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Authors’ notes: CAP uses “Black” and “African American” interchangeably throughout many of our products. We chose to capitalize “Black” in order to reflect that we are discussing a group of people and to be consistent with the capitalization of “African American.”

Additionally, a “Latinx” person is any individual with origins in Latin America. This term is preferable to “Latino,” which is not inclusive of gender or gender identity, as well as “Hispanic,” which refers to people from Spanish-speaking countries—including Spain—whereas many Latin American countries are not predominantly Spanish-speaking. That said, “Latino” and “Hispanic” are used throughout the report when the underlying source uses such terminology.

A high school education should prepare all students for their chosen next step after graduation, whether it be a two-year college, a four-year institution, or immediate entry into the workforce. Regardless of their choice, students’ mastery of mathematics during their high school education is a gateway to success. Student scores on assessments such as the National Assessment of Educational Progress (NAEP), consistently document that well before high school, American students lack proficiency in math—and these low proficiency rates on the eighth-grade assessment continue in high school. Even on international tests, math proficiency for U.S. students, compared with those in other countries, is not as high as it should be.¹ These students must take remedial math classes in college to build the basic numeracy skills required to enter credit-bearing college courses.² Most of these students never progress to any credit-bearing coursework or to a degree, dooming them to low-wage jobs that cannot sustain a family and in many cases are being phased out of the 21st century economy.³ This pattern disproportionately affects students from families with low incomes and Black and Latinx students.⁴

The widespread and persistent placement of students into remedial math education in college calls into question how effectively American schools teach math in K-12 education, especially in high school. It also emphasizes the need for higher education and K-12 systems to work together to align their math instruction strategies and content in order to ensure academic continuity. To be sure, the question of rigor and relevance is important for every subject. However, math is often a gatekeeper subject in all fields; this is particularly the case for entry into high-wage science, technology, engineering, and math (STEM) fields, including physics and computer programming.⁵ Given the current racial and gender inequities in employment in these fields, math is a particularly critical area of focus, as equitable pathways would ensure access for all into these high-wage fields.⁶ Content and curricula need to evolve in order to keep up with the needs of these fields of study and economic demands.⁷

This report looks at lessons learned from research and innovation in math instruction to make recommendations that can help effectively scale new, more effective math pathways at the federal, state, district, and institution levels. These recommendations include the following:

• The U.S. Department of Education should conduct additional research on the development and impact of math pathways.
• Congress should increase funding for the State Longitudinal Data Systems, which collect data on remedial education rates.
• States should establish specific state work groups or task forces to oversee the development, scaled implementation, and monitoring of math pathways. They should also target professional development funding in math pathways implementation, create statewide articulation agreements, and continue to craft policies that support data-informed practices in math instruction.
• Districts should address equity and access through explicit curriculum policy, ensure that high-quality math courses and teachers are in every school, and ensure that math content is aligned with the content taught in postsecondary institutions. These actions will ensure that practitioners in classrooms focus on effective math instruction instead of antiquated teaching methods, using stronger curricula and relevant content.
• Institutions of higher education (IHEs) should ease implementation of math pathways by decentering college algebra as a gatekeeper course and creating articulation agreements with K-12 districts and with other two-year and four-year institutions.

To increase access to and adequately prepare all students for the future of work, relevant actors need to intentionally implement math pathways with equity at the center. Ultimately, these combined efforts will increase students’ math proficiency and ease their progression through their chosen postsecondary pathways.

Initially designed to prepare students for calculus, college algebra courses focus on higher-level skills and have slowly become the default math courses for students, who are repeatedly pushed through the same process.¹³ However, few degree programs and only about 5 percent of today’s professions use those skills.¹⁴ For years, math experts have said that having math education focus solely on college algebra and calculus is misguided.¹⁵

High school math courses follow this same trajectory. Traditionally, students need to complete Algebra I for entry into advanced math courses in high school,¹⁶ Algebra II for high school graduation,¹⁷ and college algebra for a postsecondary credential or degree.¹⁸ Additionally, each postsecondary institution’s definition of college algebra differs, as some incorporate skills from Algebra II, some from precalculus, and others from a completely different mix.¹⁹ Despite this focus on algebra, around 80 percent of students do not need an algebra-intensive curriculum, nor calculus, to succeed in their degree programs.²⁰

Given the saturation of algebra-centered math instruction, any efforts to shift away from it as a traditional gatekeeper, as well as scale a newer strategy, would require institutions of higher education to approve math courses at other IHEs as qualifying for college credit. This move would also require significant support from the state education agency, which enforces state high school graduation requirements, to ensure that any new state-approved high school math courses count toward those graduation requirements and are equally rigorous for all students.²¹

There is a long history of developing initiatives that attempt to improve math course content, rigor, and relevancy.²² The various initiatives have responded, in part, to the relatively low and minimal growth in math scores on the National Assessment of Educational Progress for all students from 1990 to 2017, as well as on the international Trends in International Mathematics and Science Study (TIMSS) from 1995 to 2015.²³ As shown in Figures 1 and 2, low NAEP scores persist among Black, Hispanic, and American Indian/Alaska Native students, compared with white and Asian/Pacific Islander students. Figures 3 and 4 also show persistently low NAEP math scores for students at schools with a higher percentage of students eligible for free and reduced-price lunch.

