ASU College Algebra

COLLEGE ALGEBRA REDESIGN: INFUSING CONCEPTUAL ACTIVITIES AND TECHNOLOGY IN THE CLASSROOM TO PROMOTE STUDENT LEARNING

PI: Dieter ArmbrusterCo-PIs: Marilyn Carlson, April Strom, Lance Ward, Kacie Koch

AbstractThis project aims to redesign ASU’s large-enrollment College Algebra course in ways

that research suggests will improve students’ understanding, pass rates, and motivation to take additional mathematics. It will also address Arizona’s shortage of mathematics teachers through a novel training and mentoring of mathematics majors to serve as apprentice course instructors. The traditional ASU College Algebra course serves approximately 1700 students with over 80 course sections each year. Approximately 20% of ASU’s freshman class enrolls in College Algebra annually. First Year Mathematics (FYM) faculty, graduate teaching assistants, and competitively selected undergraduate students currently teach these sections. The pedagogy in this three-credit course consists of lecture-based instruction with minimal collaboration among students during class meetings. Most traditional sections do not infuse computer technology into classroom activities; however, teachers have the option of using online homework assignments. These assignments focus on students’ procedural learning, rather than conceptual understanding.

These methods of instruction are showing poor results. Over the past seven years, the percentage of students who fail or withdraw from ASU's College Algebra program has ranged from 35% to almost 50%. This is remarkable given that College Algebra repeats material that students have already taken in high school. Indeed, repetition is a large part of the problem. In a traditional College Algebra course, students receive a repeat dose of a curriculum and instructional methods that did not succeed for them in high school and are not succeeding for them at the university.

The course redesign we propose will incorporate curriculum and teaching techniques that research has shown to be more effective. Research has demonstrated that developing students’ conceptual understanding through instruction focused on student learning and sense-making provides students with powerful tools for success in mathematics, for example (Carlson, 1998; Monk, 1992; A. Thompson, Philipp, Thompson, & Boyd, 1994). National calls for redesigning College Algebra courses have also supported efforts to infuse active learning, problem solving, and data analysis into course instruction (Mathematical Association of America, 2007). Our course redesign plan incorporates two main components: (a) improving course curriculum and instruction and (b) developing a secondary certification program for competitively selected, well prepared, and carefully mentored mathematics majors who will tutor and teach the redesigned College Algebra course. We will improve curriculum and instruction by incorporating active learning in each class session with a focus on research-based conceptual activities designed to promote student interaction and understanding. The newly designed secondary mathematics certification program will prepare undergraduate mathematics majors to tutor in College Algebra during their junior year and to teach the course during their senior year. Experienced faculty from the redesign team will mentor and supervise these undergraduate teachers during their tutoring and teaching experiences.

ABOR’s investment in this redesign project will reap a double return: Students in the redesigned courses will be better prepared for subsequent mathematics courses, and our mathematics majors will be better prepared to teach high school mathematics. In addition, by

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providing future mathematics teachers with meaningful training in the most advanced teaching methods and technologies, our project will support Arizona’s school districts in their struggle to meet the quality teacher goals of federal No Child Left Behind regulations.

Our research plan will utilize multiple methods for data collection and data analysis. Using pre- and post-tests, we will compare students' success in the redesign pilot with student success in the traditional College Algebra course. In addition, we will interview students from both the pilot group and the traditional group. These videotaped interviews will focus on students' understanding of key College Algebra concepts. We will also track all College Algebra students' subsequent enrollment and success in future mathematics classes.

Cost savings from the redesign will primarily come from using undergraduates to teach and tutor the course in lieu of expensive graduate and FYM faculty. They will receive college credit, instead of salary, toward secondary certification. Faculty mentors will work closely with undergraduate teachers to help develop their knowledge and skills. Previous interventions to use carefully selected and trained undergraduates to teach College Algebra have been highly successful (Carlson, 1994). This cost savings will ultimately translate to fewer faculty being paid to teach College Algebra. Funds saved as a result of the redesign will be allocated to redesigning other mathematics courses and providing leadership training opportunities for faculty teaching redesigned courses.

