Math Coursework Research Articles

“What’s Math Got to Do with It?” Emphasizing Math as an Impediment to STEM Excellence for Black Students

Drawing on Martin’s Multilevel Framework for Analyzing Mathematics Socialization and Identity Among African Americans this study explores the mechanisms that influence Black students’ decision-making processes related to math course taking in high school. Three years of student transcript data for 1561 Black seniors in a Southern California school district were analyzed using descriptive statistics and logistic regression analyses in STATA. The findings reveal factors that impact students’ ability and desire to complete a fourth year of math in high school, interconnected with institutional, structural, identity, and parental factors. One such finding is that accelerated 8th-grade math placement significantly increases the likelihood that a student would enroll in upper-level math coursework, such as “Beyond IM3” courses in high school. The researcher also investigated the influence of the concentration of Black math teachers in a school on the likelihood of a Black student enrolling in a Beyond IM3 math course. The results of this study contribute to an understanding of the limited racial diversity in STEM fields, highlighting the role of math as a major deterrent for Black students’ interest and persistence in STEM. The findings suggest the need for policy and curriculum changes to promote equitable access to advanced math coursework for Black students, especially in the 8th grade. This study also emphasizes the need to address the structural and institutional factors that influence Black students’ decision-making processes related to math course taking in high school.

Beyond Tracking: The Relationship of Opportunity to Learn and Diminished Math Outcomes for U.S. High School Students

Background/Context: In this study, we draw on evolving definitions of opportunity to learn (OTL) to conceptualize mathematics OTL has having two main components: structural OTL, defined by gatekeeping access to specific mathematics courses through the process of tracking, and instructional OTL, defined by the learning experiences of students in their mathematics courses. We also conceptualize both of these aspects of OTL as occurring in the current educational milieu, where sociopolitical factors reward or punish specific school strategies. Purpose/Objective/Research Question/Focus of Study: This study seeks to examine, using an OTL framework, the relationship between high school math teachers’ instructional practices, students’ course tracks in mathematics, students’ perceptions of mathematics, and students’ distal measures of academic attainment, including completion of advanced math coursework and completion of a high school diploma. Research Design: Using latent class analysis, this secondary data analysis analyzed the 2009 High School Longitudinal Study data from the National Center for Educational Statistics to examine mathematics instructional OTL based on math teachers’ objectives of emphasis and its relationship to structural OTL in the form of course tracking. Findings/Results: We identified “Enriched” and “Rote Knowledge and Skills” latent classes of math OTL. Teachers providing Enriched OTL emphasize the widest variety of objectives, including cognitively demanding problem-solving and logic objectives and practical applications of mathematics, while teachers providing Rote Knowledge OTL emphasize basic computation, algorithms, and computation skills. Black students, Hispanic students, and students living in poverty were more likely to be in math OTL classes focused primarily on basic concepts, algorithms, and computation, with little to no emphasis in more applied and cognitively demanding math course objectives, and they were less likely to be enrolled in advanced ninth-grade math courses. Students in Rote Knowledge OTL courses with little to no emphasis in applied and cognitively demanding math course objectives had lower mathematics identity and self-efficacy, and math achievement. Conclusions/Recommendations: This study adds to the literature suggesting that students in the United States experience an opportunity gap rather than an achievement gap, and that opportunity gaps are both structural and instructional. This study also adds to the literature suggesting student sorting systems are inherently unequal and must be addressed through policy, leadership, and cultural shifts in both schools and districts.

Ability signals and rigorous coursework: Evidence from AP Calculus participation

Large racial gaps in rigorous math coursework enrollment are a barrier to improving college completion rates and access to careers in STEM. Perceptions of the math abilities of underrepresented minority students, whether by themselves or their schools, may contribute to such gaps. A regression discontinuity design with data on all Massachusetts public school students shows how receiving a positive ability signal affects subsequent enrollment in advanced high school math coursework. For Black or Hispanic students, particularly those with low reading scores, being labeled as “Advanced” on a 10th grade math test substantially increases the likelihood of later Advanced Placement Calculus course- and exam-taking. White or Asian students and those from higher income high schools show no such effects. Understanding how ability signals affect students’ and schools’ decisions about assignment to coursework may suggest further ways to address gaps in such enrollment.

Constructing Corequisites: How Community Colleges Structure Corequisite Math Coursework and the Implications for Student Success.