One of the most recent national initiatives, the Common Core State Standards, was created in 2010 to increase the rigor of academic standards in English language arts and mathematics in K-12 education in order to improve student preparation for college, career, and life.²⁴ The CCSS were developed through the collaboration and consensus of dozens of educational experts, who all agreed that students would benefit from a different approach to math instruction.²⁵ Within the CCSS math standards, experts anticipated the need for flexible quantitative reasoning and statistics infusion, both of which differ from algebra-heavy content but are equally rigorous.²⁶ These courses are also more directly applicable to the majority of other fields of work.

Subsequently, the CCSS developers embedded building blocks that would allow for the creation of math pathways, defined as “developmental and college-level course sequences that align to a student’s academic and career goals, and that accelerate student completion of a gateway college-level math course.”²⁷ However, chances for successful CCSS implementation by teachers in the classroom suffered as a consequence of the pushback against standardized testing as well as a lack of adequate professional development and sufficiently rigorous or aligned curricular materials.²⁸ Additionally, not every state adopted the CCSS, and many states still have different assessments, which makes it difficult to compare student progress in algebra and other courses across states.²⁹ The foundation and standards for a rigorous math education that goes beyond algebra are now mostly in place in the states that did adopt the CCSS or other college- and career-ready standards. However, there seems to be a gap between those standards and the quality of their implementation.³⁰ The CCSS intentionally defined standards but did not specify how teachers should teach in order to allow for practitioner interpretation and autonomy in instruction.³¹ Additionally, states are responsible for providing teachers with professional development on CCSS implementation, which can vary in funding, quality, and consistency.³²

While the CCSS are a K-12 education initiative, most other efforts to improve math instruction started as remedial education reform efforts in community colleges.³³ Remedial education courses build students’ basic skills in reading and math but do not offer college credit. Community college faculty and administrators began math pathways initiatives to disrupt the alarming rates of dropout from remedial courses—and subsequently college altogether.³⁴ Data from the National Center for Education Statistics from the 2015-16 school year show that about 56 percent of undergraduates at two-year institutions and 41 percent of those at four-year institutions took a remedial course after high school.³⁵ Moreover, Table 1 notes that American Indian, Black, and Hispanic students are overrepresented in remedial courses, especially in math.

Math pathways give students the option to enroll in college-level math courses that are relevant to their majors and as rigorous as traditional college algebra.³⁶ This strategy is deployed through a model called corequisite remediation, in which students are concurrently placed into two courses: an appropriate credit-bearing, college-level math course and a related support course.³⁷ There are different corequisite remediation models, as the instructors, types, and lengths of support courses can vary.³⁸ These models have shown significant promise for increasing math proficiency. West Virginia Community & Technical Colleges (WVCTC), for example, implemented a tailored corequisite remediation model, and within a year, the number of students enrolled in remedial math who also completed an associated, credit-bearing gateway course rose from 14 percent to 62 percent.³⁹ Other institutions in Georgia, Texas, Tennessee, and other states saw comparable results using similar corequisite models.⁴⁰ The consistent success of math pathways as a remedial education reform effort points to its ability to transform how math is taught in high school, as well as in grades K-8.

At the high school level, there are a few math pathways variations. One such model is the integrated math model—which consists of Mathematics I, II, and III—in which academic standards within algebra, geometry, probability, and statistics are addressed concurrently over three years.⁴¹ Other common models consist of a variation of Algebra I, Geometry, and Algebra II.⁴²

At the postsecondary level, the most common math pathways models are an algebra pathway that leads to calculus, a pathway for statistics, and a pathway for quantitative reasoning.⁴³ While the algebra pathway is important for students pursuing science, technology, engineering and mathematics careers, other high-wage STEM and non-STEM careers, such as nursing and law, require proficiency in statistics and quantitative skills.⁴⁴ Figure 5 offers examples of pathways from ninth grade to career that demonstrates how math pathways prepare students for their futures.

In the authors’ review of effective math pathways programs across the country, three main themes emerged:

1. Effective design of math courses in grades K-12 and at the postsecondary level has shown increased academic proficiency and success in postsecondary courses.
2. Reducing disparities in Black and Latinx students’ placement in postsecondary remediation could address a persistent achievement gap.
3. Faster access to credit-bearing courses through a method such as corequisite remediation increases math proficiency and reduces students’ failure rates in traditional, prerequisite remediation courses.

These three themes highlight effective methods that schools, districts, institutions of higher education, and states can implement to ensure that math pathways increase proficiency and prioritize access and equity for all students. The next subsections delve into each theme and successful case studies of math pathways implementation, as well as legislation that eased scaled implementation.

Theme 1: More effective design of and instruction in math courses

Implementation of math pathways in high school classrooms and postsecondary institutions is most effective when focused on intentional and effective instruction: how practitioners teach, what they teach, and how relevant the content is. Unfortunately, there have been a few barriers to effective pathway implementation.

Some teachers across the United States still use antiquated and ineffective teaching methods for math, such as rote memorization and noninteractive lecturing.⁴⁵ Additionally, there is some evidence that in the No Child Left Behind era of school accountability requirements, teachers were pushed to teach to the existing lower-quality standardized tests, instead of being encouraged to employ inquiry-based lessons that focused on high-level mathematical thought.⁴⁶ Teachers may also receive little support to design coherent curricula to ensure mathematical relevance for all students.⁴⁷ To improve instruction and course design, districts and schools should implement well-facilitated professional development in which teachers can discuss and update pedagogy, foster engagement and buy-in to the concept of math pathways, and increase collaboration between practitioners at high schools and two-year and four-year institutions. Districts and schools can also ensure curricular relevance by implementing flexible quantitative reasoning, statistics, and algebra-equivalent math pathways. The following example shows how a Massachusetts high school intentionally and effectively designed curricula in its math pathways development to increase student success and math proficiency.