supporting college and career readiness in...

SUPPORTING COLLEGE AND CAREER READINESS IN MATH:

A Case Study of a High School Math Transition Course in Hawai‘iMichelle Hodara, Lisa Dillman, and Shannon DavidsonEducation Northwest

Introduction

Math poses a barrier to the college and career readiness and success of many students, both while they are in high school and when they enter college. For example, nearly 60 percent of communi-ty college students are referred to developmental (remedial) math, and only about 20 percent of those students go on to complete a college-level math class (Bailey, Jeong, & Cho, 2010). Academ-ic underpreparedness in math even has a negative impact on wages and likelihood of employ-ment (Hodara & Xu, 2016).

To better support the college and career readiness and success of high school students, many states have adopted college and career readiness graduation standards, increased opportunities to experience college coursework in high school, and enhanced the college-going culture of schools (Glancy, Fulton, Anderson, Zinth, & Millard, 2014). As part of these efforts, many states also use a standardized assessment (typically administered in grade 11) to measure college and career readiness and provide early information about what students need to be college and career ready upon graduating from high school.

As of 2013, 29 states1 offered transition courses in math and/or English to grade 12 students who scored low on a college-readiness assessment and were not on track to graduate college and ca-reer ready (Barnett, Fay, Bork, & Weiss, 2013). These transition courses and related assessments are typically developed collaboratively by high schools and colleges (Wathington et al., 2012). Best practices for course design include targeting specific college-readiness standards (Barger, Murray, & Smith, 2011), promoting conceptual understanding rather than procedural fluency (Barnett, Fay, & Pheatt, 2016), and integrating real-world applications into instruction (Zinth & Millard, 2015).

1 Eight of these initiatives were statewide, meaning all public universities or community colleges in the state partnered with high schools to offer the same transition course(s), while 21 were implemented locally, meaning postsecondary institutions worked with individual schools or districts to offer courses to help high school students avoid remediation in college.

Education Northwest | Supporting College and Career Readiness in Math 2

As part of the external evaluation of GEAR UP Hawai‘i, we conducted a qualitative implementa-tion study of a transition course called Introduction to College Math. This course provides high school students who are not on track to graduate college and career ready with an opportunity to improve their math skills—and to avoid taking developmental math courses at any of the 10 Uni-versity of Hawai‘i (UH) campuses. This report is intended to inform the work of Hawai‘i Department of Education (HI DOE) math teachers and administrators, as well as the UH gateway math faculty, and can be used to highlight successes and decide ways to improve or refine the Introduction to College Math course.

The Smarter Balanced Assessment policy and the Introduction to College Math course

In Hawai‘i, a student earning a level 3 or 4 on the grade 11 Smarter Balanced Assessment (SBA) is on track to be college and career ready. Earning a level 1 or 2 means additional coursework is necessary to graduate ready for college coursework. Students who earn a level 4 on the Math SBA are exempt from placement testing at the UH campuses and can directly enroll in gateway (i.e., entry-level, credit-bearing) college math courses for science, technology, engineering, and math (STEM) and non-STEM programs. Students who earn a level 3 on the SBA are exempt from placement testing and can directly enroll in a non-STEM gateway college math course, but they must take advanced math in their senior year to enroll directly in a college math course for STEM programs. Students who earn a level 1 or 2 on the SBA must demonstrate readiness in other ways upon college enrollment (e.g., college placement exams, previous high school grades) to enroll in a gateway course or they must enroll in developmental education courses. However, students who earn a level 2 on the SBA and who receive a grade of B or higher in Introduction to College Math are exempt from placement testing and can directly enroll in non-STEM gateway college math courses at UH.

Developed by UH math faculty, Introduction to College Math is designed to help high school seniors who are not considered college and career ready (based on grade 11 SBA scores) to grad-uate from high school ready for non-STEM gateway college math courses at UH. Introduction to College Math is similar to the highest level developmental math course that prepares students for these college math courses. These courses include Math 100: Survey of Mathematics, Math 111: Math for Elementary Teachers, and Math 115: Introduction to Statistics. The course uses proj-ect-based learning and culturally engaging materials, emphasizes real-world problem solving, and works to develop nonacademic skills, such as growth mindset. Since Hawai‘i requires three years of math, the course can be taken for elective credit in the senior year. The credits count toward the Hawai‘i academic honors diploma, but do not count as college-level credits. In fall 2015, four high schools in Hawai‘i piloted the course, and in 2016/17, 15 high schools offered it. (There are 65 public high schools in the state.) See table A1 in the appendix for a description of the schools offering the course.


Study description

Research questions and data. This study examined the implementation of the course by col-lecting survey and interview data from Introduction to College Math teachers and students. The research questions and data sources for the study are described below (table 1). Table 1. Research questions and data sources for the study

Research question Data source(s)

To what extent is the course being implemented con-sistently and as originally designed across schools?

• Phone interviews with Introduction to College Math teachers

What are the successes and challenges at the 15 schools now offering the course?

• Survey administered to Introduction to College Math teachers

• Phone interviews with Introduction to College Math teachers

• Pre- and post-surveys administered to Introduc-tion to College Math students

What is the relationship between course participation and nonacademic skills (e.g., growth mindset)?

• Pre- and post-surveys administered to Introduc-tion to College Math students

All 16 Introduction to College Math teachers from the 15 high schools offering the course com-pleted the survey in November 2016. (One school had two teachers teaching different sections of the course.) We used the survey findings to focus the interview questions, and we conducted the interviews shortly after the course ended.2 Fourteen teachers from 13 high schools participated in an interview.

We worked with the teachers to administer a survey to their Introduction to College Math stu-dents to assess student perspectives on the course and nonacademic skills midway through the class in January (the pre-survey) and at the end of the class in May (post-survey). Eight schools administered the pre-survey, and six schools administered both the pre- and post-survey. Four of the schools chose not to participate in the survey, and three of the schools could not participate because they use block scheduling and therefore the course ended in December. In January, 229 students responded to the pre-survey. In May, 174 students responded to the post-survey. More details about the sample are provided below (table 2).

2 Three schools used block scheduling in which class periods were longer; therefore, the course ended in December 2016. For these schools, we conducted the interviews in January 2017. For all other schools, we conducted the inter-views in May 2017.


