A Crossroads in California K-12 Math Education

(Updated October 19, 2021.)

The state of California recently developed a new Mathematics Framework for K-12 curricula, generating considerable controversy. Much of the plan had been actually implemented in the San Francisco Unified School District (SFUSD) starting in 2014. SFUSD claims great success with the project, and its publicized statistics have often been cited as a basis for other curricula, including the new statewide plan. Currently, the plan is pending public comment.

In this post, I’ll discuss the motivations underlying this and similar reforms elsewhere in the US, and explain the views of opponents of the plan. I will focus on the San Francisco situation, and will argue that the claims made by SFUSD regarding success of the reform are incorrect and egregiously misleading. Regrettably, it will also be seen that complex racial/class/ideology issues are involved as well.

Motivation

Much of the impetus for these curricular reforms is a laudable desire to improve the math skills of underrepresented minority (URM) students. Indeed, some of the underlying dogma involves anti-racism philosophy.

Among other themes of the philosophy underlying this and other reforms in the US as to how math is taught, the following are especially notable:

• Abandon the notion of telling kids there is a “right” answer, allegedly “white supremacy culture.”
• Abandon the idea that students must show their work in their math solutions, again dismissed as “white.”
• De-emphasize, or downright discourage, offering more challenging courses, notably Calculus, to mathematically-ready students. In San Francisco, these students tend to be white or Asian.

For a while a few years ago, some of the “woke” were even decrying 2+2=4 as purely a “Western” concept, until the claim became a much-ridiculed meme. The SFUSD Board also refused to use acronyms, dismissing them as “white supremacist culture.”

To be sure, a goal of the reforms is to instill confidence in math among URM students, which we all want. The objections by some that early placement of students into ability tracks, typically in the sixth grade, is unfair and counterproductive, have some validity. And some versions of this philosophy are somewhat more nuanced. But as with any movement of this sort, subtleties are lost, and the extremists take conrol, even to the state government level.

Controversy Regarding the New Framework

The California plan, and SFUSD’s already in-place implementation, has generated much controversy, especially among STEM university faculty and parents of K-12 children. Due to my background as a university professor in computer science, a PhD in mathematics, and longtime activist in support of underrepresented minorities (URMs), I share those concerns. I believe the new curricular design will harm the very children the reforms hope to help, while significantly reducing educational quality for mainstream kids.

As of this writing, more than 800 professors, scientists and engineers have signed a petition to California Governor Newsom to revoke the new curricular plans. The governor, who has been defending against a recall effort, has to my knowledge not responded. Some, of course, would say that argues in favor of the recall, given the central importance of math in K-12 education.

Controversy Regarding the SFUSD School Board

Meanwhile, three members of the San Francisco Board of Education (BofE) are facing their own recall challenge. Issues include: BofE’s mishandling of the pandemic in terms of in-person instruction; BofE’s placing priority instead on renaming 44 schools deemed to have ideologically incorrect names (including one named for former-SF Mayor and current US Senator Dianne Feinstein); and BofE’s decision to change the admissions policy of the magnet school, Lowell HS, from test-based to random lottery.

Overview of the SFUSD Curricular Changes

The district has a slide presentation, filled with many graphs showing the impact of the reforms. Slide 2 shows the curricular path under the reforms adopted in February 2014, and implemented starting in the Fall 2014 semester. Under previous policy, students took Algebra 1 in eighth grade, now ninth. The claim was that postponing Algebra 1 by a year would reduce the failure rate. Also, tracking was discontinued, and the notion of heterogeneous classes was celebrated.

College-bound kids used to take Calculus in 12th grade, or even in 11th. Instead, under the new SFUSD program, this became difficult to arrange, and students were encouraged to take AP Statistics instead.

(See further analysis beyond the below. Note too the I analyze some of the qualitative motivations following the data report below.)

The SF BoE Claims: Algebra 1 Failure Rate

The authors of the new California Math Framework base the plan in large part on the claimed success of similar reforms implemented earlier in the SFUSD. As one educational periodical put it,

Many supporters of the new proposal point to examples, such as San Francisco Unified, which in 2014 voted to remove accelerated middle school math classes. Five years after the policy change, the San Francisco Unified graduating class of 2018-19 saw a drop in Algebra 1 repeat rates from 40% to 8%, and 30% of the students in high school were taking courses beyond Algebra 2.

