What are math pathways? In short:
Mathematics pathways refer to the course or the sequence of courses that students take to meet credit or program requirements and to prepare them to use mathematics for their careers, for making sense of the world, and for their own sense of enjoyment and empowerment.
Typically, discussions of mathematics pathways focus on the courses students take as they progress through secondary (high school) and postsecondary education (college or other career training) and how the availability of multiple pathway options allows students to take advantage of opportunities best suited to their unique needs.
The Common High School Pathway
Many high schools have some sequence of courses leading to calculus that looks like this:
Increased access to calculus has been one of the great achievments in high school mathematics over the past 40 years. Calculus is a powerful tool, and is required for most students pursuing a future in a STEM degree or career. However, only 10 to 15 percent of our students might earn STEM degrees. Are there other mathematics options worth considering for the vast majority of students pursing something else? Many people think so.
Math Pathways in Other States
Mathematics pathways have been a focus of national and state conversations now for over 10 years, including here in Colorado. Here are snapshots of pathways in other states.
Oregon's "2+1" course design places common expectations for all students to study a year of algebra, a semester of geometry, and a semester of statistics as the "core credits." Beyond those two credits, students can choose a pathway for their required third credit, which could be advanced algebra, data science, or a quantitative reasoning course. Elective options beyond the third course are available, each leading students towards a calculus pathway, a data science pathway, or a quantiatitve pathway.
Washinton's "Modern Algebra II" model requires students to take common Algebra 1 and Geometry courses and then partway through Algebra 2, students have the option of choosing a path directed towards statistics, mathematical modeling, or advanced algebra.
Ohio's pathway model requires common Algebra 1 and Geometry courses (or Math 1 and Math 2), and then a third year consisting of Algebra 2 or an equivalent. From there, up to five different paths exist for students, including options like discrete math and computer science, quantiative reasoning, and data science foundations.
Alabama's pathways include the expectation that all 9th graders take a year of geometry and data analysis. From there, most students move to Algebra I or Algebra II before getting "specialized course options" including Applications of finite mathematics, mathematical modeling, or precalculus. Notable in Alabama's pathways are the lab courses that offer students extra support in the high school courses, and the option to take Goemetry and Algebra 1 together in high school to accelerate one year.
Colorado's Math Pathways Task Force
Colorado has a task force of K-12 and higher education stakeholders working together to make recommendations for math pathways in Colorado. Groups represented by task force members include the departments of education and higher education, professional educator associations, higher education institutions, and advocacy groups.
Working along with 21 other states and the Charles A. Dana Center, Colorado's math pathways task force is working towards a future in which each student is in a mathematics pathway that, ideally:
- Aligns with their aspirations,
- Supports them with the resources needed to succeed,
- Has equitable access to and success in the courses, and
- Provides a smooth transition from secondary education to postsecondary opportunities.
Working Paper: Math Pathways: Defining Problems and Challenges in the State of Colorado
In 2023, Colorado's math pathways task force detailed two primary problems with the current state of math pathways:
Problem 1: Colorado K-12 students are typically tracked into high school math courses according to their perceived ability, regardless of their interests.
- Placement decisions are often made too early
- Students’ post-secondary plans get ignored
- Tracks are inflexible
- Tracking is opposed by NCTM, NCSM, and ASSM
Problem 2: Colorado schools typically offer one track to calculus that is privileged above all others.
- College Algebra and/or Calculus I is the only well-defined, non-dead-end pathway target in many systems
- Increased calculus enrollments is an achievement, but for students who would benefit more from other math, being on a calculus track may represent a missed opportunity
Solving these problems will require us to overcome a variety of policy-focused, practice-focused, and perception-focused challenges:
- Differences in governance structures
- Graduation guidelines vs. HEAR
- Placement rules and multiple measures
- Colorado Academic Standards
- The “Big Blur”
- Tracking and HS placement
- Students who stumble can’t get back on track
- School and teacher capacity
- Teacher preparation and professional development
- Your pathway is your “smartness”
- Beliefs that lead to segregating students by ability or demographics
- Change is too risky
The task force compiled these problems and challenges into a working paper called "Math Pathways: Defining Problems and Challenges."