Table 2. The number of students who took the pre- and post-survey per school and the range of Smarter Balanced Assessment levels

School Students who took the pre-survey

Students who took the post-survey

Range of SBA levels

Aiea High School 20 11 1–4

Kahuku High & Intermediate School 8 0 2–4

King Kekaulike High School 24 22 1–3

Leilehua High School 38 34 1–4

Molokai High School 13 8 2–4

Pahoa High & Intermediate School 5 5 2–3

Pearl City High School 96 94 1–4

Waiakea High School 25 0 1–3

Total 229 174 1–4

Note: The following schools did not participate in the survey: Castle High School, Farrington High School, Kapa‘a High School, Mililani High School, Waialua High & Intermediate School, Wai‘anae High School, and Waimea High School.

Source: Introduction to College Math pre-survey and post-survey.

We also reviewed interview data collected by Hawai‘i P–20 in 2015 from the original pilot schools.

Analysis. To analyze the data from the teacher surveys, teacher interviews, and open-ended student survey responses, we used content analysis to identify common themes within and across data sources (Mayring, 2000). To analyze the student survey data, we calculated the overall responses for all survey questions. Since the course was designed for students with an SBA level of 2, we disaggregated all pre-survey responses for this group. To understand the different experi-ences of students based on SBA level, we also show the responses of students considered on track to be college and career ready, or those who earned a level 3 or 4 on the SBA. We do not show responses for students who earned a 1 because of the small sample size.

Student participants. Student survey respondents represented the full range of SBA levels although most survey respondents reported they earned a 2 or 3 on the SBA (table 3).

Table 3. Frequency of self-reported SBA scores among respondents

SBA level Frequency Percent

1 21 9

2 86 38

3 96 42

4 19 8

Did not answer 7 3

Note: Students were asked their SBA level on the pre-survey only.

Source: Introduction to College Math pre-survey.


On the post-survey, we asked students about their postsecondary plans. Their responses revealed that most students (89%) planned to attend college. Thirty-nine percent said they were still unde-cided about their intended major. Nursing was the most common major mentioned by students (15%), followed by programs in career technical/vocational fields (11%); STEM (10%); social and behavior sciences (10%); arts, humanities, and English (6%); business and marketing (5%); and education and childcare (4%).

Key Findings and Recommendations

To what extent is the course being implemented consistently and as originally designed across schools?

• Teachers share an understanding about the purpose of Introduction to College Math, although some believe it has benefits beyond avoiding remediation for a wide range of students

• Schools use different methods to identify students and to recruit a variety of students for the course

• Students are most likely to hear about the course from a teacher and are most likely to take the course because a teacher encouraged them

What are the successes and challenges at the 15 schools now offering the course?

• Most teachers believe the course prepares students for non-STEM gateway math courses at UH campuses

• Many students like the course, and both teachers and students appreciate the opportuni-ty to connect math to meaningful, “real-world” topics

• Although teachers and students like group work and projects, they require more prepara-tion and resources and can pose challenges related to group dynamics

• Some teachers struggle to reach learners with diverse math levels in the context of a fast-paced, senior-year math course

What is the relationship between course participation and nonacademic skills (e.g., growth mindset)?

• Students and teachers report improvements in students’ confidence and growth mindset, and quantitative survey results find high levels of confidence and growth mindset across students with different SBA levels.


Recommendations for Hawai‘i Department of Education and school administrators

• Consider the implications—for instruction, advising, and math course options—of open-ing the course to students with SBA levels outside of the intended range

• Continue offering a professional learning community for transition-course teachers• Provide teachers with additional planning time or other opportunities to master the

course material

Findings: Implementation

To understand course implementation, we asked teachers about their views of Introduction to College Math’s purpose, the identification and recruitment of students, and how and why students chose to enroll in the course. We found that all teachers understood that the course allows students with an SBA level of 2 who earn a B to avoid remediation and to place directly into non-STEM gate-way math courses at UH campuses. Many teachers also viewed the course as having a larger pur-pose that could benefit many types of students. This is due, in part, to the fact that in many schools the course is either the only or one of the only alternatives to traditional senior-year math courses that build on Algebra 2 (e.g., pre-calculus, trigonometry, calculus). As a result, schools also enrolled students who did not receive a 2 on the SBA, based on various measures and methods.

Teachers share an understanding about the purpose of Introduction to College Math, although some believe it has benefits beyond avoiding remediation for a wide range of students

Hawai‘i P–20 gathered preliminary data from in-depth interviews with two Introduction to College Math instructors at pilot schools who completed their course in fall 2015.3 These early interviews suggested that school staff members—including instructors and counselors—needed a shared understanding of the course’s intended purpose.

In our follow-up study we found that there is a shared understanding of the purpose of Introduc-tion to College Math—nearly all teachers said it is to help students with an SBA level of 2 avoid remediation and enroll directly in a non-STEM gateway math course at a UH campus. Many also stated the policy tied to the course.

The purpose of the course is to help our high school students be more ready to enter

the college courses at the 100 level because in the state of Hawai‘i, you’re only required

to have three math credits, and most of them finish their junior year … They can take

it at the high school level as a high school credit, and then if they earn a B or better in

that class and they enroll in any one of the colleges within the UH system and commu-

nity colleges, they are able to access the 100 level without having to take the ACCU-

PLACER or any of the remedial math classes. (Math teacher)

3 Both instructors had taught the course in a block schedule, and the interviews took place within the last two weeks of the course.


Half of the teachers said the course also played a larger role in changing students’ math experienc-es in high school and/or preparing them to enter and succeed in college. More than a third said their department or school wanted to offer the course for these reasons. Specifically, teachers said Introduction to College Math was valuable for a broad range of students to help them “problem solve” and “build their critical-thinking skills so they can be better people, not just a better math student.” Some also said the course gave students an opportunity to practice, refine, and review important math skills in their senior year.

While the focus of the course is college and career math readiness, two teachers mentioned that it could do even more, for example by helping students pass college math. One teacher said it could even help increase college graduation (see quote). At least one school was using the course to spur an overhaul of its math scope and sequence so that students could take courses that align with their long-term academic and career goals.

For me, this was an opportunity to be part of a larger program that helps students

create that tie between high school and college, in the hopes that it would increase our

students’ matriculating, as well as actually graduating from college. (Math teacher)

Teachers who viewed Introduction to College Math as having a larger purpose also tended to say that all students benefit from it. More than a third of teachers said all students benefit from the course, even those not intending to go to college.

