Solving California's math problem

by Carol Kocivar | August 22, 2022 | 4 Comments
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Imagine you have to solve the following problem:

You have three cars filled with 8th grade math students and the college or career of their choice is 50 miles away.

  • Car A has 1 student who is beyond basic proficiency standards in math.
  • Car B has 2 students who more or less meet proficiency standards in math.
  • Car C has 7 students who are not yet meeting proficiency standards in math.

All the cars need to go at different speeds and take different paths to reach the math proficiency levels needed for their unique college and career destinations.

Essay question:

What needs to be done to provide all students with math opportunities that meet their academic potential to help them get to their college and career goals?

This is the issue drafters of California’s math frameworks face.

What is a curriculum framework?

Many, many people are involved in the important work of creating textbooks, tests, lesson plans and other educational materials. As students advance from one class to another it’s important for these materials to align with one another — and that doesn’t happen by accident.

Curriculum frameworks help educational leaders, publishers and educators harmonize their work with California’s standards, the expectations of what students should understand and be able to do as they advance. A curriculum framework is sometimes compared to a roadmap — it helps you find your way to a destination without necessarily telling you exactly how to get there.

Frameworks are meant to address how content standards can meet the needs of the broadest range of students possible, making math both rigorous and accessible. They also provide research and guidance to help schools make the best local decisions that expand math options and improve math outcomes for all students.

California’s math frameworks are in review

California’s math frameworks are in the process of a contentious revision. After several rewrites and delays, the frameworks are expected to reach the State Board of Education for approval in 2023.

The drafters of the frameworks are especially interested in solutions that support students who historically have not done well in math. An aim is to respond to the “structural barriers …[to] mathematics success: equity influences all aspects of this document.”

The frameworks incorporate equity-based teaching strategies and the use of what it calls BIG ideas and connections. The framework recommends teaching BIG ideas that allow teachers and students to explore key concepts in depth, through investigations.

What’s the right level of rigor?

Some math experts have expressed concern that the proposals do not contain enough rigor and clear pathways to higher-level math. The frameworks propose a new high school pathway called data science. In public comment, some experts expressed concern that the draft framework leaves students mathematically unprepared for any STEM major.

Nearly 1,800 STEM professionals signed an open letter to the State Board of Education warning that “Reducing access to advanced mathematics and elevating trendy but shallow courses over foundational skills would cause lasting damage to STEM education in the country and exacerbate inequality by diminishing access to the skills needed for social mobility.”

Many California students are not proficient in math

California students are all over the place in their levels of math achievement.

About 30% of 8th grade students in the state (mostly Asian, Filipino and White) meet or exceed grade-level proficiency in math. About 70% of students (predominantly students of color) have not yet reached grade-level proficiency in math. Few African American and Hispanic students end up taking the most advanced AP courses.

The table below (from a report by PACE) shows 12th grade math course participation by ethnicity.

A math problem within a math problem

Different college courses of study and career pathways require different paths of study. Some students will need five years' worth of math courses to acquire the skills they will need to pursue STEM majors and STEM careers. But high school only lasts four years. For this reason, the California Department of Education recommends different possible math sequences depending on a student’s interests and motivations.

The table below shows the possible math sequences based on the Common Core State Standards for Mathematics.

Model mathematics courses, by grade level
(based on common core state standards)








Algebra I/Mathematics I







Geometry/Mathematics II







Algebra II/Mathematics III







AP Probability and Statistics














The California Department of Education, like most state departments of education in the U.S., recognizes two primary pathways through high school math requirements. Each of these two pathways can be further compacted for students who wish to accelerate in math. Students need to be prepared to do additional work in order to compact the additional year(s)’ worth of math content into the given number of years available in high school.

California pathways through high school math

Traditional pathway

The U.S. traditional pathway consists of two algebra courses and a geometry course, with some data, probability and statistics included in each course.

Integrated approach

An integrated approach typically consists of a sequence of three courses (Math I,II and III), which include numbers, algebra, geometry, probability and statistics.

Compacted Traditional pathway

Students complete the content of 7th grade, 8th grade, and the High School Algebra I course in grades 7 and 8. This will enable them to reach calculus or other college level courses by their senior year. No content is omitted.

Compacted Integrated pathway

Students complete the content of 7th grade, 8th grade, and the Mathematics I course in grades 7 and 8. This will enable them to reach calculus or other college level courses by their senior year. No content is omitted.

Note: Most schools do not provide early middle school compacted pathways that accelerate learning. This requires students to double-up on math courses in high school or take summer programs that squeeze in a full year’s worth of math.

Accelerated math and tracking.

The proposed, revised math framework has “strong reservations against traditional tracking in the early grades.” The philosophy: High-level content should not be allocated to small numbers of students and denied to most others. Schools should offer high level mathematics in a variety of ways to all students.

These proposed frameworks concentrate on describing alternatives to traditional tracking that are aimed particularly at the needs of students who have not historically done well in math. See Appendix A: High School Pathways of California’s Common Core State Standards for Mathematics.

Graduation and college entrance requirements for math

California has several stages of math requirements that strongly influence student course choices: high school graduation requirements, university entrance requirements, and requirements for different STEM majors:

California Math Requirements

High School Graduation

Two years of mathematics (including Algebra I)

UC and CSU entrance requirements

Three years of mathematics. You can determine if the courses at your school are accepted by the UC and CSU here.

CSU course options

Math (4 years recommended) of college preparatory math including or integrating topics covered in algebra, geometry, and intermediate algebra.

UC course options

Three years of college-preparatory mathematics required (four years are strongly recommended), including or integrating topics covered in: elementary algebra, two-and three-dimensional geometry, advanced algebra.

Also acceptable are courses that address the above content areas, and include or integrate: probability, statistics or trigonometry.


applied mathematics, calculus, computer science, data science, discrete mathematics, linear algebra, pre-calculus (analytic geometry and mathematical analysis), probability, statistics and trigonometry.

The frameworks are not law. They are suggestions, but they matter. Educators are keenly aware that these suggestions will influence what a local school district provides. Curriculum and textbook companies know that aligning with the frameworks is the key to unlocking billions of dollars’ worth of sales and licensing business.

Questions & Comments

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user avatar
Carol Kocivar August 28, 2022 at 12:17 pm
Here is a link that From Stanford math that discusses this:
user avatar
Carol Kocivar August 28, 2022 at 12:24 pm
Here is one more source that contains effective strategies to teach math:
user avatar
Frida August 28, 2022 at 9:15 am
Is there any discussion regarding HOW math is taught, not just access to classes? We know that explicit reading instruction works much better than just exposing students to books. Isn’t it the same with math, don’t student need explicit math instruction as well, especially those who are struggling? We also know from reading instruction, that children do better if the teacher focuses on one area for an extended time, instead of moving back an fourth between different areas. The same should be true for math, especially for children who are struggling. Is there any research into the best way to teach math?
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