sociology program assessment - essex county...

compiled by Susan Gaulden, SLOAT Facilitator

FINAL REPORTS FOR SLOAT FALL 2010 COURSES

Final Reports for SLOAT Fall 2010 CoursesAFE 083 Troy Hamilton, Center for Academic Foundations

AFM 083 Violeta De Pierola & Arturo Vera, Center for Academic Foundations

ART 100 Barbara Pogue, Humanities

BIO 121 Jill Stein, Biology & Chemistry

BUS 101 Nate Himelstein, Business

ENG 096 Eileen De Freece, Humanities

ENG 101 Richard Bogart, Humanities

MTH 092 Eman Aboelnaga & Barbara Satterwhite, Mathematics & Physics

MTH 100 Carlos Castillo & Soraida Romero, Mathematics & Physics

MTH 127 Susan Gaulden, Mathematics & Physics

SOC 101 Akil Khalfani, Social Sciences

Members of the Student Learning Outcomes Assessment Team (SLOAT) at ECC are assigned the task of determining the level of student mastery of various SLOs (i.e., Course Goals and all associated MPOs, General Education Goals if applicable, and Program Goals if applicable) specific to their SLOAT course. This book is a compilation of the Fall 2010 SLOAT Final Reports, which each contain course-specific findings. These final reports, along with other SLOAT course assessment documents, may be found on the ECC SLO Assessment website http://sloat.mathography.org, which is maintained by Professor Ron Bannon, Mathematics & Physics.

Abstract – 1

AFE 083 Student Learning Outcomes Assessment Team (SLOAT)

Fall 2010 Final Report by Troy Hamilton

Introductio n

Academic Foundations English 083 (AFE 083) is a non-General Education course that focuses on writing, reading, and study skills. This course is designed to emphasize fluency, the writing process, sentence structure, editing and revision, paragraph and essay development, the comprehension and analysis of texts, and effective study habits and skills. The reading skills will be applied to selections of fiction and non-fiction including essays reflecting the various rhetorical modes. Study skills instruction includes emphasis on listening, note taking, following directions, understanding texts, goal setting, time management, and test taking. Special emphasis will be placed on helping students to overcome the anxieties of testing, reading, writing and studying. The following are the listed course goals for AFE 083:Upon successful completion of the course students should be able to:1. Write a five-paragraph essay.2. Utilize proper research techniques necessary to write a fully-cited research

paper using Modern Language Association (MLA) style format.

Purpose

This assessment of student learning outcomes (SLOs) conducted by Troy Hamilton seeks to assist the English instructors working for the Center for Academic Foundation to better understand exactly what topics/skills students are mastering. More than just engaging in information gathering, the desired intention of this study is to analyze and understand students’ progress for the purpose of modifying and refining how they are being taught. The hope and expectation is that after the data is shared, each instructor will be encouraged to alter and/or modify their teaching approach to meet the needs of their individual students.

Methodology

The student learning outcomes (SLO) analysis implemented in Fall of 2010 for AFE 083 was used to assess course goal 1. Each of the 5 AFE 083 instructors that participated in this assessment analyzed students’ essays to see, among other things, how well students were able to develop and sustain arguments throughout their essays. The sample population of students selected to participate in the assessment were twenty five, in total, from AFE 083 sections 001, 002, 003, DE1 and DE2. Instructors were asked to identify the first five students listed on their class roster to be part of the data

AFE 083 – 1

collection. This approach helped prevent instructors from picking only their best students to be part of the assessment. The essays reviewed in the assessment were the two essays students submitted right before the midterm and final exams were administered. The checklist rubric used for the essay assessment is given below.

Essex County College – Student Learning Outcomes Assessment Survey

AFE 083/Fall 2010

English Assignment Survey Assignment due Date_______________ Section Number____________________Assignment Topic____________________________________________________________For each of the following outcomes identified for inclusion in a paper assigned in AFE 083, please indicate their occurrence or lack of occurrence in your student’s writing:

1. The essay includes an appropriate introductory paragraph. Yes Somewhat No

2. There is an appropriate topic sentence with the author’s name and the title of the essay. Yes Somewhat No

3. A clear thesis statement was incorporated within the introductory paragraph. Yes Somewhat No

4. A relevant three-point sentence was established. Yes Somewhat No

5. Body paragraphs were well-structured. Yes Somewhat No

6. Body paragraphs were related to each other in a logical structure that supported the thesis. Yes Somewhat No

7. Proper in- text citation was utilized. Yes Somewhat No

8. The essay contained an appropriate concluding paragraph. Yes Somewhat No

AFE 083 – 2

9. The paper demonstrates an acceptable level of mechanics and language usage. Yes Somewhat No

The Measurable Course Performance Objectives (MPOs) associated with course goal 1 are as follows:

1.1 write an appropriate introductory paragraph;1.2 compose an appropriate topic sentence;1.3 construct a clear thesis statement;1.4 establish a three-point sentence;1.5 compose an appropriate topic sentence for each body paragraph;1.6 utilize in-text citation;1.7 write a concluding sentence for each body paragraph;1.8 write an appropriate concluding paragraph; and1.9 use correct grammar and syntax throughout the essay

Student achievement of MPOs 1.1 through 1.3 provides evidence of how well students are able to develop an appropriate introductory paragraph, whereas achievement of MPOs 1.4 through 1.7 and 1.9 and MPO 1.8 were used to assess the body paragraphs and the conclusion paragraph respectively.

Assessment Results for Midterm Exam:

60% of the students were able to develop an appropriate introductory paragraph (i.e., achieved MPOs 1.1 – 1.3) before the midterm exam (both the mid-term and the final exams were designed by the Humanities Division). The first three questions on the checklist rubric were formulated to assess the introductory paragraph.

63% of the students were able to develop an appropriate body paragraph utilizing MLA in-text citation (i.e., achieved MPOs 1.4 – 1.7 and 1.9) before the midterm exam. Questions 4 through 7 and 9 on the checklist rubric were formulated to assess the body paragraphs.

61% of the students were able to develop an appropriate concluding paragraph before the midterm exam. Question 8 on the checklist rubric was designed to assess student ability to develop an appropriate concluding paragraph.

AFE 083 – 3

Intro Body Conclusion0102030405060708090

100

60 63 61

Midterm Assesment

Responses

Diagram 1

These findings as displayed in Diagram 1, indicate that by the Fall 2010 midterm exam only 60% (introductory paragraph), 63% (body paragraphs), and 61% (concluding paragraph) of the sampled students attained the corresponding Measurable Performance Objectives (MPOs). For this study, if 70% of the students are able to accomplish a given objective, it is considered ‘achieved.’ In this particular study conducted prior to midterm, none of the MPOs were achieved. This implies that by the eighth week of the semester students were not performing/writing at the expected, desired level. It seems that, based on anecdotal information gathered in discussions with students after the midterm assessment, a number of factors contributed to their lack of achievement. Some of the factors reported by students were external, such as employment, financial difficulties, and child rearing. It is safe to conclude that these factors prohibited students from attending class regularly, which directly impacted their academic performance. In spite of this and based on the study findings, it is clear that AFE English instructors and Supplemental Instructors (SIs) need to come up with more effective pedagogical strategies in an effort to enhance their students performance preferably exceed 70% MPO achievability before the midterm exam.

Assessment Results for Final Exam:

By the Final Exam MPOs 1.1 thru 1.9 were achieved by the AFE students. However, this achievement might be accepted with hesitance the level of success was certainly by the narrowest of margin, especially when you factor in that AFE 083 is a developmental course.

AFE 083 – 4

MPOs Considered Achieved

71% of students were able to develop an appropriate introductory paragraph before the final exam, which is a small but considerable improvement from the midterm assessment (60%).

75% of students were able to develop an appropriate body paragraph utilizing MLA in-text citation before the final exam, which is a small but considerable improvement from the midterm assessment (63%).

71% of the students were able to develop an appropriate concluding paragraph before the final exam which is a small but considerable improvement from the midterm assessment (61%).

Intro Body Conclusion0

102030405060708090

100

71 75 71

Final Assesment

Responses

Diagram 2

Summary

As indicated in Diagrams 1 and 2, which are based on the information gathered from the assessment, AFE 083 instructors in the CAF department need to spend more time developing their students’ writing skills before the midterm exam if 70% or more of the students are to be able to achieve the course MPOs by the eighth week of the semester. This will definitely improve the writing skills of the students within CAF. When students can develop a good introductory paragraph, it is more likely that the overall structure—tone, diction and structural arguments—of the essay will be adequate as

AFE 083 – 5

MPO’s considered Achieved

well. These are some of the strategies English instructors can implement in order to improve their student’s success:

spend more class time on the pre-writing process have student engaging in timed writing drills require that the supplemental instructor (SI) spend more time

with struggling students offer more collaborative learning opportunities

AFE 083 – 6

MTH 083 Student Learning Outcomes Assessment Team (SLOAT)

Fall 2010 Final Report by Violeta De Pierola and Arturo Vera

*Introduction

Academic Foundations Math AFM 083 is a beginning mathematics course designed to take students from concrete arithmetic ideas to the more abstract algebraic forms of these ideas. One of the instructional components of AFM 083 is two mandatory sessions (one hour each) of tutoring per week and the required completion of ALEKS (computer software) assignments. AFM 083 course outline lists the following goals:

1. Demonstrate knowledge of the fundamental concepts and theories from arithmetic, algebra and geometry.

2. Utilize various problem-solving and critical-thinking techniques to set up and solve real-world applications.

3. Communicate accurate mathematical terminology and notation in written and/or oral form in order to explain strategies to solve problems as well as to interpret found solutions.

*Purpose

The purpose of the SLOAT was to determine if the students enrolled in AFM 083 are learning the goals set in the course outline. It was also meant to help the Math instructors understand how the students enrolled in the Center for Academic Foundations learn and what different teaching techniques they can use. This assessment was conducted by Violeta De Pierola and Arturo Vera and it was done based on 32 students.

*Methodology

For the Fall 2010 SLOAT the two goals that were assessed were goals 1 and 2 from the course outline. 1. Demonstrate knowledge of the fundamental concepts and theories from

arithmetic, algebra and geometry:

1.1 perform arithmetic operations on signed numbers;1.2 perform arithmetic operations on fractions;1.3 perform arithmetic operations on decimals;

AFM 083 – 1

1.4 perform arithmetic operations on percents;1.5 determine the perimeter and area for simple geometric figures;1.6 determine whether a ratio is a proportion;1.7 convert from one unit of measure to another;1.8 simplify basic algebraic operations; and1.9 solve simple linear equations involving one operation

2. Utilize various problem-solving and critical-thinking techniques to set up and solve real world applications:

2.1 apply arithmetic to solve application problems encountered in daily

life

*Population

We decided to use a total of 32 students as a sample size selected from 4 sections of AFM 083; i.e., even though we gave all of the students in the 4 sections the pre-test, questionnaire, and post-test we sampled only 32 of those students for this SLOAT study.

Since one of the purposes for this assessment was to help determine whether students taking AFM are achieving the Measureable Performance Objectives (MPOs) for this course, we decided to start by blueprinting the pre-test given to all students. From there we randomly chose 8 students from each section and kept track of those students’ questionnaire responses, quiz and test scores, and Aleks (an online homework software) statistics.

*Instrumentation

For this study we used data from 3 sources:- Blueprinted multiple-choice questions*- Questionnaires*- Statistics from Aleks *Copies of these assessment instruments used are included in

Appendix A of this report.

*Results

Pre- and Post-test ResultsGraphs comparing the scores the 32 sampled students received on the

pre- and post-tests are below.

Pre- and Post-test scores

AFM 083 – 2

1 2 3 4 5 6 7 80

102030405060708090

100

Section CW1

Pre-Test scoresPost-Test

1 2 3 4 5 6 7 80

102030405060708090

100Section 003

Pre-test scoresPost-Test

Pre- and Post-test scores (continued)

AFM 083 – 3

1 2 3 4 5 6 7 80

102030405060708090

100

Section 005

Pre-Test ScoresPost -Test

1 2 3 4 5 6 7 80

102030405060708090

100

Section 014

Pre-test ScoresPost-Test

The pre- and post-tests were given by the instructors in class. The pre-test was given on the first day of class. Students were told to try their best and were not allowed to use calculators. The post-test was also given by the

AFM 083 – 4

instructors and, by looking at the graphs above, we can see how remarkably the students’ scores changed.

In section CW1, the average score on the pre-test was 30% and 79.8% on the post-test indicating an increase of 49.8%. In section 003, the average score on the pre-test was 35.6% and 81.7 % on the post-test indicating an increase of 46.1%. In section 005, the average score on the pre-test was 20.6% and 79.1% on the post-test indicating an increase of 58.5%. In section 014, the average score for the pre-test was 28.1% and 77.5% on the post-test indicating an increase of 49.4%.

By looking at the graphs we can also see that the students scored low as they entered this course. Many different factors could have influenced this result; for example, not expecting the test, coming back to school after many years, and not being well prepared. These are just a few reasons given by the students explaining why they did not perform that well on the pre-test.

Questionnaire ResultsThe students were given two questionnaires, the first one was

conducted before they took the midterm and the second one was administered before the final. Average student responses to both questionnaires are given in Appendix B. From looking at the average responses of students’ answers to the survey, we can conclude that the students still need extra help when working on the following MPOs:

1.4 Perform arithmetic operations on fractions;1.8 Simplify basic algebraic operations;2.1 Apply arithmetic to solve application problems encountered in

daily life.

We came to this conclusion after noticing that the average student responses for each question related to these three MPOs were less than 70%. Since students need at least 70% to pass the course, the instructors should ensure that students spend more time practicing these topics.

This information is already being shared with CAF instructors and students. One such way is by creating the Class Syllabi for the Spring 2011 semester which reflect the course outlines prepared by SLOAT members. These are the following categories that we included in the syllabus:

Course Number and Name Credit Hours Prerequisites Co-requisites Course Description Course Goals Course Requirements Methods of Evaluation

AFM 083 – 5

Academic Integrity Student Code of Conduct Course Content Outline (by week)

We decided to include these elements because doing so will make the students aware of what is expected from them on day one, and they will know what they must learn by end of the semester.

*Suggestions

After reviewing all the data collected from the assessment, we realize that instructors need to spend more time reviewing fractions (adding, subtracting, multiplying and dividing), relating word problems to real life, and solving basic algebraic equations. Some suggestions to help students learn more effectively include the following:

Instructors can have SIs work with students struggling in these areas. Have the students work on Aleks at least one day per week during

tutoring time. Have the students work together while working on these difficult

topics.

AFM 083 – 6

APPENDIX A

Center Academic FoundationsAcademic Foundation Mathematics

AFM 083 Pre-test

Name: ____________________________ Date: ____________ Section: ________

1. Name the property that is illustrated4 x (3+6) = (4 x 30 + (4 x 6)

2. What is the product of 1636 and 58?

3. Write in expanded form 353, 999.

4. Write in expanded form x5.

5. What is nine thousand seventy eight in standard form?

6. The average age of students in College X is 23.58 and the average age of students in College Y is 23.5798. Which College has the lower average?

7. Express seventy one thousand seventy-one and seventy-six hundredths in decimal form.

8. Evaluate: -22 + (-11) + 11 + (-10)

9. Evaluate: d3 – b3 if b = 5; d = 6.

10. Write the following phrase, using symbols: Twice the difference of x and y

AFM 083 – Appendix A – 1


AFM 083 Midterm Questionnaire

Name: ____________________________ Date: ____________ Section:________

Please mark only one X on the one that applies to you.

1. How do you think you will do on the midterm?__ Really good __ good __ average __ not so good

On a scale from 0% - 100%:2. How comfortable do you feel rounding? (Round 8,416 to the nearest

thousand.)__ 100% __ 75% __50% __25% __0%

3. How comfortable do you feel dividing fractions? ( 38 ÷ 2

8 )__ 100% __ 75% __50% __25% __0%

4. How comfortable do you feel finding product? (Find the product of -90 and

60.)__ 100% __ 75% __50% __25% __0%

5. How comfortable do you feel with prime factorization? (Find the prime factorization of 144.) __ 100% __ 75% __50% __25% __0%

6. How comfortable do you feel finding the perimeter? (A rectangle has a length

of 26m and a width of 12m. Find the perimeter of the rectangle.)__ 100% __ 75% __50% __25% __0%

7. How comfortable do you feel evaluating expressions? (Evaluate −xy for

x=12 and y = -3.)__ 100% __ 75% __50% __25% __0%

8. How comfortable do you feel simplifying? (Simplify -8 ÷ 2 + (-6)²)__ 100% __ 75% __50% __25% __0%

9. How comfortable do you feel with absolute value? (Write in ascending order –

׀8׀ , ׀17׀ , - ׀9-׀ , ׀4-׀ )__ 100% __ 75% __50% __25% __0%


10. How comfortable are you multiplying fractions? [( 53 ) x ( 9

4 ) x ( 25 )]

__ 100% __ 75% __50% __25% __0%


AFM 083 Final Questionnaire

Name: ____________________________ Date: ____________ Section: _________


1 How do you think you will do on the final?__ Really good __ good __ average __ not so good

2. Do you think you will do better on the final then you did on the midterm?

___ yes ___ no

On a scale from 0% - 100%:3. How comfortable do you feel working with order of operations? (20-16 ÷ 4)

__ 100% __ 75% __50% __25% __0%4. How comfortable do you feel working with percents? (Write 0.818 as a

percent.)__ 100% __ 75% __50% __25% __0%

5. How comfortable do you feel solving proportions? ( 38 = 6

16 is this proportion

true?)__ 100% __ 75% __50% __25% __0%

6. How comfortable do you feel simplifying variable expressions? [4+5m+(-5m)]

__ 100% __ 75% __50% __25% __0%7. How comfortable do you feel solving equations? (Solve 2d = -12.)

__ 100% __ 75% __50% __25% __0%

8. How comfortable do you feel dividing fractions? (-110 ÷ 317 )

__ 100% __ 75% __50% __25% __0%9. How comfortable do you feel solving word problems?


(A digital camera with a regular price of $265 is on sale for 19% off the regular price. Find the sale price.)__ 100% __ 75% __50% __25% __0%

10. How comfortable do you feel multiplying exponential expressions? ( z³ * z² * z)

__ 100% __ 75% __50% __25% __0%


APPENDIX B


AFM 083 Midterm QuestionnaireName: ____________________________ Date: ____________ Section:

________Please mark only one X on the one that applies to you.

1. How do you think you will do on the midterm?__ Really good __ good __ average __ not so good

On a scale from 0% - 100%:2. How comfortable do you feel rounding? (Round 8,416 to the nearest

thousand.)85%

3. How comfortable do you feel dividing fractions? ( 38 ÷ 2

8 )67%

4. How comfortable do you feel finding product? (Find the product of -90 and 60)

73%5. How comfortable do you feel with prime factorization? (Find the prime

factorization of 144.) 80%

6. How comfortable do you feel finding the perimeter? (A rectangle has a length

of 26m and a width of 12m. Find the perimeter of the rectangle.)71%

7. How comfortable do you feel with evaluating expressions? (Evaluate −x

y for

x=12 and y = -3.)78%

8. How comfortable do you feel simplifying? (Simplify -8 ÷ 2 + (-6)²)72%

9. How comfortable do you feel with absolute value? (Write in ascending order –

AFM 083 – Appendix B – 1

׀8׀ , ׀17׀ , - ׀9-׀ , ׀4-׀ .)86%

10. How comfortable do you multiplying fractions? ( 53 ) x ( 9

4 ) x ( 25 )

62%Center Academic Foundations

Academic Foundation MathematicsAFM 083 Final Questionnaire

Name: ____________________________ Date: ____________ Section: ________


1 How do you think you will do on the final?good

2. Do you think you will do better on the final then you did on the midterm?

yesOn a scale from 0% - 100%:3. How comfortable do you feel working with order of operations? (20-16 ÷ 4)

95%4. How comfortable do you feel working with percents? (Write 0.818 as a

percent.)81%

5. How comfortable do you feel solving proportions? ( 38 = 6

16 is this proportion

true?)76%

6. How comfortable do you feel simplifying variable expressions? [4+ 5m+(-5m)]

68%7. How comfortable do you feel solving equations? (Solve 2d = -12.)

78%

8. How comfortable do you feel dividing fractions? (-110 ÷ 317 )

69%9. How comfortable do you feel solving word problems?


(A digital camera with a regular price of $265 is on sale for 19% off the regular price. Find the sale price.)69%

10. How comfortable do you feel multiplying exponential expressions? ( z³ * z² * z)

71%


SLOAT Summary 1/24/11 Prof. Barbara Pogue

ART APPRECIATION – ART 100 – 3 credit hours

ART 100 BO1 and ART 100 007 were the two classes chosen for analysis; at semester’s end (Fall 2010) there were 60 students evaluated.

The above course is both an AA and AS degree program additional requirement under the General Education category of Humanistic Perspective. The purpose of Art Appreciation is to give students an introduction to great works of world art as well as to encourage them to question the nature and relevance of art to daily life. Students are also introduced to the elements and principles of design and asked to demonstrate comprehension of the principles of design by constructing a Principles of Design booklet.

For SLOAT, I decided to focus attention on the Principles of Design booklet, as it required a wide variety of educational behaviors in comprehension, knowledge, evaluation, analysis and application: distinguishing, comparing, interpreting, identifying, deciding, classifying and explaining the various principles of design: variety and unity, symmetrical and asymmetrical balance, rhythm, scale, proportion, emphasis and subordination. Students choose two examples of each principle from popular magazines, carefully place them in a booklet, and type an explanation of why each example was chosen.

The Principles of Design booklet relates to Course Goal number 4: “prepare and present information using a computer by doing the Principles of Design booklet” (ART 100 Course Outline, p.2) and to Measurable Performance Objective number 4: “use magazines to gather examples of each of the principles of design; use computers to type up explanations of why each illustration fits the criteria for the principles; assemble images, titles and explanations, along with a cover sheet, into a booklet.” (ART 100 Course Outline, p.2)

I prepare a handout of instructions on how to do the booklet (attached) for students, as well as speak extensively on the subject and show previous examples of booklets. Students read the relevant chapter in their textbooks to further enhance their knowledge of the principles. Finally, there is one day devoted to doing the booklets in class, and then the students are required to complete the project on their own time.

For SLOAT, I prepared a checklist of how I would evaluate the booklets (attached) and got ready to check off 60 booklets to see how well the students understood the principles of design. The booklets, by their nature,

ART 100 – 1

take a long time to do, so I give the instructions about two months before the due date, which is the last week of class. The last week, I collected the booklets and used my check-off sheets to determine what grade the student would receive for his/her booklet. That’s when the problem became obvious. I discovered my so-called carefully-prepared list was totally inadequate to determine grades. Time and again, students (actually all of them) met all the check-off requirements, yet their booklets could not be given an A or a B+ grade. Many of the booklets were adequate, but lacked an indefinable something. For example, the illustration chosen might have been average or okay, but lacked subtle design qualities which would have made it superior. Or perhaps a student’s explanation, while technically correct, might have been repetitious, showed a lack of imagination or awkward rhetoric or lapses in grammar.

The result of doing the SLOAT assessment was that I discovered that all my students did understand the principles of design and all did pass the principles of design booklet assignment, but that my instrument was too crude to predict grade distinctions. Therefore, if I want to figure out what is an A, B+, B, C+, C or D grade, I’ll have to design a different instrument. The question is how do you absolutely define or measure what is a superior illustration, a very good illustration, a good one, an above-average one, a fair one, or a poor one? How do you communicate these distinctions so students will understand them? How do you design an instrument that will take these distinctions into account without being unduly cumbersome to use?

As a check on the rationale for doing the booklet, one of my final exam questions was: “On the back of this paper, evaluate the course. What worked? What didn’t? What did you like the most and the least? What did you learn the most from doing? What could I do better in the future? This question is worth 10 points…and …, you don’t have to be positive. Negative comments are also helpful.”

Out of a total of 39 responses (students who had an A average weren’t required to take the final, so there were only 39 instead of 60 students reporting), 23 commented that they learned most from either the lectures or the in-class projects such as the color wheel, the collages and the masks. Fifteen reported that the single thing they learned the most from doing was the Principles of Design booklet, and one commented that the booklet was too difficult, but that doing it was a helpful learning experience. Many students (14) didn’t like doing the oral reports; some (7) didn’t like watching the videos. Not one student reported he/she didn’t like or didn’t learn from doing the booklet. Not one chose it as something he/she learned the least from doing.

Therefore, I must conclude that students feel doing the booklet is important, but perhaps not as important as I believe it to be. Nevertheless, it is a

ART 100 – 2

valuable learning tool and I will continue to utilize it. I must try to develop a more subtle instrument for measuring the booklet itself.

ART 100 – 3

Biology 121 – Fall 2010 – SLOAT Final Report – Jill Stein

Introduction

The purpose of this assessment is to document the progress of a cohort of students taking Biology 121 during the Fall 2010 semester.

Biology 121 (Anatomy & Physiology I) is the first semester of a two semester Anatomy & Physiology sequence, and is a pre-requisite for application to the Nursing, Physical Therapist Assistant, Radiography, Dental Hygiene/Assisting, Respiratory Care and Dietary Manager Programs here at Essex County College (ECC). It is also required for admission to other area Nursing programs, such as those at Rutgers, UMDNJ, and Seton Hall. Along with the subsequent successful completion of Biology 122 (Anatomy & Physiology II), the student is able to fulfill the General Education requirement for a laboratory science sequence, and General Education goal 3 regarding Scientific Knowledge and Reasoning. The Biology 121/122 sequence can also be used to fulfill an elective requirement for the Biology major.

Approximately 21 sections, which each contain 24 students, are offered for this course in both fall and spring semesters. Four additional sections containing 24 students each are offered during the summer, bringing the total number of students enrolled in this course each year to approximately 1100.

Currently, the only pre-requisites for Biology 121 are completion of all remedial courses, if necessary, or demonstration of college level readiness in Mathematics and English. There is no college science pre-requisite. The course is content heavy, and taught at a rapid pace, a situation unfamiliar to many of our students. This can lead to a high attrition rate, a problem not just at ECC, but at colleges all over the country.1 Since mastery of this course is crucial for so many students in pursuit of their goal to become a health professional, it was chosen for this pilot assessment project.