Stanford University professor Jo Boaler, a major proponent of the Math Framework who is often cited in the press, wrote (along with coauthors)

The [SFUSD] policy shift began in earnest five years ago. As of last year, the number of middle-school students with low math-performance rates (students receiving Ds and Fs) dropped by a third. Students in the district who took Algebra 1 in eighth grade in 2014 (the last year it was offered as a stand-alone course to eighth-graders) had a repeat rate of 40 percent. By contrast, the first group of students who took Common Core Math 8 in eighth grade and Algebra 1 for the first time in ninth grade (and who graduated earlier this year) had an Algebra 1 repeat rate of 8 percent. As a result, more students in the district are taking a fourth year of high-school mathematics — and taking advanced classes beyond Algebra 2 — than ever in its history… We congratulate San Francisco Unified on its wisdom in building math sequences that serve all students increasingly well.

These numbers are taken at face value by the press, by legislators and so on. But closer inspection shows a different story.

As noted, the BoE claims a dramatic drop in the Algebra 1 failure rate, from 40% to 8%, from the year before the change to the year of the change. Anyone familiar with educational statistics knows that such a precipitous drop in a major program is virtually unheard of. Could postponing algebra by a mere one year have THAT much of an impact?

Of course, the answer is No. SFUSD declined a freedom-of-information request by a group of concerned San Franciscans to provide the details as to the specific counts that produced those 40% and 8% figures. But the district did provide some other statistics:

There appears to be no way to derive those 40% and 8% figures from the above tables provided by the district, a point conceded by an analyst in the district office. Again, the district declined to provide the numbers making up the numerators and denominators in the 40% and 8% figures.

These were analyzed by educational researcher Ze’ev Wurman, who wrote,

In [2013-]2014, under the previous system, almost 2,400 eighth-graders were placed in algebra, and almost 700 of them scored a C or below; 650 retook algebra in grade nine in 2015. In 2016, almost 3,000 ninth-grade students were placed in algebra, and almost 1,000 of them scored C or below. How many were required to retake algebra? Only 18. In other words, SFUSD changed its criterion for retaking algebra and declared victory, claiming that the change reflects improved achievement. In reality, only 67 percent of students scored an A or B after the change, compared to 70 percent before. So much for the claimed “improvement.”

The “changed criterion” was as follows, at least in part: In implementing the new plan, the district made moving on to Geometry after Algebra 1 (in effect, “passing” Algebra 1) much easier, now requiring only a passing grade in Algebra 1 rather than the old policy, which had been the passing grade AND passing a separate exam. A passing grade is nominally a D, though SFUSD encourages repeating for UC eligibility.

Statewide Test Scores Declined

The most powerful illustration of the failure of the SFUSD reforms is in the statewide test scores. The tests are taken in a student’s junior year, so the last group to take Algebra 1 in eighth grade, the class of 2018, took the exam in 2017. Here are the results, from the California government site:

test year	2017	2018	2019
% pass	53.82%	49.88%	48.61

So, scores dropped substantially in the two years after the change. As one observer put it, “The SBAC scores from 2017-2019 represent just about the closest thing you could get to a controlled experiment in the field of education. The ‘control group,’ the state of California as a whole, registered a slight increase in proficiency over the same period.”

(The tests were not held in 2020, due to the pandemic.)

Impact on Low-SES Students

Again, we see a devastating effect of the BofE policy on statewide math scores, in this case for low-Socioeconomic Status students:

test year	2015	2016	2017	2018	2019
% pass	45.00%	46.00%	49.89%	43.97%	41.66%

Again, that 2017 testing year number consisted of the last cohort of students to matriculate under the old plan. As in the previous table, the percentages are for students meeting or exceeding state standards.

So, the numbers had actually been going up under the old plan, then declined substantially after the new plan was implemented.

This and the similar chart above form a powerful indictment of the new SFUSD plan, and by extension, the pending California plan.

Note too: Children from families of means — both financial and awareness of options — are harmed less than are the more vulnerable kids. The well-off famiies can compensate for the low-quality compressed Algebra 2/Precalculus course (see below), for instance, by having their chldren take private courses, with a $700 course from APEX, or hire private tutors.

The Role of Calculus

The national College Board (a private company) offers AP examinations in a number of basic college-level subjects, including Calculus (AB, BC) and Statistics. Though AP was originally billed as a way to shorten one’s college coursework via credit-by-examination, it eventually became a major criterion for admission to selective universities. Hence the high concern among parents and students regarding difficulty in enrolling in Calculus under the new policy.

