Equity Comes for Math
The proposed changes to the California K-12 Mathematics Framework would further harm the most disadvantaged students in the state
Background
In May of 2019, the California State Board of Education (SBE) approved a timeline to revise the state’s K-12 Mathematics Framework. A curriculum framework is an implementation guide for California local educational agencies (LEAs)1 on how they should implement state standards for educational instruction. The revised California Math Framework (CMF) is currently in draft form and goes by the title “2021 Revision of the Mathematics Framework.” In other words, the CMF is the operating manual for all K-12 public schools to teach the state math standards to its 6 million students.
The first 60-day public comment period on the CMF ended on Apr. 08, 2021. Some 35,000 public comments were received during the first public comment period. The comments were reviewed by the state’s Instructional Quality Commission (IQC), an advisory board to the SBE originally established in 1927, and they reportedly approved changes to the draft Framework, but pushed back the timetable for the release of the second draft by 10 months under a withering barrage of critical comments. Typical of the criticism was a joint letter from over 600 current or former California mathematics professors; Science, Technology, Engineering, and Mathematics (STEM) instructors, professionals, venture capitalists, or business executives; and current or former education or school officials or administrators who concluded:
“California is on the verge of politicizing K-12 math in a potentially disastrous way. Its proposed Mathematics Curriculum Framework is presented as a step toward social justice and racial equity, but its effect would be the opposite—to rob all Californians, especially the poorest and most vulnerable, who always suffer most when schools fail to teach their students. As textbooks and other teaching materials approved by the State would have to follow this framework and since teachers are expected to use it as a guide, its potential to steal a promising future from our children is enormous.
The proposed framework would, in effect, de-mathematize math.”2
Progressive media organizations such as the Los Angeles Times, usually supportive of the latest progressive educational reform initiatives to emerge from Sacramento, surprisingly expressed their disapproval of the plan as well:
“In ways, the new guidelines might open a new era of intriguing mathematics education that inspires the students who were given too little opportunity to show that they, too, had ‘math brains.’ But to the extent that the framework would rein in talented students who are ready to rev forward, it could be the catalyst that prompts many families to flee the traditional public school system and seek out charter and private options. That’s not the sign of a successful new math.”3
The LA Times joined the Mercury News, the Orange County Register, and the Santa Cruz Sentinel among California newspapers that came out against the draft framework.
In response, the IQC decided at their May 19 & 20, 2021 meeting to slow down its CMF development timeline. While originally targeting CDE adoption of the final Framework revision in Nov-Dec 2021, the IQC decided instead to revise the first draft and add a second 60-day comment period from December 2021 to February 2022, with SBE approval slated for May 2022.4 The IQC has not announced when the second draft of the CMF will be released.
When completed, the CMF will replace the 2013 Mathematics Framework, which was the first guide for implementation of the then newly adopted California Common Core State Standards in Mathematics (CCSS-M.) The CCSS-M were adopted in California by the SBE in August 2010, part of a lightning fast adoption of the controversial Common Core State Standards Initiative across the United States.5
In this article I provide historical context on how the proposed changes to the 2021 CMF diverge from previous math frameworks in the state. I then argue that the proposed changes will only further disadvantage California’s already low-performing students in mathematics competency and preparedness for college and careers in STEM fields.
Common Core’s Lofty Goals
The adoption of the CCSS-M in 2010 represented a sizable shift in the teaching of elementary and high school mathematics in California. The major “instructional shifts” emphasized by the architects and supporters of Common Core were:
Greater focus on fewer topics.
Greater coherence in the standards (i.e. linking topics and thinking across grades.)
Increased rigor. The sales pitch still used to this day is the CCSS-M promoted conceptual understanding in addition to procedural skills and fluency.
Note that the third announced shift was an aspirational goal only – several educational think tanks and researchers that reviewed the CCSS-M found them less rigorous than California’s previous 1997 math standards.6 The writers and supporters of the CCSS-M overstated the rigor in the new standards at the time of their adoption and educators to this day often repeat the hollow claim that the CCSS-M were “internationally benchmarked” against standards in mathematically higher performing countries. California students suffered as a result of the actual real-world reduction in mathematical rigor.
In high school mathematics, the biggest change to the mathematics standards in California was the end to “Algebra for All.” The “Algebra for All” initiative had been a key part of the previous math standards, adopted in 1997 as a response to the disastrous experiment with “fuzzy math” during the 1989-97 period.7
According to the 1997 California math standards, Algebra I was to be taught to all students by 8th grade. But the 2010 CCSS-M standards pushed Algebra I out to 9th grade. The delay in Algebra I was baffling – the 1997 standards had witnessed remarkable success in improving the math preparedness of California high school students. As evidence of the impact of the 1997 standards, when they were first implemented in 1999, only 16% of California’s 8th graders were taking Algebra I or higher, but by 2013 (the last year before the CCSS-M were put into effect by the 2013 Mathematics Framework), that number had multiplied four-fold: 67% of 8th graders were taking Algebra I.