Methodology

Fifty students, comprising two sections, were part of the initial cohort. This number was based on the official class lists after the “no shows” were removed. Eight exams were given in class at varying intervals throughout the semester starting with the third week of class. Each exam contained a variety of short answer questions which were blueprinted to specific MPOs. Assessment methods used were direct, summative, quantitative, and objective. Multiple questions were used to assess each MPO. Each question was scored for the number of students selecting the correct answer. This number was converted to a percentage of the total number of students

BIO 121 – 1

taking the exam. Multiple percentages for each MPO were then averaged to determine the overall student success for each MPO.

Results

As shown in Figure 1 below, the number of students taking the exams declined gradually over the course of the semester, from 45 to 20. Although 50 students were registered, only 45 took the first exam, an immediate loss of 10%. Three of those five did not return to class. The other two returned to take the second exam; one dropped immediately after, and the other attended irregularly until the end of the semester. The steepest declines occurred after exams 3 (histology and integumentary system) and 4 (bone physiology). Exam 5 was given after midterm warnings were sent out, but just before the final drop date. By that time, most of the students had made their decision as to whether or not to remain in the class. Twenty students took both exams 7 and 8, although only 18 of the 20 were the same for both exams.

1 2 3 4 5 6 7 805

101520253035404550

Figure 1: Number of Students in the Cohort Who Took Each BIO 121 Exam

Exam #

# of

Stud

ents

Student success for each MPO is shown in Table 1 below. Most of the success rates are between 60-70%. Notable exceptions are Exam 2, where percentages are below 60% for all MPOs assessed, and Exam 5, where the score for MPO 2.2 is 57.5%. The material covered for Exam 2 is essentially a “crash course” in biochemistry and cell biology. Exam 5 is a practical exam on bone and joint identification.

BIO 121 – 2

Table 1: Student Success for Each MPO on Exams 1 – 8MPO

Exam 1

Exam 2

Exam 3

Exam 4

Exam 5

Exam 6

Exam 7

Exam 8

1.1 68.7 1.2 61.2 1.3 56.7 1.4 49.4 1.5 55.9 1.6 62.3 2.1 62.7 2.2 73.1 57.5 2.3 65.6 2.4 70.1 69.23.1 56.4 3.2 70.8 3.3 68.2 72.2 3.4 69.9 3.5 61.3 72.5

Students were asked to complete brief surveys after Exams 1 and 2. Thirty-nine students completed the survey after Exam 1 (see Appendix A for full results). Several students did not have a book or lab manual, but most felt that the exam was reasonable, and virtually no one felt time pressure. Unfortunately, 16 students felt that they did not study enough due to overcommitted schedules. This fact appeared repeatedly when students listed other factors which contributed to their exam scores. Students also wrote: “stress not related to class; focused more on math class; lack of sleep, nervous; didn’t make it as much of a priority as I should have; careless mistakes with reading questions; and misunderstood two questions.”

Thirty one students completed the survey after Exam 2 (see Appendix B for full results). As noted, successful completion of MPOs was generally lower on this exam. Here again, 10 students cited an overcommitted schedule, with comments including “family troubles/didn’t study,” and “crammed this past weekend and froze at test time.” Several students indicated that they did not feel that they studied the correct information.

Discussion

Biology 121 is the first part of a two semester course in Anatomy & Physiology. As such, the content is both quantitatively and qualitatively difficult to master. In addition, critical thinking and analysis are required to answer some of the questions. Anecdotally and demonstrably, many

BIO 121 – 3

students are unaccustomed to this type of course, are insufficiently prepared, and lacking in the appropriate study skills. Thus, while successful completion rates for the MPOs generally hovered between 60-70%, this was not surprising.

Successful completion rates for MPOs 1.3, 1.4, and 1.5 (Exam 2) fell below the 60% rate. These MPOs encompass biochemistry and cell biology, basic information that is crucial for success. Currently, the only pre-requisites required to take Biology 121 are successful completion of developmental math and English/reading if required, or demonstration of college level competency in these areas. Students were surveyed at the beginning of the semester to make sure that these requirements were completed (data not shown). There is no biology and/or chemistry requirement. While the course obviously provides instruction in these areas, it is quite a rapid pace of delivery for such critical information. Biology is not required for high school graduation in New Jersey2, and many students begin BIO 121 with the most rudimentary of scientific backgrounds. An in depth, detailed examination of these fundamental topics of biochemistry and cell biology, however, is provided in Biology 100, a preparatory class which may be taken while taking developmental classes, prior to the start of BIO 121. Many students should take advantage of this class, but fail to do so since it is not a requirement.

Successful completion of MPO 2.2 (Exam 5) was 57.5%. The topics covered on this exam included bone and joint anatomy. In this case, the issues are slightly different. First, the exam format is a practical exam, rather than the standard short answer to which the students have become accustomed. Students are asked to identify bones, markings, and articulations from the sample presented on the bench. Most students have never had this type of exam, and many panic at the format change. Second, the quantity of information is very large, although not as complex as the biochemistry/cell biology. Again, many students do not have the time or the skills necessary to adequately learn the material, or sufficiently recognize the time needed to master these skills until too late.

A rigorous background in Anatomy & Physiology is critical for success in the health related professions. Many students are interested in these professions, as they are ones in which well-paying jobs are available without excessive years of education. Problems similar to those noted here have been observed at other institutions. At the University of Southern Indiana, a Supplement course for students identified as high risk, for failing or withdrawing due to many of the same issues presented here, was implemented.1 Success rates (as measured by a final grade of C or better) improved for those enrolled in the Supplement. A “supplemental course,” BIO 100, already exists at ECC. Therefore, a discussion about the pre-requisites for BIO 121 should be held by the Division Curriculum Committee.

BIO 121 – 4

In addition, consideration should be given to the quantity of material on Exam 5, or possibly breaking it up into two smaller exams.

Endnotes

1. Hopper, M. 2011. Student Enrollment in a Supplement Course for Anatomy and Physiology Results in Improved Retention and Success. Journal of College Science Teaching 40 (3): 70-79.

2. Brody, Leslie. “N.J. Puts Off Plans for High School Biology Test.” Bergen Record Online 28 Dec. 2010. Web. 31 Jan 2011.

BIO 121 – 5

Appendix A – Student Survey Administered After Exam 1 in BIO 121

N=39 SCORE EARNED ON EXAM #1 ________

PLEASE ANSWER THE FOLLOWING QUESTIONS HONESTLY:

1. How prepared were you for this exam based on the work you’ve done so far? (Circle one.)

FULLY PREPARED 12 SOMEWHAT PREPARED 23NOT AT ALL PREPARED 3

2. Do you have a copy of the required textbook (or a similar book by a different author)?

YES 35 NO 4

3. Do you have a copy of the lab manual?

YES 33 NO 6

4. How much homework have you done so far this term? (Circle one.)

ALL 20 MOST(>50%) 14 SOME(<50%) 3 NONE 2

5. How did you find the level of the exam? (Circle one.)

TOO HARD 5 REASONABLE 32 TOO EASY 1

6. Did you feel rushed to complete the exam? (Circle one.)YES 1 NO 37

7. If you didn’t do as well as you’d hoped, why not? (Circle all that apply.)

TEST ANXIETY 13 INSUFFICIENT BIOLOGY BACKGROUND 7DIDN’T STUDY ENOUGH – LAZY 1 DIDN’T STUDY ENOUGH – OVERCOMMITTED SCHEDULE 16OTHER: see written report

BIO 121 – Appendix A – 1

Appendix B – Student Survey Administered After Exam 2 in BIO 121

N=31 SCORE EARNED ON EXAM #2: _____________

PLEASE ANSWER THE FOLLOWING QUESTIONS HONESTLY:

1. How did you do on this exam compared to Exam #1?

BETTER 2 ABOUT THE SAME 7 WORSE 22

2. If you did better on this exam, why was this so? (Circle all that are applicable. Leave it blank if necessary.)

STUDIED MORE HAVE THE BOOK NOW COMPLETED MORE HOMEWORK

WASN’T AS NERVOUS – KIND OF KNEW WHAT TO EXPECT 2DIDN’T MISS AS MANY CLASSES OTHER: _____________________________

3. If you did worse on this exam, why was this so? (Circle all that are

applicable. Leave it blank if necessary.)

TEST ANXIETY 7 BAD BIOLOGY BACKGROUND 7 MISSED TOO MANY CLASSES

DIDN’T STUDY ENOUGH – LAZY DIDN’T STUDY ENOUGH – OVERCOMMITTED SCHEDULE 10DIDN’T DO ENOUGH HOMEWORK 1 OTHER: 9 – see written report

4. How did you find the level of the exam? (Circle one.)TOO HARD 9 REASONABLE 20 TOO EASY 0

5. Did you feel rushed to complete the exam? (Circle one.)

YES 3 NO 27

BIO 121 – Appendix B – 1

SLOAT Assessment Final Report FALL 2010 BUS 101 Business Organization & Management

Dr. Nathan HimelsteinJanuary 28, 2011

I. The purpose to the study was to determine what questions on the departmental final exam did most students get wrong. Once these questions were ascertained we suggest that more time should be spent in reviewing the topic and concepts.

II. Methodology SLOAT ASSESSMENT PLAN

a. An item analysis from the ScanTron scoring sheets was conducted from 6 day sections. 113 scores were analyzed.

b. Dr. Nathan Himelstein used his three sections and one section from Prof. Carlos Riivera’s class, one section from Prof. Karen Scuorzo’s class and one section from Prof. Janet Foster (an adjunct instructor) were utilized in this survey. The results were scanned during the final exam period December 14 – 16, 2011.

c. Instrumentation

The questions on the departmental exam were based upon Bloom’s Taxonomy and AACSB parameters. They were chosen from the questions bank developed by McGraw-Hill from the text book used for this course “Understanding Business” by Nickels, McHugh & Mc Hugh (9th edition) and based on the chapters stated in the departmental syllabus given to all students taking the course.

d. Collection of data

All students were given a 100 question exam and answers noted on ScanTron scoring sheets. The answers were scanned and an item analysis form was fed through the machine and number of wrong responses to each question was noted.

e. Processing of Data

Each item analysis was reviewed by Dr. Nathan Himelstein and the results summarized. The questions marked wrong were noted.

BUS 101 – 1

III. Results:

Section # Mean # of Students # of Students Who Answered >10/100 Questions Incorrectly

001 78.3 16 2

002 78.7 17 1

003 80.1 15 1

006 69.6 17 16

007 77.0 22 13

009 77.8 26 20

The questions which the students marked wrong will be given to the instructors so that next semester these areas can be further explained.

The three instructors in sections 006 , 007 and 009 do not have the teaching experience that those instructing sections 001, 002 and 003 have, however those areas must be noted as indicating students having deficiency in that subject area.

Interesting to also note that the same question which had > than 10 wrong was in Sec 001 and Sec 002 not in Sec 003.

Please also note that the mean of 5 of the 6 sections are in close range of each other.

The specific questions in which more than 10 students provided the wrong answers were as follows:

Exam Question #

5. Taxes and government regulations are part of the ? environment of business. (economic and legal).

11. Which of the following prohibits monopolies, attempts to monopolize, and any restraints of trade? (Sherman Act)

23. Which of the following statements about S corporations is most accurate? (The major attraction of S corporations is that they avoid the problem of double taxation.)

BUS 101 – 2

24. A ? is two firms combining to form one company. (merger)

35. ? is the management function of creating a vision for the organization and guiding, training, coaching, and motivating employees to help achieve the goals and objectives of the organization. (Leading)

42. Henri Fayol and Max Weber are best known for heir contributions to: (organization theory).

59. The Hawthorne studies were conducted by ? and his colleagues from Harvard University. (Elton Mayo)

61. In Maslow’s hierarchy of needs, the desire for love and acceptance would fall into the category of: (social needs)

62. Herzberg found that good pay: (was a hygiene factor rather than a motivator)

78. Historically, the ? strengthened he labor unions, while the ?supported management efforts. (National Labor Relations Act, Taft-Hartley Act.)

82. The Taft-Hartley Act: (allowed individual states to pass right-to-work laws prohibiting compulsory union membership)

92. Which of the following product attributes is least emphasized on television ads? (price)

96. A firm that wants to distribute its products as widely in a market as possible would us a(n) ? distribution strategy. (intensive)

100. In evaluating the bet advertising medium to reach a specific target market the clear is (direct mail)

These areas will be shared with all faculty (full and adjunct) so that when the topics are covered these concepts should be given further emphasis in the lectures and assignments

Based on the means of the final exam, the MPOs are demonstrated in the departmental final exam.

BUS 101 – 3

ENG 096 SLOAT Fall 2010 REPORT – Submitted by: Dr. Eileen De Freece

Introduction

The use of two instruments helped measure the achievement of outcomes in ENG 096 during the Fall 2010 semester. Both were based upon Course Goals developed in the submitted revised ENG 096 course outline. The purpose of these instruments provided two outcomes: First, a rubric was used to randomly assess the achievement of essay development skills by students across the course, based upon the first Course Goal listed in the revised outline, “write a composition.” This rubric was used twice during the semester to measure any change noted in the outcome.

The second instrument was a questionnaire, completed by students in the ENG 096 sections, regarding their readiness for the mid-term essay, in order to measure, to some extent, the second Course Goal, “implement critical reading to analyze selected materials.”

Support from faculty and students was strong in this effort, and the results were interesting and worthy of consideration.

Methodology

Of the two instruments used in this study, the first was meant as a limited, random sample. Therefore, the anonymous nature of the study was made clear to the instructors who received a rubric designed to evaluate each of the Measureable Performance Outcomes (MPOs) listed in the revised ENG 096 outline under the first Course Goal, “write a composition.” Instructors were given ample copies of the rubric and asked to evaluate their students’ most recent essay for the elements, focusing on the first five students on their roster. By selecting alphabetically, the random nature of the study was maintained. Instructors rated each on a three point scale labeled, “Yes,” “Somewhat,” or “No.”

The first distribution and collection of the surveys happened in late September and October while the second was completed in December to note any changes in the outcomes. Since these questionnaires were anonymous, the Humanities Division work study students helped total results by category.

In the September/October rubric, eight ENG 096 sections participated, while just two sections participated in the December rubric. Unfortunately, timing may have been an issue in December as many instructors may have been preparing for the Divisional final essay.

ENG 096 – 1

The second instrument, a student questionnaire regarding mid-term essay preparedness, was distributed to ENG 096 instructors the week following the Divisional mid-term essay. A total of 135 students responded to the survey, a representative sample of the student enrollment in the course.

As with the essay rubric, the questionnaire was administered and evaluated anonymously; therefore, the Humanities Division’s work study students again helped tally the results for each category. The results and original instruments were returned to me and are stored in my office.

Results

Results from the rubric distributed to ENG 096 instructors and the survey administered to ENG 096 students after the mid-term essay provide insight into students’ abilities and awareness.

The questions on the rubric, distributed twice, were:

1. The paper includes an appropriate subject based upon the given writing assignment.

2. A specific topic was addressed within the assigned subject for the paper.3. A relevant thesis statement was incorporated within the introductory paragraph.4. Body paragraphs were well structured.5. Body paragraphs were related to each other in a logical structure that supported

the thesis.6. The paper contained an appropriate concluding paragraph.7. The paper approaches an acceptable level of mechanics and language usage.8. The paper demonstrates an acceptable level of mechanics and language usage.

Instructors were asked to evaluate the first five papers alphabetically, to insure randomness, and for each question respond “Yes,” “Somewhat,” or “No” in each category. The categories were drawn from the Student Learning Outcomes (SLO) in the ENG 096 revised course outline.

Results of the first distribution of the rubric during September/October 2010 follow:

1. The paper includes an appropriate subject based upon the given writing assignment.Yes 63 (61%) Somewhat 29 (28%) No 11 (11%)

ENG 096 – 2

2. A specific topic was addressed within the assigned subject for the paper.Yes 98 (89%) Somewhat 7 (6%) No 5 (5%)

3. A relevant thesis statement was incorporated within the introductory paragraph.Yes 75 (23%) Somewhat 31 (5%) No 5 (5%)

4. Body paragraphs were well structured.Yes 88 (81%) Somewhat 19 (17%) No 2 (2%)

5. Body paragraphs were related to each other in a logical structure that supported the thesis.

Yes 77 (86%) Somewhat 12 (13%) No 1 (1%)

6. The paper contained an appropriate concluding paragraph.Yes 28 (76%) Somewhat 8 (22%) No 1 (3%)

7. The paper approaches an acceptable level of mechanics and language usage.Yes 22 (65%) Somewhat 12 (35%) No 1 (1%)

8. The paper demonstrates an acceptable level of mechanics and language usage.Yes 22 (63%) Somewhat 12 (34%) No 1 (4%)

In terms of the first question, the “Yes” responses were mostly encouraging, especially for numbers 2, 4, 5 and 6 with the least positive response being for number 3 at 23%, which implies the need for thesis development in the introductory paragraph for the ENG 096 level. The other least positive responses, though exceeding 60% indicate the need for “an acceptable level of mechanics and language usage.” Question number 1, like 3, seems to point to a need for stronger critical thinking skills for this level.

The results can be charted as follows:

ENG 096 – 3

In December 2010, ENG 096 instructors were once again given the same rubric to complete for a subsequent assignment. It was anticipated that some patterns of improvement would be seen in the second study. Faculty participation was very low in the second study, which was disappointing, but timing was an issue considering faculty absorption in Divisional final essay preparation and other concerns.

December 2010 results follow:

1. The paper includes an appropriate subject based upon the given writing assignment.Yes 9 (90%) Somewhat 0 (0%) No 1 (10%)

2. A specific topic was addressed within the assigned subject for the paper.Yes 8 (80%) Somewhat 1 (10%) No 1 (10%)

3. A relevant thesis statement was incorporated within the introductory paragraph.Yes 7 (70%) Somewhat 2 (20%) No 1 (10%)

4. Body paragraphs were well structured.

ENG 096 – 4

SLOAT Essay Rubric Sept./Oct. 2010

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 2 3 4 5 6 7 8

Question Number

Stud

ent P

erce

ntag

e A

nsw

ered

YesSomewhatNo

Yes 5 (50%) Somewhat 3 (30%) No 2 (20%)

5. Body paragraphs were related to each other in a logical structure that supported the thesis.Yes 6 (60%) Somewhat 3 (30%) No 1 (10%)

6. The paper contained an appropriate concluding paragraph.Yes 5 (50%) Somewhat 2 (20%) No 3 (30%)

7. The paper approaches an acceptable level of mechanics and language usage.Yes 5 (50%) Somewhat 2 (20%) No 3 (30%)

8. The paper demonstrates an acceptable level of mechanics and language usage.Yes 5 (50%) Somewhat 2 (20%) No 3 (30%)

Although the December 2010 survey noted fewer faculty members participated, it was interesting that question number 1 presented more positive results than in the first survey with 90% marked “Yes.” And question number 3 illustrates an increase from 23% to 70%. There remains more support needed in terms of paragraph development represented in questions 4 and 5 at the end of the semester that appeared more positive in the first survey. The support for “mechanics and language usage” is evident here with 50% approaching “an acceptable level” in question 7, and 50% demonstrating “an acceptable level” in question 8. The results can be charted as follows:

ENG 096 – 5

Another instrument that was used during the Fall 2010 semester was a questionnaire that was distributed to ENG 096 students a week after taking the Divisional mid-term essay. The anonymous responses allowed students to openly consider their own preparedness for the midterm essay. Students were asked five questions dealing with their performance and preparedness. Note the following results:

1. Are you pleased with your score on the exam?Yes 20 (41%) Somewhat 12 (25%) No 17 (35%)

2. Did the professor accurately tell you what to expect on the exam before the exam date?

Yes 59 (95%) Somewhat 3 (5%) No 0 (0%)

3. Did you adequately prepare for the exam?Yes 46 (63%) Somewhat 25 (34%) No 2 (3%)If not, why not? (Circle all that apply)A. Did not have time to studyB. Did not know the exam was scheduledC. Have an overcommitted scheduleD. Did not study enough during the semester

4. Did the exam relate to what you have been learning in class?Yes 57 (93%) Somewhat 3 (5%) No 1 (2%)

ENG 096 – 6

SLOAT Essay Rubric Dec. 2010

0%10%20%30%40%50%60%70%80%90%100%

1 2 3 4 5 6 7 8

Question Number

Stud

ent P

erce

ntag

e An

swer

ed YesSomewhat

NoS

5. Do you feel confident that you will attain college level writing by semester’s end?Yes 31 (86%) Somewhat 5 (14%) No 0 (0%)


Mid-Term Student Response Questionnaire

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 2 3 4 5

Question Number

Stud

ent P

erce

ntag

e A

nsw

ered

YesSomewhatNo

Of the 135 students who responded to the mid-term questionnaire, I noted 27 responses to question number 3, A through D. Nine students checked A, 1 chose B, 12 circled C, and 7 marked off D. What is most telling here is that most responses revealed that our students have “overcommitted schedules.” Nine students who checked A admitted that they “did not have time to study,” while 7 “did not study enough during the semester.” Only 1 student “did not know the exam was scheduled.”

As can be seen, question number 1 notes that only 25% were “Somewhat” satisfied with their mid-term scores, while 35% were not pleased at all, which indicates a healthy determination to improve.

A positive response to question number 2 revealed that 95% of professors accurately explained “what to expect on the exam before the exam date.” In question number four, 93% revealed that the exam related to what was being learned in class, while question number 5 noted that 86% felt confident of attaining “college level writing by semester’s end.”

Summary

ENG 096 – 7

The evaluation of Student Learning Outcomes for ENG 096 during Fall 2010 semester proved to be a positive, enlightening experience. Both full and part-time faculty members seemed to understand and even appreciate the importance of conducting this study. Many were eager to participate. Results indicated several strengths in terms of the course structure and the effective approach taken by faculty to fulfill the course requirements.

The survey also points to the need for further support for ENG 096 students struggling with thesis development and issues with mechanics and sentence structure. Although the college offers tutorial resources in The Learning Center, at this level, students are in dire need of a separate grammar course. When one considers that the Humanities Division offers three remedial level courses (ENG 085, ENG 096, and RDG 096), it seems plausible to offer students a grammar course. Such a course would also offer support, if needed, for the college level composition courses.

ENG 096 – 8

ENG 101 SLOAT FALL 2010 REPORTSubmitted by: Prof. Richard Bogart

INTRODUCTION

Two instruments were used to measure the achievement of outcomes in ENG 101 during the Fall 2010 semester. These were based upon the Course Goals developed in the revised ENG 101 outline, and the approach developed in the plan which was submitted and approved for use. The purpose of these instruments was two-fold. The first, a rubric, was designed to randomly assess the achievement of essay development skills by students across the course. This was based upon the first of the Course Goals listed in the current outline, “write a composition.” This rubric was used twice during the semester to measure any change which took place in this outcome. The second was a questionnaire, filled out by the students in the 101 sections, regarding their readiness for the mid-term exam. This was in order to measure, to some degree, the second of the Course Goals, “recognize and use various modes of writing in order to develop expository, argumentative, and creative compositions.”

Faculty and student support were very strong for this undertaking and the results were logical and worthy of consideration.

METHODOLOGY

As stated above, two instruments were used. The first was intended for a limited sample. In order to randomize the sample, and avoid instructors weighing the results by selecting subject, the anonymous nature of the study was made clear. Instructors were given a rubric, approved by the SLOAT chair, that was designed to evaluate each of the eight Measurable Performance Outcomes (MPOs) listed under the first Course Goal, “write a composition.” Instructors were given sufficient copies of the forms and were asked to take the most recent essay which their students had submitted and to evaluate each of the first five essays, selected alphabetically to maintain the random nature of the study, for the eight elements. They rated each on a three point scale labeled, “yes,” “somewhat,” or “no.”

The first distribution and collection of questionnaires took place during October. The forms were returned to me and, since they were anonymous, work studies in the Division totaled the results by category.

This activity was repeated in December, in order to measure any changes in the outcomes.

Twenty-four sections participated in the October rubric. Fifteen sections participated in the second, which was conducted during December.

ENG 101 – 1

While the decrease in participation seems disappointing, December may have been a late point at which to conduct the survey. Some instructors may well have returned the short essays they had assigned at that point and moved onto looking strictly at research papers and preparing for the Divisional final.

The second instrument, the questionnaire regarding preparedness for the mid-term exam was distributed at the end of the week following the Divisional exam. A total of 546 students responded to the survey, therefore, representing a very significant sampling of the student enrollment in the course.

As with the essay rubric, the survey was administered and evaluated in a manner that was completely anonymous. Since there was no identifying information on the forms, work studies, again were used to total the results for each category.

The results, and original instruments, were returned to me, and the original instruments are currently stored in my office.

RESULTS

The results from the rubric distributed to ENG 101 faculty and the questionnaire distributed to ENG 101 students following the mid-term exam drew a clear picture of abilities and perceptions.

The questions on the rubric, which was distributed twice, were:

1) The paper includes an appropriate subject based upon the given writing assignment.

2) A specific topic was developed within the assigned subject for the paper.

3) An introduction provides background regarding the paper’s thesis.4) A relevant thesis statement is incorporated into the introduction.5) Body paragraphs were well-structured.6) Body paragraphs were related to each other in a logical structure that

supported the thesis.7) The paper contained an appropriate concluding paragraph.8) The paper demonstrates an acceptable level of mechanics and

language usage.

For each question, the faculty members were asked to use the first five papers alphabetically, to insure randomness, and to respond “yes, “somewhat,” or “no” for each category. The categories were directly drawn from the Student Learning Outcomes on the ENG 101 course outline.

ENG 101 – 2

For the first administration of the rubric, distributed during October of 2010, the following results were received:

1) The paper includes an appropriate subject based upon the given writing assignment.Yes 107 (91%) Somewhat 11 (9%) No 0

2) A specific topic was developed within the assigned subject for the paper.Yes 93 (74%) Somewhat 31 (25%) No 1 (1%)

3) An introduction provides background regarding the paper’s thesis.Yes 65 (50%) Somewhat 60 (46%) No 5 (4%)

4) A relevant thesis statement is incorporated into the introduction.Yes 74 (56%) Somewhat 48 (36%) No 11 (8%)

5) Body paragraphs were well-structured.Yes 54 (48%) Somewhat 50 (44%) No 9 (8%)

6) Body paragraphs were related to each other in a logical structure that supported the thesis.Yes 62 (53%) Somewhat 53 (45%) No 3 (2%)

7) The paper contained an appropriate concluding paragraph.Yes 68 (56%) Somewhat 42 (35%) No 11 (9%)

8) The paper demonstrates an acceptable level of mechanics and language usage.Yes 51 (41%) Somewhat 60 (49%) No 12 (10%)

For the first question in each of the two submissions of the rubric, the “yes” responses were overwhelming, exceeding 90% in both cases. For the remainder of the questions, responses were strong, but with the least positive responses being for questions 5 and 8, regarding “paragraph structure” and “an acceptable level of mechanics and language usage,” respectively.