Among the math AP courses, Calculus is much more rigorous than Statistics, and thus much more important for impressing university admissions committees. Here is where the timing of Algebra 1 becomes crucial:

Under the old system, a student would take Calculus in the 12th grade or even 11th. The latter is preferable, as it meant that the student would have taken a full year of Calculus before submitting her applications to college, as well having taken the AP exam. Taking the course in 12th grade would still be helpful, as the student would have a semester of Calculus and possibly a Calculus teacher’s letter of recommendation. But moving Algebra 1 from eighth grade to ninth made it impossible to take Calculus even in the 12th grade.

Compression of Algebra 2/Precalculus:

As the San Francisco postponement of Algebra 1 to ninth grade left no room for Calculus, many parents were up in arms. There was a major backlash especially among Asian and white parents in the district, and indeed Asians have been in the forefront of the current recall drive to remove three members of the BofE.

The BofE responded by combining Algebra 2 and Precalculus, each a year long, into one single-year course. The title of the new course is Algebra 2/Precalculus Compression. As the name implies, that meant either skimping on or skipping over many topics in each course. According to one source, the compressed version is missing 25% of basic topics, and missing all advanced topics.

In other words, the basic quality of instruction was compromised.

The SF BoE Claims: Advanced Math Enrollment: AP Calculus vs. AP Statistics

The BofE decided to funnel students into AP Statistics courses instead of AP Calculus. Slide 9 in the BofE presentation shows the increase in AP Stat enrollment, at the expense of AP Calculus.

AP Stat is much, much less mathematically rigorous than Calculus. The college courses it would count toward are of the “Statistics for English majors” type, with absolutely minimal math content. To claim it as “Advanced Math” as the BofE does in Slide 9 is highly misleading.

The BofE’s reasoning was that in this era of Big Data, Statistics is more relevant than Calculus to most students, so the course would among other things prepare some students for careers in Data Science. As a statistician and former Statistics professor, I consider this very highly misleading.

A college Statistics or Data Science major requires Calculus and further advanced math, notably linear algebra. AP Calculus would thus be valuable. By contrast, AP Stat would typically not count as credit toward a Statistics or Data Science major; it is too watered-down.

I do agree that understanding Statistics is important for an informed citizenry. However, very few high school teachers have the depth to teach this subject to that end. Though the math content is minimal, the subject is riddled with subtleties, ignorance of which can lead one seriously astray. Frankly, I do not believe this is a proper topic for high school curricula.

Mode of Instruction

The BofE’s obsession with eliminating tracking led to vast disparities between the least- and most-skilled students within the same classroom. This was justified by the research of the academic cited earlier, Jo Boaler, who wrote (apparently not about SFUSD),

This article describes the ways in which the mathematics department of an urban, ethnically diverse school, brought about high and equitable mathematics achievement. The teachers employed heterogeneous grouping and complex instruction, an approach designed to counter status differences in classrooms. As part of this approach teachers encouraged multi-dimensional classrooms, valued the perspectives of different students, and encouraged students to be responsible for each another. The work of students and teachers at Railside was equitable partly because students achieved more equitable outcomes on tests, but also because students learned to act in more equitable ways in their classrooms. Students learned to appreciate the contributions of students from different cultural groups, genders and attainment levels, a behavior that I have termed relational equity. This article describes the teaching practices that enabled the department to bring about such important achievements.

Note that the overriding theme here is ideology and racial justice, rather than improved math skills. Dr. Boaler did indeed claim improvement in the latter, but I am always skeptical about statistics unless I see the raw data. It does sound plausible to me that the experiment did improve the motivation of the weaker students, resulting in improved performance. But there are other ways to motivate kids than weakening the curriculum.

One of the tenets of this “kumbaya” teaching philosophy is to have students work in groups. My experience over several decades of teaching is that this does not work; it is too passive. It is worthwhile as an instructional supplement, but should not be the main focus.

Race, Class and Ideology Issues

Earlier, we noted that many in the URM educational community view the math curricular reforms in racial/class terms, e.g. with obtaining the right answer and showing one’s work being dismissed as “white.” This is a key point.

BofE member Alison Collins has been under fire for making a series of anti-Asian tweets, which is especially concerning in light of the wave of anti-Asian violence in recent months. (Asians make up 35% of the San Francisco student body.) Some of her tweets that have been much quoted are that Asians “use white supremacy thinking to get ahead,” are “house n*****s”, and “hoard resources.” Collins was not on the board when the math curriculum was changed (she was a parent advocate) and when she made the tweets, but her comments are consistent with the general views in the “woke” education/activist community nationwide that there is an “Asian problem.” California legislator Cristina Garcia, for instance, exclaimed, “This makes me feel like I want to punch the next Asian person I see in the face,” an astonishing remark from an elected official, again especially with the current spate of anti-Asian violence.