States and broad-access colleges are rapidly scaling corequisite coursework-a model where students concurrently enroll in college-level and developmental coursework-in response to dismal completion rates in traditional "developmental" sequences. At community colleges, evidence suggests that corequisite reforms can dramatically improve students' completion of required college-level courses, but colleges often implement new programing and sequences with limited information. We analyzed administrative data from Texas community colleges implementing a statewide corequisite mandate. Our results illustrate (a) how colleges structured corequisite courses in response to the statewide mandate and (b) how corequisite coursework characteristics predicted student outcomes. Our results suggest that some corequisite coursework elements-including mixed-ability college-level classes, higher credits for the developmental education (dev-ed) corequisite support course, and using the same instructor across both the college-level and dev-ed course-improve students' probability of passing college-level math, though these course design elements do not appear to predict long-term outcomes like persistence in college.

College Readiness, Early Post-secondary Academic Performance and the GED Degree: Evidence from Kentucky

Abstract We use detailed administrative data from Kentucky to provide robust descriptive evidence on the relationship between the General Educational Development (GED) degree, college readiness, and early post-secondary (PSE) academic performance. Following previous work in this area, we address selection issues by focusing on a sample of students who are identified as at-risk prior to high school entry. Our results suggest the GED credential is not a credible signal of PSE readiness, particularly in mathematics. GED graduates attain a lower first semester GPA and are also less likely to re-enroll in second semester courses. We also find that changes made to the GED exam in 2014 to enhance student readiness in PSE institutions did not yield meaningful improvements. Finally, we investigate the extent to which differences in math coursework can explain estimated GED-related math readiness gaps, finding coursework to account for about for about 40 percent of the observed gap.

Faculty attitudes toward technology-driven instruction in developmental mathematics

Innovation in instructional technology has contributed to the rapid implementation of technology-driven instructional platforms, particularly in developmental math coursework (Bickerstaff et al., 2016). In this phenomenological study, we investigate how faculty perceive and respond to a mandated, technology-driven instructional model for developmental math coursework at public colleges in Tennessee. Through interviews with faculty members across four colleges, we find that many faculty agreed that technology helped them to better track student performance, provide more targeted assistance, and communicate directly with students. Faculty also expressed concerns that technology provides the opportunity or temptation to game the system, interfering with true learning, and that students with the greatest needs may not be well served by the instructional model. We draw policy implications related to the role of educators in the development and implementation of curricular policy, provision and requirements for ongoing professional development, and postsecondary learning accountability.

Heterogeneity in the Effects of College Course Placement

Traditionally colleges have relied on standalone non-credit-bearing developmental education (DE) to support students academically and ensure readiness for college-level courses. As emerging evidence has raised concerns about the effectiveness of DE courses, colleges and states have been experimenting with approaches that place students into credit-bearing coursework more quickly. To better understand which types of students might be most likely to benefit from being placed into college-level math coursework, this study examines heterogeneity in the causal effects of placement into college-level courses using a regression discontinuity design and administrative data from the state of Texas. We focus on student characteristics that are related to academic preparation or might signal a student’s likelihood of success or need for additional support and might therefore be factors considered for placement into college-level courses under “holistic advising” or “multiple measures” initiatives. We find heterogeneity in outcomes for many of the measures we examined. Students who declared an academic major designation, had bachelor’s degree aspirations, tested below college readiness on multiple subjects, were designated as Limited English Proficiency (LEP), and/or were economically disadvantaged status were more likely to benefit from placement into college-level math. Part-time enrollment or being over the age of 21 were associated with reduced benefits from placement into college-level math. We do not find any heterogeneity in outcomes for our high school achievement measure, three or more years of math taken in high school.

Context and Implications Document for: Recruitment to STEM studies: The roles of curriculum reforms, flexibility of choice, and attitudes

Context and Implications Document for: Recruitment to STEM studies: The roles of curriculum reforms, flexibility of choice, and attitudes

College Readiness, Early Post-Secondary Academic Performance and the GED Degree: Evidence from Kentucky

The General Education Development (GED) certificate is recognized as a credible alternative to a high school diploma in the US. In this paper, we use detailed administrative data from the state of Kentucky to measure the efficacy of a GED degree. We examine the association between the GED college readiness and early post-secondary academic performance. Following previous work in this area, we address selection issues by focusing on a sample of students who are identified as at-risk prior to high school entry. Our results suggest the GED credential is not a credible signal of PSE readiness, particularly in the area of mathematics. GED graduates attain a lower first semester GPA and are also less likely to re-enroll in second semester courses. Differences in the highest level of high school math coursework between GED holders and traditional graduates account for a majority of the observed GED related math-readiness disparities. We also test whether the substantial changes made to the GED exam in 2014 improved student readiness in PSE institutions, however we find no meaningful improvements in PSE math readiness.