I think any student can benefit from the course. I have students who got a 4 on the SBA

and students who got a 1 and everything in between, and they all take away something

from the course. I think for the 1s, maybe they really hated math before, but they know

they want to go to college, so this is giving them a new way to experience math where

they can learn that they don’t actually hate math as much as they think they do. The

2s benefit from the course because if they get a B or better, then they can go into the

100-level class without taking the placement exam. And the 3s and the 4s, I think, ben-

efit most from the projects and just getting to use math in a little bit more of a fun way

rather than a traditional textbook way. (Math teacher)

Schools use different methods to identify and recruit students for the course

Nearly all the teachers thought different types of students benefited from the course, and per-haps as a result, only two schools said that their target population for the course was exclusively students who had earned a level 2 on the SBA. One teacher described tension at their high school regarding who should take Introduction to College Math. This teacher felt that it made more sense for a larger group of students—not just those who earned a level 2 on the SBA—to take the course because of the lack of senior-year math options at the school.

Honestly, at our school, it’s not like the average student is getting above a 2 … we proba-

bly have 300 or so people who got 1s. Saying that we’ll put the 2s in the course and we’ll

put the 1s in trig and pre-calculus is insanity. It’s insane. I understand that you get the

most benefit out of the course if you have a 2, but if you got a 1, you probably get no ben-

efit out of being forced to take trig and pre-calculus. Yes, there is a very specific benefit

for a very small group of people, but there is much broader benefit for our average senior

at our school. (Math teacher)


Schools used multiple measures to identify students for the course, in part because the target population is much broader than students with a level 2 and in part because they do not receive SBA scores when they are registering students for classes the following year. The complete list of measures schools reported using to identify students for participation in Introduction to College Math is shown below (table 4). While eight schools reported recruiting students with an SBA level of 2, only two schools reported relying solely on this measure. Other measures included: identi-fying whether students have non-STEM college major and/or career goals; using the STAR test as a proxy for SBA level; relying on previous grades in math (e.g., whether a student passed algebra I, earned less than a B in algebra II, or had a GPA lower than 2.5); and using other SBA levels. Two schools reported telling all seniors about the course.

Table 4. Measures schools used to identify students for participation in the Introduction to College Math course

Number of schools that used this combination of measures

SBA level 2

Non-STEM goals

Previous grades

SBA level 1

SBA level 3 and/

or 4

STAR None; all seniors are told about the course

2 X

1 X* X* X

1 X* X X* X

1 X X

1 X X X X

1 X X X

1 X X

1 X

1 X X

1 X

2 X

Number of schools that used the

measure:

8 4 4 3 3 2 2

* Indicates that schools did not have students’ SBA levels during course registration, but later used them to verify that the “right” students were in the course.

Source: Authors’ analysis of teacher interview data.

Students are most likely to hear about the course from a teacher and to take the course because a teacher encouraged it

The preliminary data gathered at pilot schools in fall 2015 suggested that information about the Introduction to College Math course was mostly traveling by word of mouth and that schools might need to engage counselors to more actively recruit students. In contrast, the current data show that few students with an SBA level of 2 first heard about the course from a friend, suggest-


ing that those students were more likely to learn about the course through recruitment efforts than through informal channels. Counselors still played a reduced role in sharing information, however (figure 1). Most schools reported relying on grade 11 math teachers to recruit students, typically by conducting group information sessions for students and families and/or by meeting with students individually to discuss the best option for a senior-year math course. Students with an SBA level of 3 or 4 were slightly less likely to hear about the course from teachers and counsel-ors and much more likely to hear about it from friends, suggesting that formal recruitment efforts were not directed at these students.

Figure 1. Students are most likely to hear about the course from a teacher

Note: Responses to question: “How did you first hear about the Introduction to College Math course?” Sample includes all students who took the pre-survey (N = 229). Respondents could check all that apply. SBA level 1 is not shown to protect student privacy. See table A2 in appendix for overall responses.


Students cited many reasons for enrolling in Introduction to College Math (figure 2). The top four reasons were: a teacher or counselor encouraged it, they thought it would help them prepare for college, they were interested in the experience of taking a college course,4 and they were interested in the subject or material. In open-ended responses, which we categorized under “Interested in the subject or material,” students said they enrolled in the course to learn life skills, such as “writing a check.”

Students with a level 2 SBA score were slightly more likely than their peers with level 3 or 4 scores to enroll in Introduction to College Math because their teacher or counselor encouraged it and much less likely to enroll because a friend or family member encouraged it. This aligns with the data on how students first heard about the course. Other notable findings also illustrate differenc-es based on SBA level. For example, more than a quarter of students with an SBA level of 3 or 4 said they took it to avoid another math class, compared with only 14 percent of students with an SBA level of 2, suggesting that students considered on track to be college and career ready were

4 Introduction to College Math is not a credit-bearing college course, but is similar to the highest level developmental education course at UH that prepares students for non-STEM gateway math.

65%57%

30%17%

14%34%

Math teacher

Counselor

Friend

SBA Level 2

SBA Level 3 or 4

0 20 40 60 80 100


looking for senior-year math options that were not necessarily in the traditional algebra sequence. As one student stated, “I took [Introduction to College Math] because my next step was trigonom-etry or Algebra 3, which is very difficult to me, so I took this class instead.” Finally, 10 percent of students with an SBA level of 3 or 4 did not seem to understand the new placement exam policies, since they said they took the course to waive the placement exam requirement, even though the placement exam is already waived for students with a 3 or 4.

Figure 2. Students enroll in the course for a variety of reasons

Note: Responses to question: “Why did you originally decide to enroll in the Introduction to College Math course?” Sample includes all students who took the pre-survey (N = 229). Respondents could check all that apply. SBA level 1 is not shown to protect student privacy. See table A3 in the appendix for overall responses.


48%40%

36%41%

31%33%

28%36%

17%25%

14%27%

13%32%

12%10%

10%11%

My teacher or counselor encouraged it

I thought it would help me prepare for college

I was interested in the experience of taking a college course

I was interested in the subject or material

I like the Introduction to College Math teacher

I was trying to avoid a specific other math class

My friends or family encouraged it

I wanted to waive the Compass test requirement

I wanted to be challenged

SBA Level 2

SBA Level 3 or 4

0 20 40 60 80 100


Findings: Successes and Challenges

Most teachers and students liked the course and believed it was effective because of its emphasis on applied math, development of nonacademic skills, and alignment with college-level math. The primary challenges, as identified by teachers, included how to address students’ varying levels of math skill, the timing of the course in the senior year, and the pace of the curriculum.

Most teachers believe the course prepares students for non-STEM gateway math courses

Nearly three-quarters of the teachers were confident that students who earned a B in Introduction to College Math would be prepared to do well in non-STEM gateway math courses at a UH cam-pus. They attributed the course’s effectiveness to the emphasis on applied math and conceptual understanding, development of nonacademic skills, and alignment with college-level math. More than a third of teachers mentioned that the course helps students develop critical-thinking skills and gain a deeper understanding of practical math concepts.

