# REL Central Ask A REL Response

#### Math

**December 2020**

**Question**

What is the relationship between high school math course sequencing and future academic success?

**Response**

Following an established research protocol, REL Central conducted a search for research reports as well as descriptive study articles to help answer the question. The resources included ERIC and other federally funded databases and organizations, research institutions, academic databases, and general Internet search engines. (For details, please see the methods section at the end of this memo.)

References are listed in alphabetical order, not necessarily in order of relevance. We have not evaluated the quality of the references provided in this response, and we offer them only for your information. We compiled the references from the most commonly used resources of research, but they are not comprehensive and other relevant sources may exist.

**Research References**

Asim, M., Kurlaender, M., & Reed, S. (2019). *12th grade course-taking and the distribution of opportunity for college readiness in mathematics*.
Policy Analysis for California Education. Retrieved from
https://eric.ed.gov/?id=ED600439

*From the ERIC abstract:*

“In this report, the authors explore the patterns in mathematics course-taking among California public high school seniors. They describe what courses students are enrolled in and how course participation varies by key student characteristics, such as race/ethnicity, socioeconomic status, and performance level on the state’s 11th grade assessments. The authors also explore course-taking patterns for students eligible for California’s public four-year colleges–California State University (CSU) and the University of California (UC), and for applicants and admitted students at the CSU and UC. The findings demonstrate that although a large majority of college-bound students enrolled in math in their final year of high school, advanced math pathways were not equally accessed among our high school seniors. These disparities in enrollment patterns by race/ethnicity and school characteristics likely contribute to disparities in postsecondary access and success.”

Brown, J., Dalton, B., Laird, J., & Ifill, N. (2018).
*Paths through mathematics and science: Patterns and relationships in high school coursetaking* (NCES 2018-118).
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. Retrieved from
https://ies.ed.gov/pubsearch/pubsinfo.asp?pubid=2018118

*From the executive summary:*

“This report examines mathematics and science coursetaking in high school by providing a description of coursetaking within each of the mathematics and science subject areas across the high school years, as well as by showing the association between early mathematics coursetaking and subsequent science coursetaking. The report also describes coursetaking in engineering and technology, and the associations between coursetaking in these subject areas and in mathematics and science. Data on high school graduates from the National Assessment of Educational Progress’s (NAEP’s) High School Transcript Study (HSTS) serve as the basis for the report.”

Burdman, P. (2015). *Degrees of freedom: Diversifying math requirements for college readiness and graduation*.
Policy Analysis for California Education; LearningWorks. Retrieved from
https://eric.ed.gov/?id=ED564291

*From the ERIC abstract:*

“Since the mid-20th century, the standard U.S. high school and college math curriculum has been based on two years of algebra and a year of geometry, preparing students to take classes in pre-calculus followed by calculus. Students’ math pursuits have been differentiated primarily by how far or how rapidly they proceed along a clearly defined trajectory that has changed little since then. Evolutions in various disciplines and in learning sciences are calling into question the relevance and utility of this trajectory as a requirement for all students. The emerging movement is toward differentiated ‘math pathways’ with distinct trajectories tied to students’ goals. Alternatives emphasizing statistics, modeling, computer science, and quantitative reasoning that are cropping up in high schools and colleges are beginning to challenge the dominance of the familiar math sequence. The drive toward acknowledging the importance of multiple domains within math is prompted largely by two developments: (1) technological tectonics; and (2) demand for deeper learning. Decisions about math requirements and expectations will have a major impact on the academic opportunities of millions of students nationally. This is the first report in ‘Degrees of Freedom,’ a series that explores the role of math as a gatekeeper in higher education. This report examines the move toward differentiated math pathways linked to students’ academic majors, highlights some obstacles to implementing them, and discusses some principles for addressing those obstacles.”