Importance of math prerequisites for performance in introductory physics

Previous work has looked at the relationship between high school preparation and student performance in calculus-based introductory mechanics (physics 1) courses. Here, we extend that work to look at performance in introductory calculus-based electricity and magnetism (physics 2), and we look at the significance of what college math courses have been completed in addition to high school preparation. Using multiple linear regression including these measures of prior preparation, we examine the correlation between taking various math courses in college and final exam scores in introductory physics courses at a highly selective west coast university. In physics 1, we find that prior college math coursework is not a predictor of physics 1 final exam score. In physics 2, we find that having taken a course in vector calculus is a strong predictor of physics 2 exam performance (effect size=0.58 standard deviations, p<0.001), even when controlling for students’ physics 1 final exam scores (effect size=0.27 standard deviations, p<0.01). These effect sizes are similar in magnitude to other measures of students’ incoming physics and math preparation. Qualitative analysis of student exams from physics 2 reveal that this “vector calculus gap” is due to differences in reasoning about vectors and geometry and some differences in conceptual understanding of circuits, as vector calculus itself is not required to perform well on the final exam. That is, basic reasoning related to vector calculus appears to be important, but the formalisms of vector calculus do not.Received 10 November 2020Accepted 1 February 2021DOI:https://doi.org/10.1103/PhysRevPhysEducRes.17.010108Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasStudent preparationPhysics Education Research

Suspended in context: School discipline, STEM course taking, and school racial/ethnic composition

STEM curricula and school disciplinary regimes are key foundations of the transition to adulthood, and they may be connected within school contexts in ways that reflect and exacerbate the intergenerational transmission of inequality. This study examines such connections with particular attention to student race/ethnicity and the racial/ethnic composition of high schools. Bivariate probit analyses of the High School Longitudinal Study of 2009 and the Civil Rights Data Collection of 2012 revealed that early suspension was associated with truncated trajectories of Calculus course taking later in high school while taking Algebra I in grade 9 was associated with avoiding suspension. The proportion of disciplinary cases of racial/ethnic peers was associated with the math coursework of boys and the proportion of Calculus enrollment moderated the association between Algebra I in 9th grade and suspension during high school for girls. These results confirm the value of studying the interplay of formal and informal processes of schooling.

Inside the Math Trap: Chronic Math Tracking From High School to Community College

Examining linked academic transcripts from urban community colleges and their feeder high schools, we identify math course-taking patterns that span sectors. We highlight stifled mobility and chronic repetition of math coursework in the transition to college, and we identify “math traps” from which students do not escape. Math mobility was limited, math repetition was rampant, and nearly half of students found themselves in math traps. All else equal, being trapped in math was significantly linked to race/ethnicity, suggesting that these forms of chronic math tracking across sectors expose previously undocumented forms of inequality in educational experiences.

Beyond Predictive Validity: A Mixed Method Study of Self-directed Developmental Education Placement at a Small Community College

ABSTRACT Colleges across the country struggle with determining the most appropriate means of placing students into math and English coursework. Most colleges utilize a single high-stakes standardized placement exam to assess incoming students and use strict cut-scores to determine students’ placement. However, the ability of these tests to accurately place students has been called into question. A small, but growing, number of colleges allow students to have more input into their placement through self-directed placement (SDP) policies, which are typically based on a self-assessment tool that asks students to reflect on their content-related practices, abilities, and beliefs or attitudes. This mixed methods research study explored the experiences of a small community college that implemented SDP as part of a larger multiple measures placement process. Data were examined through the lens of Messick’s conceptualization of validity and revealed evidence that both supported and challenged the validity of placement decisions made from SDP. When designing SDP instruments, we recommend that colleges ensure that SDP tools reflect the skills and knowledge that students need to be ready for the college-level courses at each particular institution, rather than relying heavily on SDP instruments developed by other institutions. We also recommend that colleges adopt a holistic approach to students’ self-assessment. Our findings indicate a need to consider a shift in the dominant conversation on placement methods from a focus almost exclusively on predictive validity toward a more comprehensive, and potentially more robust, holistic consideration of qualitative and quantitative validity evidence.

The Effectiveness of Model Rocketry to Teach Science and Quantitative Content to Students in a Non-Science Majors Course at the College Level: An Example from a Planetary Geology Course

Engaging non-science majors in a college-level science course can prove challenging. In turn, this can make it difficult to effectively teach science and math content. However, topics related to planetary exploration have a unique way of capturing one’s imagination and may serve to robustly engage non-science majors. In this contribution, I 1) describe a model rocketry lab module, I have created and implemented into an introductory-level planetary geology course and 2) quantify student learning gains as a result of this module. This module builds on model rocketry lesson plans for science and math coursework at the K-12 level (e.g., [1] [2]) and involves students working in groups to 1) design and build model rockets to carry out a theoretical mission that addresses a science question the students have developed, 2) launch their rockets and collect related data, 3) synthesize and evaluate their data, and 4) report their results in both oral and written forms. The tasks of building and launching the model rocket serve as a vehicle that allows students to employ the scientific process while learning about planetary mission design and applying geologic and quantitative skills useful to answering a science-related question. Quantification of student learning gains shows that through this lab module, students significantly improved their quantitative and scientific reasoning skills. Results from student questionnaires showed a significant increase in student interest and confidence in addressing scientific questions as well as an understanding of how planetary missions are designed and conducted.