Students are making connections between math and real life … projects are getting stu-

dents to apply some of the content but also practice other important skills. (Math teacher)

I really like the thought process to get students to really think, to interpret things.

They’re uncomfortable. It makes them really uneasy, but at the same time, when they

actually do get it, the discussion we have in class is so much richer because now

they’re using their words to describe mathematical things. (Math teacher)

About a third of the math teachers described positive changes they noticed in students’ mindsets, essential skills, and habits—specifically, more confidence, resilience, motivation, and excitement about math.

I would say they have really grown from first quarter to now, when I look back. They are

excited about coming to class. I think they can tell you from the three quarters of doing

this class that, yes, they realize that math is important and it ties into certain things, but

it’s really about your growth, your grit. It’s really that that gets you through things. (Math

teacher)

It has been great to hear comments from students who now feel more confident and

positive in their own math skills. They have gained a better understanding of basic math

concepts and have experienced the importance of thinking through and reasoning ab-

stractly. (Math teacher)

I believe taking a class like this has exposed them to another side of math that perhaps, if

anything, makes them a little bit more flexible and a little bit more resilient. (Math teacher)


A few teachers said their students liked the course and would be prepared for college-level math because Introduction to College Math was developed by postsecondary faculty:

The [Introduction to College Math] curriculum was developed by the community

colleges, and it required a little bit of thought. It wasn’t just a worksheet of problems—

somebody actually put the effort in the application of writing. A lot of the [student]

complaints were “There was too much writing; why do we have to write?” But any-

body who could actually get a B, I think—you know, in college, you have to be able to

communicate and express yourself, so I think that’s a good indicator that they’ll do OK.

(Math teacher)

My students liked [the course]. They liked the idea that it was a thought process more

than just doing numbers. It was this big thought process. I think they kind of got the

idea. I think it was also a bigger sell when some of my students went on a college visit

and they went to Hilo and walked in a college classroom and saw their high school

textbook being used as a college book. They’re going, ‘Oh yeah, this is a college class!’

(Math teacher)

Finally, a few teachers said they were not sure whether the course would prepare students for non-STEM gateway math because they were not certain about the curriculum and expectations for college-level math. This information was covered during the Math Summit, but may reflect gaps in understanding that arise when teachers are either unable to attend the summit or unable to retain all the information covered.

I’m not going to give a good answer for [whether students who earn a B are prepared

for college-level math] because I don’t know what the college-level math entails. (Math

teacher)

Many students like the course, and both teachers and students appreciate the opportunity to connect math to meaningful, “real-world” topics

In the post-survey, we asked student to identify the components of the course they found most useful for learning the content. Between 60 and 86 percent of students cited each aspect of the course as helpful or very helpful (figure 3). Meanwhile, about a quarter of students used the open-ended comments to share that they thought everything about the course was helpful, using words and phrases like “Beneficial,” “Best math class ever,” and “Would take again.”

It is one of the top-three classes that made learning easier and more enjoyable than the

other classes. (Student)


Figure 3. A majority of students rated every aspect of the course helpful or very helpful in learning the course content

Note: Responses to question: “How helpful or not helpful were the following course components in learning the course content?” Sample includes all students who took the post-survey (N = 174). Respondents could check all that apply. See table A4 in the appendix for all responses.

Source: Introduction to College Math post-survey.

In addition, slightly more than 10 percent of students used the open-ended survey responses to emphasize how helpful their teachers were in helping them understand and engage with the course content.

I rate this class a 10 because my teacher was very good at getting our class involved

and understanding what we were learning. (Student)

Math isn’t my best subject, but I really did enjoy this class. It was very unique com-

pared to other regular math classes I have taken in the past. The learning style, motto,

environment, and projects were different, which made class more interesting. I appre-

ciate the effort the teacher put in and the positive attitude she had. (Student)

Nearly a third of students also said they were learning topics that would be helpful to them in their lives, making Introduction to College Math seem meaningful and relevant. Meanwhile, most interviewed teachers said their favorite thing about the course was the opportunity to teach real-world math.5

Intro to College Math helped me understand math used in the real world instead of just

equations. (Student)

Right now, a lot of students are working through the financial math section. They’re

5 Other teachers said their favorite thing about teaching Introduction to College Math was working with seniors, that the curriculum was given to them, that their students liked math, and that they did not experience behavior problems because the students had chosen to take the course.

35% 51%

43% 43%

41% 44%

43% 38%

38% 35%

51% 21%

34% 31%

37% 23%

Group work

Daily assignments/homework

Quizzes

Exams

Projects

Other resources

Study group (outside of class)

Introduction to College Mathematics textbook

Helpful

Very Helpful

0 20 40 60 80 100


like, “I had no idea about this kind of stuff. This is kind of important, right?” And I’m

like, “Yeah, financial math is really important.” A lot of people don’t know it very well,

but it is something to understand how loans work and how loan repayments work and

what happens when you pay more to your principal and how much actually goes to

your principal and how much you’re overpaying if you actually take the loan for the

full term … I like the fact that these are students that don’t typically like math. They’re

wanting to take this course to kind of end their math suffering. It’s cool to see them

actually like a math course. (Math teacher)

When asked how the course compared with their other math classes, many teachers said

they preferred Introduction to College Math because of the emphasis on applied math

and its larger purpose, as opposed to other grade 12 math classes that are focused on

preparing for an Advanced Placement exam. One teacher described how instruction is

different in Introduction to College Math:

When you walk in, you might not even notice sometimes that it’s a math class because

we’re talking about a lot of outside experiences in relation to the math. The conver-

sations are not as formal; there’s not as much lecture. It’s just different. I’m more of a

facilitator instead of a teacher. (Math teacher)

Box 1. Examples of Introduction to College Math projects

• FINANCIAL GOALS: “They are supposed to pretend like they are working adults,” and “What would their goal be in the next 10 years, and what would they do to achieve their goals?”

• T-SHIRT DESIGN: “They got to talk to the owner and ask questions and look at what was marketable—what design would sell to more people—and do a little bit of market research. They came up with their own design … We looked at ratios and proportions, scaling.”

• SNACK PACK: “I give them a unit price list from Costco, and they are instructed that they are going to get $25 as a group to spend their money, and they have to build a snack pack from that $25, and they have to use their fallacies to sell the snack pack. Eventually, I’ll go to Costco and buy all the materials, disperse it to them, and they create their snack packs …They’re instructed that if they don’t make a prof-it, they fail. The group with the largest profit will earn a prize. The reason I do that project first is because I take the proceeds from that project to fund the majority of the other projects throughout the year.”