IntroductionDevelopment of students’ conceptual understanding through instruction focused on

inquiry methods that promote sense making of key ideas provides students with powerful tools for success in mathematics (Carlson, 1998; Monk, 1992; A. Thompson et al., 1994). National calls for redesigning current College Algebra courses have also supported efforts to infuse active learning, problem solving, and data analysis into course instruction as a way of building stronger conceptions of College Algebra topics (American Mathematical Association of Two-Year Colleges, 2006; Mathematical Association of America, 2007). Our proposed redesign of ASU’s College Algebra program adopts research-based recommendations for teaching College Algebra conceptually with meaningful activities designed to promote critical thinking, collaborations and communication among students.

Over the past seven years, the percentage of students who fail or withdraw from ASU's College Algebra program has been unacceptably high, ranging from 35% to almost 50%. This failure affects the lives of hundreds of ASU students, who often drop out of the university after failing their initial mathematics course. Their lack of success can be traced in part to the students' own lack of preparation, coupled with their guaranteed acceptance into the College Algebra course. But the problem is magnified when the course concepts, which these students have already encountered in their high school coursework, are re-taught to them using the techniques and teaching styles that did not work the first time. That is the situation currently in ASU College Algebra; under-prepared students are receiving a repeat dose of a curriculum and instructional methods that did not succeed for them in high school and are currently not succeeding for them at the university. Our course redesign thus intends to take a fresh approach by adopting methods, technology and curricula that mathematics education research points to as effective. Using the research to guide us, we intend to align the instructional delivery, curriculum and tools of ASU’s College Algebra program with the best knowledge and most current tools that have proven successful for College Algebra students in this nation and internationally. By improving the experiences of large numbers of students in freshman mathematics at ASU we will contribute to

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improving the retention rate of ASU students. This effort will also open doors to subsequent courses for students who have never had the opportunity to pass College Algebra before. By making the course more relevant we anticipate that we will also improve these students’ views about the importance and usefulness of mathematics in a broad range of decisions they will be confronting during their lifetimes.

The current ASU College Algebra course consists largely of skill-based tasks, which mostly require memorization of the procedures essential for completing these tasks. Yet research strongly suggests that memorizing mathematical procedures leaves students with little understanding of the important concepts necessary for success in future mathematics courses. Our redesign project will focus more on the key ideas of College Algebra than on repetitive calculation exercises. Among the key ideas we will explore are variation, covariation, rate of change, function, additive reasoning, and multiplicative reasoning. These ideas are central to College Algebra and foundational for students’ success in calculus (Oehrtman, Carlson, & Thompson, in press).

Additionally, mathematics education research has illuminated the importance of instruction that focuses on student inquiry and applying mathematical concepts in real-world contexts. In contrast to the traditional College Algebra course, our redesign project will infuse contextual applications in every class session. These applications will require students to grapple with the mathematics and make sense of the concepts through a process of inquiry and reflection. This engagement of students in class activities will shift instruction in the course from a more teacher-centered to a more student-centered experience. They too will help students see the relevance and usefulness of mathematics in science explorations. Our project will produce a comprehensively redesigned model for College Algebra, incorporating training workshops, enhanced curriculum, computer-based instructional supports, and revised assessments. Over the course of several years, we hope to create a national model for instruction not only in College Algebra, but in the entire range of entry-level college mathematics courses, with the knowledge and tools acquired from this project laying the foundation for improvements we plan to make in both precalculus and calculus.

College Algebra Redesign: A Model for SuccessCentral to our mission in this redesign effort is the idea of shifting instruction in the

classroom to be more student-centered as opposed to traditional courses in which the center of instruction lies with the teacher. This active role of learning will require students to engage in meaningful collaborative activities inside and outside of the classroom environment. Our vision of this redesign incorporates classroom activities that provide opportunities for students to collect their own data using calculator-based technology and to work with hands-on manipulatives to make sense of the mathematics. In this effort we are guided by our team’s deep familiarity with the literature in mathematics education research. Indeed, teaming mathematics faculty with mathematics education researchers is a particular strength of our project, one that will expand the university’s human capacity to deliver quality instructional experiences.