ENG 101 – 3


1 2 3 4 5 6 7 80.0%

10.0%20.0%30.0%40.0%50.0%60.0%70.0%80.0%90.0%

100.0%

SLOAT Short Paper Rubric - October 2010

Yes Somewhat No

As can be clearly seen from the chart, there were very few “no” answers given. This may indicate a relatively strong level of preparation for the course, either in earlier education, or, when applicable, in developmental programs. The weakest scores in paragraph structure and mechanics would, however, indicate a need to look to those areas and discuss ways in which support services could be provided, perhaps outside of the traditional classroom setting, for students still struggling in those areas.

In December 2010, ENG 101 instructors were once again given the same rubric to fill out for a subsequent assignment. It was anticipated that some patterns of improvement would be seen in the second study.

Participation was still healthy, if a little lower, for this attempt. December is busy month with classes preparing for the Divisional final exam, which may offer some explanation.

The results for the December 2010 rubric were as follows:

1) The paper includes an appropriate subject based upon the given writing assignment.Yes 71 (95%) Somewhat 4 (5%) No 0

2) A specific topic was developed within the assigned subject for the paper.Yes 66 (85%) Somewhat 15 (20%) No 0

3) An introduction provides background regarding the paper’s thesis.Yes 60 (80%) Somewhat 20 (15%) No 0

ENG 101 – 4

4) A relevant thesis statement is incorporated into the introduction.Yes 60 (80%) Somewhat 19 (14%) No 1 (1%)

5) Body paragraphs were well-structured.Yes 52 (69%) Somewhat 19 (25%) No 4 (5%)

6) Body paragraphs were related to each other in a logical structure that supported the thesis.Yes 52 (69%) Somewhat 21 (28%) No 2 (3%)

7) The paper contained an appropriate concluding paragraph.Yes 50 (64%) Somewhat 20 (26%) No 8 (10%)

8) The paper demonstrates an acceptable level of mechanics and language usage.Yes 34 (45%) Somewhat 38 (51%) No 3 (4%)

The results for the December 2010 rubric can be charted as follows:

1 2 3 4 5 6 7 80%

10%20%30%40%50%60%70%80%90%

100%

SLOAT Short Paper Rubric -- December 2010

Yes Somewhat No

While the sample size for the December study is smaller, there is apparent improvement reflected both in the data and the charts above from the October to the December rubrics.

Regarding criteria 5, “paragraph structure,” the “yes” evaluations rose from 48% to 69%. In the area of mechanics and sentence structure, however (criteria 8), there was a more limited improvement with the “yes” score moving only from 41% to 45% and the “somewhat” score moving from 49% to 51%.

ENG 101 – 5

Again, the issue of supplemental support for ENG 101 students, relevant to mechanics and sentence structure, should be explored.

Another instrument that was used during the Fall 2010 semester was a questionnaire which was to be distributed to ENG 101 students following the mid-term exam. Both instruments were conducted in a completely anonymous fashion. Doing so with this instrument, in particular, is vital to encouraging open participation by both students and faculty members.

That open participation appears to be the case in that students were often very open to identifying their own failure to study sufficiently as a factor in their mid-term exam performance.

Students were asked four questions dealing with their performance and preparedness for the exam. The results of the questionnaire are as follows:

1) Are you pleased with your grade on the exam?Yes 331 (62%) Somewhat 114 (22%) No 85 (16%)

2) Did you prepare adequately for the exam?Yes 321 (59%) Somewhat 195 (36%) No 27 (5%)

If not, why not? (Circle all that apply)a) Did not have time to studyb) Did not know the exam was scheduledc) Have an overcommitted scheduled) Did not study enough during the semester

3) Did the exam relate to what you have been learning in class?Yes 426 (78%) Somewhat 85 (16%) No 35 (6%)

4) Did your instructor accurately tell you what to expect on the exam prior to the exam date?Yes 449 (83%) Somewhat 72 (13%) No 19 (4%)

While students did respond to the choices from a to d under question 2, practicality did not permit me to fully analyze the results, although I have maintained the questionnaire themselves. As you can see, approximately 545 students responded individually to the questionnaire.My review of the questionnaires, however, indicates that the clear majority of answers under the number 2 choices fell into the categories of the last two

ENG 101 – 6

choices, either being over-committed or not having studied enough during the semester.

Interestingly, a number of students responded to the “a to d” choice in spite of the fact that they had responded to the initial question with a “yes.” This conditional approach to conducting a survey question may not have communicated well with a number of students.

As can be seen, 84% of the respondents indicated that they were at least “somewhat” satisfied with their mid-term exam score while only 62% were satisfied enough to choose “yes.” Assuming that those who fell into either category had probably passed the exam, the number of students in the “somewhat” category may very well indicate a healthy determination to do better in the upcoming final.

As can be seen, a very minimal 4% indicated that their instructor had not accurately told them “what to expect on the exam prior to the exam date.” This very low percentage would have to be viewed as “outliers” and an indication that students do feel informed of the nature of the exam. A strong 83% gave that category a solid “yes.”

Another positive sign is the fact that 78% strongly indicated that the exam was related to course work with a Yes, while only 6% indicated that it was not.

SUMMARY

The evaluation of Student Learning Outcomes for ENG 101 during the Fall 2010 semester was certainly a positive experience. Faculty members, both full and part time, appeared to understand the important nature of the study and were willing to cooperate.

The results were predictable and indicated several strengths regarding the structure of the course and the appropriate approach taken by the faculty to the fulfillment of the course requirements.

The survey also indicated the need for greater support for many students who are struggling with issues of mechanics and sentence structure. Since this is not the case with more than 40% of the students, the results would not indicate the need for greater emphasis on these factors in the course. At this level, such work would probably be best approached in a prescriptive manner rather than a class-wide manner.

The College, of course, already has several opportunities available for this type of directed work including the student access of the Learning Center.

ENG 101 – 7

The possibility of more being needed, however, should be considered. One possibility might be a separate “grammar” course for students on the Freshman Composition level, similar to the course that has been offered at Rutgers-Newark in the past.

ENG 101 – 8

ESSEX COUNTY COLLEGE

STUDENT LEARNING OUTCOMES (SLO) ASSESSMENT REPORTMTH 092 – Elementary Algebra

FALL 2010

PREPARED BY:Dr. Eman Y. Aboelnaga Pr. Barbara Satterwhite

Dr. Alvin Williams

MTH 092 – 1

INTRODUCTIONAccording to Linda Suskie in her book Assessing Student Learning: a

common sense guide, 2nd edition, assessment is the ongoing process of: (1) establishing clear, measurable expected student learning outcomes; (2) ensuring that students have sufficient opportunities to achieve those outcomes; (3) systematically gathering, analyzing, and interpreting evidence to determine how well students’ learning matches our expectations; and (4) using the results to understand and improve student learning. Assessment can be achieved in a variety of diverse processes.

This report focuses mainly on student learning outcomes assessment of the course MTH 092, an Elementary Algebra course offered by the Mathematics and Physics Department at ECC. In addition, social factors governing students’ perceptions of their performance were also investigated. The types of assessment used, as well as the methodology and administration of the assessment tools used, are all described. The results and findings are presented and explained. Finally, in order to “close the loop”, feedback based on the findings is suggested in an effort to initiate positive change and improve student learning.

1.1 PURPOSEMTH 092, Elementary Algebra, is one of the most important courses at

ECC. It is the second level in a remedial math sequence that is a prerequisite for 100-level (i.e., college-level) mathematics courses. Furthermore, it is a prerequisite for many other majors and courses available at ECC. These include Nursing, Biology, Chemistry, Engineering, Computer Science, Radiography, in addition to many social science majors. Therefore, the importance of assessing student learning outcomes and correlating them to measurable course performance objectives cannot be underestimated. As co-course coordinators of MTH 092, we are aware that there are many factors that contribute to student success, i.e., student learning. As members of SLOAT in Fall 2010, we endeavored, by choosing three forms of assessment, to investigate some of these factors. These forms of assessment will be discussed in detail in the following sections. Our goal is to use our findings to provide insight into some of the factors that affect student success thereby suggesting possible improvements for future semesters. Furthermore, we hope that by sharing our results and suggestions, we will jumpstart a discourse that will include the exchange of ideas, initiation of other assessment tasks, and is overall focused on the improvement of our MTH 092 course.

METHODOLOGY2.1 POPULATION

MTH 092 – 2

Based on our initial assessment plan, we decided to assess ten sections of MTH 092 with an approximate average of 30 students in each section. This gave us a sample size of approximately 300 students. We hoped to ensure at least a 5% margin error (278 out of 1000 corresponds to a 5% margin error) (Suskie). We attempted to sample a variety of sections. However, based on the response we received from professors willing to participate, the breakdown was as follows:

Professor Sections

Campus Daytime/Evening

Full-time/ Adjunct

Eman Aboelnaga 006 and 028

Main Campus Daytime Full-time

Barbara Satterwhite 009 and 012


Susan Gaulden 011 and 019


Nasser Moheb 003 and 014


Shohreh Andresky CW2 West Essex Daytime Full-time

Gordon Nanton 3WC West Essex Evening Adjunct

As is evident from the table, 80% of the sections were day time courses taught at the Main Campus by full-time professors.

2.2 ADMINISTRATIONAs co-course coordinators of MTH 092, we chose to assess the

following student learning outcomes (SLOs): SLO #1: Course Goal 1: Demonstrate knowledge of the fundamental

concepts and theories from algebra and geometry. SLO #2: Course Goal 2: Utilize various problem-solving and critical-

thinking techniques to set up and solve real-world applications.These correspond to the following measurable course performance objectives (MPOs):

1. Demonstrate knowledge of the fundamental concepts and theories from algebra and geometry.1.1 simplify and evaluate variable expressions;1.2 translate verbal expressions into variable expressions;1.3 perform basic operations on polynomial, rational, and exponential

expressions;1.4 factor polynomial expressions;1.5 solve linear, literal, and factorable quadratic equations;

MTH 092 – 3

1.6 graph a line in the Rectangular Coordinate System;1.7 identify and find the slope and intercepts of a line; and 1.8 find the equation of a line based on given geometric properties

2. Utilize problem-solving and critical-thinking techniques to set up and solve real-world applications. 2.1 apply algebraic methods to solve varied real-world applications

(such as integer problems, uniform motion problems, and perimeter and area problems) that can be modeled by a linear equation or a quadratic equation

We chose three forms of assessment. The first was an anonymous survey designed to investigate students’ attitudes towards math, their classmates, and their professor, as well as their perception of their progress and standing in the class. This is an indirect, summative, and subjective type of assessment based on the input of the students. The second form of assessment was an indirect, process, and objective type of assessment designed to investigate the correlation, if any, between the number of absences and the final grade and between use/completion of online homework and the final grade. Our last form of assessment was direct, summative, and objective, and was designed to measure the student learning outcomes mentioned earlier.

Regarding the first form of assessment: the attitudinal survey, we developed several drafts before finally choosing one that best expressed the issues we were investigating. We initially intended to have it ready to administer by late October after Midterms or early November. We then sent it to Dr. Alvin Williams who then modified the form of questioning in order to make it easier to calibrate. He then provided us with ScanTron-like answer sheets that corresponded to our questionnaire. The next step was to deliver the questionnaires to the participating instructors along with detailed instructions regarding their administration. This process took more time than anticipated so that the questionnaire was actually administered in late November. Students were asked to keep them anonymous and were given about 15 minutes of class time to complete them. We then assembled all the questionnaire answer sheets and delivered them to Dr. Williams. He calibrated the results and provided us with a breakdown of the percentages of students’ answers for each question. We then analyzed the results and formed conclusions and suggestions for future change. These will be discussed further in the Results section.

In order to gather information for our second form of assessment, we prepared an Excel spreadsheet template requesting information from each participating instructor as follows:

MTH 092 – 4

Instructor: Eman Aboelnaga SLOAT Coordinators:Section: 006 Eman AboelnagaTotal # of Students: 25 Barbara Satterwhite

Student ID# Absences Online HW Final GradeAgunanna, Princess O. 9000- 0 yes BBryant Jr., Aniko 9000- 31 no FChung, Claudia R. 9000- 8 yes DColey, Tyler C. 9000- 7 no DDesilhomme, Jean H 9000- 1 yes B

This information was sent to Dr. Williams, where he proceeded to statistically analyze it. He sent the results back to us and we formed conclusions and suggestions for future change.

Finally, since our third form of assessment was designed to measure student learning outcomes, we decided to blueprint the MTH 092 cumulative final exam to all of the MPOs from the entire set of course goals stated earlier. However, for the purpose of this study, the original plan was to increase the number of multiple choice questions so that every MPO corresponding to SLOs 1 and 2 were addressed within the multiple choice section of the final exam. This means that every specific MPO under Course goals 1 and 2 (CG 1 and CG 2) was mapped to a multiple choice question. This allows us to use ScanTron-like sheets in order to collect the data. When preparing the final exam, we found that it was going to be confusing to make application problems (i.e., word problems) multiple choice when neither the students nor the instructors were used to such a situation. We decided to map the MPOs from the first goal to ten multiple choice questions (a reasonable amount of multiple choice questions for a MTH 092 final exam) and hold off on assessing the second course goal. On the day of the final exam, participating professors were provided with a ScanTron-like answer sheet for each of their students. They were requested to have their students answer the multiple choice questions on the actual exam as well as on the ScanTron-like answer sheets. Repeated instructions were given to the students to bubble in their answers carefully and completely and to include the version of the exam that they completed. Despite that, some submitted answer sheets were still found to be incorrectly filled out. After final exams were completed, participating professors were asked to submit their ScanTron-like answer sheets to us. We delivered them to Dr. Williams who

MTH 092 – 5

calibrated the results, providing us with a spreadsheet with the percentages of students who had answered each question correctly, thereby “mastering” that corresponding MPO. Details and results are discussed in the results section of this report.

2.2.1 INSTRUMENTATION2.2.1.1 ATTITUDINAL SURVEY

An anonymous questionnaire was administered to ten sections of MTH 092 within the last week of November and the first week of December. The questions as well as the calibrated results performed by Dr. Alvin Williams are included in Appendix A. 2.2.1.2 RUBRICS

In order to gather information on attendance and use of online homework, we formed an Excel spreadsheet template that professors involved in the study could use to input the students’ information. A sample was shown in section 2.2 of this report. Regarding the grading rubric for the final exam, the ten questions assessed were all multiple choice. The following table illustrates the question along with the MPO it is being mapped to. MPO # - Topic/Skill Sample Final Exam question(s)

used to determine MPO acquisition

(1.1) simplify and evaluate variable expressions

Evaluate the variable expression when b = -2 and c = -1:

(1.2) translate verbal expressions into variable expressions

Translate the following into a variable expression, then simplify: a number added to the difference between twice the number and twenty

(1.3) perform basic operations on polynomial, rational, and exponential expressions

Simplify:

Simplify:

Simplify: (1.4) factor polynomial expressions Factor bz + 3b – 2z – 6 (1.5) solve linear, literal, and

factorable quadratic equations Solve: (1.6) graph a line in the Rectangular

Coordinate SystemGraph: 2x – 3y = -6

(1.7) identify and find the slope and intercepts of a line

Find the slope and y-intercept of the

MTH 092 – 6

line (1.8) find the equation of a line

based on given geometric properties

Find the equation of the line that contains the point (4, -8) and has slope -3.

Each question assessed an MPO of the course and a correct answer was taken as the student having mastered the objective. If the student answered incorrectly, then that MPO was considered not mastered. The results by exam version as well as mean results are referenced in the Results section. The multiple-choice portion of the MTH 092 final exam – Fall 2010, version 1 used in this assessment can be found in Appendix B.

RESULTS3.1 FINDINGS3.1.1 ATTITUDINAL SURVEY

We developed the SLOAT Student Questionnaire for MTH 092 Elementary Algebra to determine how influential social factors are over MTH 092 students' academic performance or if social factors influence their performance at all. We considered two possible social factors which could influence students: the instructor of the class and the other students in the class. Thus we wanted to determine whether the professor or classmates had the more dominant influence on a student. Furthermore, we looked at whether social factors influence which section of MTH 092 a student registers for, and if so, which is the more powerful social factor. Additionally, we asked questions investigating students' attitudes towards the discipline of mathematics, their confidence level in math, and their knowledge of studying math. Finally, we wanted to see how a student's attitude towards their instructor and fellow classmates does (or does not) affect their performance in MTH 092.

Questions 1, 7, and 12 were designed to investigate the importance of social factors in MTH 092 enrollment, and the results indicated that social factors are not very influential in students' decision to register for a particular section of MTH 092. Only 5% of students registered for their section of MTH 092 because they wanted to take the course with a classmate enrolled in that section, while 29% of students registered because they wanted to take a course with the Professor who instructs their section. Yet question 1's results show that 60% of students chose to take MTH 092 to fulfill a math requirement, and another 30% were repeating the course. The questionnaire responses indicate that students are more likely motivated by the need to fulfill graduation requirements than by the desire to take a certain instructor's course or to take MTH 092 with a friend. However students are more likely to register for a section because they like the

MTH 092 – 7

instructor instead of registering because they like another student in that section.

Questions 2 and 5 show that many students have negative feelings about the discipline of mathematics and low confidence in their math skills before coming to ECC. It was found that almost half (46%) of students disliked math or were anxious about math and roughly the same percentage of students were not very confident or not confident at all in their ability to study math. MTH 092 instructors should be mindful of the prevalence of negative feelings towards math among new students, so that they can better help them to build their confidence level in math. However, questions 3 and 6 reveal that 52% of students feel that they now know how to study math, and approximately 75% of students are either somewhat confident in math or very confident in math at present. The results convey that students' confidence level in math increases dramatically at ECC, as well as their ability to study mathematics.

In examining what might cause the change in students’ ability to study math, question 4 asked where students would go for help if they did not know how to study math. The student responses show that the majority (59%) of students would ask their professor for help. Thus, if we can attribute the rise in confidence level of the students to any social factor, it would be the instructor since they are the ones whom students ask for help from the most.

In analyzing students' attitudes towards their MTH 092 instructor and towards the other students, we found that the overwhelming majority (76%) of students surveyed consider it important that they like their Professor. Comparatively, approximately 16% of students consider it important that they like their classmates. Therefore, the students surveyed indicated that they care significantly more about who is instructing their class, than who is taking the class with them. The importance of one's professor over one's classmates was reflected in the responses to questions 10 and 15 as well. Almost half of the students surveyed indicated that their like or dislike of their professor affects their performance in the course. The vast majority (73%) of students did not agree that their like or dislike of their classmates affects their performance in the course. The responses to questions 10 and 15 emphasize the fact that many students feel that it is important to like their professor, and that their attitude towards their professor will directly affect their performance. Few students consider their like or dislike of their classmates important, and even fewer agree that their like or dislike of their classmates has an effect on their academic performance. Interestingly, an overwhelming majority of students (86%) like their professor for MTH 092, while a lesser but still strong majority (63%) like their classmates, and 78% of students were passing MTH 092 with a grade of C or better.

MTH 092 – 8

Thus, in analyzing these responses, one can see the importance of the professor, not just pedagogically, but as the most important social factor influencing a student's academic performance. Consequently, MTH 092 instructors may be able to use their prominent social position in the classroom to help improve their students' academic performance. Professors are in a position to exercise their social influence upon their students' in a positive way, so as to build a rapport with their students which not only makes the students more comfortable with the professor, but also makes the professor more comfortable with the students. This attitudinal survey should serve as another means of learning more about our students and their mindset. If we can become more familiar with our students and maintain our professionalism at the same time, we can then hope to reach them in ways we may have never considered or have underutilized up until now.

3.1.2 ATTENDANCE AND HOMEWORKThe belief that lack of attendance and homework completion adversely

affects a student’s grade tends to be widely held by many faculty members. As course coordinators and faculty members, we also hold this belief; particularly in a mathematics course where topics, for the most part, are sequential. In other words, the following class is dependent on mastery of the previous class’s content. Furthermore, a thorough understanding of mathematics includes a conceptual understanding of the topics, the ability to apply this conceptual understanding to a problem, and the necessary skills to solve it. Homework is a tool that is used to develop and harness these attributes.

Therefore, as part of our student learning outcomes assessment plan, we decided to assess the correlation, if any, between attendance, homework, and final grade. The MTH 092 sample contained the following data: Student Name, ID#, Number of Absences, Use of Online Homework (yes/no), and Final Grade. This sample included 210 students from nine sections that completed the course for the Fall 2010 semester. Two forms of analysis were conducted.

First, a regression analysis was performed that looked at the group of investigated variables specified above. In this case, the MTH 092 final grade was considered to be a dependent variable while the number of absences and use of online homework were each considered independent variables. Regression analysis reflected how the typical value of the dependent variable (the MTH 092 final grade) changed when any one of the independent variables (absences or online homework use) were varied, while the other independent variables were fixed. It was found that the only variable that affected the MTH 092 grade in a statistically significant way was the number of absences. The independent variable, online homework

MTH 092 – 9

use, did not affect the variability in MTH 092 grades in a statistically significant way for this particular sample.

Second, the variables were investigated further using an Independent Samples T-Test to discover which variables were significantly different statistically between the group of students that passed with a MTH 092 grade of “C” or higher and the group of students that did not pass. The analysis showed that the number of absences variable was significantly different between the two groups. The online homework variable was found to not be significantly different between the group of students that passed and the group that did not pass.

As a result, one can conclude that for this sample size, students that received passing grades in MTH 092 were found to have excellent attendance. Regarding the lack of statistical significance for the online homework variable, several factors could account for this. Only three out of the nine sections used online homework. That does not mean that the other sections did not do homework; they just did not do homework online. Furthermore, within the three sections in which online homework was used, some of the students simply did not participate in it, claiming a shortage of funds in order to purchase the book or purchase a webaccess number (a requirement for online homework use). These factors, as well as other issues, need to be addressed further. 3.1.3 FINAL EXAM

As a third form of assessment, the MTH 092 final exam was blueprinted to the measurable course performance objectives. This is the process by which each of the questions on a test is mapped to a measurable course performance objective (MPO). This allows the creator of the exam to ensure that the exam focuses on the most important course content, helping to determine what should be covered on the exam, and to document the extent to which students have achieved each MPO.

The sample size corresponding to the Fall 2010 ten sections of MTH 092 included 148 students that took the final exam. By the time of the final exam, some of the students had stopped attending although they were still registered for the course. There were ten different versions of the MTH 092 final exam. In order to facilitate assessment of ten sections, it was decided to formally assess the first course goal (CG): Demonstrate knowledge of the fundamental concepts and theories from algebra and geometry. This CG is the most comprehensive and includes the important topics covered in a MTH 092 course. These fundamental concepts and theories are stated as MPOs below.

1.1 simplify and evaluate variable expressions;1.2 translate verbal expressions into variable expressions;

MTH 092 – 10

1.3 perform basic operations on polynomial, rational, and exponential expressions;

1.4 factor polynomial expressions;1.5 solve linear, literal, and factorable quadratic equations;1.6 graph a line in the Rectangular Coordinate System;1.7 identify and find the slope and intercepts of a line; and 1.8 find the equation of a line based on given geometric properties

Each of these MPOs was mapped to one of ten multiple choice questions in the first part of the final exam. A ScanTron-like answer sheet was used to collect data from the ten sections on these first ten multiple-choice questions of the final exam. The non-multiple choice parts of the exam addressed the remaining MPOS, as well as the first one, but since they were open ended were not included in the ScanTron-like results.

The results were calibrated separately by version, and then a comprehensive score was found using the data from all ten versions. These results are summarized in the following graph:

MPO 1.1 MPO 1.2 MPO 1.3 MPO 1.4 MPO 1.5 MPO 1.6 MPO 1.7 MPO 1.80

102030405060708090

100

MasteredNot Mastered

One can see that the highest percentage of students, (88.52%), mastered MPO 1.4: Factor polynomial expressions. One reason for this is that the MTH 092 curriculum allots a reasonable amount of time for this topic. Furthermore, it is a skill that is frequently required within other topics in 092, so students become very familiar with it. The MPOs with the smallest percentages of students that mastered them were the following:MPO Description % mastered

MTH 092 – 11

1.5 Solve linear, literal, and quadratic equations that are factorable

58.11

1.6 Graph a line in the Rectangular Coordinate System 51.351.8 Find the equation of a line based on given geometric

properties62.84

One can attribute these results to several, potential factors. MPO 1.6 and 1.8 topics are both covered in the last two weeks of the semester. Usually by then, attendance has dwindled. Therefore, some of the students taking the final exam have barely been exposed to these topics. Furthermore, it is the only chapter that students have not been tested on prior to the final exam. As for MPO 1.5, the question has to do with solving a linear equation, usually a concept that the majority of students master. However, this question included fractions, a topic that many students coming into MTH 092 have difficulty with. It would be interesting in future semester final exams to modify this question to include a linear equation without fractions and to compare the results.

3.2 DISSEMINATION OF FINDINGSBenefit from this assessment can only be gained by sharing the results

with other MTH 092 professors and discussing ways that change can be implemented. As course coordinators of MTH 092, we hope that this report will be made available to all full-time as well as adjunct professors of MTH 092. We will make this report available online and perhaps the MAP division can provide hard copies for those that require them. Furthermore, this final report will be accessible on the ECC SLO Assessment website, http://sloat.mathography.org, and we can also establish a folder within Dropbox that can be accessible to all MAP faculty, where other professors can add files where they have conducted assessment studies. The next step is to share these results at a forum where ideas, thoughts, etc. can be exchanged in order to effect positive change.

3.3 CLOSING THE LOOP – Suggestions for Change3.3.1 ATTITUDINAL SURVEY

As the results of the questionnaire suggest, if professors are better liked by their students, this factor may have an effect on students’ academic performance. The following are suggestions whereby instructors can improve their rapport and interaction with the students.