• STOCK MARKET SIMULATION: “They bought stocks [and] investments, tracked it for a few weeks, and then saw the net gain or net loss.”

• SHARK TANK: “They had to calculate their expense and revenue linear models, and then they had to be able to explain the scope of it—what it means, the intercept … With those two models, they then had to use their systems of equation knowledge to find where their company would potentially break even with their money. Once they did all that, they had to put together a solid presentation where they would ask for a certain amount of money to start their company and then in return give equity back to investors, a portion of their company—so they kind of had to calculate that, as well. Then they had to do a presentation. I had a bunch of people come in, the principal, VP, counselors, other math teachers, and they were like the sharks. The students presented to them, and it was determined whether they would invest in their company or not.”


Although teachers and students like group work and projects, they require more preparation and resources and can pose challenges related to group dynamics

Teachers and students like applying math to real-world problems through group work and proj-ects, but implementing project-based learning was also the most common challenge identified by interviewed teachers. Nearly a third of teachers mentioned either the extensive prep time and resources involved or the difficulty of managing group dynamics, particularly in a classroom with a lot of variation in students’ skill level.

Managing the curriculum and the projects is tough—especially while teaching other

courses. (Math teacher)

The projects are a challenge. Just being the nature of projects, you have to work in

groups. Some people don’t want to do the work. Others want to get the A. What do you

do? [If] the A person ends up doing [all the work]? That’s awful … I still have to figure

out how to make [projects] work for the students. (Math teacher)

Several students echoed this sentiment.

Group work was never good because I felt sometimes I did most of the work. (Student)

Group work … didn’t help because the people I was with were all smarter than I was,

and they did most of the math. (Student)

Despite these challenges, however, most students felt group work was “very helpful” or “helpful” for their learning (see figure 3), and nearly half of students wanted more hands-on learning (table 5). More hands-on learning was a top suggestion for course improvement across all high schools. Even though many teachers reported using more hands-on learning in the class than their other math classes, and students discussed the frequency and breadth of projects in the course, stu-dents wanted even more hands-on learning.

My ratings for this class were very good because we did projects and used group work

to help us learn. (Student)


Table 5. Nearly half of students said more hands-on learning would have made the Introduc-tion to College Math course better

What would have made the Introduction to College Math course better?

Percentage selected

More hands-on learning 45%

More interesting or relevant material 39%

More group work 29%

Slower pace or more time for each lesson 28%

Nothing 17%

More projects 16%

Fewer projects 16%

Fewer quizzes 13%

More challenging work 11%

Less challenging work 10%

More quizzes 7%

Other* 2%

*Includes “A teacher that cared,” “Handouts explaining the concepts or a directory of websites that will assist those who need more help understanding,” “More instruction/board time,” and “I feel I would have had an easier time if we had some type of class briefing on each assignment and new concepts.”

Note: Sample includes all students who took the post-survey (N = 174). Respondents could check all that apply.


Some teachers struggle to reach students with varying ability levels in the context of a fast-paced, senior-year math course

Course pacing. The course is meant to be fast-paced, both to align with college-level courses and to prepare students for the challenge of taking those courses in the future. According to 28 percent of students, Introduction to College Math would be better if it were taught at a slower pace (see table 5), but in open-ended comments, student opinions on the pace varied. For some, the fast pace meant they could cover a lot of information, and it contributed to their learning. For others, it was difficult to keep up and/or retain the lessons.

The Introduction to College Math course was fast-paced and easy to learn. (Student)

I wished it would’ve been more slow-paced … we would go through a different lesson

every day, and I still hadn’t gotten a full understanding of the topic [from] the previous

day. (Student)

Several teachers also noted that they struggled to adjust their instruction to reach different learn-ers in the same classroom. Given students’ varying ability levels and experiences, these teachers found it difficult to appropriately differentiate instruction and find a balanced approach to rigor.

The challenge arises with the range of backgrounds and skill levels in my classes, which

can be quite significant across students and varied from lesson to lesson. (Math teacher)


Motivation in the senior year. Finally, the timing of the course in the senior year present-ed some challenges, and nearly all the teachers mentioned that some of their students lacked motivation. As one teacher said, “Seniors, in general, sometimes tend to be a little lazier.” Some students stopped attending or turning in assignments because the course was an elective and they didn’t need it to graduate. Motivation seemed to be lowest among students who decided not to go to college or had been accepted to a college outside the UH system, in which case the SBA policy would not apply.

About 50 percent really liked it. They saw the value in it. They put a lot of effort into it,

especially when I told them if they got a B in this class, it speaks well for their future

math in college. About half of them really bought into that, and half of them were just

getting through their senior year, doing as little as possible. (Math teacher)

Survey responses appeared to capture the perspectives of more motivated seniors. Nearly three-quarters of survey respondents were very satisfied (33%) or somewhat satisfied (41%) with their level of effort in the course, while the remaining were neither satisfied nor dissatisfied (14%), somewhat dissatisfied (7%), or very dissatisfied (2%). Mirroring these results, a quarter of students said they spent less than one hour per week studying or completing homework for the class.

Findings: Nonacademic Skills

Students and teachers report improvements in students’ confidence and growth mindset, and quantitative survey results find high levels of confidence and growth mindset across students with different SBA levels.

Teachers and students reported a focus on nonacademic skills in the course. Several students said the course improved their growth mindset and their belief in their ability to learn math.

This class overall was a great experience. It really helped challenge me to want to do

better. I believe it will do the same for those who don’t really enjoy math too much. It was

definitely a positive learning experience that helped me grow my math skills. (Student)

Math is not my best subject, but this class helped me understand some things that I’ve

struggled with in the past. You also learn a lot of life lessons, and I really enjoyed that.

It makes you push yourself, and it teaches you not to give up to get the results that

you’re satisfied with. (Student)

About a third of teachers also reported observing improvements in students’ confidence and growth mindset. A teacher described how the course builds students’ growth mindset, which is essential to success:

It doesn’t matter if you can or can’t in the moment, but thinking that you can, you’re

going to be able to figure it out; that’s what I kind of saw in them, especially in the last

few weeks. (Math teacher)


The survey confirmed the teacher and student interviews. Midway through the course, the ma-jority of students were mostly or completely confident in their ability to do well in the class (table 6). Across most measures of confidence, students with an SBA level of 2 or SBA level of 3 or 4 reported similar levels of confidence. The lowest percentage of students (62%) selected mostly or completely confident for the item: “I can master the hardest topics in this class.” This was also the only area where students with an SBA level of 2 had significantly lower confidence than students with an SBA level of 3 or 4, meaning we can be confident that the differences in responses are unlikely due to chance alone. This finding suggests that teachers may want to focus on supporting students with an SBA level of 2 when it comes to the most difficult topics.