In the language of ABOR’s RFP, our College Algebra redesign project is best described as a supplemental model since the basic structure of the traditional course will remain while being augmented with instruction that focuses on understanding and using foundational ideas through active learning during class. All class sessions will continue to be conducted in the face-to-face format and students will meet in class three hours per week. However, in-class instruction will be student-centered with less emphasis on the traditional lecture format currently used in

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College Algebra at ASU. During class students will be engaged in activities that are scaffolded to promote inquiry. Similar to the traditional course, enrollment will remain capped at 20 students per section.

Relative to the five principles of successful course redesign cited by NCAT, this project has been designed to maximize success in College Algebra by reforming the curriculum and instruction. The project will also contribute to the development of a new program for secondary mathematics teacher certification.

Redesigning the whole course: Our project will redesign the entire College Algebra curriculum at ASU using innovative instructional activities based on research. In an effort to maintain consistency and improve quality of instruction among the course sections, we plan to implement the use of PowerPoint presentations for instructors to use in scaffolding classroom activities and the major conceptual issues that should emerge from the classroom discussions. These presentations will be made available for students to download and use as class notes. The use of structured lessons for all sections will decrease the amount of “course-drift” that many past projects experienced. Consistent with Florida Gulf Coast University’s redesign model, our course will use a common syllabus, textbook, and course website for scheduling assignments and sharing course materials. Faculty experts will design course activities into approximately seven modules, which we describe later in this proposal. Faculty will also revise existing assessments (chapter tests and final exam) to align with the new course objectives.

Encouraging active learning: Class activities will engage students in meaningful collaboration to discuss solution approaches for tasks designed to develop students’ understanding of key concepts of the course. Students will consistently be required to present their ways of thinking about problem situations to each other and to the entire class. Students will focus on learning key ideas through inquiry and making sense of data and contextual situations, both inside and outside the classroom. Furthermore, online homework assignments will require students to take an active role in learning procedural and skill-based tasks in order to prepare them for upcoming classroom activities. These online assignments will also provide students with tutorial support and reinforce concepts previously learned in the course.

Provide students with individualized assistance: The college algebra redesign project will encompass learner-centered classrooms that allow instructors to facilitate individual student learning during class sessions. (This is in contrast to the current situation in which instructors lecture about the content and illustrate procedures for obtaining answers to problems, while paying little attention to individual learning.) Offering individualized assistance during class can help instructors learn what areas are most difficult for students. This allows instructors to help students, either individually or collectively, at the time the difficulty is known rather than requiring students to seek help outside of class (which they often do not). This improves quality of the course instruction and reduces costs by replacing expensive labor (full-time faculty and graduate students) with inexpensive labor (undergraduates) to aid in outside tutoring. For our project, we plan to leverage pre-service mathematics teachers by offering them credit to tutor in the ASU Mathematics Tutor Center and/or the CRESMET Tutor Center. Institutions such as the University of Alabama and Virginia Tech have also successfully incorporated undergraduate assistants and peer tutors in

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their mathematics tutoring centers. Our project will further utilize undergraduate mathematics majors who wish to obtain secondary certification by teaching College Algebra as part of their field experience. In addition, the online tutorial support provided by the software will be available to students 24 hours a day, every day. Such automated tutorial support will free instructors from spending class time on low level skills and procedures, thus allowing for greater attention to individual student development of key concepts.

Build in ongoing assessment and prompt (automated) feedback: Our team will adopt course management software, called WileyPLUS, to facilitate online homework assignments and assessments. Students will use the software to complete assignments designed to prepare them for an upcoming week of classwork. Instructors will use these assignments to assess students’ procedural knowledge prior to beginning the conceptual lessons each week. The software provides immediate feedback on each student’s progress and also graphs the progress of the entire class. Instructors can gauge students’ level of engagement and understanding to further prepare class instruction to meet the needs of the class. This component of our redesign project is similar to the University of Massachusetts Amherst’s plan of requiring students to complete low-stakes assessment prior to class to reduce the amount of class time spent on tasks understood by students, thus utilizing class time more efficiently.