First of all, simply learning the students’ names is one fundamental mean of establishing a personal connection with each student. Most students realize that it is not easy to remember as many names as instructors have students, so when a professor takes the time to remember a student’s name, it communicates that the professor cares about the student as an individual. Second, an instructor should attempt or take the time to recognize a

MTH 092 – 12

student’s special gifts or academic strengths. By acknowledging their academic strengths, the instructor not only communicates that he/she is interested in the student as an individual, but also that the instructor would like the student to use his/her strengths to succeed. Another way of showing concern may be if the student seems out of character on a particular day. It may be that the student is dealing with an overwhelming situation that does not allow him/her to focus. While instructors are not expected to be social workers or counselors, a helpful action could be to send the student to the appropriate areas in the College that can help the student with his/her particular problem. There are many avenues to explore when considering ways to reach our students in order to help them succeed. Knowing that instructors are one of the instrumental figures in the classroom whom the students have high regard for should motivate us to try these, as well as other methods in order to better impact our students.3.3.2 ATTENDANCE/ONLINE HOMEWORK

As previously mentioned in this report, attendance had a strong correlation to final grade. The better the grade was, the lower the number of absences that a student had. As MTH 092 instructors, we should share these results with our students. Furthermore, we can assign a grade value to number of absences, and even to number of late arrivals to class. When a student consistently walks in to class fifteen minutes late, he/she has usually missed the introduction or basis for a concept and so will most likely be weak in conceptual understanding. I, personally, have assigned 5% of the overall course grade to attendance and participation in the past, and have found that it is a good motivator. I also counted three late arrivals to class as an absence.

Regarding online homework, this study showed that it did not have a statistical significance on the overall course grade. As mentioned before, only one-third of the sections analyzed used online homework. Therefore, it is difficult to make any conclusive results from this study. For next semester, perhaps it would be beneficial to assess more sections that use online homework regularly. Furthermore, a survey could be administered before the end of the semester to investigate student’s attitudes towards online homework. After several semesters of using it, one of the factors that I have informally discovered is that many of the students who didn’t use it claimed financial reasons. If a student does not purchase a new book package from the ECC bookstore, then he/she would have to purchase a webaccess number online costing anywhere from $35 to $50. The MAP division should work with the publishers to keep these costs down so that students are not turned away from using online homework due to financial constraints. Furthermore, students have mentioned in the past that some of them do not have frequent, convenient access to a computer. These issues warrant further investigation that can be conducted within future assessment studies for MTH 092.

MTH 092 – 13

3.3.3 FINAL EXAMAs previously mentioned, MPOs 1.5, 1.6, and 1.8 showed the lowest

level of student mastery. MPO 1.6 and 1.8 are covered during the last two weeks of the semester when some students stop coming or have “given up.” Professors could administrate a quiz towards the end of the chapter before the final exam leaving time to return and review the quiz before finals. That way, students receive an opportunity to be assessed on the topic before the final exam. As for MPO 1.5, as mentioned previously, future final exams could assess the topic of linear equations with fractions and without fractions. Results can then be compared. This will provide insight regarding whether the issue is with respect to weakness dealing with fractions or solving linear equations. Furthermore, the Spring 2011 MTH 092 Final Exam could include assessment of non-multiple choice questions in order to assess student mastery of application problems.

MTH 092 – 14

APPENDIX A

MTH 092 – Appendix A – 1

APPENDIX BESSEX COUNTY COLLEGE

DIVISION OF MATHEMATICS AND PHYSICSMTH 092 - FINAL EXAM - Fall 2010

Name: ____________________________ Date: ____________ Section: _____

Telephone #________________________________ ID # __________________________

Part I MULTIPLE CHOICE. Problems (1-10) are each worth THREE (3) points. Place the letter of the correct answer in the blank provided to the left of the question. Write out the solution to the problem in the space provided. No partial credit.

___ 1. Evaluate the variable expression when b = –16 and c = 4.

A) 52 B) 160 C) 88 D) 153 E) 17

___ 2. Translate the following into a variable expression, then simplify:a number added to the difference between twice the number and three

A) D)

B) E)

C)

___ 3.

Solve: y + =

A) B) C) D)

MTH 092 – Appendix B – 1

___ 4.Simplify:

A) B) C) D) E)

___ 5.

Simplify:

A) B) C) D)

___ 6.

Simplify

A) B) C) D)

___ 7. Find the equation of the line that contains the point (1, –1) and has slope –4.

A) D) B) E) C)


___ 8.

Find the slope and y-intercept of the line 1

A)

Slope y-intercept (1, 0)B)

Slope y-intercept (0, –1)C)

Slope y-intercept (0, 1)D)

Slope y-intercept (- 1, 0)

___ 9. Factor:

A) D)

B) E)

C)


___ 10. Graph:

A)

B)

C)


D)

E)


MTH 100 SLOAT ASSESSMENT STUDY REPORT (Fall 2010)prepared by the MTH 100 Course Coordinators: Soraida Romero & Carlos

Castillo

I. Introduction:A comprehensive assessment study on MTH 100 at Essex County

College was conducted in fall 2010 as part of SLOAT (Student Learning Outcomes Assessment Team.) The principal coordinators for this study were two full-time faculty members of the Math and Physics Division (MAP): Carlos Castillo, Instructor of Mathematics, and Soraida Romero, Professor of Mathematics; another important contributor to this study was Alvin Williams, Associate Professor of Mathematics, who did all the statistical analysis for the study.

a. Purpose: The purpose of this study was two-fold. First, the study attempted to

determine whether MTH 100 students are indeed learning all four (4) Course Goals (CGs) that were established by the Math Department for this course. Under each CG, there are also specific Measurable Performance Objectives (MPOs) that students are expected to attain; these CGs also assess specific General Education Goals (GEGs) established by the College. The list of these CGs for MTH 100 and the MPOs contained in each with the relevant CGs in parenthesis for each are listed below:

CG #1: Demonstrate knowledge of the fundamental concepts and theories from algebra and geometry, (GEG 2)(1.1) Solve linear equations(1.2) Solve literal equations(1.3) Solve rational equations(1.4) Solve radical equations(1.5) Solve quadratic equations(1.6) Solve linear inequalities(1.7) Solve systems of equations(1.8) Factor polynomials(1.9) Simplify exponential expressions(1.10) Perform basic operations on polynomials(1.11) Perform basic operations on rational expressions(1.12) Perform basic operations on radical expressions(1.13) Perform basic operations on complex numbers(1.14) Find the equation of a line based on given geometric

properties(1.15) Graph a line in the Rectangular Coordinate System(1.16) Graph a parabola in the Rectangular Coordinate System

MTH 100 – 1

(1.17) Graph a circle in the Rectangular Coordinate System(1.18) Determine whether a given relation is a function, find its

domain, and use function notation CG #2: Utilize various problem-solving and critical-thinking techniques

together with algebra to set up and solve application problems taken from a variety of disciplines, (GEG 2)(2.1) Apply algebraic methods to solve varied real-world applications

(such as, consecutive integer problems, coin/stamp problems, distance problems, investment problems, area problems, and work problems) that can be modeled by a linear equation, quadratic equation, rational equation or system of equations.

CG #3: Communicate accurate mathematical terminology and notation in written and/or oral form in order to explain strategies to solve problems as well as to interpret found solutions.(GEG 1) (3.1) Write and explain solutions to application problems related to

the course material using appropriate mathematical terminology and notation.

CG #4: Use calculators effectively as a tool to solve such problems as those described above, (GEG 2) (4.1) Use a calculator to perform basic arithmetic operations,

evaluate powers and find the square root of a number.

The second purpose of this study was to ascertain what factors or variables impede some students from performing well in mathematics. Some of the variables to be investigated in this study include student’s prior math background, study habits, placement, attendance, going to tutoring, participation with on-line homework package, etc.

II. Methodology:a. Population sample used -

Based on information gathered from Linda Suskie’s book on Assessing Student Learning: a common sense guide, 2nd edition, we decided to use 10 sections of MTH 100 for our study to ensure a 5% margin of error. While the study started with 405 students, the sample population was reduced to 314 since 91/405 or 22% of the students were voided out of their MTH 100 class and got no grade by the end of the semester. Using representative random sampling, the following ten sections and instructors of MTH 100 were selected to participate in this study conducted in Fall 2010.

MTH 100 – 2

Day Sections at the Main Campus:MTH 100-002 TRF 10-11:20 (adjunct instructor Jayson Swanson)MTH 100-004 TRF 10-11:20 (adjunct instructor Douglas Platt)MTH 100-005 TRF 1-2:20 (full-time instructor Soraida Romero)MTH 100-007 TRF 1-2:20 (adjunct instructor Alex Taran)MTH 100-013 TRF 11:30-12:50 (full-time instructor Ron Bannon)MTH 100-016 TRF 7-8:20 AM (full-time instructor Soraida Romero)

Evening Sections at the Main Campus:MTH 100-OEC MW 7:25-9:10 (adjunct instructor Jose Iglesias)MTH 100-OGC MW 5:15-7 (adjunct instructor Mathew Cherian)

Day Section at the West Essex Campus:MTH 100-CW2 MWF 11:30-12:50 (full-time instructor Shohreh Andresky)

Evening Section at the West Essex Campus:MTH 100-CWC MW 5:35-7:20 (full-time instructor Shohreh Andresky)

b. Instrumentation – There were three different methods used to gather data for this study. These were as follows:

i. Multiple-choice questions blue-printed with MPOsii. A Student Questionnaireiii. Data obtained from IT

i. Multiple-choice questions blue-printed with MPOs –

As a means of determining whether students taking MTH 100 are meeting the Measureable Performance Objectives (MPOs) for this course, Professors Castillo and Romero decided to include eight multiple-choice questions blue-printed to the MPOs in each of the 4 Departmental exams for MTH 100 given out during the fall 2010 semester. ScanTron sheets prepared by Prof. Williams (including Student Name, Student ID and a section to place the answer for each of the 8 multiple-choice questions) were included in each exam packet to facilitate the easy grading of these multiple-choice questions. The time-line for administrating these 4 tests was: Test #1, late September; Test #2 (Midterm), late October; Test #3 (Midterm), late November; and Test #4 (Final), late December. After each exam period was over, the instructor returned the completed ScanTron sheets to Prof. Castillo who first verified that each sheet had a student name and ID number, after which he submitted all these ScanTron sheets

MTH 100 – 3

to Prof. Williams for statistical analysis. See Appendix A for a listing of the multiple-choice questions used in each test and the corresponding MPO associated with each of these questions.

ii. A Student Questionnaire –In order to ascertain what factors impede student progress, the two

course coordinators along with Alvin Williams designed a student questionnaire consisting of twenty-four multiple-choice questions. These questions were formed to investigate students’ prior math background, study habits, class attendance, tutoring attendance, on-line homework package participation, etc. The questionnaires were packaged together with a Disclosure Statement, prepared by Prof. Romero, which informed the students that their responses would be kept confidential and used only for the purposes of this SLOAT study. Since it was felt that some students may not feel comfortable answering the questions truthfully if their instructor administered the questionnaire, other full-time professors were asked to come to the 10 classes, ask the instructor to leave, give each student a copy of the Disclosure Statement as well as read it to them, then administer the surveys; the professors who assisted were Professors Andresky, Castillo, DeLaTorre, Gaulden, Romero, and Rozak. The completed questionnaires were then gathered by Professor Castillo and submitted to Prof. Williams for statistical analysis. See Appendix B for a copy of the student questionnaire.

iii. Data Obtained from IT –

Student attendance, instructor, class location and time, prerequisite completion, and others variables may have an influence on a student’s final grade. To determine whether there is a significant correlation between factors such as these and a student’s final grade, a spreadsheet containing student information was required. In late September, Prof. Romero requested the following data from the Office of Information Technology (IT) for all 314 students participating in this study: name, ID number, MTH 100 section, Placement Test scores, and all math courses taken at ECC up to the MTH 100 class being taken in fall 2010 including the grades earned in each and the semester when taken. The requested data was first received in early October, and then re-submitted in early November when it was noted that some information was missing. Throughout the month of November, Prof. Romero organized the data and created an Excel spreadsheet that was used for further analysis of the data. In late December, each instructor who participated in this study submitted a complete list of all their students, their ID numbers, their final grade for the course, number of absences in the class, and indicated if the student participated in on-line homework for the course. This data was returned to Prof. Romero who then added it to the student spreadsheet that had been prepared earlier. This completed spreadsheet was

MTH 100 – 4

subsequently submitted to Prof. Williams to determine any significant correlations.III. Results obtained from the three different methods used to

gather data for this study:

(a) Results from multiple-choice questions blue-printed with MPOs – Out of the original 314 students chosen to participate in this MTH 100

study, 300, 294, 207, and 206 students took test 1, the midterm, test 2, and the final exam, respectively. Each test or exam consisted of 22 or 23 questions including 8 multiple-choice questions used to examine for the acquisition of 8 MPOs, not all necessarily distinct. At the end of the fall 2010 semester, all 21 MPOs were eventually tested. Each MPO, the question(s) used to determine its acquisition, the average percentage score of students who met the particular MPO, and the number of students who answered the question(s) relating to it are listed in the table found in Appendix A. It was found that of the 21 MPOs that were tested, 15 out of the 21 MPOs (71.4%) were met with students scoring an average of 70 percent or more. An average score of 70 percent or higher on a given MPO is considered a success.

The MPOs that were acquired include:1.1 Solve linear equations1.2 Solve literal equations1.3 Solve rational equations1.4 Solve radical equations1.6 Solve linear inequalities1.8 Factor polynomials1.9 Simplify exponential expressions1.10 Perform basic operations on polynomials1.11 Perform basic operations on rational expressions1.13 Perform basic operations on complex numbers1.14 Find the equation of a line based on given geometric properties1.15 Graph a line in the Rectangular Coordinate System1.16 Graph a parabola in the Rectangular Coordinate System1.17 Graph a circle in the Rectangular Coordinate System1.18 Determine whether a given relation is a function, find its domain,

and use function notation

There were 6 out of the 21 MPOs (28.6 %) that failed to be acquired in the study. These are listed below with the average score of students who met the MPO, followed by a description of the reason why the MPO was probably not met.

(1.5) Solve quadratic equations. (average score: 63.11 %)

MTH 100 – 5

Students may have had a difficult time solving the quadratic equation on the final exam since to solve it required the use of the quadratic formula, a formula which they may have forgotten, or the use of completing the square technique, which students usually avoid. In fact, it is possible that perhaps some students may have used the quadratic formula correctly and arrived at the following solution . However, they may not have understood that implies that the quadratic equation has two answers namely: . Perhaps this MPO can be met if the instructor highlights the details of writing solutions and provides the Quadratic Formula to the students.

(1.7) Solve systems of equations. (average score: 68.37 %)The liberty of choosing any method to solve the question on system of

equations may have confused some students. The question was designed so that the substitution method was the most convenient method to use. However, since the graphing method and the substitution method are taught in the same lecture, students’ exposure to the substitution method may have been inadequate. Since the addition method is taught separately in another lecture and it is the method that most students prefer, it is possible that students would have used this method and perhaps have obtained the correct answer had the problem been set up in the traditional way to facilitate the use of this addition method. Since this MPO was met by over 68% of the students in the sample, perhaps it can be met the next time if it is tested by simply setting up the equations the traditional way.

(1.12) Perform basic operations on radical expressions. (average score: 61.86 %)

The topic of radicals is first covered in MTH 100 and not in any of the prerequisite courses: MTH 086 and MTH 092. Also, the chapter on radicals is taught towards the end of MTH 100 and generally difficult for students to understand especially since a good deal of terminology is used. Since we have so many topics in MTH 100 that were already covered in MTH 092, it may be the proper time to revise the course outline to include the chapter on radicals at a much earlier time to allow students time to master this important topic of college algebra.

(2.1) Apply algebraic methods to solve varied real-world applications that can be

modeled by a linear equation, quadratic equation, rational equation or system of equations. (average score: 68.00 %)

Regardless of the math course, students have a hard time solving word problems especially setting up the proper equation to solve it. However, since this MPO was met by 68 % of 500 students (not all distinct), it is a

MTH 100 – 6

positive sign that this MPO can be met from next semester and on with some improvements on how to teach word problem-solving techniques.

(3.1) Write and explain solutions to application problems related to the course material using appropriate mathematical terminology and notation. (average score: 58.69 %)

With regards to the MPO requiring the verbal explanation of an answer, no question in the MTH 100 homework set requires a student to verbally explain their answer. As a result, it may be the case that many instructors do not emphasize that theory is vital for their understanding of the subject. Students become satisfied arriving at an answer and not interested in the explanation of their answer since they may feel that only teachers have to explain answers. Since this was the MPO that was met by the lowest percent of students, it is important that the Department look at ways of getting students to practice more on verbal explanations of solutions.

(4.1) Use a calculator to perform basic arithmetic operations, evaluate powers and find the square root of a number. (average score: 68.33 %)

The question on finding the distance between two points then using the calculator to get the answer may have been a poorly chosen problem to determine if students know how to use the calculator to perform an operation. Students may have forgotten the formula and perhaps this is the reason why they responded incorrectly; as a result, one cannot determine if an incorrect response to this question is on account of not knowing the distance formula or how to use it or else not knowing how to use the calculator properly to get the square root of a number to get the correct answer. However, since this MPO was met by 68% of the students, perhaps next time a more carefully selected problem can be used to test this MPO.

(b) Results from the student questionnaire –

The student questionnaire was conducted the first week of December 2010 since it was felt that by this time most students who had withdrawn or stopped coming to class would no longer be attending. There were 172 students who completed the questionnaire (n = 172 or 55% of the sample population in this study.) The student responses to each question on the student questionnaire are shown in Appendix C.

Prof. Williams did a statistical analysis on the results of this

questionnaire to determine whether there is a significant correlation between the following:

(1) Grades earned in MTH 100 and prior math background of student before coming to ECC (see question #4 on questionnaire.)

MTH 100 – 7

(2) Grades earned in MTH 100 and math attitude of student (see question #19 on questionnaire.)

(3) Grades earned in MTH 100 and student using tutoring facilities (see question #8 on questionnaire.)

(4) Grades earned in MTH 100 and student having a textbook for the course (see question #6 on questionnaire.)

(5) Grades earned in MTH 100 and student perception of their amount of absences (see question #5 on questionnaire.)

(6) Grades earned in MTH 100 and student perception of their meeting course pre-requisites (see question #2 on questionnaire.)

(7) Actual grade earned in MTH 100 and student perception of the grade they will be getting in MTH 100 (see question # 1 on questionnaire.)

(8) Grades earned in MTH 100 and student perception of how much homework they have done in the course (see question #7 on questionnaire.)

(9) Teacher reporting of student participation with on-line homework vs. their perception of their involvement with this on-line homework (see question #11 on questionnaire.)

(10) Grade earned in MTH 100 and student perception of math being useful (see question # 17 on student questionnaire.)

(11) Grade earned in MTH 100 and student perception of math being applied to topics in their major (see question # 18 on student questionnaire.)

Prof. Williams performed a regression analysis on the entire group of variables listed above by using a reduced data set containing only those 172 students who responded to the survey. In statistics, regression analysis includes techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable (MTH 100 Grade) and one or more independent variables. More specifically, regression analysis helps us understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. In this way, the analysis discovers "predictors" of the dependent variable (grade in MTH 100.) From this regression analysis made by Prof. Williams, it was discovered that the predictors of the MTH 100 grade from among the above variables entered were Q1 (Perception of grade earned) and Q5 (Perception of absences). Quite surprisingly, the other remaining variables did not affect the variability of the MTH 100 grade in a statistically significant way.

Since three weeks before the end of the semester students should be well aware of how they are performing in the course, they apparently predicted what their final grade would be; therefore having students’ perception of their final grade as a predictor of the actual grade is to be expected. Attendance is also a predictor of performance implying that a

MTH 100 – 8

student’s attendance and their final grade are directly proportional. In other words, the more lectures students attended, the higher their grade.

A further study, an Independent Samples T-Test, was then done to compare groups of students that passed and students that did not pass. The T-Test found that the following variables are significantly different between groups of passing and non-passing students in this study: Actual number of absences submitted by the professor; Q1 (Student perception of grade earned); Q5 (Student perception of absences); Q7 (Student perception of homework done); Q16 (Student perception of math test anxiety); and Q23 (Student perception of need for more time to take tests).

Since homework is usually 0, 5, or 10 percent of a student’s final grade, students may feel that homework will have a minimal impact on their final grade. The T-Test shows, however, that the students who did most of their homework performed better than those who completed a minimal part of their homework. A student’s lack of preparation from doing little to no homework may cause anxiousness during a test. Even though some MAP faculty members have offered workshops on dealing with math text anxiety, these workshops have not been well attended; since the T-test results indicate that students with math text anxiety are not performing as well as those without it, perhaps these workshops should be continued. Also, the lack of sufficient time to complete tests certainly does not help students with math anxiety. The T-Test confirms that many students, in general, need more time to take tests.

(c) Results from student data obtained from IT – Using the Student Data Spreadsheet for the 314 students involved in

this study, the data was analyzed to determine success rates based upon the following variables:

(1) Grades earned by students and the type of instructor for MTH 100 (that is, if there is a difference in success rates by those students who took MTH 100 with a full-time instructor and those who took it with an adjunct instructor.)

(2) Grades earned by students and the time of day for MTH 100 (that is, if there is a difference in success rates by those students who took MTH 100 during the day and those that took it in the evening.)

(3) Grades earned by students and the location where students took MTH 100 (that is, if there is a difference in success rates by those students who took MTH 100 at the Main Campus and those who took MTH 100 at the West Essex Campus.)

(4) Grades earned by students and student placement (that is, if there is a difference in MTH 100 success rates between those

MTH 100 – 9

students who were initially placed correctly on their first math course at ECC on the basis of placement test scores and those who were not correctly placed.)

(5) Grades earned by students and meeting MTH 100 pre-requisites (that is, if there is a difference in MTH 100 success rates between those students who met the MTH 100 pre-requisite of passing MTH 092 or being placed into MTH 100 on the basis of placement test scores and those students who did not meet the MTH 100 pre-requisite.)

(6) Grades earned by students in MTH 100 and their grade earned in MTH 092 (that is, if there is a difference in MTH 100 success rates between those students who earned B or higher in MTH 092 and those that earned less than B in MTH 092.)

(7) Grades earned in MTH 100 and the track where students started taking math at ECC (that is, if there is a difference in MTH 100 success rates between those students who started with AFM – track 1, those who started with MTH 086- track 2, those that started with MTH 092 – track 3, and those who started with MTH 100 – track 4.)

(8) Grades earned in MTH 100 and leaving a gap between math courses at ECC (that is, if there is a difference in MTH 100 success rates between those students who do leave a gap between math courses at ECC and those that do not leave a gap between their math courses.)

(9) Grades earned in MTH 100 and number of absences incurred in MTH 100 (that is, if there is a difference in MTH 100 success rates between those students who have few absences (three or less) and those students who have excessive absences (four or more).

(10) Grades earned in MTH 100 and participation with on-line homework (that is, if there is a difference in MTH 100 success rates between those students who participated with on-line homework and those who did not participate.)

The following results from this analysis were noted for the 314 students in this study:

(1) Grades earned by students and the type of instructor for MTH 100: Of the 314 students, 142/314 or 45% were taught by full-time faculty and 172/314 or 55% by adjuncts. The success rate of students taught by full-time faculty was 78/142 or 55% and that of the adjunct faculty was 61/172 or 35% as is shown below.

MTH 100 – 10

Adjunts Full-Time0%

20%

40%

60%

35%

55%

Success Rate and Instructor

Succ

ess

Rate

Discussion: It appears that students in this study learned better from full-time than adjunct faculty and this was confirmed by the regression analysis conducted by Prof. Williams where it was found that the type of instructor the student had in our study (full-time vs. adjunct) was a top predictor of the MTH 100 grade obtained by the student.

(2) Grades earned by students and the time of day for MTH 100:Of the 314 students, 227/314 or 72% took MTH 100 during the day and 87/314 or 28% during the evening. The success rate of day students was 100/227 or 44% and that of the evening students was 38/87 or 44% as is shown below.

Day Evening

-20%

0%

20%

40%

60%

44% 44%

Success Rate and Time of Day

Succ

ess

Rate

Discussion: It appears that is in this study there is no difference in success rate based on the time the class was taken (day vs. evening). This was confirmed by the statistical analysis conducted by Prof. Williams with no significant correlation being found between the time the course was taken and success rate.

(3) Grades earned by students and the location where students took MTH 100:

MTH 100 – 11

Of the 314 students, 258/314 or 82% took MTH 100 in the Main Campus and 56/314 or 18% took MTH 100 in the West Essex Campus. The success rate of the main campus students was 112/258 or 43%; that of the WEC students was 30/56 or 54% as is shown below.

Main WEC0%

20%

40%

60%

43%

54%

Success Rate and LocationSu

cces

s R

ate

Discussion: It appeared that in this study the MTH 100 success rate was higher for those students in the sample taking the course at the West Essex campus than those taking it in the main campus. This could be due to the fact that many students in the West Essex Campus come from suburban high schools where they may have had more a rigorous mathematics education program than those students who take math in inner-city high schools like Newark.

(4) Grades earned by students and student placement: On the basis of their placement score, 256/314 or 82% of the students were placed correctly into their math courses; 36/314 or 11% of the students were placed incorrectly and the remaining 7 % includes those 22/314 students that did not take the placement test. According to the Testing Office policy, those students who are exempt from taking the math placement test are those who had taken the SAT and/or transferred in a college-level math course and are therefore considered prepared to take college level math courses; therefore, this would make those 22 students who did not take the placement test as also being properly placed. Thus the percent of students who were placed correctly into MTH 100 in this SLOAT study would then be higher at 89%. The success rate in MTH 100 for those students who were not placed correctly was 16/36 or 44%; also the success rate of the group of students who were placed correctly (either on the basis of the placement test or the Testing office exemption policy) was 121/278 or 44% as is shown below.

MTH 100 – 12

Correct Incorrect

-20%

0%

20%

40%

60%

44% 44%

Success Rate and Student Placement

Succ

ess

Rate

Discussion: In our SLOAT study it was found that there was no difference in success rates in MTH 100 by those students that were placed correctly and those that were not placed correctly. Perhaps this is due to the fact the number of students who were not placed correctly was quite small (36) especially in comparison to those that were placed correctly (278).