Table 6. Across SBA levels, Introduction to College Math students have a high level of confi-dence in their course performance

Percentage of students who indicated they were “mostly confident” or completely confident”

Overall SBA level 2 SBA level 3 or 4

I have what it takes to be successful in this class 89% 90% 96%

I can do well on future assignments in this class 89% 91% 91%

I can meet all the learning goals my teacher sets 86% 91% 90%

I can understand the material even when it’s difficult 79% 79% 84%

I can master the hardest topics in this class* 62% 54% 72%

*Represents differences in means between the SBA level 2 and SBA level 3 or 4 are statistically significant (p <0.001).

Note: Sample includes all students who took the pre-survey (N = 229). Respondents could select: “Not at all confi-dent,” “A little confident,” ”Mostly confident,” “Completely confident.”


We asked students to report their “growth mindset,” or their underlying beliefs about learning and intelligence. A student with a growth mindset believes he or she can develop better skills by putting in extra effort and is therefore more likely to work harder, leading to higher achievement (Dweck, 2006). The majority of students reported a growth mindset across all items and there were no statistical differences across SBA levels (table 7). Responses reflect that a portion of the students (between 13% and 28% depending on the item) report a fixed mindset, suggesting that developing students’ growth mindset is still an important area for teachers to focus on throughout the course with students of all levels.


Table 7. Across SBA levels, most Introduction to College Math students report a growth mindset

Percentage of students who indicated “mostly true” or “completely true”


Responses to positively worded items

My intelligence in math is something that I can change through challenging myself

84% 83% 86%

Responses to negatively worded items

There are some things in math that I am not capable of learning

20% 21% 18%

If I am not naturally smart in math, I will never do well in it

13% 14% 15%

I can learn new things in Introduction to College Math, but that won’t change how good I am at math

28% 27% 29%

Note: Sample includes all students who took the pre-survey (N = 229). Respondents could select: “Not at all true,” “A little true,” ”Mostly true,” or “Completely true.” No differences in means between the SBA level 2 and SBA level 3 or 4 are statistically significant.


Recommendations for Consideration

The Introduction to College Math course has been successful in terms of teacher and student experiences and perceptions of its impact on students’ college and career readiness. Hawai‘i P–20 is tracking the outcomes of Introduction to College Math students and will demonstrate to what extent students are enrolling and passing college math courses at UH. As the course continues to scale across the state and schools implement a new transition course in English, we offer the fol-lowing three recommendations for how HI DOE and high school administrators can increase their support for Introduction to College Math teachers and students. UH gateway math faculty may also want to advocate for these recommendations to ensure the course is successful.

Consider the implications—on instruction, advising, and course options—of opening the course to students with SBA levels outside of the intended range

Implications for instruction. Many teachers view the course as having a larger purpose. They see its curriculum and approach as having the power to improve students’ overall experience of math, which ultimately improves their ability to succeed in college and in life. Because they believe the course is beneficial for many types of students, they are more likely to identify and recruit students from a range of SBA levels, not just students who have a level 2. While this reflects positively on the course’s popularity and potential to impact a wide variety of students, we recom-mend that school administrators consider the implications of opening the course to a wider range of students. For example, teachers need to be prepared for the difficulties that arise from extend-ing the course beyond its intended implementation.


This issue is not limited to teachers in our sample. In a case study of transition courses in four states, Barnett and colleagues (2016) found that deciding which students to recruit and enroll was a common challenge. In most cases, these courses were designed for the express purpose of pre-paring students whose assessment scores were below a specific target for being college and ca-reer ready in math in grade 11. However, similar to schools and teachers in our study, other states have found that there are gaps in availability of senior-year math courses—both for students who score below the target and for those who score above it but are not interested in pursuing advanced math courses. Furthermore, sometimes schools receive information about student test scores after scheduling and enrollment decisions have already been made for the following school year. Barnett and colleagues (2016) did not offer solutions to these problems. Instead, they called on transition programs to consider critical questions about identifying the best approaches to teaching students with a broad range of ability levels. One of the most important questions is whether it is better to differentiate instruction to meet the needs of all students within one course or to attend to their needs in separate courses. This is a question that HI DOE may want to address.

Implications for advising. Teachers and administrators may also want to discuss this issue with counselors and other advisors who help place students into appropriate courses and pre-pare them to apply to and enroll in college. Ideally, the student advising process is informed by a shared understanding of the intent and expectations of the Introduction to College Math course. This issue is not limited to counselors, however. In math, many students appear to receive guid-ance from their current math teacher as to which course in the math sequence they should take next. In our study, a few teachers said that grade 11 math teachers needed a better understanding of the purpose of Introduction to College Math so it does not become a catchall for students who are not necessarily interested in taking the course or who do not understand the purpose of the course. For example, some students with an SBA level of 3 or 4 said they took the course to waive the placement exam requirement.

I think one issue that we need to work on and refine at our school is not making this

class like a dumping ground for any student. Some teachers will put any student in

this class even if they really should be taking a higher level class. What happened is we

had some students who were really high level and then some students who were really

low level. It made it kind of tough because some students would struggle with basic

concepts, but some students would be really bored by it because they got it in, like, a

few minutes. (Math teacher)

Schools may also want to examine how they are identifying students for the course. They can look to other schools for strategies to help them target the course to a specific student population or otherwise inform their course advising protocols. For example, schools that use the STAR test and/or previous grades as proxies for the SBA could share this strategy with other schools that are looking for better identification and advising procedures to ensure the course is helping the school meet its objectives.


Implications for math course options. The popularity of Introduction to College Math emphasizes the need for more senior-year elective math options that get students excited about math and better prepare them for the math they will see in college and in their careers. HI DOE may want to consider additional senior-year math options for students that do not build on Alge-bra 2, such as an applied math course tailored for students who receive a 1 on the SBA. In addition to traditional courses like college Algebra, schools may also want to examine the possibility of offering dual-credit or other college-level elective math options for students who receive a 3 or 4.