Ensure sufficient time-on-task and monitor student progress: Through the use of computerized assessment, instructors can monitor students’ progress on online assessments by investigating students’ time on assignment and number of task retakes. The course management software allows instructors to oversee individual student progress while also assessing class progress outside of the classroom. Similar to the universities of Alabama and Idaho, attendance will be mandatory for College Algebra students. Study groups will be encouraged outside of class.

Our redesign team will align the new curriculum, instructional methods, and assessments with the most recent research knowledge of the experiences students need to: (a) continue taking and succeeding in undergraduate mathematics courses; (b) develop an understanding of fundamental concepts (such as variable, rate of change, function) needed for understanding calculus; (c) become better mathematical thinkers and problem solvers, acquire improved communication abilities, and (d) acquire improved confidence in their ability to persevere in solving complex problems. This redesign project will require the retraining of all ASU faculty and graduate students who teach College Algebra. These faculty and graduate students currently use mostly traditional lecture format and have no knowledge of the body of research that has revealed instructional sequences that lead to students’ understanding the key ideas of the course. The workshop models and tools that are designed and used to retrain College Algebra instructors in realizing the goals stated above will be institutionalized to ensure that the course redesign and improvement is sustained. The broad dissemination of what will be a research-tested model for College Algebra will set in motion a new approach for revising undergraduate mathematics courses at ASU.

Learning MaterialsAll faculty in the course redesign are committed to employing research-based materials

that have been successfully used to prepare students for beginning calculus. Additional materials supported by research to enhance secondary mathematics and science teachers’ understanding of

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ASU College Algebra

the function concept will be implemented in this course. These materials will be revised and scaffolded to meet the needs of College Algebra students. The faculty are also committed to enhancing these materials by including computer-based supports and improved training for ASU instructors and graduate students who teach College Algebra. Since the faculty, graduate and undergraduate students who teach College Algebra at ASU and elsewhere tend to change from year to year, we are committed to developing tools and workshops that will ensure that as new teachers are assigned to the course, they too are trained to provide quality, coherent, and meaningful instruction.

The focus for this project will be on redesigning instructor training and instructional formats rather than authoring new curricular materials. The curricular groundwork has been laid for the College Algebra pilot materials. Our efforts will concentrate on adapting these materials to the College Algebra audience.

The College Algebra redesign course will be organized into seven modules: Proportional Reasoning, Covariation I, Linear Functions, Composition, Quadratic Functions, Covariation II, and Exponential/Logarithmic Functions. Each module will consist of the following components:

Lesson Logic: This in-depth lesson narrative provides instructors with the important ideas contained in the lesson along with helpful hints on the type of conceptual questions to address during the activity. The lesson logic is for College Algebra instructors only, not students.

PowerPoint Presentation: The lesson will be formatted into a PowerPoint presentation, which will pose various problems for students to work on within their respective groups. Students will be provided opportunities to justify their reasoning on whiteboards for other students in the class to view. Activities will also involve a hands-on component where students are required to collect and analyze their own data using calculator-based technology (e.g., Texas Instruments Calculator-Based Laboratory). In addition, visual simulations of the mathematics will be included in the activities. Instructors will demonstrate various mathematical ideas using instructional software such as Geometer’s Sketchpad, Graphing Calculator, and Fathom. The PowerPoint presentation will be made available for students to download as class notes.

Reflective Homework: These assignments will be designed to promote student reflection on the topics learned in class. This writing-intensive homework will serve as a method of formative assessment to gather information about whether students were able to make important connections during in-class activities.

Online Homework: These homework assignments will prepare students for the upcoming class activities, thus freeing time for in-class instruction to focus more on the conceptual aspects of algebra. Online assessments will gauge students’ learning of the mathematical procedures and concepts and will provide the instructors with immediate feedback on class progress.

Sample Activity: The Box ProblemOne example of a problem often taught in traditional College Algebra courses is the Box

Problem. This problem involves key ideas about variation and covariation. Understanding these ideas helps students to grasp functional relationships as they relate to contextual situations. Yet traditional courses typically overlook these powerful ideas and simply focus on more procedural components of the problem. An example of the traditional Box Problem is illustrated below.