(5) Grades earned by students and meeting MTH 100 pre-requisites :Of the 314 students, 259/314 or 82% of the students met the pre-requisites for all their math courses taken up to MTH 100; 33/314 or 11% did not meet the pre-requisite for at least one math course; and, 22/314 or 7% did not take the placement test so we do not know if they met pre-requisites or not. The success rate of those students that did not meet pre-requisites was 12/33 or 36% and 117/259 or 45% for those that did meet the pre-requisites; also, 10/22 of 45% of the students for whom meeting pre-requisites was unknown were successful in MTH 100. This is shown below.

Met Not Met

-20%

0%

20%

40%

60%

45%

36%

Success Rate and Meeting Pre-requisites

Succ

ess

Rat

e

MTH 100 – 13

Discussion: In this study, it appears that meeting pre-requisites for MTH 100 gives a student a better chance for success in MTH 100.

(6) Grades earned by students in MTH 100 and their grade earned in MTH 092:Of the 314 students in the sample, 209/314 or 67% of them took MTH 092. Of these 209 students in the sample that took MTH 092 before they took MTH 100, 102/209 or 49% earned grades less than B in MTH 092 and 107/209 or 51% earned a grade of B or higher. The MTH 100 success rate of those students who obtained a grade of B or higher in MTH 092 was 62/107 or 58% while that of the 28/102 who got a grade lower than B in MTH 092 is significantly lower at 27%. This is shown below.

B or higher Less than B

-20%

0%

20%

40%

60% 58%

27%

Success Rate and Grade in MTH 092

Succ

ess

Rate

Thus it would appear that a student who gets a good grade in MTH 092 is more than twice as likely to pass than one who barely passed MTH 092.

(7) Grades earned in MTH 100 and the track where students started taking math at ECC:Of the 314 students, 27/314 or 9% of the students started their math courses with AFM 083 (Track 1); 166/314 or 53% started with MTH 086 (Track 2); 31/314 or 10% started with MTH 092 (Track 3); and, 90/314 or 29% started with MTH 100 (Track 4). The success rate of the 27 students that started with AFM 083 was 8/27 or 30%; that of the 166 students that started with MTH 086 (Track 2) was 72/166 or 43%; that of the 31 students that started with MTH 092 (Track 3) was 16/31 or 52%; and finally that of the 90 students who started with MTH 100 (Track 4) was 45/90 or 50 % . This is shown in the chart below.

MTH 100 – 14

Track 1 Track 2 Track 3 Track 40%

20%

40%

60%

30%

43%

52% 50%

Success Rate and Math Track

Succ

ess

Rate

Discussion: In this study it appears that the students that performed the best were those that started with MTH 092 (Track 3); the second most successful group included those who started with MTH 100 (Track 4); the third most successful group consisted of those that started with MTH 086 and the track that did the poorest included those who started with AFM 083.

(8) Grades earned in MTH 100 and leaving a gap between math courses at ECC:Of the 314 students, 115/314 or 37% students left at least one gap between one math course and the next in the sequence and 199/314 or 63% did not leave a gap between math courses. Comparing the success rates of those that left gaps and those that did not, we noted the following: 44/115 or 38% of those students who left gaps passed while 95/199 or 48% of those that did not leave the gap passed. This is shown below.

Left Gaps No Gaps0%

20%

40%

60%

38%

48%

Success Rate and GapsBetween

Math Courses

Succ

ess

Rate

MTH 100 – 15

Discussion: In this study it appears that leaving gaps between previous math courses which are pre-requisites for MTH 100 lowers the chances of a student passing MTH 100.

(9) Grades earned in MTH 100 and number of absences incurred in MTH 100:Of the 314 students, 38/314 or 12% had no absences, 73/314 or 23% were absent one to three times, 48/314 or 15% were absent 4 to 6 times, 71/ 314 or 23% had 7 or more absences, and 84/314 or 27% stopped attending. This means that only 35% of the students had three absences or less with the remaining 65% of students having 4 or more absences, or stopped attending. When comparing the success rate of students with amounts of absences, the following was noted.

None 1 to 3 4 to 6 7 or more0%

10%20%30%40%50%60%70%80%90%

100% 97%

73%63%

25%

Success Rate and Absences

Succ

ess

Rate

Discussion: This table clearly suggests that as the number of absences increase, the success rate in the course dramatically decreases. This was confirmed by the regression analysis conducted by Prof. Williams; the data noted that number of absences incurred by the students was a statistical predictor of the MTH 100 grade received by these students.

(10) Grades earned in MTH 100 and participation with on-line homework :Of the 314 students in the sample, 111/314 or 35% participated with on-line homework and 203/314 or 65% did not. Of those 111 that used this homework software, 55/ 111 or 50% earned grades of 60% or higher on this on-line homework and 56/111 or 50% earned grades less than 60% on this homework. When comparing the success rate of students who participated with on-line homework and those that did not, the following was noted: those

MTH 100 – 16

who participated with on-line homework and received a grade of 60% or higher had a success rate in MTH 100 of 43/55 or 78% whereas those who participated and received a grade below 60% had a MTH 100 success rate of 12/56 or 21%. Also, comparing the success rate of all those who participated with on-line homework and those that did not, we note the following.

Participated Not participate0%

20%

40%

60%

50%

41%

Success Rates and on-line homework

Succ

ess

Rate

Discussion: The data obtained from this study suggests that those who participated with on-line homework have a higher success rate in MTH 100 and in particular those who score well (above 60%) on this on-line homework seem to have a much higher chance of success in MTH 100.

Other Findings:Math Courses Repeated: 88/314 or 28% of the students in the study

repeated at least one math course. Of these repeating students, 7/88 or 8% repeated MTH 086; 13/88 or 15% repeated MTH 092; and 75/88 or 85% are repeating MTH 100. The success rate of all those students repeating MTH 100 was 36/75 or 48%; thus, persistence does seem to pay off and students who fail MTH 100 once should be encouraged to repeat the course.

Retention in the study: While the study started with 405 students, the sample population was reduced to 314 since 91/405 or 22% of the students were voided out of their MTH 100 class and got no grade by the end of the semester. Of these 314 students remaining in the study, one month later when Test #1 was given, only 300/314 or 96% took this test; two months later, only 294/314 or 94% took Test 2 (Midterm); three months later, 207/314 or 66% took Test #3; and finally, by the end of the semester, 206/314 or 66% took Test #4 (Final). If we define retention as the number of students who stay until the end, take the final exam and get a grade for a course, then 206/314 students or 66% of the sample of students in the study were retained in the course until its completion.

MTH 100 – 17

Grades Obtained by students in this study: Of the 314 students, 35/314 or 11% earned an A ; 26/314 or 8% earned a B+; 30/314 or 10% earned a B; 24/314 or 8% earned a C+; 25/314 or 8% earned a C; 15/314 or 5% earned a D; 91/314 or 29% earned an F; 67/314 or 21% earned W; and 1/314 or 0.3% earned a grade of I. Since Success Rates are determined by those students that earned grades of C or higher, this indicates a 45% success rate for this sample of students. The following table shows the breakdown of grades in this study.

C or higher D or F W or I

-20%

0%

20%

40%

60%

45%

34%

21%

Grades Earned in this Study

Gra

des

Earn

ed

Summary of Findings from the Student Background Data Analyzed: Of the 10 variables investigated, the above data shows that there were a

number of variables that do seem to affect student success rates in MTH 100. These are: type of instructor, location where class is taken, meeting pre-requisites for the course, gaps between math courses taken, math track where started, grade in MTH 092, participation with on-line homework, and number of absences incurred by the student. The two variables that did not show a difference in student success rates are: the initial student math placement on the basis of the placement test score and the time of day when the course is taken. The statistical analysis of this student background data conducted by Prof. Williams found that there was indeed a significant correlation between those students who passed the course and those who were taught by full-time faculty. Since full-time faculty have more expertise in mathematics, have more experience teaching math, as well as are more accessible to students, it is not unusual that students perform better when taught by full-time over adjunct faculty. This result stresses the need for the Department to hire more full-time faculty and decrease the number of sections taught by adjuncts.

IV. Summary, Conclusion and Recommendations:

MTH 100 – 18

An intensive study on MTH 100 considering many factors impacting student success in this course was done by Professor Soraida Romero, Professor Carlos Castillo and Dr. Alvin Williams of the MAP Division during the fall 2010 semester as part of the Student Learning Outcomes Team (SLOAT). To determine whether students taking MTH 100 are meeting the Measurable Performance Objectives (MPOs) for this course, Professors Castillo and Romero included eight multiple-choice questions blue-printed to the MPOs in each of the 4 Departmental exams for MTH 100 given out during the fall 2010 semester. By the end of the semester, Professors Castillo and Romero were able to test for the acquisition of all 21 measurable performance objectives in MTH 100. Of the 21 MPOs that were tested, 15 out of the 21 (15/21 = 71.4 %) had the given MPO met by 70 % or more of the students who answered the question(s) relating to that MPO. As a result, 6 out of the 21 (6/21 = 28.6 %) MPOs failed to be acquired. The MPOs which failed to be acquired are described in the first part of the Results section and the following suggestions may help future students acquire these MPOs:

The Department should consider including in the MTH 100 final exam a formula sheet consisting of the distance formula, the quadratic formula, the area of a rectangle, and the Pythagorean Theorem in order to ensure that student errors are not based on forgetting formulas.

Each instructor should devote more time to solving a system of equations by the substitution method. In addition, a supplemental worksheet containing several systems of equations will be designed for use by all interested instructors. The instructions on this worksheet will not be conventional and will be as follows: Solve each system of equations by both the substitution method and the addition method. Which method was more convenient? What would you change to make the less convenient method become more convenient?

Instead of teaching the chapter on radicals towards the end of the course, a suggestion will be made to the curriculum committee to include this chapter at a much earlier time. To help this transition go smoothly, the coordinators of MTH 086, MTH 092, and MTH 100 should meet with the curriculum committee and talk about a considerable restructuring of all three courses.

In order to facilitate the process of learning how to solve word problems, seminars should be conducted by the Math and Physics Department open to all instructors (part-time and full-time) to discuss strategies and best-practices for teaching how to solve word problems using algebra.

A supplemental worksheet containing problems requiring a verbal explanation will be designed and made available for use by all interested instructors.

MTH 100 – 19

Professors Castillo, Romero and Williams designed a student questionnaire consisting of twenty-four multiple-choice questions formed to investigate students’ prior math background, study habits, class attendance, tutoring attendance, on-line homework package participation, etc. It was found that the top predictors of the MTH 100 grade from among all the variables of the questionnaire were Q1 (Perception of grade earned) and Q5 (Perception of absences). Prof. Williams also conducted an Independent Samples T-Test to compare groups of students that passed and students that did not pass. The T-Test found that the following variables are significantly different between groups of passing and non-passing students: Actual number of absences, Q1 (Student perception of grade earned), Q5 (Student perception of absences), Q7 (Student perception of homework done), Q16 (Student perception of math test anxiety), and Q23 (Student perception of need for more time to take tests). Given these study results, Professors Castillo, Romero, and Williams make the following recommendations:

On the first day of class, all MTH 100 instructors should stress to their students that our research has shown that students who get good grades in MTH 100 are ones that have excellent attendance and complete their homework assignments.

Every semester, the Math Department should offer workshops on dealing with test anxiety. Professors Ming McCall and Kathleen Powell have conducted seminars on text anxiety in the past and will be asked to continue offering similar seminars in the near future.

The Math Department should consider making arrangements that would allow more time on exams (particularly high stakes exams like Midterms and Finals). If not, the exam committee should consider reducing the number of questions asked on each test to allow students enough time to take the test.

Professor Romero did her own study on success rates using control variables such as student’s prior math background, study habits, attendance, going to tutoring, and participation with an on-line homework package, among others. Of the 10 variables investigated from student’s background data gathered from the Office of Institutional Research, 8 out of the 10 appeared to affect student success rate in MTH 100. These are: type of instructor, location where class is taken, meeting pre-requisites for the course, gaps between math courses taken, math track where started, grade in MTH 092, participation with on-line homework, and number of absences incurred by the student. The two variables that did not show a difference in student success rates are: the initial student math placement on the basis of the placement test score and the time of day when the course is taken. The statistical analysis of student background data conducted by Prof. Williams found that two variables, whether the instructor was a full-time or adjunct faculty, and the actual number of absences of students, were the only variables that affected the MTH 100 grade in a statistically significant way. It

MTH 100 – 20

is not surprising that being taught by a full-time faculty member and the number of absences incurred by students were top predictors of the MTH 100 grade of students. On the basis of these results from student background data, Professors Castillo, Romero and Williams make the following recommendations:

Since students, in general, earned better grades with full time instructors than with adjuncts, it is the appropriate time to hire new full-time faculty. Full-time faculty members are much more available to students than adjunct faculty since each member holds regular office hours as well as office hours by appointment to assist students. In contrast to full-time faculty, adjuncts are not required to hold office hours and while many of them do volunteer their time to help their students it is clear that their poor compensation, job status, and other job commitments make it nearly impossible for all of them to do this on a regular basis.

All students should satisfy the pre-requisite for MTH 100 before taking this course. Since it was found that those students who start with MTH 092 generally do better in MTH 100, if a number of years have passed since a student last studied algebra, then that student should take MTH 092 before MTH 100 to review elementary algebra before taking college algebra. Also students should be encouraged to do well in MTH 092, that is get a grade of B or higher in MTH 092, to give them the strongest background in elementary algebra which will best enable them to succeed in college algebra. Also, since it was found that those students who score less than a B in MTH 092 have a lower success rate in MTH 100, these students may want to consider taking an easier college-level math course, like MTH 101 or 103, to satisfy the math requirement for their major.

Students who get low math test scores on the College placement test should be advised to take MTH 086 rather than AFM 083 to review arithmetic concepts since the success rate in MTH 086 is much higher than that of AFM 083. This could be due to the fact that MTH 086 is taught by members of the Math Department while AFM 083 is taught by instructors who do not have the same expertise in mathematics as well as the experience in teaching math as the instructors in the Math Department. Also, if AFM 083 is to continue being offered at the College, assessment studies need to be conducted to determine the success rate of these students who take AFM 083 not only in AFM 083 but also in their subsequent math courses.

Students should avoid gaps between the math courses taken prior to MTH 100 so that they do not forget important topics, concepts and rules as they move up from one course to the next.

Students should try to use on-line homework software and if so, try to get a score of 60% or higher; this would give them additional practice on course material on top of the regularly assigned homework.

MTH 100 – 21

Students should definitely limit the number of absences in MTH 100 to less than 3. Too much material is covered in MTH 100 in a somewhat rapid pace so that important topics are missed for each absence incurred by students, lessening their chance of success in the course.

MTH 100 – 22

APPENDIX A: Multiple-Choice Questions Included in Each MTH 100 SLOAT Test (to test acquisition of MPOs):

(MPO #) TopicQuestion(s) used to determine

MPO acquisition(test in which question was

asked)

Average Student Score

on MPO

# of students

who answered

the question(s) relating to

MPO

(1.1) Solve linear equations

Solve for n: (Test 1)

Find the solution of 11x – 2 = 3x + 5. (Test 1)

Solve for x:

(Midterm)

79.21 % 594

(1.2) Solve literal equations

Solve for m: (Test 1)

70.33 % 300

(1.3) Solve rational equations

Solve for x:

(Test 2)85.51 % 207

(1.4) Solve radical equations

Solve for x: (Final)

79.61 % 206

(1.5) Solve quadratic equations

Solve the quadratic equation: (Final)

63.11 % 206

(1.6) Solve linear inequalities

Solve the inequality:. Write the

solution in set-builder notation.

(Test 1)

81.34 % 300

(1.7) Solve systems of equations

Solve the system:

(Midterm)

68.37 % 294

(1.8) Factor polynomials Factor completely:

(Midterm)

84.01 % 294

(1.9) Simplify exponential expressions

Simplify:

(Midterm)

Simplify:

84.43 % 501


(Test 2)

Simplify: (Test 2)



asked)


on MPO

# of students

who answered


MPO

(1.10) Perform basic operations on polynomials

Multiply:

(Midterm)91.16 % 294

(1.11) Perform basic operations on rational expressions

Simplify:

(Test 2)

92.57 % 207

(1.12) Perform basic operations on radical expressions

Simplify: (Test 2)

Simplify: (Test 2)

Simplify: (Final)

61.86 % 413

(1.13) Perform basic operations on complex numbers

Simplify: (Final) 73.30 % 206

(1.14) Find the equation of a line based on given geometric properties

Find the equation of the line that contains the point (0, 4) and has slope 8.(Test 1)

85.33 % 300

(1.15) Graph a line in the Rectangular Coordinate System

Graph:

(Midterm)

75.85 % 294

(1.16) Graph a parabola in the Rectangular Coordinate System

Find the vertex and axis of symmetry, and then graph the parabola given by:

(Final)

77.19 % 206

(1.17) Graph a circle in the Rectangular Coordinate System

Find the center and radius, then match the graph of the

81.63 % 206


circle given by the equation:



asked)


on MPO

# of students

who answered


MPO

(1.18) Determine whether a given relation is a function, find its domain, and use function notation

Find the range of the function defined by the equation and the given domain.

(Test 1) What value(s) are excluded

from the domain of the

function ? Explain your answer.(Test 1)

Given , evaluate .(Midterm)

Find the domain of the following function:

(Test 2)

Given , find (Test 2)

78.78 % 801

(2.1) Apply algebraic methods to solve varied real-world applications (such as, consecutive integer problems, coin/stamp problems, distance problems, investment problems, area problems, and

Which algebraic equation can be used to solve the following problem: An herbalist has 5 oz of herbs costing $8 per ounce. How many ounces of herbs costing $2 per ounce should be mixed with the 5 oz to produce a mixture costing $6

68.00 % 500


work problems) that can be modeled by a linear equation, quadratic equation, rational equation or system of equations.

per ounce? (Midterm)

The length of a rectangle is 7 in. more than twice its width. Its area is 60 in2. If x is used to represent the measure of the width, which algebraic equation can be used to find the dimensions of the rectangle? (Final)



asked)


on MPO

# of students

who answered


MPO(3.1) Write and explain solutions to application problems related to the course material using appropriate mathematical terminology and notation.

Are the lines and parallel,

perpendicular, or neither? Explain your answer.(Final)

58.69 % 506

(4.1) Use a calculator to perform basic arithmetic operations, evaluate powers and find the square root of a number.

Find the distance (to the nearest hundredth between the points

(–4, 2) and (4, –5). (Test 1)

68.33 % 300


APPENDIX B


APPENDIX C

MTH 100 – Appendix C – 1

MTH 127 Student Learning Outcomes Assessment Team (SLOAT)Fall 2010 Final Report by Susan Gaulden

Introduction

MTH 127 is a basic calculus course designed for Business majors who plan on transferring to colleges or universities that require calculus for their Business Bachelor’s Degrees. MTH 127 is a very intense course, as it numerous covers topics ranging from pre-calculus concepts to using simple ordinary differential equations to mathematically model various business-type applications. The MTH 127 course outline lists the course goals as follows:

1. demonstrate knowledge of the fundamental concepts and theories from pre-calculus, calculus, and introductory ordinary-differential equations;

2. utilize various pre-calculus, calculus, and introductory differential equation problem-solving and critical-thinking techniques to set up and solve applied problems in finance, economics, geometry, sciences, and other fields;

3. communicate accurate mathematical terminology and notation in written and/or oral form in order to explain strategies to solve problems as well as to interpret found solutions; and

4. use graphing calculators effectively as a tool to solve such problems as those described above.

SLOAT Assessment Plan

The SLOAT Fall 2010 MTH 127 Student Learning Outcomes (SLO) assessment, which was conducted by Susan Gaulden, focused on course goals 1 and 2 only. Data was collected on the performance of all students attending MTH 127 section 001 (Susan Gaulden’s section), which originally included 37 students but was ended with only 25 students at the conclusion of the semester. Although this is a small sample size, it is important to note that only 2 sections of MTH 127 were offered in Fall 2010 and only a total of 69 students were enrolled at the start of the semester. Thus, the initial sample size was 37/69 or approximately 54% of the entire MTH 127 student population.

Almost all questions from 6 tests given in class throughout the semester and from the cumulative final exam in MTH 127 section 001 were blueprinted to the specific measurable course performance objectives (MPOs) that correspond to course goals 1 and 2. These tests and the final exam – showing the question-to-MPO blueprint as well as collected SLO data – are included as Appendix A in this report. Also, the day before each test was

MTH 127 – 1

given in MTH 127 section 001, all students present were asked to complete brief surveys to self-assess their abilities to accomplish the MPOs that were included on the next day’s test. In addition to students reporting their level of confidence with specific skills on the surveys, they also were asked to identify barriers that exist in their lives and prevent them from excelling at math, to list practices that would help them do better at math, to indicate things that the instructor could do differently to improve the class, and address other similar concerns. These surveys, including the results of the surveys, are included as Appendix B in this report.

Assessment Results/Findings

Survey (Student Perception) Results – As mentioned above, the results of the surveys are given in their entirety in Appendix B of this report, but interesting results from the student surveys include the following:

53% of respondents indicated that they have test anxiety and 36% don’t study enough because of overcommitted schedules. Both of these items were reported as barriers that keep students from excelling in math.

36% of respondents offered that they should do more practice and an additional 25% said they should study more to improve their chances of success in math. This means that 61% of the students in MTH 127 felt that they needed to work harder on their own to achieve better results in the course.

Although 42% of respondents asked the instructor to slow down and to not assume they know the material from MTH 100 even though that is the course prerequisite, 25% of respondents felt that the instructor needed to improve ‘nothing’ at all to help students do better at math.

Regarding the survey components, which required students to self-assess their abilities to accomplish the MPOs that were included on the next day’s test, the following noteworthy results were reported: (NOTE : The percentages given in parentheses below indicate the number of students who agreed with the statement ‘I know how to do this’ for the given skill/math topic on the survey.)

Students were very confident in their self-assessed abilities to perform the following skills: evaluate polynomial functions (MPO 1.1, 97%), calculate derivatives using the product rule (MPO 1.5, 93%), solve quadratic equations (MPO 1.2, 83%), and calculate derivatives using the quotient rule (MPO 1.5, 81%).

MTH 127 – 2

Students were least confident in their self-assessed abilities to perform the following skills: solve related rates problems (MPO 2.3, 15%), determine a specified volume of revolution (MPO 1.8, 23%), calculate derivatives using logarithmic differentiation (MPO 1.5, 26%), and calculate derivatives of logarithmic functions (MPO 1.5, 27%).

Student self-assessment seemed to significantly overestimate their abilities to perform the following skills: evaluate polynomial functions (MPO 1.1, 97% perceived they knew how to do this versus only 47% who actually knew how to do this on Test 1), graph a function – indicate the relative extrema, inflection points, concavity, and y-intercept (MPO 1.1, 63% perceived they knew how to do this versus only 23% who actually knew how to do this on Test 3), solve logarithmic equations (MPO 1.2, 70% perceived they knew how to do this versus only 36% who actually knew how to do this on Test 4), and solve exponential equations (MPO 1.2, 78% perceived they knew how to do this versus only 54% who actually knew how to do this on Test 4).

Student self-assessment seemed to significantly underestimate their abilities to perform the following skills: solve elasticity of demand problems (MPO 2.6, only 33% perceived they knew how to do this versus 91% who actually knew how to do this on Test 5), integrate functions (MPO 1.7, only 41% perceived they knew how to do this versus 96% who actually knew how to do this on Test 5), calculate definite integrals by applying the Fundamental Theorem of Calculus (MPO 1.7, only 45% perceived they knew how to do this versus 91% who actually knew how to do this on Test 5), and solve growth and decay problems (MPO 2.5, only 55% perceived they knew how to do this versus 100% who actually knew how to do this on Test 5).

‘Indirect’ Factors that Affect Student Learning – Anecdotally, most instructors describe attendance as having a significant impact on student performance in classes. As was mentioned above (see Assessment Plan section), the initial enrollment of MTH 127 Section 001 included 37 students, but only 25 students completed the class. This means that 12 students (32%) withdrew from (did not complete) the class. Attendance data for these 12 non-completers, along with those who completed (did not withdraw from) MTH 127 Section 001 students, are given in the table below. NOTE : For students who withdrew from the class, the % of classes missed is calculated by dividing the # of absences up to the given test date by the number of classes held up to that point in the semester. On average, students who withdrew missed 27.8% of the classes held up to that point in the semester.

MTH 127 – 3

Final Course Grade

# of Student

s

# of Classes Missed Average # (%) of Classes Missed

A 10 0, 1, 1, 1, 2, 3, 4, 5, 5, 10 3.2 (7.6%)B+ 2 0, 1 0.5 (1.2%)B 3 1, 2, 3 2.0 (4.8%)C+ 4 1, 6, 6, 9 5.5 (13.1%)C 0 not applicableD 4 1, 1, 11, 21 8.5 (20.2%)F 2 26, 30 28 (66.7%)

W 12

1 withdrew before Test 1: 6 6 (75.0%)4* withdrew before Test 2: 0, 1, 2, 4 1.8 (11.7%)1 withdrew before Test 3: 4 4 (18.2%)2 withdrew before Test 4: 2, 6 4 (14.3%)4 withdrew immediately after Test 4: 2, 5, 8, 8 5.8 (19.8%)

Data from the above table is presented in the bar graph below. This data (given in the table above or the graph below) seems to support the hypothesis that students who miss more class sessions do not perform as well in the class. In fact, students who passed the class were absent from 7.6% of the sessions on average in contrast to the 25.3% of sessions on average missed by students who did not pass the class. This finding should be shared with students who enroll in MTH 127 early in the semester so they are warned that attending class can significantly increase their chance of succeeding in the course.

MTH 127 – 4

A B+ B C+ D F W

7.6%1.2% 4.8%

13.1%20.2%

66.7%

27.8%

The Effect of Missing Classes on Final Course Grade in MTH 127

% of Classes Missed

Blueprinted Tests/Exam (Student Performance) Results – On every test and the final exam, all questions were blueprinted to the MPOs related to course goals 1 or 2 that were covered on that test/exam. (See Appendix A for blueprinted tests and final exam as well as collected data.) Each student, based on his/her answers on each of the blue-printed questions, was classified by Susan Gaulden, the instructor/grader, as falling into one of the three following categories: knows how to do this, has some idea how to do this but needs more practice, or does not know how to do this. Note that often there was more than one question on a given test/exam that blueprinted to a specific MPO. For example, there were 2 questions on Test 4 involving solving exponential equations. In this case, a student who got both questions correct was counted as ‘knowing how to do this’, a student who got one of the questions correct or both of the questions partly correct was counted as ‘having some idea how to do this but needing more practice’, and a student who got both questions wrong was counted as ‘not knowing how to do this.’ The number of students in each category was tallied for each test and for the final exam.