The delay in teaching of Algebra I in CCSS-M espoused in the 2013 Mathematics Framework was justified by a questionable reading of a key 2011 study by Trish Williams, et al. entitled “Preparation, Placement, Proficiency: Improving Middle Grades Math Performance.”8 In addressing the issue of course placement in mathematics and to justify the recommendation to delay teaching of Algebra I, the authors of the 2013 Mathematics Framework wrote about the 2011 Williams paper:
“Algebra I refers to courses that were in place under the 1997 California mathematics standards, prior to the adoption of the CA CCSSM. A big difference is that the CA CCSSM have rigorous grade-eight standards, but the California standards adopted in 1997 did not have specific standards for grade eight. Over the past decade, there has been a dramatic increase in the number and proportion of eighth-grade students enrolled in Algebra I in California. Williams et al. (2011) reported that, between 2003 and 2009, the percentage of grade-eight students taking Algebra I increased from 32 percent to 54 percent. Although the increase in grade-eight enrollment in Algebra I resulted in greater percentages of grade-eight students achieving either ‘Proficient’ or ‘Advanced’ on the Algebra I California Standards Test, it also led to larger numbers of grade-eight students achieving ‘Far Below Basic’ or ‘Below Basic’ on the test (Williams et al. 2011). Williams et al. (2011) concluded that the practice of placing all eighth-graders in Algebra I, regardless of their preparation, sets up many students to fail.”9
To paraphrase the fallacious logic used by Williams and the 2013 Framework authors, a greater percentage of California 8th graders took Algebra I in 2009 than in 2003, but greater numbers of students performed poorly. They compared the percentage in one year, to the number in another. In other words, they compared apples and oranges. More than two times as many California students were taking Algebra I by 8th grade in 2009 than had taken it in 2003. It is a mathematical truism that if a larger percentage of a group does something, then a larger number of that group will do that thing. Larger numbers of students took Algebra I and larger numbers were represented in all seven of the performance bands on the end-of-course Algebra I California Standards Test’s (CST), not just in the lowest performing bands:
The authors should have instead compared the percentage of students in performance bands on the Algebra I CST over time. If the researchers had looked at the data, they would have seen that a larger percentage of students performed well (defined as “Proficient” or above in the performance bands) on the Algebra I CST in 2009 than in 2003, and a lower percentage of students performed poorly (defined as “Below Basic or below” in the same performance bands.) In other words, including Algebra I in the 8th grade curriculum actually improved overall student performance.
Minority students were the biggest beneficiaries of the “Algebra for All” movement – five times as many African-American students, and six times as many Hispanic and lower socio-economic status students were deemed “Proficient or above” in Algebra I by 2013, while the improvement rate for all students was only 3X.10 This may in part have been due to the phenomenon observed by some scholars that minority students were misplaced in higher math courses in high school,11 a practice that was attempted to be remedied by the California Mathematics Placement Act of 2015. Put succinctly, raising the standards for all students helped raise the achievement results more for those who had been held back by inequitable placement practices. This success should be kept in mind when considering the proposed changes in the 2021 CMF.
While the Algebra I benchmark is the most prominent metric to indicate the success of the 1997 California math standards, downstream effects in higher math courses were also observed. More students took and completed Geometry, Algebra 2, Pre-Calculus, and Advanced Placement (AP) Calculus during the pre-Common Core period from 1999 to 2013.12 And as would be expected, more students were prepared for entry into college, particularly in STEM majors. Math remediation rates at the California State University (CSU) system13 dropped from 54% in 1998 to 28% by 2014:
Common Core’s Inferior Results
With the switch to the Common Core math standards completed for most public school districts across California by 2013, the remarkable gains realized from the 1997 California math standards were wiped out with breathtaking speed. Enrollment in Algebra I or above by 8th grade plummeted from 67% in 2013 to below 20% four years later. Historically marginalized minorities fell even further than the average – the rate for Black students dropped from 47% to 18% and for Hispanic students from 52% to 12% over the same period.