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ASU College Algebra

The Box Problem (Larson & Hostetler, 2004)An open box is to be made from a piece of paper (8.5” by 11”) by cutting equal squares of length

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x from the corners and turning up the sides. Find the following:1. Verify that the volume of the box is given by the function

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V (x) = x 8.5 − 2x( ) 11− 2x( ) .2. Determine the domain of the function

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V .3. Sketch the graph of the function and estimate the value of

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x for which

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V (x) is maximum.

In this traditional format of the problem, students are provided the function first with additional follow-up questions about domain of the function, as well as the function’s graph. With this task, students are not required to think deeply about how the volume changes with respect to changes in the size of the cutout. Connections among the size of cutout, respective changes in length, respective changes in width and respective changes in volume are largely ignored. The focus of the traditional version of this task is on the procedural and abstract algebraic components of the situation with little to no emphasis on the meaning of the variables.

In contrast, the redesign course will utilize the Box Problem in a very different way to illuminate the important components of variation and covariation. As students come to grasp the ideas of variation and covariation, they are building conceptions of the algebraic representation of the function. In addition, the redesigned Box Problem will engage the students in hands-on and active learning. They will first create physical boxes with various cutout sizes to help bridge the conceptual gap between the size of cutout

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x and the volume of the box,

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V (x) . This knowledge will be used to create the algebraic function. The sample slides below illustrate the introduction to the Box Problem that we will use in the redesigned course.

The next portion of the discussion for the Box Problem in the redesigned course will be geared to simulating the changing box with the changing size of cutout. This computer-aided simulation provides a powerful opportunity for students to visualize the size of the box as the cutout size changes dynamically. Sample slides below illustrate this portion of the activity.

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ASU College Algebra

The redesigned Box Problem will focus on the meanings of the formula and variables, such as the meaning of

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x , the meaning of

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11− 2x and the meaning of

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8.5 − 2x as they relate to the physical dimension of the box. The lesson will engage students in generalizing the arithmetic processes and building the algebraic formula from concrete models of the boxes to more abstract forms such as the algebraic representation of

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V (x) = x 11− 2x( ) 8.5 − 2x( ) . In this activity, students will also discover how to conceptualize how two variables change in tandem with one another by using a teaching strategy known as the Finger Tool. Developed by ASU Professor Patrick Thompson, the Finger Tool involves having students move their index fingers—each of which represents a changing quantity, one independent and one dependent—along imagined

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x and

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y axes. This helps students to grasp the coordination of the changes in the dependent variable with respect to changes in the independent variable. As when responding to the traditionally taught Box Problem, students will also discuss the maximum volume of the box. However, the explorations leading up to this question should assure that students understand the meaning of both the algebraic procedures and graph as they relate to the real context of the box.

Furthermore, students will be prompted to continue reflecting on related ideas. We will prompt them to find different-sized boxes with the same volume and values of the cutout for which the volume increases. This will help illuminate ideas about the physical nature of the box by providing meaning of how two different sized cutouts can produce the same volume but different orientations of the box. The activity will also include discussion about amounts of change relative to ideas of covariation and multiple representations of function.

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ASU College Algebra

In summary, the redesigned College Algebra course will extend traditional problems into classroom activities with rich, probing questions embedded in contextualized and meaningful problem situations. The redesigned Box Problem illuminates the kinds of questions students will tackle during class where the center of instruction is shifted from the teacher to the student. Our redesign team will continue modeling such activities to provide more meaningful and productive experiences for students in College Algebra.

Cost Reduction StrategyStudent enrollment at ASU is currently growing and all indicators suggest this enrollment

will continue as the university strives to accommodate an unprecedented number of students enrolled. As a result, the number of students who need to take College Algebra will undoubtedly parallel the growth of the university. To accommodate this growth without increasing the number of faculty hired to teach College Algebra, the redesign project utilizes undergraduate mathematics majors as teachers of College Algebra for their field experience toward secondary mathematics certification. The cost savings of this project is calculated to be $243,744 per year, given we project that half of all College Algebra sections will be taught by undergraduate teachers. The change in teaching personnel will allow the enrollment of College Algebra to increase without increasing the number of expensive faculty.