Data was collected for the entire class to determine which course objectives were achieved by the most students and which were mastered by the fewest students. Since questions related to the same MPO often appeared on more than one test or the final exam, it is important to clarify how the percentages of students who ‘know how to do this’, who ‘have some idea how to do this’, and who ‘do not know how to do this’ were calculated for each MPO. An example of such calculations is given below.

MTH 127 – 5

MPO 1.3 actually involves the following 2 distinct skills: determining limits and determining continuity and/or differentiability of a function at a specified value. Limit questions were present on Test 2 and continuity/differentiability questions were asked on both Test 2 and on the final exam. On Test 2, 25 students got the limit questions correct, 6 got them somewhat correct, and 0 got them incorrect. On Test 2, 18 students got the continuity/differentiability questions correct, 8 got the somewhat correct, and 5 got them incorrect. On the final exam, 7 students got the continuity/differentiability questions correct, 5 got the somewhat correct, and 8 got them incorrect. This means that overall, the percentages of students in each classification (‘know how to do this’, ‘have some idea how to do this’, and ‘do not know how to do this’) – where this means MPO 1.3 –

are calculated as follows: 25+18+7(25+6+0 )+ (18+8+5 )+(7+5+8 )

≈¿ ¿ 61% know how

to do MPO 1.3, 6+8+5

(25+6+0 )+ (18+8+5 )+(7+5+8 )≈¿ ¿

23% have some idea how to

do MPO 1.3, and 0+5+8

(25+6+0 )+ (18+8+5 )+(7+5+8 )≈¿ ¿

16% do not know how to do MPO 1.3.

In this SLOAT study, an MPO is considered to be achieved if at least 70% of the students were counted as ‘knowing how to do this’ on blueprinted questions from all relevant tests/exams. An MPO is partially achieved if between 50% and 70% of the students were counted as ‘knowing how to do this’ on blueprinted questions from all relevant tests/exams. And an MPO is not achieved if less than half of the students were counted as ‘knowing how to do this’ on blueprinted questions from all relevant tests/exams. Although the entire data, which includes the percentages of each classification of students on each test and on the final exam, is included in Appendix B, the results of the analysis grouped by course goal and organized by MPO are as follows:

Course Goal 1 : demonstrate knowledge of the fundamental concepts and theories from pre-calculus, calculus, and introductory ordinary-differential equationsMPO 1.1 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 1.1, evaluate and graph (using the first-derivative and second-derivative tests as appropriate) polynomial, piecewise, composite, exponential, logarithmic, and multi-variable functions, were classified as follows: 52% know how to do this, 32% have some idea how to do this, and 15% do not know how to do this.

MTH 127 – 6

It can be concluded, then, that students only partially achieved this MPO. It is important to note the following specifics: students performed best on evaluating multi-variable functions (100% correctly answered this question on the final exam); many students did well on graphing polynomial functions (68% correctly answered this question on Test 2) and evaluating piecewise functions (64% correctly answered this question on Test 1); students had difficulty mastering graphing piecewise functions (34% incorrectly answered this question on Test 1).MPO 1.2 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 1.2, solve linear, quadratic, exponential, and logarithmic equations, were classified as follows: 70% know how to do this, 21% have some idea how to do this, and 12% do not know how to do this. It can be concluded, then, that students achieved this MPO. It is important to note the following specifics: 100% correctly solved exponential equations, 75% correctly solved quadratic equations, and 70% correctly solved logarithmic equations on the final exam.MPO 1.3 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 1.3, determine limits, continuity, and differentiability of given functions at specified values, were classified as follows: 61% know how to do this, 23% have some idea how to do this, and 16% do not know how to do this. It can be concluded, then, that students partially achieved this MPO. It is important to note the following specifics: students performed best on determining limits (81% correctly answered these questions on Test 2) and worst on determining continuity and/or differentiability of a function at a specified value (40% incorrectly answered this question on the final exam).MPO 1.4 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 1.4, determine a derivative of a function by using limits and difference quotients, were classified as follows: 38% know how to do this, 13% have some idea how to do this, and 50% do not know how to do this. It can be concluded, then, that students did not achieve this MPO. It is important to note the following specifics: although 52% of the students correctly answered this question on Test 1, all of the students who answered a related extra credit question on the final exam answered it incorrectly. This means that students certainly seem to forget how to calculate derivatives by using the definition of the derivative once they have learned some of the other (shortcut) rules of differentiation such as the power rule, the product rule, the chain rule, etc.MPO 1.5 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 1.5, calculate first, second, or partial derivatives of polynomial, rational, exponential, and logarithmic functions by using rules of differentiation including the product, quotient, and chain rules and implicit and logarithmic differentiation, were classified

MTH 127 – 7

as follows: 55% know how to do this, 28% have some idea how to do this, and 17% do not know how to do this. It can be concluded, then, that students partially achieved this MPO. It is important to note the following specifics: students performed best on calculating derivatives using the product, quotient, and chain rules (80% correctly answered questions requiring differentiation via the product and quotient rules on Test 3 and 79% correctly answered questions requiring the chain rule on Test 4) and on calculating the derivatives of exponential functions (68% correctly answered these questions on Test 4); students had difficulty calculating derivatives of logarithmic functions (32% incorrectly answered this question on Test 4) and calculating derivatives using logarithmic differentiation (32% incorrectly answered this question on Test 4).MPO 1.6 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 1.6, calculate Riemann sums to estimate definite integrals, were classified as follows: 83% know how to do this, 17% have some idea how to do this, and 0% do not know how to do this. It can be concluded, then, that students achieved this MPO.MPO 1.7 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 1.7, apply the Fundamental Theorem of Calculus to calculate integrals of single variable functions and determine the areas between given curves, were classified as follows: 60% know how to do this, 29% have some idea how to do this, and 10% do not know how to do this. It can be concluded, then, that students partially achieved this MPO. It is important to note the following specifics: students performed best on calculating definite integrals by applying the Fundamental Theorem of Calculus (74% correctly answered these questions on Test 5 and the final exam); all students at least had some idea how to determine the area between curves (35% answered this question correctly and 65% answered this question somewhat correctly on Test 6); and although 96% of the students got the integrating function questions correct on Test 5, 35% incorrectly answered this question on the final exam.MPO 1.8 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 1.8, determine a specified volume of revolution, were classified as follows: 63% know how to do this, 25% have some idea how to do this, and 13% do not know how to do this. It can be concluded, then, that students partially achieved this MPO.

The MPO analysis for course goal 1 given in detail above is summarized in the chart below. It is notable that for course goal 1, 2 (25%) of the MPOs were achieved, 5 (62.5%) of the MPOs were partially achieved, and 1 (12.5%) of the MPOs was not achieved.

Course Goal MPO achieved

partially

not achieve

MTH 127 – 8

achieved d

1 Demonstrate knowledge of the fundamental concepts and theories from pre-calculus, calculus, and introductory ordinary-differential equations.

1.1 evaluate and graph (using the first-derivative and second-derivative tests as appropriate) polynomial, piecewise, composite, exponential, logarithmic, and multi-variable functions

ü

1.2 solve linear, quadratic, exponential, and logarithmic equations

ü

1.3 determine limits, continuity, and differentiability of given functions at specified values

ü

1.4 determine a derivative of a function by using limits and difference quotients

ü

1.5 calculate first, second, or partial derivatives of polynomial, rational, exponential, and logarithmic functions by using rules of differentiation including the product, quotient, and chain rules and implicit and logarithmic differentiation

ü

1.6 calculate Riemann sums to estimate definite integrals ü

1.7 apply the Fundamental Theorem of Calculus to calculate integrals of single variable functions and determine the areas between given curves

ü

1.8 determine a specified volume of revolution ü

Course Goal 2 : utilize various pre-calculus, calculus, and introductory differential equation problem-solving and critical-thinking techniques to set up and solve applied problems in finance, economics, geometry, sciences, and other fieldsMPO 2.1 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 2.1, solve compound interest, present value, and future value problems, were classified as follows: 68% know how to do this, 21% have some idea how to do this, and 11% do not know how to do this. It can be concluded, then, that students partially achieved this MPO. It is important to note the following specifics: students performed best on solving present value and compound interest problems (91% correctly answered present-value problems and 87% correctly answered compound-interest problems on Test 5); students had difficulty solving continuous-stream-future-value problems (25% incorrectly answered this question on Test 6).

MTH 127 – 9

MPO 2.2 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 2.2, solve marginal cost, marginal profit, and marginal revenue problems by using differentiation and integration as necessary, were classified as follows: 70% know how to do this, 30% have some idea how to do this, and 0% do not know how to do this. It can be concluded, then, that students achieved this MPO.MPO 2.3 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 2.3, solve rate-of-change and related rates problems, were classified as follows: 30% know how to do this, 32% have some idea how to do this, and 38% do not know how to do this. It can be concluded, then, that students did not achieve this MPO. It is important to note the following specifics: students performed much better on rate-of-change problems (52% correctly answered this problem on Test 2) than on related-rates problems (55% incorrectly answered this problem on the final exam).MPO 2.4 overall, students answering the questions on any given test/exam throughout the semester that addressed MPO 2.4, solve optimization problems (in geometry, finance, inventory control, etc.) including those involving functions of several variables, were classified as follows: 60% know how to do this, 20% have some idea how to do this, and 20% do not know how to do this. It can be concluded, then, that students partially achieved this MPO. It is important to note the following specifics: 67% of students answered the economic order quantity (EOQ), i.e., inventory control problem, correctly and an additional 13% answered this problem somewhat correctly on Test 3.MPO 2.5 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 2.5, solve growth and decay problems (in finance, biology, chemistry, physics, etc.), were classified as follows: 100% know how to do this, 0% have some idea how to do this, and 0% do not know how to do this. It can be concluded, then, that students achieved this MPO.MPO 2.6 overall, students answering questions on any given test/exam throughout the semester that addressed MPO 2.6, solve elasticity of demand problems, as follows: 72% know how to do this, 12% have some idea how to do this, and 16% do not know how to do this. It can be concluded, then, that students achieved this MPO.

The MPO analysis for course goal 2 given in detail above is summarized in the chart below. It is notable for course goal 2, 3 (50%) of the MPOs were achieved, 2 (33.3%) of the MPOs were partially achieved, and 1 (16.7%) of the MPOs was not achieved.

Course Goal MPO achieved partially achieved

not achieved

2 Utilize various 2.1 solve compound interest, ü

MTH 127 – 10

pre-calculus, calculus, and introductory differential equation problem-solving and critical-thinking techniques to set up and solve applied problems in finance, economics, geometry, sciences, and other fields.

present value, and future value problems2.2 solve marginal cost, marginal profit, and marginal revenue problems by using differentiation and integration as necessary

ü

2.3 solve rate-of-change and related rates problems ü

2.4 solve optimization problems (in geometry, finance, inventory control, etc.) including those involving functions of several variables

ü

2.5 solve growth and decay problems (in finance, biology, chemistry, physics, etc.)

ü

2.6 solve elasticity of demand problems ü

The bar graph below presents the level of student achievement in MTH 127 of the various MPOs for course goals 1 and 2. As can be seen in the bar graph, when course goals 1 and 2 are examined collectively, 5 (36%) of the MPOs were achieved, 7 (50%) of the MPOs were partially achieved, and 2 (14%) of the MPOs were not achieved,

achieved partially achieved not achieved0

1

2

3

4

5

6

7

8

5

7

2

Level of Student Achievement of MPOs forCourse Goals 1 and 2 in MTH 127

# of MPOs

Interpretation of Results/Findings

Many MTH 127 students self-reported that they need to spend more time studying and practicing the content covered in the course. More than half of the students in the cohort also indicated that they have test anxiety, which may keep them from excelling at math. To address these issues, it is recommended that some class time be dedicated to and/or extra credit assignments be made that help students learn appropriate study skills and how to alleviate some of their test anxiety. Ideally, this information would be shared with students early on in the semester – even before the first test.

Students also need to be warned that some of the topics they perceive to be ‘easy’ may not be as easy as they think. When this occurs students

MTH 127 – 11

sometimes do not spend time on these topics since they assume they will easily get these problems correct on the tests. To address this situation, students should especially be encouraged to spend time practicing topics such as evaluating polynomial functions, graphing functions (by using the First and Second Derivative Tests), and solving exponential and logarithmic equations, as these are the skills that students most overestimated their abilities to perform. It is suggested that questions on these topics, as well as the topic students perceived as the most difficult (e.g., solving related rates problems, determining volumes of revolution, and calculating derivatives of logarithmic functions and using logarithmic differentiation), be given as in-class group problem sets prior to the relevant tests.

In this SLOAT study, students achieved the 5 MPOs listed below. It is recommended that the instructional techniques pertaining to these skills not be changed, as it seems that they are working reasonably well.

MPO 1.2 solve linear, quadratic, exponential, and logarithmic equations

MPO 1.6 calculate Riemann sums to estimate definite integrals

MPO 2.2 solve marginal cost, marginal profit, and marginal revenue problems by using differentiation and integration as necessary

MPO 2.5 solve growth and decay problems (in finance, biology, chemistry, physics, etc.)

MPO 2.6 solve elasticity of demand problems

Furthermore, students partially achieved the 7 MPOs listed below. Specific recommendations to improve student mastery for each skill/topic are given below as necessary.

MPO 1.1 evaluate and graph (using the first-derivative and second-derivative tests as appropriate) polynomial, piecewise, composite, exponential, logarithmic, and multi-variable functions Recommendation: Teach how to graph piecewise functions in the same class as evaluating piecewise functions is taught – use index cards to block off intervals of the x-axis that are not satisfied by each piece’s condition; include questions on graphing piecewise functions on an in-class small group assignment, the MPO 1.1 skill that students had the most difficulty mastering.

MPO 1.3 determine limits, continuity, and differentiability of given functions at specified values Recommendation: Spend some more class time on determining continuity and differentiability of functions at specified values – ask students to evaluate functions

MTH 127 – 12

and slopes of tangent lines at points of discontinuity to have them see graphically that these function values do not exist.

MPO 1.5 calculate first, second, or partial derivatives of polynomial, rational, exponential, and logarithmic functions by using rules of differentiation including the product, quotient, and chain rules and implicit and logarithmic differentiation Recommendation: Include questions on calculating derivatives of logarithmic functions and using logarithmic differentiation on an in-class small group assignment, the MPO 1.5 skills that students had the most difficulty mastering.

MPO 1.7 apply the Fundamental Theorem of Calculus to calculate integrals of single variable functions and determine the areas between given curves Recommendation: Have students identify (via a check-off list) which problems require differentiation and which require integration while reviewing for the final exam since some students incorrectly took derivatives instead of integrating on the final exam integration questions.

MPO 1.8 determine a specified volume of revolution Recommendation: Include questions on determining volumes of revolution on an in-class small group assignment.

MPO 2.1 solve compound interest, present value, and future value problems Recommendation: Have students distinguish between future value and continuous-stream-future-value problems; ensure that they know which formula is applicable in which instance.

MPO 2.4 solve optimization problems (in geometry, finance, inventory control, etc.) including those involving functions of several variables Recommendation: Include optimization problems on an in-class small group assignment; also be sure to give students choices of optimization problems on tests/the final exam.

Lastly, students did not achieve the 2 MPOs listed below. Specific recommendations to improve student mastery for each skill/topic are given as necessary.

MPO 1.4 determine a derivative of a function by using limits and difference quotients Recommendation: Discuss with MAP colleagues who teach this course if this concept, which is certainly more theoretical than practical, should be included as a MTH 127 MPO. The difficulty with this topic is that once students

MTH 127 – 13

learn the ‘shortcut’ rules for taking derivatives, they no longer rely on the more cumbersome method of applying the definition. If this is kept as an MPO, it is suggested that students be given a take-home or open book in-class assignment, which can be evaluated for student mastery of this performance objective, rather than collecting data from such questions on tests/the final exam.

MPO 2.3 solve rate-of-change and related rates problems Recommendation: Spend more time covering related rate problems in class; distribute a supplemental handout with many more example problems on this topic as it is sparsely covered in the textbook; have students work through these problems by explicitly showing each of the following steps for every related rates problem they attempt: 1) draw a picture (if necessary) illustrating the problem; 2) identify variables and constants given or asked for in the problem; 3) identify rates given or asked for in the problem; 4) write an algebraic equation relating all variables and constants given in the problem; 5) implicitly differentiation the equation with respect to time; 6) substitute known values for the variables and rates; and 7) solve for the unknown variable or rate.

It is recommended that data be collected and analyzed that pertain to the specific measurable course performance objectives (MPOs) of course goals 3 and 4 to determine the level of student achievement on these mathematical topics/skills.

Summary

Students reported needing to spend more time practicing and studying for MTH 127, as well as some guidance to deal with test anxiety. In this SLOAT study, student achievement of two of the four course goals was determined. These two goals are as follows: 1) demonstrate knowledge of the fundamental concepts and theories from pre-calculus, calculus, and introductory ordinary-differential equations; and 2) utilize various pre-calculus, calculus, and introductory differential equation problem-solving and critical-thinking techniques to set up and solve applied problems in finance, economics, geometry, sciences, and other fields. Students achieved 2, partially achieved 5, and did not achieve 1 of the 8 measurable performance objectives related to course goal 1. Furthermore, students achieved 3, partially achieved 2, and did not achieve 1 of the 6 measurable performance objectives related to course goal 2. This means that students are certainly

MTH 127 – 14

learning some required content/skills in MTH 127, but they are not necessarily mastering it to a desired level.

Recommendations for student learning and teaching improvement consist of the following:

adopt specific teaching strategies for certain skills

spend more class time on identified content as well as guiding students to enhance study skills and address test anxiety

distribute necessary supplemental handouts with more examples for certain topics (e.g., related rates problems)

require students to write out the steps to solve certain application problems (e.g., related rates problems)

have students complete in-class small group assignments that include questions on specific topics

ask students to (on sight) determine/distinguish between mathematical skills necessary to solve various problems

give students choices of similar application problems on tests so they are able to exert their preference and still apply the same math to show their abilities

collect some SLO assessment data from instruments other than tests/exams (e.g., in-class work, selected homework, etc.)

NOTE : Course-embedded SLO assessment is most valuable when findings and recommendations are shared with and solicited from colleagues who are also familiar with the course. For this reason, the data collected and analyzed in the MTH 127 SLOAT study as well as recommendations made to improve student learning and teaching will be shared with other mathematics instructors at a Division meeting in early Spring 2011. Some elements of the SLOAT experience, the MTH 127 SLOAT assessment plan, and the actual SLO findings will be reported to College faculty at the ECC SLO Assessment Symposium in February 2011.

MTH 127 – 15

MTH 127 SLOAT Final Report – APPENDIX A


Name: ____________________________ September 24, 2010

Test #1 on Sections 0.1 – 0.6 & 1.1 – 1.2 Math 127 Dr. Gaulden

1) Compute f (1 ) and f (2 ) given

f ( x )={π x2 for x<2

1+x for 2≤x≤2 .5

4 x for 2 . 5<x (8 points)

2) Describe the domain of

8 x( x−1 ) ( x−2 ) . (8 points)

3) Given f ( x )=x6 and g ( x )= x

1−x , calculate f composed with g; that is determine f (g ( x ) ) . (8 points)

4) If g ( t )=4 t−t2, find

g ( t+h )−g ( t )h and simplify. (8 points)

5) Find the equation of the line that is perpendicular to y+x=0 and contains the point (2, 0). (8 points)

6) Find the points of intersection of the curves y=2x2−5 x−6 and y=3 x+4 . (10 points)

7) Find the point on the graph of y=x2 where the tangent line is parallel to the line

2 x+3 y=4 . (10 points)

8) In some cities you can rent a car for $18 per day and $.20 per mile. If the car is to be rented for one day, express the total rental expense as a function of the number x of miles driven. (10 points)

9) Assume that a couple invests $1000 upon the birth of their daughter. Assume that the investment earns 6.8% compounded annually. What will the investment be worth on the

daughter’s 18th birthday? (HINT : where A is the amount in the account, P is the principal invested, r is the annual interest rate, n is the number of interest periods per year, and t is the number of years. ) (10 points)


PLEASE show all work to receive full credit. That means that if you do not show all work, you will not receive full credit. Work carefully and neatly. Good luck!

10)CHOOSE and complete ONE of the two problems below. You must you show your work to receive maximum credit. PLEASE NOTE : If you complete more than one part, only the first one shown will be graded unless otherwise indicated. (10 points)

a) An average sale at a small florist shop is $21, so the shop’s weekly revenue function is R ( x )=21 x , where x is the number of sales in 1 week. The corresponding weekly cost is C ( x )=9 x+800 dollars. If the profit is $1000 for 1 week, what is the revenue for 1 week?

OR

b) A frozen yogurt stand makes a profit of P ( x )=. 40 x−80 dollars when selling x scoops of yogurt per day. How many more scoops of yogurt will have to be sold to raise the daily profits from $30 to $40?

11)CHOOSE and complete ONE of the two problems below. You must you show your work to receive maximum credit. PLEASE NOTE : If you complete more than one part, only the first one shown will be graded unless otherwise indicated. (10 points)

a) After t hours of operation, an assembly line has assembled A (t )=20 t−1

2t2

power lawn mowers, 0≤t≤10 . Suppose that the factory’s cost of manufacturing x units is C ( x ) dollars, where C ( x )=3000+80 x . What is the cost of the first 2 hours of operation?

ORb) When the owner of a gas station sets the price of 1 gallon of unleaded gasoline at

$4.10, he can sell approximately 1500 gallons per day. When he sets the price at $4.25 per gallon, he can sell approximately 1250 gallons per day. Let G ( x ) denote the number of gallons of unleaded gasoline sold per day when the price is x dollars. Assume that G ( x ) is a linear function of x. Approximately how many gallons will be sold per day if the price is set at $4.35 per gallon?

Extra Credit:

1) Sketch the graph of the function

f ( x )={3 for x<2

2 x+1 for x≥2 (2 points)

2) Is the point (12

, 25 ) on the graph of the function

g ( x )= 3 x−1x2+1 ? (2 points)

3) An office supply firm finds that the number of fax machines sold in year x is given

approximately by the function f ( x )=50+4 x+ 1

2x2

, where x=0 corresponds to 1990. Find the number of fax machines sold in 1992. (2 points)


SLO Assessment Results for Test 1:

Skill/Math Topic (part of specified MPO): blueprinted questions from

the test

Students who ‘knew how to do

this’

Students who ‘had some idea how to do this but

need more practice’

Students who ‘did not know how to

do this’

Evaluate polynomial functions (MPO 1.1): questions 3, 4, 10, 11, EC2 & EC3 17 = 47% 15 = 42% 4 = 11%Evaluate piecewise functions (MPO 1.1):question 1 23 = 64% 5 = 14% 8 = 22%Graph piecewise functions (MPO 1.1):question EC1 10 = 34% 9 = 31% 10 = 34%Solve quadratic functions (MPO 1.2):question 6 29 = 81% 5 = 14% 1 = 3%Solve compound interest problems (MPO 2.1):question 9

24 = 67% 9 = 25% 3 = 8%

NOTE : Questions 2, 5, 7 & 8 were not blueprinted on this test.


Name: ____________________________ October 12, 2010


1) Determine each limit below if it exists. If either limit does not exist, be sure to state so and indicate why. (4 points each)

a)limx→1

(1−6 x )

b)limx→0

x2+3 xx

2) Differentiate each of the expressions below with respect to x. (8 points each)

a)y=x7+3 x+7−2

x

b) y= (2x+4 )3

3) Calculate the second derivative of f ( x )= (3 x+1 )5 . (8 points)

4) Find the slope of the tangent line to the curve y=x3+3 x−8 at (2 , 6 ) . (8 points)

5) Let P ( x ) be the profit (in dollars) from manufacturing and selling x luxury cars. Interpret P (100 )=90 , 000 and P

' (100 )=1200 . (NOTE : This means you should write one or two sentences that gives the meaning of each equation.) (8 points)

6) Determine whether the piecewise function

f ( x )={2 x−1 for 0≤x≤1

1 for 1<x is continuous and/or differentiable at . Be sure to show all work to justify your answers. (10 points)

7) An analysis of the daily output of a factory assembly line shows that about

60 t+ t2− 112

t3

units are produced after t hours of work, 0≤t≤8 . What is the rate of production (in units per hour) when t=2? (10 points)



xfy A

B

C

DE

F

8) An object moving in a straight line travels s (t ) kilometers in t hours, where s ( t )=2 t2+4 t. What is the object’s velocity when t=6 , and what is the object’s acceleration when t=6 ? (10 points)

9) Refer to the graph below to answer the following questions: (2 points each)

a. At which labeled points is the function increasing?

b. At which labeled points is the graph concave up?

c. Which labeled point has the most positive slope?

10)Sketch a graph of each function with properties described below. (8 points each)

a. f (2 )=1 ; { f ' (2 )=0¿ ; concave up for all x

b. (0 , 6 ) , (2 , 3 ) and (4 ,0 ) are on the graph; f' (0 )=0 and { f ' (4 )=0¿ ; f

' ' ( x )<0 for x<2 ,f ' ' (2 )=0 , and { f ' ' ( x )>0 for x>2¿

Extra Credit: (2 points each)

1) Let f ( x )= x2−7 x+10

x−5 , x≠5

. If possible, define f ( x ) at x=5 in a way that makes f ( x ) continuous for all x.

2) Let S ( x ) represent the total sales (in thousands of dollars) for the month x in the year 2005 at a certain department store. Represent “at the end of March, the sales for this month dropped to $80,000 and were falling by about $200 a day“ by equations involving S and {S '¿ .