Not all districts adopted the CCSS-M the same way. Some districts in higher income areas that had worked hard to achieve “Algebra for All” gains under the previous 1997 California math standards did not move Algebra I out to 9th grade as the CCSS-M advised most schools to do, and to this day see more than 50% of their students complete Algebra I by 8th grade.15 Most other high-performing districts that do not outright achieve >50% of students in Algebra I or above by 8th grade retain multiple math pathways in middle and high school that allow some of their students to accelerate in mathematics. This practice of providing multiple pathways based on ability, called tracking, is among the primary pedagogical practices targeted for elimination in the 2021 draft CMF. Meanwhile, most lower-performing school districts, as well as many average and high-performing ones, followed the CCSS-M’s recommendation to delay the teaching of Algebra I until 9th grade.
As demonstrated by the effects of the 2010 CCSS-M and 2013 Mathematics Framework reviewed above, slowing the progression to higher math had a devastating downstream effect on college readiness. Though more students took AP math exams (i.e. AP Calculus AB, AP Calculus BC, and AP Statistics) as the popularity of the AP program continued to grow, the pass rate (score of 3 or above) declined after 2013. Math remediation rates for California graduates at universities increased after the adoption of Common Core. Realizing California students were less prepared for college, the CDE prompted the CSU chancellor to issue an executive order ending the CSU math placement exam in 2017, over the principled objection of CSU STEM professors.16 The SBE and Common Core’s supporters asserted that California high school graduates were adequately prepared for college math requirements in spite of the lack of placement testing. Real-world results, however, showed students less prepared, resulting in CSU amending its graduation math requirements to accept non-Algebra based courses such as statistics and computer science.
And just as minority students had benefitted the most from the 1997 California math standards, they suffered the most from changes ushered in by the CCSS-M. After the adoption of CCSS-M, AP Calculus AB and BC success rates (i.e. a score of 3 or higher) for Black students dropped far more than for other ethnic groups.
Given the dismal failure of the CCSS-M to improve college readiness of California’s nearly 2 million public high school students, one might expect the CDE to have learned from its mistake and either returned to the previous 1997 standards, or changed direction allowing LEAs more latitude in reversing the damage caused by the CCSS-M. Instead, the CDE appears to have given up on actual mathematics education and instead capitulated to the political agenda of progressive math reformers and activists at the vanguard of the math equity movement.
The Push for Equity
The shift in the California’s math direction from actual math education to social justice is boldly proclaimed in chapter 1 of the new CMF:
“A fundamental aim of this framework is to respond (sic) issues of inequity in mathematics learning; equity influences all aspects of this document.”17
The authors then lay out their equity battle plan for transforming the CMF, listing the principles that guided their work:
“Some overarching principles that guide work towards equity in mathematics include the following:
Access to an engaging and humanizing education — a socio-cultural, human endeavor — is a universal right, central among civil rights.
All students deserve powerful mathematics; we reject ideas of natural gifts and talents (Cimpian et al, 2015; Boaler, 2019) and the “cult of the genius” (Ellenberg, 2015).
The belief that “I treat everyone the same” is insufficient: Active efforts in mathematics teaching are required in order to counter the cultural forces that have led to and continue to perpetuate current inequities (Langer-Osuna, 2011).
Student engagement must be a design goal of mathematics curriculum design, co-equal with content goals.
Mathematics pathways must open mathematics to all students, eliminating option-limiting tracking.
Students’ cultural backgrounds, experiences, and language are resources for learning mathematics (González, Moll, & Amanti, 2006; Turner & Celedón-Pattichis, 2011; Moschkovich, 2013).
All students, regardless of background, language of origin, differences, or foundational knowledge are capable and deserving of depth of understanding and engagement in rich mathematics tasks.”
Thereupon follows the authors’ plans to reimagine public K-12 mathematics education in California. Remember that the purpose of a curriculum framework is to provide a guide for LEAs to implement the already existing and unchanged 2010 mathematics standards. Instead the 2021 CMF spends over 800 pages failing to address California’s extant K-12 math standards – the CCSS-M – and introducing instead a vision for reforming mathematics instruction through fanciful theories backed up by dubious studies. Many of the changes recommended not only stray from the CCSS-M, they introduce whole-cloth new courses of study and a third pathway (the Mathematics: Investigating & Connecting or MIC) for high school math. Targeted for elimination are tracking, acceleration, gifted programs, the “mathematics pathway system” (i.e. creating different pathways in middle and high school for students of different math aptitude and goals), Algebra 2, Calculus, “rote procedures”, accuracy, direct instruction, timed tests, and anything that the 2021 draft CMF authors believe results in disparate outcomes by race, gender or other protected class of students.
Where did this shift of focus to achieve “math equity” come from?