Additionally, the team will develop training materials and workshops to provide new teachers will the necessary knowledge for teaching College Algebra using the redesigned materials. These materials will be developed by a team of experienced researchers and faculty who will share instructional materials to eliminate duplication of effort in course curriculum construction. These materials will be provided through a course management website for instructors to use. Not only will this save the university money in funding teachers to create new course materials, it will also increase new-instructor support of the project, since they will not be required to develop their own set of materials independently.

Funds saved as a result of the redesign project will be used toward continued redesign of other first year mathematics courses at ASU (i.e., Precalculus, Brief Calculus). The cost savings will also provide training opportunities for future College Algebra teachers (FYM faculty, faculty mentors, and undergraduate mathematics majors).

Redesign Project TimelineThe timeline for the College Algebra redesign project can be categorized into four

phases. Phase 1 is the planning stage during which the leadership team, composed of ASU faculty and mathematics education researchers, will work to revise current curricular activities and research tasks for the College Algebra audience. We plan to organize the course material

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ASU College Algebra

into seven modules and create online assignments to align with these modules (using course management software which accompanies the course textbook). Furthermore, the leadership team will begin training instructors in the new teaching strategies and use of conceptually focused curricular materials to support the instructors in providing effective instruction for the redesigned course. The leadership and instructional team will work together throughout the summer and fall sessions to continue refining the course materials.

Phase 2 will involve piloting the new College Algebra course with 10 sections during the spring 2008 semester. The leadership team will conduct data collection through pre- and post-test assessments and clinical interviews to ascertain the effectiveness of the redesigned course as compared to the traditional course. The leadership team will continue training new instructors during this phase.

The leadership team will continue course revision during Phase 3 of summer 2008. The team will analyze the data collected during the pilot study, and use that data to inform the refinement of both the curriculum and instructor training as they prepare for full implementation in Phase 4. The project is planned for full implementation of all College Algebra sections at ASU to be taught using the redesigned model developed during the 2008-2009 academic year. The Department of Mathematics and Statistics has committed to support a full implementation, which will involve their providing the necessary support to carry out the redesigned College Algebra beginning in Fall 2008.

In addition to training teachers, the leadership team will work during Phase 2 with undergraduate mathematics majors seeking secondary certification. Since the secondary certification program is new to ASU, the team will first focus on recruiting and then training undergraduate assistants in tutoring College Algebra. This will serve as an important part of their preparation for teaching the course. During Phase 3, undergraduates will be assigned to faculty mentors to further prepare for teaching College Algebra during Phase 4 of the project and beyond. The undergraduate mathematics majors will meet weekly with their mentor during their teaching semesters to continuously reflect on their teaching practice. Figure 1 illustrates the College Algebra redesign project timeline’s four phases.

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Figure 1: College Algebra redesign timeline.

Phase 1Planning stage, revise curriculum, author online materials

Phase 2Pilot 10 sections of revised college algebra, collect data (assessments, interviews)

Phase 3Continue course revision based on preliminary findings

Phase 4Full implementation of revised college algebra

Summer 2007 – Fall 2007 Spring 2008 Summer 2008 Fall 2008

ASU College Algebra

Redesign Research Plan: Measuring SuccessThe effectiveness of the pilot course will be compared with the current instructional

approach during the first semester of its implementation, using valid tools and methods to compare the redesigned sections with the current sections. Our research plan consists of two components: (a) researching the College Algebra students and (b) researching the College Algebra redesign teachers.