3) Use the definition of a derivative – that is, f ' ( x )= lim

h→0

f ( x+h )− f ( x )h – to compute

the derivative of f ( x )=x3.




the test


this’




do this’

Graph a function with given properties where information is given about its first and second derivatives (MPO 1.1):Questions 9 & 10

21 = 68% 8 = 26% 2 = 6%

Determine limits (MPO 1.3):question 1 25 = 81% 6 = 19% 0 = 0%Determine whether a function is continuous and/or differentiable at a specified value for x (MPO 1.3):question 6 & EC1

18 = 58% 8 = 26% 5 = 16%

Use the definition of a derivative to compute a derivative (MPO 1.4):question EC3

12 = 52% 4 = 17% 7 = 30%

Determine first and second derivatives (MPO 1.5):questions 2, 3 & 4

13 = 42% 17 = 55% 1 = 3%

Solve rate-of-change problems (MPO 2.3):questions 5, 7, 8 & EC2

16 = 52% 11 = 35% 4 = 13%


Name: ____________________________ October 26, 2010


1) Find the derivative dydx of each of the following: (10 points each)

a) y= (x−2 )5 ( x+1 )2

b)y= x−1

x+1

c)y=u

2+ 2

u if u=x−x2

d) y5−3 x2=x

2) Find two positive numbers, x and y, whose sum is 100 and whose product is as large as possible. (10 points)

3) Given the cost function C ( x )=x3−6 x2+13 x+15 , find the minimum marginal cost. (10 points)

4) The monthly advertising revenue A and the monthly circulation x of a magazine are

related approximately by the equation A=6√x2−400 , x≥20 , where A is given in thousands of dollars and x is measured in thousands of copies sold. At what rate is the advertising revenue changing if the current circulation is x=25 thousand copies and the circulation is growing at the rate of 2 thousand copies per month? (10 points)

5) The length, x, of the edge of a cube is increasing. For what value of x is dVdt equal to 12

times the rate of increase of x? (NOTE : Volumecube=length3) (10 points)

6) Sketch the curve y=x 4−6 x2. Be sure to include all relevant details on the graph

including at least the following: relative extrema, inflection points, concavity, and y-intercept. (10 points)

7) A California distributor of sporting equipment expects to sell 10,000 cases of tennis balls during the coming year at a steady rate. Yearly carry costs (to be computed on the average number of cases in stock during the year) are $10 per case, and the cost of placing an order with the manufacturer is $80. Determine the economic order quantity



(EOQ), that is, the order quantity that minimizes the inventory costs and then find the minimum inventory cost. (10 points)


1) Find the quadratic function f ( x )=ax2+bx+c that goes through (2 , 0 ) and has a local maximum at (0 , 1 ) .

2) Let f ( x ) , g ( x ) , and h (x ) be differentiable functions. Find a formula for the derivative of f ( x ) g (x ) h ( x ) .

3) A sugar refinery can produce x tons of sugar per week at a weekly cost of 0 . 1 x2+5 x+2250 dollars. Find the level of production for which the average cost is at a minimum.



the test


this’




do this’

Graph a function – indicate the relative extrema, inflection points, concavity, and y-intercept (MPO 1.1):question 6

7 = 23% 17 = 57% 6 = 20%

Calculate derivatives using the product rule (MPO 1.5):question 1a & EC2

24 = 80% 3 = 10% 3 = 10%

Calculate derivatives using the quotient rule (MPO 1.5):question 1b

24 = 80% 2 = 7% 4 = 13%

Calculate derivatives using the chain rule (MPO 1.5):question 1c

10 = 48% 5 = 24% 6 = 29%

Calculate derivatives using implicit differentiation (MPO 1.5):question 1d

18 = 62% 4 = 14% 7 = 24%

Solve related rates problems (MPO 2.3)questions 4 & 5 1 = 3% 13 = 43% 16 = 53%Solve optimization problems (MPO 2.4):questions 2, 3 & EC3 17 = 57% 9 = 30% 4 = 13%Solve economic order quantity problems (EOQ) (MPO 2.4)question 7

20 = 67% 4 = 13% 6 = 20%


NOTE : Question EC1 was not blueprinted on this test.


Name: ____________________________ November 11, 2010

Test #4 on Sections 4.1 – 4.6 Math 127 Dr. Gaulden

1) Solve each equation below for x. Please be sure to give exact (not rounded) values. (6 points each)

a) 3 (2.7 )5 x=8 . 1

b) e2 x=5

c)ln ( 4− x )=1

2

d) ln ( x+1 )− ln ( x−2 )=1

2) Find dydx given the following: (6 points each)

a) y= e4 x

4+x

b) y=ex (1+x )2

c) y=ln (e5 x+1 )

d)y= ln( x−1

x+1 )

e)y=ln ( x+1 )4

e x−1

f)y= ( x+1 ) (2 x+1 ) (3 x+1 )

√4 x+1 (NOTE : You may use logarithmic differentiation.)

3) Find the slope of the tangent line to the curve y=xe x at (0 , 0 ) . (10 points)

4) Find the coordinates of the minimum point of y=−5 x+e x. (10 points)



5) If the demand equation for a certain commodity is p=45

ln x , determine the marginal revenue function for this commodity, and compute the marginal revenue when x=20 . (10 points)

6) A painting purchased in 1998 for $100,000 is estimated to be worth v ( t )=100 , 000 et5

dollars after t years. At what rate will the painting be appreciating in 2008? (10 points)


1) Find the point on the graph of y=e−x where the tangent line has slope – 2.

2) Find values of h and k for which the graph of y=hekx passes through the points (1,6 ) and

(4 , 48 ) .



the test


this’




do this’

Solve exponential equations (MPO 1.2):questions 1a & 1b 15 = 54% 11 = 39% 2 = 7%Solve logarithmic equations (MPO 1.2):questions 1c & 1d 10 = 36% 12 = 43% 6 = 21%Calculate derivatives of exponential functions (MPO 1.5):questions 2a, 2b & 4

19 = 68% 7 = 25% 2 = 7%

Calculate derivatives of logarithmic functions (MPO 1.5):questions 2c, 2d, 2e & 5

5 = 18% 14 = 50% 9 = 32%

Calculate derivatives using logarithmic differentiation (MPO 1.5):question 2f

12 = 43% 7 = 25% 9 = 32%

Calculate derivatives using the product rule (MPO 1.5):questions 2b & 3

17 = 61% 9 = 32% 2 = 7%

Calculate derivatives using the quotient rule (MPO 1.5):question 2a

17 = 61% 9 = 32% 2 = 7%

Calculate derivatives using the chain rule (MPO 1.5):

22 = 79% 4 = 14% 2 = 7%


questions 2a, 2c & 6

Name: ____________________________ DUE TUESDAY, November 30, 2010

Take-Home Test on Sections 5.1 – 5.3 & 6.1 – 6.3 Math 127 Dr. Gaulden

1) Determine each integral given below. (5 points each)

a)∫(4 x3+1

2 √x−3)dx

b)∫1

e

(2 x−1x )dx

2) Find all functions f ( x ) such that f' ( x )=3 x2+e− x

and f (0 )=2 . (10 points)

3) Find the exact area (do not approximate with a Riemann sum and do not use a calculator and round your answer) under the curve y=x2

from x=0 to x=5 . (10 points)

4) Use a Riemann sum to approximate the area under the graph of y=x3 in the interval

0≤x≤2 with n=4 (that is, 4 subintervals or “panels”) and use midpoints of subintervals. (10 points)

5) How much money must you invest now at 6.2% interest compounded continuously to have $10,000 at the end of 8 years? (10 points)

6) An investment grows at a continuous 10% rate per year. In how many years will the value of the investment double? (10 points)

7) A movie theater has a seating capacity of 3,000 people. The number of people attending a

show at price p dollars per ticket is q=16 , 000

p−1200

. Currently the price is $8 per ticket. If the price is lowered, will revenue increase or decrease? (10 points)

8) Suppose that the marginal cost function of a computer manufacturer is

C ' ( x )=45

x2−x+150 dollars per unit at production level x (where x is measured in units of

100 computers). Determine the total cost of producing 10 additional units if 10 units are currently being produced. (10 points)



9) Let P ( t ) be the population (in millions) of a certain city t years after 1992, and suppose that P ( t ) satisfies the differential equation P

' (t )=. 03 P ( t ) , P (0 )=4 . Approximately what was the population in 2000? (10 points)

10) A ball is thrown upward from a height of 192 feet above the ground, with an initial velocity of 64 feet per second. From physics it is known that the velocity at time t is v (t )=64−32 t feet per second. How high will the ball go? (Hint: You must find s (t ) , the function giving the height of the ball at time t, first to answer this question.) (10 points)SLO Assessment Results for Test 5:


the test


this’




do this’

Calculate Riemann sums to estimate definite integrals (MPO 1.6):question 4

19 = 83% 4 = 17% 0 = 0%

Integrate functions (MPO 1.7):questions 1a & 2 22 = 96% 1 = 4% 0 = 0%Calculate definite integrals by applying the Fundamental Theorem of Calculus (MPO 1.7):questions 1b, 3 & 8

21 = 91% 2 = 9% 0 = 0%

Solve compound interest problems (MPO 2.1):question 6

21 = 91% 2 = 9% 0 = 0%

Solve present value problems (MPO 2.1):question 5 20 = 87% 3 = 13% 0 = 0%Solve growth and decay problems (MPO 2.5):question 9

23 = 100% 0 = 0% 0 = 0%

Solve elasticity of demand problems (MPO 2.6)question 7

21 = 91% 1 = 4% 1 = 4%


Name: ____________________________ December 10, 2010

Test #6 on Sections 6.4 – 6.5 & 7.1 – 7.3 (+ 7.4 for extra credit only) Math 127 Dr. Gaulden

1) Let f ( x , y )=x2−3 xy− y2. Compute f (5 ,−2 ) (10 points)

2) The value of residential property for tax purposes is usually much lower than its actual market value. If v is the market value, the assessed value for real estate taxes might be only 40% of v. Suppose that the property tax, T, in a community is given by the function

T= f (r , v , x )= r100

(0 .40v−x ), where v is the estimated market value of a property (in

dollars), x is a homeowner’s exemption (a number of dollars depending on the type of property), and r is the tax rate (stated in dollars per hundred dollars) of net assessed value. Determine the real estate tax on a property valued at $200,000 with a homeowner’s exemption of $5000, assuming a tax rate of $3.00 per hundred dollars of net assessed value. (10 points)

3) Set up the integral (DO NOT SOLVE!) used to find the area of the region between the

curves y=8 x2 and y=√ x . (10 points)

4) Determine the area of the region bounded by the curves y=x2 and y=x . (12

points)

5) Draw the level curve of the function f ( x , y )=x− y containing the point (0 , 0 ) . (10 points)

6) Find ∂ f∂ x

and ∂ f∂ z

if f ( x , y , z )=x z e yz

. (12 points)

7) Find all point(s) ( x , y ) where f ( x , y )=3 x2−6 xy+ y3−9 y has a possible relative maximum or minimum. Then use the second-derivative test to determine, if possible, the nature of f ( x , y ) at the point(s). If the second–derivative test is inconclusive, so state. (12 points)

8) CHOOSE and complete ONE of the problems below. NOTE : If you complete more than one, only the first will be graded unless otherwise indicated. (12 points)

a) An investment pays 10% interest compounded continuously. If money is invested steadily at the rate of $5000 per year, how much time is required until the value of the investment reaches $140,000?



ORb) Find the volume of the solid of revolution generated by revolving about the x-axis the

region under the curve y=e−x from x=0 to x=1 .

9) CHOOSE and complete ONE of the problems below. NOTE : If you complete more than one, only the first will be graded unless otherwise indicated. (12 points)a) A company manufactures and sells two products, I and II, that sell for $10 and $9 per

unit, respectively. The cost of producing x units of product I and y units of product II is 400+2 x+3 y+0 .01 (3 x2+xy+3 y2 ) . Find the values of x and y that maximize the company’s profits. (RECALL : Profit = Revenue – Cost)

OR

b) A farmer can produce f ( x , y )=200√6 x2+ y2 units of produce by utilizing x units of

labor and y units of capital. (The capital is used to rent or purchase land, materials, and equipment.) Calculate the marginal productivities of labor and capital when x=10 and y=5 .

Extra Credit:

1) Find a formula C ( x , y , z ) that gives the cost of materials for a closed rectangular box with length x feet, width y feet, and height z feet. Assume that the material for the top and bottom costs $3 per square foot and the material for the sides costs $5 per square foot. (3 points)

2) Minimize x2+3 y2+10 subject to the constraint 8−x− y=0 . (NOTE : The Lagrange

multiplier method may be used to solve this problem.) (3 points)



the test


this’




do this’

Evaluate multi-variable functions (MPO 1.1):questions 1 & 2

14 = 70% 6 = 30% 0 = 0%

Determine relative minima and relative maxima of multi-variable functions (MPO 1.1):question 7

4 = 20% 12 = 60% 4 = 20%

Calculate partial derivatives (MPO 1.5):questions 6 & 9b 6 = 30% 13 = 65% 1 = 5%Determine the areas between curves (MPO 1.7):questions 3 & 4

7 = 35% 13 = 65% 0 = 0%

Determine a specified volume of revolution (MPO 1.8):question 8b

5 = 63% 2 = 25% 1 = 13%


Solve continuous income stream future value problems (MPO 2.1):question 8a

3 = 25% 6 = 50% 3 = 25%

Solve optimization problems (MPO 2.4)questions 9a & EC2 7 = 54% 2 = 15% 4 = 31%

NOTE : Questions 5 & EC1 were not blueprinted on this test.Name: ________________________________ December 16, 2010

Math 127 FINAL EXAMINATION Dr. Gaulden

1) Differentiate as indicated below. (6 points each)

a) Given y= (2x+4 )3+ x−1

x+1+ x√ x+1

, determine dydx .

b) Given y= ( x+1 ) (2 x+1 ) (3 x+1 )

√4 x+1 , use logarithmic differentiation to determine dydx .

c) Given f ( x , y , z )=xy 2 z , evaluate ∂ f∂ y at ( x , y , z )=(2 ,−1 ,3 ) .

2) Integrate as indicated below. (6 points each)

a)∫(x √x−4 x3+ 1

3 x+ x

2 )dx

b)∫0

1

4 e−3 x dx NOTE : Do not round your answer – give the exact value.

3) Determine the function values/continuity as indicated below. (8 points each)

a) Let g ( x , y , z )= x

y−z . Compute g (2 ,3 , 4 ) .

b) Givenf ( x )={2 x−1 for 0≤x≤1

1 for 1< x , determine whether f ( x ) is continuous at x=1 . Be sure

to show adequate work to justify your answer and receive full credit.

4) Solve each equation below. (8 points each)


PLEASE show all work to receive full credit. That means that if you do not show all work, full credit will not be given. Work carefully and neatly. Good luck!

a)ln ( 4− x )=1

2

b) e x2−2 x=e8

5) A movie theater has a seating capacity of 3000 people. The number of people attending

a show at price p dollars per ticket is q=18000

p−1500

. Currently, the price is $6 per ticket. If the price is lowered, will revenue increase or decrease? Be sure to show adequate work to justify your answer and receive full credit. (9 points)

6) Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 2 p3+x2=4500 . Determine the rate at which sales are changing at a time when x=50 , p=10 , and the price is falling at the rate of $0.50 per week. (9 points)

7) Choose and complete ONE of the two problems below. (NOTE : If you complete both problems, only the first one will be graded.) (10 points)a) Suppose that the marginal cost function of a handbag manufacturer is

C ' ( x )= 332

x2−x+200 dollars per unit at production level x (where x is measured in

units of 100 handbags). Find the total cost of producing 6 additional units if 2 units are currently being produced.

ORb) Let C ( x )=12 x+1100 denote the total cost (in dollars) of manufacturing x units of a

certain commodity per day. What is the total cost if the production is set at 10 units per day? Also, what is the marginal cost?

8) Choose and complete ONE of the two problems below. (NOTE : If you complete both problems, only the first one will be graded.) (10 points)

a) Shakespear’s Pizza sells 1000 large vegi pizzas per week for $18 a pizza. When the owner offers a $5 discount, the weekly sales increase to 1500. Assume a linear relation between the weekly sales A ( x ) and the discount x. Find the value of x that maximizes the weekly revenue.

ORb) $1000 is deposited in a savings account at 6% interest compounded continuously.

How many years are required for the balance in the account to reach $2500?


1) Use limits (the definition of the derivative) to compute f' (3 ) where f ( x )=x2+1 . NOTE :

To receive credit for this problem, limits (the definition of the derivative) and not the power rule must be used to compute f

' (3 ) .


2) 100 shares of a technology stock were purchased on January 2, 1990, for $1200 and sold on January 2, 1998, for $12,500. What rate of interest compounded continuously did this investment earn?

SLO Assessment Results for the Final Exam:

Skill/Math Topic (part of specified MPO): blueprinted questions from the

final exam

Students who ‘knew how to

do this’

Students who ‘had some

idea how to do this but need more practice’


do this’

Evaluate multi-variable functions (MPO 1.1)question 3a

20 = 100% 0 = 0% 0 = 0%

Solve quadratic equations (MPO 1.2)question 4b 15 = 75% 0 = 0% 5 = 25%Solve exponential equations (MPO 1.2)question 4b 20 = 100% 0 = 0% 0 = 0%Solve logarithmic equations (MPO 1.2)question 4a 14 = 70% 3 = 15% 3 = 15%Determine whether a function is continuous at a specified value of x (MPO 1.3)question 3b

7 = 35% 5 = 25% 8 = 40%

Determine the derivative of a function by using limits and difference quotients (MPO 1.4)question EC1

0 = 0% 0 = 0% 9 = 100%

Calculate derivatives using the product rule (MPO 1.5):question 1a

7 = 35% 5 = 25% 8 = 40%

Calculate derivatives using the quotient rule (MPO 1.5):question 1a

9 = 45% 5 = 25% 6 = 30%

Calculate derivatives using the chain rule (MPO 1.5):question 1a

13 = 65% 5 = 25% 2 = 10%

Calculate derivatives using logarithmic differentiation (MPO 1.5):question 1b

8 = 40% 6 = 30% 6 = 30%

Calculate partial derivatives (MPO 1.5):question 1c 11 = 55% 4 = 20% 5 = 25%Integrate functions (MPO 1.7):question 2a 3 = 15% 10 = 50% 7 = 35%Calculate definite integrals by applying the Fundamental Theorem of Calculus (MPO 1.7)question 2b

11 = 55% 5 = 25% 4 = 20%

Solve compound interest problems (MPO 2.1)

10 = 50% 4 = 20% 6 = 30%


questions 8b & EC2Solve marginal cost problems (MPO 2.2)question 7a or 7b 14 = 70% 6 = 30% 0 = 0%Solve related rates problems (MPO 2.3)question 6 7 = 35% 2 = 10% 11 = 55%Solve optimization problems (MPO 2.4)question 8a 1 = 50% 0 = 0% 1 = 50%Solve elasticity of demand problems (MPO 2.6)question 5

10 = 50% 4 = 20% 6 = 30%


MTH 127 OVERALL STUDENT LEARNING OUTCOMES (SLOs) RESULTS

(including data from all tests & the final exam)

MPO

Specific Skill / Math TopicStudents

who ‘knew how to do

this’



Students who

‘did not know how to do this’

MPO 1.1 evaluate and graph (using the first-derivative and second-derivative tests as appropriate) polynomial, piecewise, composite, exponential, logarithmic, and multi-variable functions

Evaluate polynomial functions. T1: 17 = 47% T1: 15 = 42% T1: 4 = 11%

Evaluate piecewise functions. T1: 23 = 64% T1: 5 = 14% T1: 8 = 22%

Graph piecewise functions. T1: 10 = 34% T1: 9 = 31% T1: 10 = 34%

Graph polynomial functions. T2: 21 = 68%T3: 7 = 23%

T2: 8 = 26%T3: 17 = 57%

T2: 2 = 6%T3: 6 = 20%


Evaluate multi-variable functions.T6: 14 = 70%FE: 20 = 100%

T6: 6 = 30%FE: 0 = 0%

T6: 0 = 0%FE: 0 = 0%

Determine relative minima and relative maxima of multivariable functions. T6: 4 = 20% T6: 12 = 60% T6: 4 = 20%

MPO Specific Skill / Math TopicStudents


this’



Students who


MPO 1.2 solve linear, quadratic, exponential, and logarithmic equations Solve quadratic equations. T1: 29 = 81%

FE: 15 = 75%T1: 5 = 14%FE: 0 = 0%

T1: 1 = 3%FE: 5 = 25%

Solve exponential equations.T4: 15 = 54%FE: 20 = 100%

T4: 11 = 39%FE: 0 = 0%

T4: 2 = 7%FE: 0 = 0%

Solve logarithmic equations. T4: 10 = 36%FE: 14 = 70%

T4: 12 = 43%FE: 3 = 15%

T4: 6 = 21%FE: 3 = 15%

MPO 1.3 determine limits, continuity, and differentiability of given functions at specified values

Determine limits. T2: 25 = 81% T2: 6 = 19% T2: 0 = 0%


Determine continuity and/or differentiability of a function at a specified value.

T2: 18 = 58%FE: 7 = 35%

T2: 8 = 26%FE: 5 = 25%

T2: 5 = 16%FE: 8 = 40%



this’

Students who ‘had some

idea how to do this but need more practice’

Students who

‘did not know how to

do this’

MPO 1.4 determine a derivative of a function by using limits and difference quotients

Use the definition of a derivative to compute a derivative.

T2: 12 = 52%FE: 0 = 0%

T2: 4 = 17%FE: 0 = 0%

T2: 7 = 30%FE: 9 = 100%

MPO 1.5 calculate first, second, or partial derivatives of polynomial, rational, exponential, and logarithmic functions by using rules of differentiation including the product, quotient, and chain rules and implicit and logarithmic differentiation

Calculate first and second derivatives. T2: 13 = 42% T2: 17 = 55% T2: 1 = 3%

Calculate derivatives using the product rule.T3: 24 = 80%T4: 17 = 61%FE: 7 = 35%

T3: 3 = 10%T4: 9 = 32%FE: 5 = 25%

T3: 3 = 10%T4: 2 = 7%FE: 8 = 40%

Calculate derivatives using the quotient rule.T3: 24 = 80%T4: 17 = 61%FE: 9 = 45%

T3: 2 = 7%T4: 9 = 32%FE: 5 = 25%

T3: 4 = 13%T4: 2 = 7%FE: 6 = 30%

Calculate derivatives using the chain rule.T3: 10 = 48%T4: 22 = 79%FE: 13 = 65%

T3: 5 = 24%T4: 4 = 14%FE: 5 = 25%

T3: 6 = 29%T4: 2 = 7%FE: 2 = 10%

Calculate derivatives of exponential functions. T4: 19 = 68% T4: 7 = 25% T4: 2 = 7%

Calculate derivatives of logarithmic functions. T4: 5 = 18% T4: 14 = 50% T4: 9 = 32%

Calculate derivatives using implicit differentiation. T3: 18 = 62% T3: 4 = 14% T3: 7 = 24%

Calculate derivatives using logarithmic differentiation.

T4: 12 = 43%FE: 8 = 40%

T4: 7 = 25%FE: 6 = 30%

T4: 9 = 32%FE: 6 = 30%


Calculate partial derivatives. T6: 6 = 30%FE: 11 = 55%

T4: 13 = 65%FE: 4 = 20%

T4: 1 = 5%FE: 5 = 25%



this’



Students who


MPO 1.6 calculate Riemann sums to estimate definite integrals

Calculate Riemann sums to estimate definite integrals. T5: 19 = 83% T5: 4 = 17% T5: 0 = 0%

MPO 1.7 apply the Fundamental Theorem of Calculus to calculate integrals of single variable functions and determine the areas between given curves

Integrate functions. T5: 22 = 96%FE: 3 = 15%

T5: 1 = 4%FE: 10 = 50%

T5: 0 = 0%FE: 7 = 35%

Calculate definite integrals by applying the Fundamental Theorem of Calculus.

T5: 21 = 91%FE: 11 = 55%

T5: 2 = 9%FE: 5 = 25%

T5: 0 = 0%FE: 4 = 20%

Determine the area between given curves. T6: 7 = 35% T6: 13 = 65% T6: 0 = 0%

MPO 1.8 determine a specified volume of revolution

Determine a specified volume of revolution. T6: 5 = 63% T6: 2 = 25% T6: 1 = 13%

MPO 2.1 solve compound interest, present value, and future value problems

Solve compound interest problems.T1: 24 = 67%T5: 21 = 91%FE: 10 = 50%

T1: 9 = 25%T5: 2 = 9%FE: 4 = 20%

T1: 3 = 8%T5: 0 = 0%FE: 6: 30%


Solve present value problems. T5: 20 = 87% T5: 3 = 13% T5: 0 = 0%

Solve continuous stream future value problems. T6: 3 = 25% T6: 6 = 50% T6: 3 = 25%



this’



Students who


MPO 2.2 solve marginal cost, marginal profit, and marginal revenue problems by using differentiation and integration as necessary Solve marginal cost, marginal profit,

and marginal revenue problems by using differentiation and integration as necessary

FE: 14 = 70% FE: 6 = 30% FE: 0 = 0%

MPO 2.3 solve rate-of-change and related rates problems

Solve rate-of-change problems. T2: 16 = 52% T2: 11 = 35% T2: 4 = 13%

Solve related rates problems. T3: 1 = 3%FE: 7 = 35%

T3: 13 = 43%FE: 2 = 10%

T3: 16 = 53%FE: 11 = 55%


MPO 2.4 solve optimization problems (in geometry, finance, inventory control, etc.) including those involving functions of several variables

Solve optimization problems.T3: 17 = 57%T6: 7 = 54%FE: 1 = 50%

T3: 9 = 30%T6: 2 = 15%FE: 0 = 0%

T3: 4 = 13%T6: 4 = 31%FE: 1 = 50%

Solve economic order quantity (EOQ) – i.e., inventory control – problems. T3: 20 = 67% T3: 4 = 13% T3: 6 = 20%

MPO 2.5 solve growth and decay problems (in finance, biology, chemistry, physics, etc.)