Dual‐Credit Courses and the Road to College: Experimental Evidence from Tennessee

AbstractDual‐credit courses expose high school students to college‐level content and provide the opportunity to earn college credits, in part to smooth the transition to college. With the Tennessee Department of Education, we conduct the first randomized controlled trial of the effects of dual‐credit math coursework on a range of high school and college outcomes. We find that the dual‐credit advanced algebra course alters students’ subsequent high school math course‐taking, reducing enrollment in remedial math and boosting enrollment in precalculus and Advanced Placement math courses. We fail to detect an effect of the dual‐credit math course on overall rates of college enrollment. However, the course induces some students to choose four‐year universities instead of two‐year colleges, particularly for those in the middle of the math achievement distribution and those first exposed to the opportunity to take the course in eleventh rather than twelfth grade. We see limited evidence of improvements in early math performance during college.

The Labor of Division: Returns to Compulsory High School Math Coursework

Despite great focus on and public investment in STEM education, little causal evidence connects quantitative coursework to students' economic outcomes. I show that state changes in minimum high school math requirements substantially increase black students' completed math coursework and their later earnings. The marginal student's return to an additional math course is 10 percent, roughly half the return to a year of high school, and is partly explained by a shift toward more cognitively skilled occupations. Whites' coursework and earnings are unaffected. Rigorous standards for quantitative coursework can close meaningful portions of racial gaps in economic outcomes.

Toward the Next Generation of Scholarship: Challenges and Opportunities for Full Participation in PhD Training in Economics

A great advantage of our rigorous doctoral training is that as PhD economists we speak a common language that allows for efficient vetting and quick dissemination of ideas and insights. But what good is sophisticated grammar and a powerful vocabulary if the contents of our narratives are lacking? Our top three criteria for admissions to PhD programs are prior coursework in math, the quantitative GRE score, and prior coursework in economics. To attract top talent and prevent becoming a stagnant discipline that loses the influence we have in society and academia, students' creativity, originality, and drive should receive more weight.

Can Math Competency Predict Success in Nursing School?

Nursing research into math competency and the impact it has on success in nursing school has produced mixed results. This retrospective comparative study investigated whether math coursework predicted program completion in an associate degree nursing program. Review of student transcripts (n=473) found that how a student performed in calculus and precalculus courses, and a student’s overall total math GPA was associated with program completion. Grades in algebra & trigonometry or statistics courses had no effect on graduation rates.

Improving Placement Accuracy in California’s Community Colleges Using Multiple Measures of High School Achievement

Objective: Standardized placement tests remain the primary means by which new community college students are assessed and placed in the hierarchy of math and English coursework. A growing body of evidence indicates that placement tests tend to underestimate students’ likelihood of achieving passing grades in college-level courses, leading to students being misplaced in developmental coursework, slowing their academic progress, and increasing their likelihood of dropping out of college. This article discusses the results of a statewide research effort to improve the accuracy of student placement in math and English in the California Community College system. Method: Decision tree methods were applied to high school and college transcript data to identify key measures of high school achievement that predict performance in nine levels of community college math courses (three developmental and six college level) and four levels of community college English courses (three developmental and one college level). Results: Cumulative high school grade point average (GPA) is the most consistently useful predictor of performance across levels of math and English coursework, and a higher GPA is necessary to signal readiness for college-level coursework in math than is necessary to signal readiness for college-level coursework in English. In addition, cumulative GPA combined with specific indications of progress in the high school curriculum is frequently useful for predicting performance in math among direct matriculants and for predicting performance in both math and English among nondirect matriculants. Conclusion: Drawing on the findings, placement rules that colleges can apply directly in their placement processes are developed and validated.

An intervention to support mathematics self-efficacy in middle school

Findings from recent studies suggest that students’ pathways into mathematics-related careers begin as early as middle school when students are forming lasting self-perceptions of their academic abilities. Middle school is also a time when students begin making choices about future coursework in math, science, and technology that will have long-term implications for their academic and career achievements. Because important self-efficacy beliefs are forming and young adolescents are making decisions that impact career choice, it is important to provide support for students early in their schooling to maximize student potential and consideration of mathematics education and mathematics-related careers. Supporting self-efficacy for math is important for most middle school students but may be crucial for girls who often experience significant declines in their feelings of competence in this domain. Middle school teachers have an opportunity to support student learning beyond the academic curriculum, and this article describes how a self-efficacy intervention can support important skills, attitudes, and dispositions necessary for mathematics achievement and consideration of mathematics-related careers.