Research of StudentsOur research plan is focused on the conceptual development and learning of College

Algebra students in the redesign course as compared to students in the traditional course. Among our primary tools for measuring student achievement will be the Precalculus Concept Assessment (PCA) instrument, developed by Marilyn Carlson and identified through more than a decade of testing as a valid assessment tool for determining if students have acquired an understanding of the major concepts of College Algebra and precalculus mathematics (Carlson, Oehrtman, & Engelke, 2007). In their study, Carlson, Oehrtman, and Engelke reported that 85% of students who received a score of 11 or higher on the PCA succeeded in first semester calculus, while 80% of students who received a score lower than 11 on the PCA either withdrew or failed first semester calculus. Therefore, the PCA instrument was integrated into this research to provide insight on students’ understanding of precalculus concepts, such as the concept of function, before and after their College Algebra experience. Students in both the pilot course and the traditional course will be assessed using the PCA as a pre- and post-test assessment instrument and their results will be compared to determine the effectiveness of the redesign course materials. Finally, we will administer a previously developed and validated tool, the Views About Mathematics Survey (VAMS), to assess shifts in students’ confidence and views about the methods and nature of mathematics. Results of the pilot group will be compared to those of the traditional group.

In addition to the quantitative measures listed above, the team will also collect qualitative data to provide a more in-depth investigation of students’ understanding of College Algebra. We will conduct clinical interviews for College Algebra students from both the pilot group and the traditional group. A total of 10 students from each group will be selected to participate in this study. Each student will be interviewed three times at various points in the semester to study their conceptual growth on specific topics relative to College Algebra. The interview protocol will include conceptual tasks designed to measure students’ ways of thinking about College Algebra topics such as variable, rate of change, covariational reasoning, additive reasoning, and multiplicative reasoning. Research has shown that these algebra concepts are foundational to building a profound understanding of the function concept, which is central to the college algebra and precalculus curriculum (Carlson, 1998; Carlson, Jacobs, Coe, Larsen, & Hsu, 2002; Confrey & Smith, 1994, 1995; Monk, 1992; P. Thompson, 1994). This qualitative data will be compared with the quantitative data to provide a more holistic picture of the effectiveness of the redesigned College Algebra course. The qualitative data will also provide the instructional team with evidence of student thinking throughout critical points of the semester to help refine course instruction as necessary.

Research of Redesign TeachersThe team will also investigate the development of the teachers as they prepare for and

implement the redesigned course materials. This data will be used to enhance teacher training materials and workshops as we prepare to expand our redesign efforts for improving course

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instruction in precalculus and brief calculus courses. Of the 10 College Algebra redesign pilot sections, the leadership team will intensely

focus on at least two sections to investigate the effectiveness of the materials and instruction for enhancing students’ learning of the concepts. These focus sections will be videotaped during each class session with one camera on each student group and another on the teacher. This video data will be reviewed and analyzed to further enhance the teacher training materials for future implementations of the course. Video cases will be used in training workshops to showcase exemplary models of conceptual learning inside the classroom. Moreover, all instructors for the pilot redesign will be evaluated using the Reformed Teaching Observation Protocol (RTOP) created by the Arizona Collaborative for Excellence in the Preparation of Teachers. The measurement tool provides valuable information about the nature of teaching and will allow the redesign team to facilitate in the development of the teachers from the redesign group.

In summary, the redesign project will incorporate multiple methods of data collection. For investigating students, we will collect data from (a) PCA pre- and post-test for redesign and traditional courses, (b) clinical interviews of students from both redesign and traditional sections, and (c) VAMS assessment of students’ views of mathematics. For investigating the redesign teachers, we will collect data from (a) RTOP pre- and post-evaluation of redesign instructors and (b) videotape focus sections of College Algebra.

Timeline of Research PlanData collection for the project is planned throughout the semester during the pilot phase

of the project. Two focus sections of the redesign course will be videotaped throughout the semester. Instructors will be evaluated using the RTOP during the first week of the semester and again at the end of the course. Students from both the redesign group and the traditional group will be assessed using the PCA and VAMS during the first and last week of the semester. Student volunteers will be interviewed at the beginning of the course, during the middle of the course and again at the end of the course. Figure 2 illustrates this timeline.

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PCA Pre-test

VAMSPre-Survey

RTOP Pre-evaluation

Student Interview 1

Week 1 Week 7 Week 10Week 4 Week 14

Student Interview 2 Student Interview 3

PCA Post-test

RTOP Post-evaluation

VAMSPost-Survey

Videotape Focus Sections (2) of Redesign Course

Figure 2: Redesign research timeline.

ASU College Algebra

REFERENCES

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