The National Academies of Science, Engineering, and Medicine hosted a workshop and webinar on increasing student success in developmental mathematics on March 18-19 in Washington, D.C. With a packed two days of talks and panels, I found myself wondering how community college math requirements differ from the requirements at four-year institutions. I pondered this after watching Michelle Hodara's presentation titled "Student Demographics and Course-taking Experiences in Developmental Mathematics." In her commissioned paper, she answered two questions asked by the committee: What is known about college students in developmental mathematics? And how has the population changed during the last decade? Hodara also considered how research can better characterize this population of students.

To answer these questions, she used the Beginning Postsecondary Students (BPS) Longitudinal Study dataset. The survey, conducted by the U.S. Department of Education (NCES), includes various background characteristics such as high school preparation, college experiences, financial aid, and postsecondary outcomes. Though the dataset is very useful, there are limitations because the information for the 2003-04 data is self-reported rather than observational, and the information for the year 2011-12 represents an early period of developmental mathematics reform.

Hodara’s analysis showed that in 2003-04, 42% of college entrants took developmental mathematics across all types of institutions. This proportion was similar in 2011-12, although there was a significant increase in the proportion of entrants who took developmental mathematics in their first year at for-profit four-year colleges and at public two-year colleges. Although Hodara did not give reasons for the significant change in the enrollment in for-profit four-year institutions, I wondered if changes in math placement and requirements since 2003-04, or the more aggressive marketing of the four-year for-profit institutions may explain the increases.

To address the question of who is represented in developmental mathematics courses, Hodara disaggregated the information by historically underrepresented student groups, including students of color, students who first learned to speak another language other than English, students who are foreign-born or have foreign-born parents, students whose parent(s)’ highest degree is a high school diploma or less, and students who have a Pell Grant. She found that developmental mathematics students in 2011-12 were more likely to be from historically underrepresented student groups compared to developmental mathematics students in 2003-04. With that key takeaway, Hodara suggests the developmental mathematics population has become more diverse over time. However, the diversification of the developmental mathematics population may be a reflection of the increased diversification of the college population in general. At the same time, it is important to question whether we are seeing an overrepresentation of historically underrepresented students in developmental mathematics.

Hodara addressed the issue of overrepresentation by using a composition index defined as the ratio between the percentage of the specific student group in the developmental mathematics population compared to the percentage of the group in the overall population. A ratio greater than one implies a higher proportion of that student group enrolled in developmental mathematics than what would be in the overall student population.

In 2011-12 at public four-year colleges, overrepresentation in developmental mathematics occurred for American Indian/Alaska Native (2.1), Native Hawaiian/Pacific Islander (2.0), Black/African American (1.7), Hispanic/Latinx (1.6), and students receiving Pell grants (1.4). In comparison in 2011-12 at public two-year colleges, there was a significantly smaller range in the index across various categories, and thus a smaller degree of overrepresentation, which can be explained because, in general, two-year colleges receive more underrepresented students. The analysis showed public two-year colleges having an overrepresentation in developmental mathematics occurring for Black/African American students (1.3), American Indian/Alaska Native (1.1), and students receiving Pell Grants (1.1).

Hodara had access to restricted transcript data, which allowed her to study first-time college students’ backgrounds, course-taking patterns in college including developmental mathematics, and college outcomes. She used two common measures of college readiness including students’ completion of Algebra 2 or higher in high school and those who received a B-minus in high school or higher. Surprisingly, 68% of the developmental mathematics student population had completed Algebra 2 or higher and 55% of the developmental mathematics student population had a B-minus GPA in high school or higher. These high percentages indicate that the majority of students leaving high school should be ready for college-level mathematics—and yet, they are enrolled in developmental mathematics!

