In 2015, the California Legislature passed aspirational legislation, the California Math Placement Act SB-359, which language includes:

The California State Legislature declares that:

1. Pupil achievement in mathematics is important to prepare pupils for college and their future careers, especially those careers in the fields of science, technology, engineering, and mathematics (STEM).
2. Placement in appropriate mathematics courses is critically important for a pupil during his or her middle and high school years.
3. New research shows that it is less common for pupils of color, even high-achieving pupils of color, to reach calculus by grade 12 compared to their white and Asian peers.
4. All pupils, regardless of race, ethnicity, gender, or socioeconomic background, deserve an equal chance to advance in mathematics.

The proposed framework’s guidance conflicts with these aspirational goals. Its guidance deters students from reaching and completing calculus in the 12th grade; which it labels ‘a rush to calculus’ (Ch. 1 Lines 432, 440-441), by universally delaying Algebra 1 / Integrated Math 1 until grade 9, while recommending that all students be in the same math classes in grades 6-10. (Ch. 9, Lines 1042-1043), (Ch. 8, Lines 246-249)

For background, the traditional pathway in US mathematics education in grades 8-12 is the following (CMF Critique):

• Algebra 1 (taken mostly either in 8th grade or 9th grade, with 24% of students nationally taking it before 9th grade). It has been a longstanding goal of the US Department of Education and many organizations to increase the number of students taking Algebra 1 in 8th grade.
• Geometry.
• Algebra 2.
• Precalculus.
• AP Calculus.

Note: Integrated Math (IM) is an existing reorganization of the traditional pathway. It consists of three courses Integrated Math 1, Integrated Math 2, and Integrated Math 3 which together cover Algebra 1, Geometry, and Algebra 2 (with trigonometry) in an integrated way. Math 3 is fairly similar¹ to Algebra 2. (CMF Critique)

Each course listed above is a year long math course.

Delaying Algebra 1 / Integrated Math 1 until grade 9 holds students back, precluding most from completing calculus in high school, as students have only 4 years to complete the 5 year progression.

Recommending that all students be in the same math classes in grades 6-10, regardless of whether their interest, ability, or level warrants advancement, also holds students back.

These two prongs of the draft framework’s guidance, that students attend the same math classes in grades 6-10, and that Algebra 1/Integrated Math 1 be delayed to grade 9, effectively decelerates math in public schools in California.

Though the 2013 Math Framework gave students’ options to ‘accelerate’ in middle school by enrolling in Algebra 1 in 8th grade (see CCSSI Appendix, page 3, options 3 & 4), the draft framework removes those options. It justifies this deceleration by claiming that prior Frameworks and others erred ‘...because of an incorrect conclusion that Calculus is an important high-school goal.’ (Ch. 8, Lines 121-123)

Strangely, though the draft framework claims that completing Calculus is not ‘...an important high-school goal..,’ (Ch. 8 Lines 121-123), it attempts to shoehorn in a workaround for students — to complete Calculus in high school. It claims that students need not take Precalculus prior to taking Calculus (Ch. 8 Line 843-847):

“Research has shown that taking a precalculus class does not increase success in calculus (Sonnert & Sadler, 2014), and recent innovative approaches for students in California community colleges have shown that students who move from Algebra 2 to supported calculus classes are more successful than those who go through prerequisite courses (Mejia, Rodriguez, & Johnson, 2016).”

According to STEM professionals though, ‘..skipping precalculus is only feasible for very few advanced students..,’ and the research that the draft framework cites for this claim does not support its conclusion at all.

The Math Placement Act sets calculus completion as an important high school goal, recognizing that “Placement in appropriate mathematics courses is critically important for a pupil during his or her middle and high school years.”

According to a recent RealClearEducation article, ‘The Proposed California Mathematics Framework Lacks Research Evidence,’

“For the 15 years prior to 2014, California’s educational standards were on par with international standards, under which most students would take Algebra I in middle school, typically in grades seven or eight. California once had great success in closing on that goal.”

The draft framework clashes with one of its underlying studies on this point. Burris, Heubert, & Levin, 2006², argues for math acceleration — not deceleration — advocating enrolling all students in Algebra 1 in 8th grade.

From Burris, et al:

• In other words, the belief that underlies their work is that a school's accelerated and enriched "best curriculum," reserved for its highest achievers, is the best curriculum for all students. (Burris, Heubert, Levin, 2006, pg. 106)

• Such findings regarding American mathematics curricula led SIMS scholar Edward Kifer (1993) and TIMSS scholar William Schmidt (2004) to propose that all students take an algebra-based course in the eighth grade. (Burris, Heubert, Levin, 2006, pg. 107)

• Third, this study does not stand in isolation. Rather, it confirms the findings of other studies suggesting that an enriched, accelerated curriculum is more beneficial to at-risk learners and low-achieving students than a traditional remedial curriculum that slows down instruction (Bloom et al., 2001; Heubert & Hauser, 1999; Kifer et al., 1993; Mason et. al., 1992; Peterson, 1989; White et al., 1996). (Burris, Heubert, Levin, 2006, pg. 132)

Eliminating the option to ‘accelerate’ and enroll in Algebra 1 / Integrated Math 1 in grade 8 in California public schools will likely lead to:

• Students with financial means taking outside math classes to complete calculus in 12th grade, while students without financial means do not
• California students being disadvantaged when applying to college, and to college STEM programs versus students from other states or countries
• California students being disadvantaged when taking standardized tests like the PSAT/ SAT/ACT versus students from other states

Clearly CA students have been able to complete Algebra 1 / Integrated Math 1 in 8th grade and calculus in 12th grade before, in past decades. The opportunity to take AP Calculus in high school makes students more competitive to get into college, to compete for internships in college, and allows them to graduate more quickly. Retaining these pathways to excellence is important for the California public school system.

The California Math Placement Act was meant to encourage mathematics excellence and achievement as well as the appropriate mathematics placement to do so. The draft 2022 California Math Framework’s guidance will do damage to these aspirations, holding students back, while lowering overall math standards.