Continue offering a professional learning community for transition-course teachers

Teachers universally appreciate the instructional and curricular materials provided by Hawai‘i P–20, as well as the Introduction to College Math teacher trainings. The most common type of support requested by the teachers we interviewed was an ongoing professional learning community.6

P–20 has been great in terms of resources. All the materials, whether it was a home-

work assignment, all of the assessments—all of those resources were very, very helpful

for a person just starting out … Having that and P–20 in terms of being able to source

funds to help with the projects—that made such a big difference in terms of the kinds

of projects we could consider. It doesn’t make money a constraint. That was also help-

ful. I guess, to some degree, when we get together for training, the two professors are

always there. They are part of the actual authors/designers of the curriculum. They are

always introducing new ways of looking at stuff. (Math teacher)

I’d like an opportunity to network more with the teachers who are teaching the course,

because I feel like this would be our PLC, and because we’re not at the same school,

it’s difficult to meet. Sometimes, I send out emails to touch base, but I don’t always get

emails back. I do like when we have the training sessions and we’re able to talk to each

other about things that are going well, what we can improve on, project ideas from

other people. I would like that more. (Math teacher)

Previous research has also demonstrated that teachers desire and appreciate ongoing professional learning to support instruction of transition courses. Generally, studies recommend that states develop statewide plans for targeted professional development to ensure teachers understand the standards and how to teach them, along with the knowledge and skills students need to master (Barger, Murray, & Smith, 2011; Zinth & Millard, 2015). Other states have employed strategies such as job-embedded professional learning communities for ongoing support (Barger, Murray, & Smith, 2011; Barnett, Fay, & Pheatt, 2016), online professional development portals and/or archived we-binars that teachers can access, and the inclusion of other school personnel (e.g., counselors) who also need to understand the importance of the course (Barger, Murray, & Smith, 2011). Additionally, several states have maintained ongoing contact between college faculty and high school teachers throughout the year to get feedback from the course instructors (Barger, Murray, & Smith, 2011).

6 Other requests by teachers included more online materials and resources; additions or revisions to the course materials, including supplemental or differentiated assignments; a teacher’s edition of the textbook; and revisions to the materials for the last three units of the course. Over a third of interviewed teachers said they did not need any additional support.


We recommend that HI DOE continue to provide an ongoing professional learning community for veteran and new Introduction to College Math teachers so they can share strategies and learn together. Professional development could focus on the following specific aspects:

• Growth mindset: New Introduction to College Math instructors are mastering a great deal of unfamiliar content and pedagogy at once, and they may benefit from deeper learning on how to continuously promote their students’ growth mindset. Because the research evidence on growth mindset is strong, there are many resources that can help teachers learn how to cultivate this skill in their students—and how to conduct their own measurements. The Mindset Scholars Network (http://mindsetscholarsnetwork.org) offers access to a rich array of resources (many of them free) that teachers can use.

• Project-based learning: Since many of the teachers are teaching a wide variety of students, professional development should also incorporate strategies for differentiating and managing group dynamics.

• Expectations and curriculum of UH math courses: Although existing professional development—including the Math Summit—have provided information about col-lege-level math, a professional learning community could help to address the gaps in understanding that persist. The professional learning community should continue to provide opportunities for more communication with UH faculty members, particularly college math teachers.

I kind of graduate them on, and I don’t really know what happens at the community

college level. It would be good to have some communication with the college level

to see what the Math 100 class looks like—what they need to know for that, what the

standards are, what they cover in the remedial class. Because that’s essentially what

we’re doing. We’re doing the remedial class here at the high school as opposed to when

they’re in college. Having some alignment with them would be good … I don’t even

know the numbers. I don’t know much beyond the math system at the high school

level, so I think that would be good education for the teachers so we can answer these

questions for our students—if you take Math 75 or whatever in college, this is what

you’re going to be learning. If you take Math 100, this is what you’re going to be learn-

ing, and this is what you need to know beforehand. I guess, as a high school teacher,

we can probably research that ourselves, but it would also be good to have some com-

munication at the college level. (Math teacher)

Provide teachers with additional planning time or other opportunities to master the course material

Some teachers reported feeling overwhelmed by the demands of teaching Introduction to Col-lege Math, and they expressed a desire for additional preparation time to master the unfamiliar material while juggling their other responsibilities. Previous studies have also shown that transi-tion-course teachers sometimes struggle to balance breadth and depth in the curriculum. Some of the recommended best practices—learning by doing, allowing students to reach answers on their own—require time that inhibits teachers’ ability to cover all the course topics (Wathington et al., 2012). Meanwhile, other studies have shown that transition courses can present teachers with


a confusing mix of goals. For example, the curriculum may focus on college readiness, but the directive may be to prepare students for an assessment. Ultimately, some teachers have struggled to make decisions about which aspects of these courses to prioritize (Barnett, Fay, & Pheatt, 2016).

If possible, allowing teachers to teach multiple sections of the course might relieve some of the lesson-planning burden and create an opportunity for trial and error between sections, which could ultimately benefit implementation of the course. Schools may also want to consider offering extra planning time and opportunities for professional development for teacher who are new to these types of courses.

Conclusion

Introduction to College Math represents an innovative strategy for improving students’ readiness for college math, thereby addressing a major barrier to college completion for many students. Moving forward, considering the implications of opening the course to students with SBA levels outside of the intended range, continuing to offer a professional learning community for transi-tion-course teachers, and providing teachers with additional planning time and opportunities to master the course materials will help support Introduction to College Math teachers and students. Qualitative research on implementation can also continue to inform improvements to the course, while quantitative causal research can identify the effect of the course on specific student out-comes. For example, quantitative findings can help determine who the course is most benefitting, which can improve identification of the target population. Rigorous research can also identify the course’s impact on college math enrollment and completion and longer term outcomes of college persistence and completion. Demonstrating that Introduction to College Math has long-term positive impacts on students can help make the case for scaling it across schools, replicating the model for other subjects, and supporting sustainability and improvement by continuing profes-sional development for teachers.


References

Bailey, T., Jeong, D. W., & Cho, S.-W. (2010). Referral, enrollment, and completion in developmen-tal education sequences in community colleges. Economics of Education Review, 29(2), 255–270.

Barger, K., Murray, R., & Smith, J. (with Blanco, C., & Root, M.). (2011). State college and career read-iness initiative: Statewide transitional courses for college readiness. Atlanta, GA: Southern Regional Education Board.