It was distressing to learn that the percentage of students who completed Algebra 2 or higher math classes in high school and took developmental math in their first year was vastly different when looking at public two-year colleges versus four-year colleges, and that there was a wide variation by race and ethnicity. For instance, in public four-year institutions, the percentage of students with the same level of college readiness who took developmental math in their first year of college included the highest proportion (Native American/Alaskan Natives at 37%) and the lowest proportion (White students at 10% and Students who did not receive a Pell grant at 10%). In public two-year institutions, the gap between the highest percentages of students with the same level of college readiness who took developmental math in their first year of college was 41% for Black/African American students at 27% for White students and 26% for students who did not receive a Pell Grant.

Overall, these findings suggest that there is an overrepresentation of students of color and of low-income students at both public two- and four-year institutions. However, it is striking that there are more students attending community colleges who have completed Algebra 2 and are still taking developmental mathematics than there are at four-year colleges. In my opinion, this should force the consideration of two ideas: (1) successful completion of Algebra 2 in high school signals college readiness; and (2) community colleges might be imposing more rigorous, and perhaps unnecessary, standards for their students’ entrance into college-level mathematics.

A few audience members considered this latter idea and suggested that it could be happening because of concerns that receiving institutions will judge their students’ coursework harshly. Four-year colleges in certain areas often will not accept students’ developmental math-course credits as college credits, labeling them as elective credits instead. This forces community colleges to impose higher requirements for their developmental courses and entrance into college-level mathematics. An individual at the workshop suggested that even when faculties consider developmental mathematics restructuring at the institutional level, they weigh the judgment of the receiving institution highly in their minds, which skews their decision-making process.

No one in the audience considered the first idea, which considered what college readiness is and whether successfully completing Algebra 2 should be enough to be considered ready for college. When I consider this idea, I think about how secondary education has changed within the last couple of decades. While high schools are trying to incorporate new standards and assessment policies, for example, standards-based grading and exam retaking, they may be failing to consider how low or high they are setting the bar for students, as well as the overall effect on college readiness. The differences in state graduation requirements for high school math must be considered as well. Specifically, many states only require two or three years of math in high school and do not have specific courses. Therefore, there may be several students who are succeeding in Algebra 2 by their junior year in high school and spend a whole academic year without math education before enrolling in college math courses. This one example should change our interpretation of readiness, especially when we see that 68% of developmental mathematics students have taken Algebra 2 or higher in high school. When considering how many paths students can take to becoming a college student enrolled in a developmental math course, I am not sure that completing Algebra 2 in high school is enough to measure readiness for college.

One must also consider that without a complete, national consensus regarding how many years of math a high school student needs to graduate, and what content specific math courses will contain, that it’s almost impossible to know that a high school graduate from one school has roughly the same skills in mathematics as students nationwide. The same Algebra 2 could be labeled “Math 3” at a high school and have a vastly different emphasis on topics but still be considered Algebra 2 for survey data. This is one reason why many colleges incorporate their own placement test in mathematics. Thus, it would be interesting to know if an institutional-level placement test was involved in placing a percentage of the 68% of students who completed Algebra 2 and enrolled in developmental mathematics their first year because some element of the two-year college mathematics requirements is placing more students of color and low-income students in developmental mathematics than at four-year colleges.

Ultimately, there is more to consider when looking at who is represented in developmental mathematics; investigating college readiness and community college math-placement requirements may be a more pressing concern. Thus, I would encourage college faculty to collect data that include student measures of college readiness and their enrollment in developmental mathematics. Then disaggregate those data based on student characteristics that include race/ethnicity, gender, first language, age, and income status to discern if there is an overrepresentation of any particular group of students at their institution in developmental mathematics. Mining this type of data, as Dr. Hodara did, is helpful for a national representation of who is enrolled in developmental mathematics. As for answering questions at a college departmental level, specific institutional data will help faculty consider their institutional context and potential areas for change.

**References:**

Hodara, M. (2019). *Understanding the developmental mathematics student population: Findings from a nationally representative sample of first‐time college entrants*. Workshop on Increasing Student Success in Developmental Mathematics. National Academies of Science, Engineering, and Medicine, Washington D.C.

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