Look no further than the sources referenced by the CMF’s authors. 48 references in Chapter 1 include such reputable mathematics journals as:
International Journal of Environmental & Science Education
Social Psychology of Education
Journal of Urban Mathematics Education
Journal of Latinos and Education
Even more illuminating, fully one-sixth of the 48 references in the first chapter alone are to articles (many in unrefereed journals) and books by the CMF’s lead writer – Jo Boaler.
A Pathway to Equitable Math Instruction
As revealing as the first chapter is in outlining the CMF’s objectives, Chapter 9 reveals the primary source of the push for equity. The title of Chapter 9 of the CMF is “Supporting Equitable and Engaging Mathematics Instructions.” Our first clue to the primary driver of equity is the chapter’s preface:
Note to reader: The use of the non-binary, singular pronouns they, them, their, theirs, themself, and themselves in this framework is intentional.
The practice of introducing one’s preferred personal pronouns has become commonplace as an act of performative allyship – to indicate that the speaker is familiar with and conversant in social justice language, ideology, and expectations. The use of first-person plural pronouns in prose forms a similar function – announcing to the reader that the authors are fully versed in proper woke etiquette and what follows is aligned with social justice presuppositions.
The chapter’s authors make no attempt to disguise their intent. They proclaim it on page 8:
“Mathematics education has a long history of inequitable access to rich learning (see Chapter 1 and Chapter 2 for more discussion of this topic). It is incumbent on all in education to seek or create professional learning experiences that are designed to help teachers challenge and overcome the legacy practices that continue to perpetuate these inequities in access and attainment. Even when professional learning is designed with a different primary focus (mathematical practices, particular instructional routines, or teaching from big ideas, for instance), the implementation of these ideas should reflect culturally relevant and sustaining ways, and include awareness of and attention to the impacts of unconscious bias on students’ experiences in the mathematics classroom.
More importantly, the field should prioritize professional learning opportunities that focus primarily on equity in mathematics education; equity cannot be an afterthought to more traditional mathematics content-centered offerings that do nothing to address the fact that ‘Black, Latinx, Indigenous, women, and poor students, have experienced long histories of underrepresentation in mathematics and mathematics-related domains’ (Martin, 2019; see also Martin, Anderson, & Shah, 2017). Inequities caused by systemic issues means that a ‘culture of exclusion’ persists even in equity-oriented teaching (Louie, 2017). Many of the stories that we use to define mathematics, and to talk about who does or is good at mathematics, are highly racialized and English language-centric, and are experienced that way by students (Lue & Turner, 2020). This means students’ mathematics identities are shaped in part by a culture of societal and institutionalized racism. Professional learning in mathematics can respond to these realities and aim for more than incremental change (which does little to change the framing narratives that drive inequities).”18
So according to the chapter’s authors, professional mathematics education should focus on achieving social justice, not secondary, less important objectives like mathematical practices or instructional routines. “Equity cannot be an afterthought.”
In the very next paragraph, the source of these rather radical proclamations is revealed:
A Pathway to Equitable Math Instruction (Education Trust West, 2020) is a guide to building equity in mathematics teaching (see https://equitablemath.org). It was developed by California educators through a comprehensive partnership of mathematics education and equity organizations. While written specifically to address grades 6–8, the broad outline of the path that is outlined is applicable to all grades:
Stride 1: Dismantling Racism in Mathematics Instruction: Exercises for educators to reflect on their own biases to transform their instructional practice
Stride 2: Fostering Deep Understanding: Methods for deepening content understanding and relevance through crafted mathematics discussions
Stride 3: Creating Conditions to Thrive: Environments and practices that support students’ social, emotional and academic development
Stride 4: Connecting Critical Intersections: The interconnectedness of English language learning and the development of mathematical thinking
Stride 5: Sustaining Equitable Practice: Coaching structures that support mathematics educators in their ongoing centering of equity principles
A cursory detour into the writings of A Pathway to Equitable Math Instruction reveal some startling assertions:
“White supremacy culture shows up in math classrooms when... The focus is on getting the ‘right’ answer.”
“The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so. Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict.”
One of the five strides asks teachers to engage ‘instructional coaches’ who have “the potential to scale their impact to a number of classrooms and students in order to dismantle the culture of white supremacy that exists within the math classroom.”19
A callout box on page 12 of Chapter 9 of the CMF describes “Characteristics of Antiracist Mathematics Educators”:
“Design a Culturally Sustaining Math Space
Center Ethnomathematics
Make Rigor Accessible Through Strong and Thoughtful Scaffolding
Prepare Students of Color to Close the Gap in Access to Stem (sic) Fields
Embrace and Encourage Multiple and Varying Ways of Sharing, Showing, and Communicating Knowledge
Support Students to Reclaim their Mathematical Ancestry”
Chapter 9 does not help us to understand what is a “culturally sustaining math space” or “mathematical ancestry.”