Barnett, E. A., Fay, M. P., Bork, R. H., & Weiss, M. J. (2013). Reshaping the college transition: States that offer early college readiness assessments and transition curricula. Retrieved from Columbia University, Teachers College, Community College Research Center website: http://ccrc.tc.columbia.edu/publications/reshaping-the-college-transition-state-scan.html

Barnett, E. A., Fay, M. P., & Pheatt, L. (2016). Implementation of high school-to-college transition courses in four states. Retrieved from Columbia University, Teachers College, Community College Research Center website: http://ccrc.tc.columbia.edu/publications/implementa-tion-transition-courses-four-states.html

Dweck, C. S. (2006). Mindset: The new psychology of success. New York, NY: Random House Incorporated.

Glancy, E., Fulton, M., Anderson, L., Zinth, J. D., & Millard, M. (2014). Blueprint for college readiness: A 50-state policy analysis. Retrieved from Education Commission of the States website: http://www.ecs.org/bpcr/html/educationissues/blueprint/blueprint-intro.html

Hodara, M., & Xu, D. (2016). Does developmental education improve labor market outcomes? Evi-dence from two states. American Educational Research Journal, 53(3), 781–813.

Mayring, P. (2000). Qualitative content analysis. Forum: Qualitative Social Research, 1(2). Retrieved from http://www.qualitative-research.net/index.php/fqs/article/view/1089/2386

Wathington, H. D., Barnett, E. A., Fay, M. P., Mitchell, C., Pretlow, J., & Bork, R. H. (2012). Preparing stu-dents for college learning and work: Investigating the capstone course component of Virgin-ia’s college and career readiness initiative [NCPR working paper]. Retrieved from Columbia University, Teachers College, Community College Research Center website: http://ccrc.tc.columbia.edu/publications/capstone-courses-virginia.html

Zinth, J., & Millard, M. (2015). Using assessments to inform 12th-grade interventions and accelera-tions. Retrieved from Education Commission of the States website: https://www.ecs.org/using-assessments-to-inform-12th-grade-interventions-and-accelerations/

http://ccrc.tc.columbia.edu/publications/reshaping-the-college-transition-state-scan.html

http://ccrc.tc.columbia.edu/publications/reshaping-the-college-transition-state-scan.html

http://ccrc.tc.columbia.edu/publications/implementation-transition-courses-four-states.html

http://ccrc.tc.columbia.edu/publications/implementation-transition-courses-four-states.html

http://www.ecs.org/bpcr/html/educationissues/blueprint/blueprint-intro.html

http://www.qualitative-research.net/index.php/fqs/article/view/1089/2386

http://ccrc.tc.columbia.edu/publications/capstone-courses-virginia.html

http://ccrc.tc.columbia.edu/publications/capstone-courses-virginia.html

https://www.ecs.org/using-assessments-to-inform-12th-grade-interventions-and-accelerations/

https://www.ecs.org/using-assessments-to-inform-12th-grade-interventions-and-accelerations/


Appendix

Table A1. Schools offering the Introduction to College Math course (descriptive data)

2015/16 high school seniors

High school Island Fall enrollment

2015/16

% FRPL 2015/16

On-time graduation

College- ready on

ACT math

Enrolled at two-year college

Enrolled at four-year

college

Aiea High School Oahu 1,048 47% 87% 19% 26% 27%

Castle High School Oahu 1,179 43% 84% 24% 34% 21%

Farrington High School Oahu 2,376 60% 75% 17% 30% 17%

Kapa‘a High School Kauai 1,046 45% 91% 18% 34% 24%

Kahuku High School & Intermediate School

Oahu 1,379 47% 83% 21% 18% 23%

King Kekaulike High School

Maui 1,043 47% 82% 15% 5% 48%

Leilehua High School Oahu 1,699 52% 80% 22% 20% 28%

Millilani High School Oahu 2,514 17% 93% 43% 27% 45%

Molokai High School Molokai 340 69%* 89% 21% 11% 47%

Pāhoa High & Intermediate School

Hawaii 576 85% 74% 21% 19% 19%

Pearl City High School Oahu 1,639 30% 83% 28% 32% 28%

Waiākea High School Hawaii 1,197 49% 88% 25% 24% 32%

Waialua High & Intermediate School

Oahu 672 46% 82% 21% 24% 28%

Wai‘anae High School Oahu 1,803 69% 72% 12% 19% 16%

Waimea High School Kauai 578 48% 85% 16% 37% 22%

*Sixty-nine percent (enrollment 353) for 2014/15; no percent indicated for 2015/16.

Source: Fall enrollment and percent free or reduced-price lunch (FRPL) are from the 2016 School Status Improvement Report http://arch.k12.hi.us/school/ssir/ssir.html#. All other data are from Hawai‘i P–20 college and career readiness indicator reports http://www.p20hawaii.org/resources/college-and-career-readiness-indicators-reports/ccri-2016-data/.

Table A2. How students first heard about Introduction to College Math


Math instructor 63% 65% 57%

Friend 25% 14% 34%

Counselor 23% 30% 17%

Other* 4% 3% 3%

*Includes parent/guardian, poster/flyer, email, mailing, and open-ended responses (e.g., “I saw it as an elective and decided to try it out,” “Registration paper,” “Registrar,” and “I got put in this class”).

Note: Respondents could check all that apply. SBA level 1 is not shown to protect student privacy.



Table A3. Why students decided to enroll in Introduction to College Math


My teacher or counselor encouraged it 44% 48% 40%

I thought it would help me prepare for college 40% 36% 41%

I was interested in the subject or material 33% 28% 36%

I was interested in the experience of taking a college course 31% 31% 33%

My friends or family encouraged it 23% 13% 32%

I was trying to avoid a specific other math class 22% 14% 27%

I like the Introduction to College Math teacher 20% 17% 25%

I wanted to be challenged 11% 10% 11%

I wanted to waive the Compass test requirement 11% 12% 10%

Other* 5% 2% 6%

*Includes: The class was assigned to me and the following open-ended responses: “I skipped a lot of school last year,” “To graduate with academic honors,” “Better understanding of the material I was taught,” “Kind of like a review of what I’ve learned in the past,” and “I didn’t want a gap in math before I graduated.”

Note: Respondents could check all that apply. SBA level 1 is not shown to protect student privacy.


Table A4. Student responses to how helpful or not helpful the following course components were in learning the course content

I did not do/use this

Not helpful Somewhat helpful

Helpful Very helpful

Group work 2% 5% 8% 35% 50%

Daily assignments/homework 1% 0% 14% 43% 43%

Quizzes 2% 3% 12% 40% 43%

Exams 1% 5% 14% 43% 38%

Projects 1% 8% 20% 37% 35%

Introduction to College Mathematics textbook 6% 10% 28% 35% 21%

Study group (outside of class) 27% 10% 16% 25% 23%

Other resources 20% 5% 18% 41% 17%


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