Burdman, P. (2015). *Degrees of freedom: Varying routes to math readiness and the challenge of intersegmental alignment*.
Policy Analysis for California Education; LearningWorks. Retrieved from
https://eric.ed.gov/?id=ED564295

*From the ERIC abstract:*

“The conventional algebra-intensive math curriculum commonly dictates students’ options for entering and completing college, including their ability to transfer from two-year to four-year institutions. The assumption that higher-level algebra is necessary for college success has led some equity advocates to promote algebra for all students. Nearly half of states require two years of algebra for high school graduation, and the Common Core State Standards being implemented in the majority of states have a similar emphasis. While the intent has been to raise achievement, the hidden underbelly of high algebra expectations has been swelling enrollment in college developmental (also known as remedial) math over the last few decades, especially at community colleges. This is the second report in ‘Degrees of Freedom,’ a series that explores the role of math as a gatekeeper in higher education. It highlights experiments with alternative remedial math sequences at community colleges in California and the particular challenges of aligning them with four-year university requirements for students seeking to transfer from community colleges. This report also examines math alignment from high school through college, revealing an underlying misalignment of existing requirements, and shows how the resulting restrictions serve to ration access to higher education. Recommendations for improving the status quo are included.”

Finkelstein, N., Fong, A., Tiffany-Morales, J., Shields, P., & Huang, M. (2012).
*College bound in middle school & high school? How math course sequences matter*. Center for the Future of Teaching and Learning at WestEd. Retrieved from
https://eric.ed.gov/?id=ED538053

*From the ERIC abstract:*

“As California competes for jobs in an increasingly competitive global economy, the state faces a looming shortage of highly educated workers (PPIC, 2012). For a variety of reasons, the need for individuals with degrees in science, technology, engineering, and mathematics (STEM) is of particular concern. Nowhere is this more true than in the discipline of mathematics where understanding develops cumulatively, requiring that students master progressively more complex building-block concepts and skills in order to be successful in each next-higher-level course. Prior research confirms that success in high-level mathematics in high school is predictive of postsecondary success and careers in STEM fields. This study, funded by the S. D. Bechtel, Jr. Foundation and the Noyce Foundation, digs deeper into this middle-and high-school connection as it applies to STEM, in order to better understand the degree to which California students stay on the trajectory for STEM-related attendance eligibility at California's public universities and, if students veer off the trajectory, to better understand when and why. Thus, researchers examined math and science course-taking patterns for a representative cohort of some 24,000 California students who were enrolled in grade 7 in 2004/05 and stayed in their district through grade 12 in 2009/10. Although the study looked at students' science course-taking, this report focuses more tightly on the mathematics-related findings, partly because it turns out that course-taking patterns and performance in science are quite similar to, though less complex than, those in mathematics and partly because mathematical understanding, while not sufficient, is essential to student success in some key high school science courses, such as chemistry and physics. The math findings include: (1) Math performance in grade 7 is predictive of high-school math course-taking; (2) While the majority of students who achieved at least Proficient on their math CSTs are those who took algebra 1 in grade 8, geometry in grade 9, and algebra 2 in grade 10, in general this accelerated pathway does not support students who are not proficient in math in grade 7; (3) Many students repeat algebra, but few repeaters achieve proficiency on their second attempt; (4) Districts are keenly aware of poor student performance in mathematics but less aware of coursetaking [sic] patterns; and (5) Districts feel great urgency to improve algebra outcomes.”

