Mathematics Pathways

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At PreK-12 in Colorado, pathways have become a common topic of discussion for mathematics teachers and specialists, with an increasing number of people looking to innovate and resolve long-standing issues affecting access, achievement, relevancy, and equity in mathematics learning, especially in high school.

For preschool through 12th grade, Colorado statutes require academic standards to describe what students should know and be able to do in mathematics. While there are progressions of learning inherent in these standards, described as coherence connections, the state does not dictate the content of individual courses or the construction of mathematics pathways. Generally, schools offer a daily math class or learning time in PreK-8, with the content of each class aligned to the academic standards for that grade.

In high school, opportunities to learn mathematics vary more. Most schools use the "traditional" sequence of Algebra 1, Geometry, and Algebra 2, while others offer an "integrated" sequence, which may be called Mathematics 1, Mathematics 2, and Mathematics 3, or something similar. Opportunities to learn mathematics vary even more for 11th and 12th graders, with some pursuing courses like precalculus or statistics, some taking college math courses through concurrent enrollment opportunities, some pursuing credit through AP courses, typically in calculus or statistics, and others earning math credit for courses like consumer math, computer-aided design and drafting, construction math, computer programming, nursing, or other postsecondary and workforce readiness (PWR) related classes for which a school district has determined some amount of math credit can be earned.

Typical traditional and integrated mathematics pathways.

In Catalyzing Change, NCTM makes the following key recommendation for the organization of high school mathematics:

High schools should offer continuous four-year mathematics pathways with all students studying mathematics each year, including two to three years of mathematics in a common shared pathway focusing on the Essential Concepts, to ensure the highest-quality mathematics education for all students. (p. 83)

NCTM outlines two possible pathways:

• Pathway A is the "Geometry First" pathway. The first semester of 9th grade would focus on Essential Concepts in geometry and measurement, followed by a focus on the Essential Concepts in statistics in the second semester of 9th grade. All 9th graders would start at the same point and build on their study of geometry and statistics in 8th grade. In the following three semesters (10th grade and the first half of 11th grade), students would focus on the Essential Concepts of algebra, building on their study of algebra in middle school. The remaining 1.5 years of high school math would include the study of mathematics in courses to serve students' future needs and interests.
• Pathway B is the "Integrated Approach" pathway. During the first year, students would study geometry and measurement, descriptive statistics, and graphing in the coordinate plane. Like Pathway A, all 9th graders would start at the same point. In the second year, students would continue their study of algebra, including exponential equations and functions. In the third year, students would analyze function families related to quadratic and exponential functions, as well as study statistical inference and probability. This could be a semester-long or year-long experience, depending on pacing. The remaining year or 1.5 years of high school math would include the study of mathematics in courses to serve students' future needs and interests.