Many of the 35,000 public comments received on the first draft of the CMF focused on the overtly political focus of Chapter 9. The CDE writes that the IQC responded by removing the reference to A Pathway to Equitable Math Instruction20, though the supposed changes to the first draft have not been published yet.
A Framework for Mathematics or a Framework for Social Justice?
Given the overt pedigree of the 2021 draft CMF to social justice organizations, scholarship, and advocates, and its failure to achieve its stated purpose of guiding public schools and districts in implementing the 2010 CCSS-M standards, is it any wonder that a veritable army of parents, educators, STEM professionals, concerned citizens, and organizations have risen up and voiced concerns about it? The response of the IQC so far has been meager and tone-deaf. It purports to have removed “a reference” to some objectionable material, but there is no proof of even that modest response. The CDE’s FAQ on the CMF provides equally tepid responses to similar concerns about eliminating math programs and opportunities for gifted students, eliminating math acceleration prior to 11th grade, and ending LEA’s freedom to offer Algebra I or Integrated Math 1 prior to 9th grade. The tepid response is not only concerning, but is contradicted by the very policy recommendations contained within the CMF itself.
How the CDE responds in the announced second draft of the CMF will speak volumes as to the state’s true intent and how well it listens to the concerns of California citizens.
In the next article in this series, I will address some of the more troubling pedagogical claims and cited research sources in the CMF.
A Local Education Agency is a public board of education or other public authority within a state that maintains administrative control of public elementary or secondary schools in a city, county, township, school district, or other political subdivision. Source: https://edsource.org/glossary/local-education-agency-lea
The joint letter , titled “Replace the Proposed New California Mathematics Framework,” was hosted on the Independent Institute’s website and continues to solicit signatories. When the joint letter was first presented to California Governor Gavin Newsom, State Superintendent of Schools Tony Thurmond, the State Board of Education, and the Instructional Quality Commission, there were about 650 signatories. That number has grown to 852 as of Sep. 01, 2021.
“Editorial: Adding up California’s new-new-newest math,” Los Angeles Times, June 03, 2021.
Mathematics Framework FAQs: Information and frequently asked questions questions about the draft Mathematics Framework. https://www.cde.ca.gov/ci/ma/cf/mathfwfaqs.asp
41 of the 50 US states adopted the Common Core State Standards in 2010, and by the next year 46 of the 50 United States had adopted either the English or mathematics parts of the Common Core standards. However, grass-roots opposition soon emerged and since 2011 nine states have repealed the Common Core standards -- Alabama, Arizona, Florida, Indiana, New Jersey, Oklahoma, and South Carolina. https://en.wikipedia.org/wiki/Common_Core_State_Standards_Initiative
In 2010, the Thomas B. Fordham Institute graded the 1997 California math standards an “A”, writing that, “California’s (mathematics) standards could well serve as a model for internationally competitive national standards.” Fordham found California one of a handful of states with standards superior to the CCSS-M slated to replace them at the time.
The standards used during the 1989-97 period were based on 1989 National Council of Teachers of Mathematics (NCTM)’s curriculum and evaluation standards.
Williams, Trish, Edward Haertel, Michael W. Kirst, Matthew Rosin, and Mary Perry. “Preparation, Placement, Proficiency: Improving Middle Grades Math Performance.” Policy and Practice Brief, EdSource, February 2011. Mountain View, CA.
Evers and Wurman, (2018).
Niu Gao and Sara Adan, “Math Placement in California’s Public Schools,” Public Policy Institute, November 2016.
Evers and Wurman, (2018).
The California State University system enrolls over 485,000 students in 23 campuses across California.
As an aside, note the steep rise in math remediation rate during the pre-1997 California math standards era – the “fuzzy math” experiment based on the disastrous 1989 NCTM standards.
Los Gatos-Saratoga Join Union High School District, home to Los Gatos and Saratoga High Schools which year after year are rated among the best public high schools in California has close to 80% of its students in at least Algebra I by 8th grade while nearby Palo Alto Unified School District has over 50% of its 8th graders in Algebra I or above.
Larry Gordon, “Cal State trustees leave intact remedial education reforms while officials warn of tuition hike,” EdSource, Nov. 07, 2017.
Paul Bond, “Math Suffers From White Supremacy, According to a Bill-Gates Funded Course,” Newsweek, Feb. 23, 2021.
Mathematics Framework FAQs, Ibid.