Fong, A. B., Jaquet, K., & Finkelstein, N. (2014).
*Who repeats algebra I, and how does initial performance relate to improvement when the course is repeated?* (REL 2015–059).
U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory West. Retrieved from
https://eric.ed.gov/?id=ED548534

*From the ERIC abstract:*

“This REL West study explores the prevalence of students repeating Algebra I, who is most likely to repeat the course, and the level of improvement for students who repeat. Using six years of data from a cohort of 3,400 first-time seventh grade students in a California school district, authors found that 44 percent of students repeated algebra I. Overall, student performance improved on average by approximately one-half of a letter grade and a little less than one-third of a performance level on the CST when students repeated the course. But when the data was disaggregated based on initial performance in the class, higher-achieving students experienced variation in improvement levels. Repeating students who initially received average course grades of at least a ‘C’ in Algebra I earned higher CST scores but lower course grades on average when they repeated the course. Students who initially scored Proficient on the Algebra I CST experienced increases in course grades but declines in CST scores on average when they repeated the course. Overall, these findings show that lower-performing students are likely to experience improvements in grades and CST scores when they repeat Algebra I, but that higher-performing students are likely to experience improvements on some measures of performance and declines on others when they repeat the course.”

Klute, M., Dougherty, B., & Van Dine, D. (2020).
*What grade 7 foundational knowledge and skills are associated with Missouri students’ Algebra I achievement in grade 8?* (REL 2020–023).
U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Central. Retrieved from
https://eric.ed.gov/?&id=ED606821

*From the ERIC abstract:*

“To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational knowledge and skills required for success in advanced math courses. This leaves educators to determine which students are ready for Algebra I in grade 8 and which are not. To inform strategies that address this challenge, this study examined whether student knowledge in five math domains in grade 7 was associated with Algebra I achievement in grade 8. It found that students’ scores in all five domains were associated with Algebra I achievement. The “expressions and equations” domain had the strongest association. The association between the “number system” domain and Algebra I achievement was stronger for English learner students than for non English learner students. The associations between the five grade 7 domains and Algebra I achievement did not significantly differ for students who were receiving special education services and those who were not.”

Koon, S., & Davis, M. (2019).
*Math course sequences in grades 6–11 and math achievement in Mississippi* (REL 2019–007).
U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Southeast. Retrieved from
https://eric.ed.gov/?id=ED597299

*From the ERIC abstract:*

“Effective with the 2014/15 school year, Mississippi adopted new academic standards and courses aligned to these new standards. The new courses included both a subject-specific mathematics sequence (that is, algebra I, geometry, and algebra II) as well as an integrated mathematics sequence (that is, integrated I, integrated II, and integrated III). In addition to differences in course content, students also could elect to begin their sequences at different grades (for example, algebra in grade 8 versus grade 9) and complete their sequences in different order. The Mississippi Department of Education is interested in understanding the student and school demographic profiles by mathematics sequences (for example, integrated versus subject specific) which were followed under these new course options. Findings from this study will provide this information and will inform professional development activities at the state and school district levels for individuals responsible for advising students and for providing mathematics instruction, facilitate discussions across districts with similar demographic profiles but differences in mathematics sequences and mathematics achievement, and, if needed, help determine the likely number of students who would be affected by future changes to the approved courses list in Mississippi. Research Questions: The study will be guided by the following research questions: (1) What are the mathematics sequences taken by students who started grade 9 in 2014/15?; (2) How are mathematics sequences related to student demographic characteristics for students who started grade 9 in 2014/15?; and (3) How are mathematics sequences related to college-ready performance on the American College Testing (ACT) Mathematics for students who started grade 9 in 2014/15? Study Design: The statistical package ‘TraMineR’ will be used to both identify and group similar mathematics sequences taken by students, and then examine how the sequences are related to explanatory factors (for example, gender, race/ethnicity) in correlational analyses. Associations between mathematics sequence and college-ready performance will be modeled using multilevel logistic regression analyses. The sample for this study includes students who entered high school in 2014/15 in the Mississippi public school system under the state’s new mathematics standards and continued enrollment through grade 11 in 2016/17.”

Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2015).
*Teaching strategies for improving algebra knowledge in middle and high school students* (NCEE 2015-4010).
U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance. Retrieved from
https://eric.ed.gov/?id=ED555576

*From the ERIC abstract:*

“Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, ‘Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students.’ The methods and examples included in the guide focus on helping students analyze solved problems, recognize structure, and utilize alternative approaches to solving algebra problems. Each recommendation includes the level of supporting research evidence behind it, examples to use in class, and solutions to potential implementation roadblocks. Teachers can implement these strategies in conjunction with existing standards or curricula. In addition, these strategies can be utilized for all students learning algebra in grades 6–12 and in diverse contexts, including during both formative and summative assessment. Administrators and professional development providers can use the guide to implement evidence-based instruction and align instruction with state standards or to prompt teacher discussion in professional learning communities.”

Yamaguchi, R., Jonas, D. L., Schmidt, R. A., Sieber, M., Buffington, P., Neumayer DePiper, J., & Araoz, C. (2020).
*Algebra I and college preparatory diploma outcomes among Virginia students who completed Algebra I in grades 7–9* (REL 2021–038).
U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Appalachia. Retrieve from
https://eric.ed.gov/?id=ED608303

*From the ERIC abstract:*

“Education leaders in Virginia use early access to Algebra I as one method to provide students more time to take college preparatory courses in high school, thereby increasing students’ likelihood of graduating prepared for college and careers. Yet, little data are available for these leaders to examine whether their approach is warranted. Members of the Regional Educational Laboratory Appalachia Student Success in Mathematics partnership are interested in learning more about students who complete Algebra I in grades 7-9 and their outcomes. This study examined whether these students passed the Algebra I state assessment and whether they earned a college preparatory diploma. The study used administrative data to calculate descriptive statistics for one cohort of Virginia grade 5 students who completed Algebra I in grades 7-9. The results for the overall study population are presented by students’ proficiency level on the grade 5 math state assessment and disaggregated for economically disadvantaged students and English learner students. Among students in the overall study population who scored at the advanced proficient level in grade 5 math and completed Algebra I in grade 7, 90 percent passed Algebra I, and 80 percent earned a college preparatory diploma. The percentage of economically disadvantaged students who passed Algebra I was 10 percentage points lower than the percentage of the overall study population, and the percentage who earned a college preparatory diploma was 18 percentage points lower. There were similar differences in performance for students who completed Algebra I in grade 8 or 9. The study findings suggest the need to better understand Algebra I placement policies and practices and whether they unintentionally contribute to differences in student access to Algebra I and subsequent outcomes.”

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**See more …**

#### Methods

**Keywords and Strings**

The following keywords and search strings were used to search the reference databases and other sources:

- math + pathways
- math + pathways + “high school”
- math + sequence
- math + sequence + “high school”
- “mathematics achievement”
- “mathematics curriculum”
- “mathematics instruction”
- “secondary school mathematics”

**Databases and Resources**

REL Central searched ERIC for relevant references. ERIC is a free online library, sponsored by the Institute of Education Sciences, of over 1.6 million citations of education research. Additionally, we searched Google Scholar and Google.

**Reference Search and Selection Criteria**

When searching for and reviewing references, REL Central considered the following criteria:

**Date of the Publication:**The search and review included references published between 2010 and 2020.**Search Priorities of Reference Sources:**Search priority was given to ERIC, followed by Google Scholar and Google.**Methodology:**The following methodological priorities/considerations were used in the review and selection of the references: (a) study types, such as randomized controlled trials, quasi-experiments, surveys, descriptive analyses, and literature reviews; and (b) target population and sample.

This memorandum is one in a series of quick-turnaround responses to specific questions posed by educational stakeholders in the Central Region (Colorado, Kansas, Missouri, Nebraska, North Dakota, South Dakota, Wyoming), which is served by the Regional Educational Laboratory Central at Marzano Research. This memorandum was prepared by REL Central under a contract with the U.S. Department of Education’s Institute of Education Sciences (IES), Contract ED-IES-17-C-0005, administered by Marzano Research. Its content does not necessarily reflect the views or policies of IES or the U.S. Department of Education nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government.