Solve growth and decay problems. T5: 23 = 100% T5: 0 = 0% T5: 0 = 0%



this’



Students who


MPO 2.6 solve elasticity of demand problems Solve elasticity of demand problems. T5:21 = 91%

FE: 10 = 50%T5:1 = 4%FE: 4 = 20%

T5: 1 = 4%FE: 6 = 30%

MPO 3.1 write and explain solutions to application problems including related rates, optimization, inventory control, growth and decay, and elasticity of demand problems NOT ASSESSED IN FALL 2010

NOT ASSESSED IN FALL 2010

MTH 127 – Appendix A –

24

MPO 4.1 use the GRAPH feature to display polynomial, piecewise, composite, exponential, logarithmic, and multi-variable functions

MPO 4.2 use the TABLE feature to determine account balances for given compound interest problems

NOT ASSESSED IN FALL 2010

NOTE : FE = final exam

MTH 127 SLOAT Final Report – APPENDIX B


STUDENTS…I NEED YOUR INPUT!! – Test 1Please answer the following questions honestly so that I can improve my performance as a math professor.<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>1. What barriers in your life keep you from excelling at math? (Circle ALL

that apply.)TEST ANXIETY: 19 (= 53%)DON’T STUDY ENOUGH – OVERCOMMITTED SCHEDULE: 13 (= 36%)DON’T STUDY ENOUGH – LAZY: 9 (= 25%) BAD MATH BACKGROUND: 5 (= 14%)MATH PHOBIA: 5 (= 14%)MISSED TOO MANY CLASSES ALREADY: 2 (= 6%)OTHER(S):left a gap between math classes/too long since I took a math course: 2 (= 6%)

need to review more of the prerequisite material: 1 (= 3%)know shortcuts but not the foundations or basics: 1 (= 3%)not enough time: 1 (= 3%)too much homework: 1 (= 3%)do the problems too fast: 1 (= 3%)have problems with concentration & focus: 1 (= 3%)

2. What can you do differently to help you do better at math?Do more practice: 13 (= 36%)Study more/have more time to study – I have a 4 year old: 9 (= 25%)Seek help/ask questions/find resources to improve my skills/find support

from classmates, the professor, tutoring/go to tutors/visit STEM more: 7 (= 19%)

Do my homework/do my homework before class then review one night before the test/pay attention more to the homework: 4 (= 11%)

Spend more time at school practicing math: 1 (= 3%)Study more & be less lazy: 1 (= 3%)Apply myself in class & at home: 1 (= 3%)Read the book more: 1 (= 3%)Pay more attention in class: 1 (= 3%)Make sure I attend each class so I won’t have to play catch up: 1 (= 3%)Cut my work hours: 1 (= 3%)Have better time management/set a fixed time 1 – 2 hours/day to review

class: 3 (= 1%)Take math separately from other study-intensive courses: 1 (= 3%)Leave no gaps between math courses: 1 (= 3%)Sleep well before tests: 1 (= 3%)Slow down on tests: 1 (= 3%)


Reduce anxiety (tests especially): 1 (= 3%)Nothing: 1 (= 3%)

3. What can I do differently to help you do better at math?

Slow down/slow down sometimes – don’t assume that because we came from math 100 that we know it. Not every teacher takes the time to make sure we are really ready for calculus: 15 (= 42%)

Nothing/you give good lessons/cannot think of anything. I think you are a great professor. I like the fact that we review homework – it is very helpful/keep doing the great job you are doing: 9 (= 25%)

Give reviews for tests: 3 (= 8%)Make homework mandatory/collect homework (even if you don’t check it)

– this will force us to do it diligently: 2 (= 6%)Explain more: 2 (= 6%)Solve more problems: 2 (= 6%)Don’t “assume” ever: 2 (= 6%)Encourage students to study more: 1 (= 3%)Give less tests: 1 (= 3%)Give easier tests: 1 (= 3%)Speed up the class: 1 (= 3%)Reinforce what we’ve learned by examples: 1 (= 3%)Be more patient: 1 (= 3%)Give one-on-one classes: 1 (= 3%)Cover less material in class: 1 (= 3%)Assess students for those topics in math they know/don’t know: 1 (= 3%)

Please indicate your confidence level regarding your ability to perform the following MTH 127 content skills by placing an X in the correct column for each row:

Skill / Math Topic I know how to do this.

I have some idea how to do this but

need more practice.

I do not know how to do this.

Evaluate polynomial functions.

Ex: Given f ( x )=x+1 find f (1 )34 = 97% 1 = 3% 0 = 0%

Evaluate piecewise functions. 18 = 55% 14 = 42% 1 = 3%


Ex: Given f ( x )={x−1 for x≤2

x2 for x>2 find f (1 )



need more practice.


Graph piecewise functions.

Ex: Graph f ( x )={x−1 for x≤2

x2 for x>2

16 = 46% 15 = 43% 4 = 11%

Solve quadratic equations.

Ex: Solve x2−4 x−5=029 = 83% 5 = 14% 1 = 3%

Solve compound interest problems.

Ex: Determine the amount of money in an account if $10,000 is invested in an account with a 4% interest rate that is compounded monthly for 3 years.

16 = 46% 17 = 49% 2 = 6%


STUDENTS…I NEED YOUR INPUT AGAIN!! – Test 2Please answer the following questions honestly so that I can improve my performance as a math professor.<><><><><><><><><><><><><><><><><><><><><><><>

<><><><><><><><><>

1. How do you think you will do on this test (Test #2) compared to Test #1?BETTER: 11 (= 42%) ABOUT THE SAME: 7 (= 27%) WORSE: 8 (= 31%)

2. If you think you will do better, why? (Circle all that are applicable. Leave it blank if necessary.)STUDYING MORE: 9 (= 82%) HAVE THE BOOK NOW: 0 (= 0%) DOING MORE HOMEWORK: 5 (= 45%) NOT MISSING AS MANY CLASSES: 1 (9%)NOT AS NERVOUS – KIND OF KNOW WHAT TO EXPECT: 4 (36%) RECEIVED HELPFUL TUTORING (IF SO, WHERE ____): 1 “Tech Support” – STEM? (= 9%)OTHER: ______________________________________: 0 (= 0%)

3. If you think you will do worse on this test, why? (Circle all that are

applicable. Leave it blank if necessary.)

HARDER MATH TOPICS ON TEST 2: 5 (= 63%) MISSING TOO MANY CLASSES: 0 (= 0%)NOT DOING ENOUGH HOMEWORK: 2 (= 25%) NOT STUDYING ENOUGH – LAZY: 2 (=

25%)NOT STUDYING ENOUGH – OVERCOMMITTED SCHEDULE: 3 (= 38%)BAD MATH BACKGROUND CATCHING UP WITH ME: 1 (= 13%) OTHER: ____: 1 “Teacher’s too fast” (= 13%)

ADDITIONAL HELPFUL COMMENTS CAN BE WRITTEN BELOW 3 – Go slower, explain more./You are going too fast. Write step by step. Please slow down. / Please slow down.

2 – Can we get a mini study guide with some problems like 10 with an answer sheet. I think it will help a lot of us since the book sucks./We need a better book.

1 – Some concepts are very hard to grasp.




I have some idea how to do this but need more practice.


Determine limits.

Ex: Find limx→2

x2−4x−2 .

15 = 58% 8 = 31% 3 = 12%

Determine first and second derivatives.

Ex: Find f ' and { f ' ' ¿given that f ( x )= (2 x−3 )7−√5 x+1 .

14 = 54% 11 = 42% 1 = 4%

Determine whether a function is continuous and/or differentiable at a specified value for x.

Ex: Is f ( x )={x−5 for 0≤x≤2

−3 for x>2 continuous and/or differentiable at x=2 ?

8 = 31% 15 = 58% 3 = 12%

Solve rate-of-change problems.

Ex: Determine the velocity and acceleration after 2 seconds if the position function is s ( t )=16 t2−4 t+1 feet.

15 = 58% 6 = 23% 5 = 19%

Graph a function with given properties where information is given about its first and second derivatives.

Ex: Sketch a graph of f ( x ) given thatf (1 )=3 , { f ' (1 )<0 , and { f ¿ ' ' (1 )>0¿ .

9 = 35% 14 = 54% 3 = 12%

Use the definition of a derivative to compute a derivative.

10 = 38% 8 = 31% 8 = 31%


Ex: Find the derivative of f ( x )=x2

by using the definition of the derivation – that is, usef ' ( x )= lim

h→0

f ( x+h )− f ( x )h .

STUDENTS…I NEED YOUR INPUT AGAIN!! – Test 3


Skill / Math TopicI know

how to do this.


need more practice.


Graph a function – indicate the relative extrema, inflection points, concavity, and y-intercept.

Ex: Graph the curve y=1

3x3−2 x2+3 x+1

17 = 63% 7 = 26% 3 = 11%

Calculate derivatives using the product rule.

Ex: Determine y ' if y=x3 (2 x−1 )9 .25 = 93% 1 = 4% 1 = 4%

Calculate derivatives using the quotient rule.

Ex: Determine y ' if y= 2x−5

3 x2+1 .

22 = 81% 4 = 15% 1 = 4%

Calculate derivatives using the chain rule.

Ex: Determine dydx if

y=u5−√u and u=x2+2 x .

15 = 56% 8 = 30% 4 = 15%

Calculate derivatives using implicit differentiation.

12 = 44% 11=41% 4 = 15%


Ex: Determine dydx if x3 y2=3 x−5 .

Solve optimization problems.

Ex: Find the maximum of Q=xy if x+ y=5 .

15 = 56% 11=41% 1 = 4%

Skill / Math TopicI know

how to do this.


need more practice.


Solve economic order quantity (EOQ) problems.

Ex: A furniture store expects to sell 640 sofas at a steady rate next year. The manager of the store plans to order these sofas from the manufacturer by placing several orders of the same size spaced equally throughout the year. The ordering cost for each delivery is $160, and carrying costs, based on the average number of sofas in inventory, amount to $32 per year for one sofa. Determine the economic order quantity that minimizes the inventory cost and then find the minimum inventory cost.

11 = 41% 14=52% 2 = 7%

Solve related rates problems.

Ex: Suppose that the price p (in dollars) and the demand x (in thousands of units) of a commodity satisfy the demand equation 6 p+x+xp=94 . How fast is the demand changing at a time when x=4 , p=9 , and the price is rising at the rate of $2 per week?

4 = 15% 17=63% 6 = 22%


ADDITIONAL HELPFUL COMMENTS CAN BE WRITTEN BELOW don’t know what else to dostudy guide for final is complicated for meI have a bad feeling about this test I need to focus more in the next test. Also need more rest before the test. It’s all my fault.






I do not know how to

do this.

Solve exponential equations.

Ex: Solve 24− x=8 or e1−3 x= 4 .18 = 78% 4 = 17% 1 = 4%

Solve logarithmic equations.

Ex: Solve ln 3 x=2 or 4−ln x=0 .16 = 70% 5 = 22% 2 = 9%

Calculate derivatives of exponential functions.

Ex: Determine y ' if

y=ex2−5 x+4 or y= e4 x

4+x .

9 = 39% 12 = 52% 2 = 9%

Calculate derivatives of logarithmic functions.

Ex: Determine y ' if y= ln (6 x2−3 x+1 ) or y=(1+ ln x )3 .

6 = 27% 12 = 55% 4 = 18%

Calculate derivatives using logarithmic differentiation.

Ex: Determine y ' if

y= (3 x−8 )9 (2x+5 )4√ x−1( x+11)3

6 = 26% 13= 57% 4 = 17%

Calculate derivatives using the product rule.

Ex: Determine y ' if y=xe x.

14 = 61% 9 = 39% 0 = 0%

Calculate derivatives using the quotient rule. 14 = 61% 8 = 35% 1 = 4%


Ex: Determine y ' if y=ln x

x .




do this.

Calculate derivatives using the chain rule.

Ex: Determine dydx if y=e3 x+1

.

14 = 61% 8 = 35% 1 = 4%

ADDITIONAL HELPFUL COMMENTS CAN BE WRITTEN BELOW

Too fast!!!Your job is well detail-oriented and well-organized. Keep it up.I think this test will be easier than the previous one. This class ought to be separated in two. Maybe I’m just complaining.







do this.

Integrate functions.

Ex: Determine

∫(5 x4− 2x+ 3√ x−7)dx

.

9 = 41% 12 = 55% 1 = 5%

Calculate Riemann sums to estimate definite integrals.

Ex: Approximate the area under the curve y=x2

in the interval −1≤x≤3 with n=4subintervals/panels and use the left endpoints of the subintervals/panels.

12 = 55% 9 = 41% 1 = 5%

Calculate definite integrals by applying the Fundamental Theorem of Calculus.

Ex: Determine

∫1

3

(5 x4−2x+ 3√ x−7)dx

.

10 = 45% 11 = 50% 1 = 5%

Solve compound interest problems.

Ex: $1000 is deposited in a savings account at 6% interest compounded continuously. How many years are required for the balance in the account to reach $2500?

13 = 62% 7 = 33% 1 = 5%





do this.

Solve present value problems.

Ex: How much money must you invest now at 4.5% interest compounded continuously to have $10,000 at the end of 5 years?

11 = 52% 10= 48% 0 = 0%

Solve growth and decay problems.

Ex: After t hours there are P ( t ) cells present in a culture, where P ( t )=5000 e0 . 2t

. When will 20,000 cells be present?

12 = 55% 10= 45% 0 = 0%

Solve elasticity of demand problems.

Ex: An electronic store can sell q=10 , 000

p+50−30

cellular phones at a price p dollars per phone. The current price is $150. If the price is lowered slightly, will revenue increase or decrease?

7 = 33% 10= 48% 4 = 19%


NOTE : Test 5 was a take-home test, which students were given 4 days to complete.






need more practice.


Evaluate multi-variable functions.

Ex: Let f ( x )=√x2+2 y2 and

determine f (0 ,−1 ) .

7 = 54% 6 = 46% 0 = 0%

Determine the areas between curves.

Ex: Determine the area of the region bounded by y=x3 and y=2 x2.

6 = 46% 7 = 54% 0 = 0%

Calculate partial derivatives.

Ex: Let f ( x , y , z )=zex

y and

determine ∂ f∂ y .

6 = 46% 7 = 54% 0 = 0%

Determine relative minima and relative maxima of multivariable functions.

Ex: Determine the possible relative maxima and minima points of the function f ( x , y )=6 xy2−2 x3−3 y4

and use the second-derivative test to

4 = 31% 7 = 54% 2 = 15%


classify each point.



need more practice.


Solve continuous income stream future value problems.

Ex: Suppose that money is deposited daily into a savings account at an annual rate of $2000. If the account pays 6% interest compounded continuously, approximately how much will be in the account at the end of 2 years?

6 = 46% 5 = 38% 2 = 15%

Determine a specified volume of revolution.

Ex: Find the volume of the solid of revolution generated by revolving about the x-axis the region under the curve y=kx from x=0 to x=h .

3 = 23% 6 = 46% 4 = 31%

Solve optimization problems.

Ex: A monopolist manufactures and sells two competing products, I and II, that cost $30 and $20 per unit, respectively, to produce. The revenue from marketing x units of product I and y units of product II is 98 x+112 y−. 04 xy−. 1 x2−. 2 y2 . Find the values of x and y that maximize the monopolist’s profits.

4 = 36% 5 = 45% 2 = 18%



ESSEX COUNTY COLLEGE

Fall 2010

SOC 101 Assessment SLOAT Report – Social Sciences

Division

SOC 101 – 1

SOC 101 Fall 2010 AssessmentPrepared by Akil Kokayi Khalfani, Ph.D.

he Social Sciences Division at Essex County College administered an assessment instrument for all students taking Introduction to Sociology (SOC 101) for the 2010 Fall semester. The instrument was

administered in 23 sections of SOC 101. These sections were taught by adjunct instructors. No full-time faculty taught this course in the Fall.

TThe Division was asked to conduct an assessment of a few sections by

sampling the Introduction to Sociology classes for the semester, however the Division decided to conduct a census of the available 23 sections for the semester. This approach allowed us to assess approximately 715 students, who represent a great diversity of students from the College because the course in a popular general education requirement for many degree programs across the College.

Course Description: This class will help students critically analyze the world through a sociological lens. The major theories and methodologies used by sociologists to understand the social world will be examined and applied. The assessment instrument contained a set of three questions that were

designed to assess the students’ understanding of some of the core tenets of the Sociology course. The questions represented a subset of the final exam students took at the end of the semester. There was a rubric designed to analyze and quantify the performance of the Intro students. These questions were designed to assess the first Measurable Performance Objectives from the SOC 101 course outline. The faculty members collected and tallied the data, which was then submitted back to the Division for analysis.

There may be a couple of challenges with the design of the instrument and the way it was administered and evaluated. However, we are confident that this method and these data will provide the Division with a valuable baseline to assess the effectiveness of the teaching and learning in the Introduction to Sociology classes at the College. We intend to use the findings to help in the decision-making process about using a universal final exam for all introductory sociology courses at the college.

SOC 101 – 2

Data from four classes had to be discarded because it was clear that the faculty did not understand how to use the instrument or how to properly tally data from the instrument. As the administrators of the instrument, we must take steps to ensure that adjunct and full-time faculty are properly trained and that we produce clearer instructions for them. Faculty may also require additional time to adequately compile data.

For this first assessment, the instrument was implemented in a variety of formats. Some faculty incorporated the instrument into an existing final exam, while others administered it independently. These different formats may have impacted the outcome of the findings; however we do not have enough information to assess the potential impact of this point at this time.

We analyzed data on approximately 490 students from 18 sections out of the 715 students from 23 sections who took the assessment instrument. Data from five additional sections representing 225 students had to be removed due to reporting errors. These numbers do not reflect enrollment numbers for all SOC 101 classes for the Fall. They only represent the numbers of students who took the instrument on the day that the final exam or the assessment instrument was given and who were enrolled in the classes where these data were properly computed. (The rubric used to grade this instrument follows this report.) Figures 1 – 5 illustrate the findings for this analysis. The questions used in this analysis are as follows:

1. Identify and explain the three major sociological theories and name the major theorists behind each.

A. Conflict TheoryB. Structural Functional TheoryC. Symbolic Interaction Theory

2. State three major contributions to the field of sociology by W.E.B. Du Bois.

A. Students needed to identify 3 of 4 possible contributions to get full credit

3. Who coined the term “Sociological Imagination;” and what does it mean?

This instrument was designed to test student achievement of the first Course Goal and part of the second Course Goal for Introduction to Sociology. Additionally the instrument assessed all of the related

SOC 101 – 3

Measurable Performance Objectives (MPOs) for Course Goal 1 and part of Course Goal 2 as illustrated below:

1. Recognize and describe sociological concepts and terms:1.1 articulate the three major sociological theories: Conflict,

Structural Functional, and Symbolic Interaction;1.2 explain and apply the concept of the sociological imagination;

and1.3 discuss the methods used for sociological analysis

2. Recognize the names of important figures in the development of sociology and recognize and explain theories and concepts they espoused or critiqued: 2.1 identify early European and American sociological thinkers, such

as Marx and Du Bois;2.2 describe the contributions of the Atlanta Sociological Laboratory

and the Chicago School and identify the central scholars who brought recognition to these institutions; and

MPOs 1.1 and 2.1 were tested directly by question 1. We wanted to see if students fully grasped the three components of each sociological perspective: 1) the names of each of the three major theoretical perspectives; 2) the names of one or two proponents of a given theory; and 3) the basic concepts behind each theory. By looking at the rubric, you will see that the point totals for questions 1 and 3 are cumulative. If the student correctly answered step 1, they earned 1 point for the section. They received one additional point for each correct component or sociological theory tested by this MPO. Question 1 contained three 3-point components where each theoretical perspective was worth 3 points for a total of 9 points possible in the section. MPO 2.1 is additionally assessed by question 2 as it focuses specifically on W.E.B. Du Bois, who was one of the founding fathers of American sociology.

MPO 1.2 was directly assessed in question number 3 by looking at the works of sociologist C. Wright Mills. Mills wrote the book Sociological Imagination in 1959. Question 3 was structured like question 1 in that it offered students three cumulative point opportunities. Each student received one point for mentioning C. Wright Mills’s name; one point for identifying the terms history and biography as they relate to the sociological imagination; and a final point for a total possibility of 3 points for briefly explaining the concept of the sociological imagination.

SOC 101 – 4

MPO 1.3 was indirectly assessed by question 2. Students would have had to know something about sociological methodology to correctly answer the question about Du Bois because one of the correct answers for question 2 was that Du Bois along with the Atlanta University Sociology Department developed the idea of method and theory triangulation. This approach to research can improve the reliability and validity of the finding.

MPO 2.2 was directly assessed in question 2 on W.E.B. Du Bois. He was the preeminent scholar affiliated with the Atlanta University Sociological Laboratory. Students who answered this question correctly would have to have some understanding about the differences between the sociology programs at Atlanta University and the University of Chicago. There were 4 possible answers to this question. If a student answered three questions correctly, they earned full credit.

DATA ANALYSISQuestion 1

The first pattern we notice in these data is that on average only 50% of the students are able to articulate their understanding of the three major sociological perspectives, including the name of the theory, the authors and a brief description of the perspective. However, a great majority of the students were able to list at least one of the three components of the three major sociological perspectives. This demonstrates that MPO 1.1 and 2.1 are being addressed in the class, but that more attention needs to be stressed on them throughout the semester. Figures 1a, 1b, and 1c, illustrate these similarities.

These data also show that in certain classes students had a propensity to answer the first step in this section, thereby awarding them only one point. It is not clear if this is due to how the question was administered, poor communication between the student and the professor, or maybe because the professor did not fully understand how to use the assessment instrument. Further analysis would be necessary to ascertain this information.

SOC 101 – 5

24%

26%

50%

Conflict Theory

Q1A.1 Q1A.2 Q1A.3

27%

26%

47%

Structural Functional Theory

Q1B.1 Q1B.2 Q1B.3

26%

20%

54%

Symbolic Interaction Theory

Q1C.1 Q1C.2 Q1C.3

Figure 1A Figure 1B Figure 1C

Question 2

Figure 2 on the next page represents data from question 2 on W.E.B. Du Bois. This question directly tests two MPOs from the second course goal: 2.1 and 2.2. The first MPO assessed whether students knew that Du Bois was an important figure in the founding of American sociology. The second MPO directly assess a student’s knowledge about the Atlanta Sociological Laboratory. Although the institution was started 1895 two year prior to the arrival of Du Bois, he was the most prominent sociologist at Atlanta University after the department’s founding. Students could state any 3 of 4 possible answers to receive full credit for this question.

The question on Du Bois also indirectly assessed MPO 1.3 which examined students’ understanding of sociological methodology. Du Bois helped to develop the ideas of method and theory triangulation, so in the process of studying about his contribution to sociology they would acquire some knowledge about methodology.

Out of the 490 students who took the assessment, less than 50% correctly chose any single correct answer. Below in Table 1, we can see the numerical distribution of the correct answers. Figure 2 illustrates the percent distribution for this question, where we see that the majority of the correct answers centered on Du Bois’s ethnographic work and his contribution to the University of Atlanta.

It is not clear if the students did not answer the question or if they answered it incorrectly. We would need to look at the exam in addition to the summary sheets we received from the faculty members to make this distinction.

SOC 101 – 6

Table 1: Numerical Distribution of Correct Answers for Question 2

1) If the student mentions Method and/or Theory Triangulation 148

2) If the student says Du Bois was one of the founding fathers of American Sociology

160

3) If the student says Du Bois began the ethnographic study of race in the U.S. 224

4) If the student says Du Bois developed the Atlanta Sociological Laboratory or sociology at Atlanta University

205

Object 272

Figure 2

Question 3

Data from question 3 assessed MPO 1.2. We were testing to see if students understood the concept of the sociological imagination and knew that C. Wright Mills coined the term. Figure 3 shows that 65% of the students attained this level of proficiency. An additional 19% of the students knew about Mills and at least the basic tenets of the concept. This means that 84% of the students had a good understanding of the sociological imagination which is an essential notion in sociology.

We had to do some extra cleaning of these data because two classes had insufficient data inputted for this question.

SOC 101 – 7

Q3.116%

Q3.219%

Q3.365%

Sociological Imagination

Figure 3

SUGGESTIONS

These data suggest that there is certainly room for improvement for establishing a greater level of proficiency on the basic ideas and Course Goals in the Introduction to Sociology course at the College. It is also clear that in certain professor’s classes a higher level of proficiency was achieved than in other. We may want to further observe the lower performing professors’ classes to coach them on ways to improve their teaching outcomes. It may be useful to have more frequent quizzes that employ these concepts as they relate to latter chapters. Particularly where the three major theories are concerned, we may want to more thoroughly explore them in subsequent chapters so that students develop a better grasp of the theories.

Further testing of these Course Goals will provide us with better data for assessing student performance in Sociology program and in the Social Sciences Division in general. This analysis gives us a usable baseline, although not a perfect one, to begin looking towards long-term goals in the program.

SOC 101 – 8

APPENDIX A

Rubric for Questions ALL SOC 101 Courses – Fall 20101. Explain the three major sociological theories and identify the major

theorists behind each.2. State three major contributions to the field of sociology by W.E.B. Du Bois.3. Who coined the term “Sociological Imagination;” and what does it mean?

List Section Number ____________________

Question 1 (3 Points possible for each section & a total 9 points possible)

Possible Points

Adjusted number of Students

receiving this grade

If the student says Conflict Theory 1 118If the student says Conflict Theory and Karl Marx or C. Wright Mills 2 129If the student says Conflict Theory and Karl Marx or C. Wright Mills; and states that this theory assumes that society is based on a series of conflicting relationships ideas.

3 243

If the students mentions Structural Functional Theory 1 117If the students mentions Structural Functional Theory and Auguste Comte, Emile Durkheim or Herbert Spencer

2 113

If the students mentions Structural Functional Theory and Auguste Comte, Emile Durkheim or Herbert Spencer; and states that this theory sees society as an organism with certain structures and related functions.

3 201

SOC 101 – Appendix A – 1

If the students mentions Symbolic Interaction Theory 1 106If the students mentions Symbolic Interaction Theory and George Herbert Mead, W.I. Thomas or Charles Cooley

2 83

If the students mentions Symbolic Interaction Theory, George Herbert Mead, W.I. Thomas or Charles Cooley, and state that this is a micro level theory that examines the relationships between individuals, and individuals and society.

3 219

Question 2 (3 Points possible) [There are 4 possible answers, but credit is only given for up to 3.]

Possible Points



If the student mentions Method and/or Theory Triangulation 1 148If the student says Du Bois was the founding father of American sociology 1 160If the student says Du Bois began ethnographic study of race in the U.S. 1 224If the student says Du Bois developed the Atlanta Sociological Laboratory or sociology at Atlanta University

1 205

Question 3 (3 Points possible) Possible Points



If the student mentions C. Wright Mills 1 80If the student mentions C. Wright Mills and mention that the Sociological Imagination has to do with history and biography

2 74

If the student mentions C. Wright Mills and explains how the Sociological Imagination has to do with history and biography and/or explain that it helps us understand the use of perspective when examining the world and social phenomena.

3 191


Grand totalNumber of

classesError in the tabulation of the assessment tool 5Missing data 23 unusable classes because of missing or erroneous data 3


sociology program assessment - essex county...

Documents