One aspect of the national conversation that especially rankles the “woke” activists is the notion of Asians as the Model Minority. Many Black (and some Asian) activists commonly use the term white adjacency to decry Asians’ (and others’) perceived status as “honorary whites.” The term is quite prevalent in “woke” literature on race, used for example repeatedly in this book review. Here is a typical view:

Chow says the model minority myth-based on the stereotype that Asian Americans are hard working, law-abiding individuals and the false perception that such qualities have led to their success over other racial groups — has played a significant role in creating a wedge between Asian Americans and other BIPOC communities. “We were painted as an example, a ‘good minority.’ And then there were examples of ‘bad minorities,’ and that was perpetuated, which created even more divide,” Chow says. He says that among the earlier generation of Asian Americans who immigrated to the U.S., many assimilated to white adjacency in hopes that it would be the quickest path to safety and stability in the country.

Of course, this view is far off the mark. Asian immigrants proceed in the US exactly as they had in Asia, placing a high premium on education and hard work in the economy; it’s not a matter of “defensive assimilation” at all. But as can be seen above, the Asians are viewed as sad “white wannabes” and racial traitors by the “woke.” Collins wrote, “Many Asian Am. believe they benefit from the ‘model minority’ BS,” and, as noted, called Asians “house n*****s.”

AP is basically an elitist institution. The high schools with a lot of offerings are typically populated by well-off students who aspire to Ivy League universities. This elitist nature of AP ties into Collins’ remark about the Asian students “using white supremacy thinking to get ahead.” Indeed, ironically, the AP website is titled “Get Ahead with AP.” AP Calculus in San Francisco, taken mainly by Asians and whites, was thus viewed with disfavor, and replaced by the more plebian — and much less mathematically challenging — AP Statistics.

Many URM teachers put ideology ahead of the 3 Rs. LA Teachers Union President Cecily Myart-Cruz told LA Magazine,

“There is no such thing as learning loss,” she responds when asked how her insistence on keeping L.A.’s schools mostly locked down over the last year and a half may have impacted the city’s 600,000 kindergarten through 12th-grade students. “Our kids didn’t lose anything. It’s OK that our babies may not have learned all their times tables. They learned resilience. They learned survival. They learned critical-thinking skills. They know the difference between a riot and a protest. They know the words insurrection and coup.“

To Be Clear

A few points to make sure readers of this post know where I am coming from:

• I myself once proposed a lottery for Lowell admission. My version was less extreme than that of the BofE, as under my plan test scores would still be used to some extent, but I support the idea in principle. What I object to is the apparent anti-Asian motivation for the policy.
• I oppose tracking of students. The decision of whether a student takes a more sophisticated math course should be up to the parents and the child, not the diktat of some teacher.
• I agree with a point made by Collins that some Asian immigrants have unhealthy attitudes toward Blacks and Latinos.
• I am not a fan of the Tiger Mom view of educating kids.

However, none of this changes my view that the BofE took a tragic wrong turn in adopting its current policy.

Summary and Conclusions

The proposed California Math Framework is modeled largely on the San Francisco curriculum, and its claimed justification is largely the claims of “success” in San Francisco. Yet those latter claims do not stand up to close scrutiny, and the quality of instruction has been demonstrably reduced:

• The much-vaunted failure rate reduction from 40% to 8%, is not borne out by the data at all. The district cannot or will not show the details of those numbers, and they concede the numbers are not consistent with the data that the district did provide.
• SFUSD performance on the statewide math test declined substantially after the math policy change.
• Access to Calculus for the more-skilled students greatly deteriorated. In order to accommodate the policy change, a two-year course sequence leading to Calculus was shoehorned into a single year, with much topical material being jettisoned.
• The reforms, in both SFUSD and nationwide, appear to be driven in significant part by ideology regarding race and class, rather than sound science.

Clearly, the SFUSD policy is a failure, and thus the California plan thus needs a thorough re-assessment, with genuine collaboration with stakeholders, not unilateral decree by ideologues.

The Economist reported in August 2021

…”net exits” from San Francisco (those leaving minus those arriving) rose by 649% — from 5,200 to nearly 39,000 — in the last three quarters of 2020.

Most of the ills of the city have ideological roots: the “woke” takeover of the schools, seen above; alarming levels of unbridled crime, ranging from overt, unchallenged shoplifting to horrifying attacks on Asian seniors, all viewed as due to the “woke” DA, who also is facing a recall; vast “tent cities” of the homeless, with broad-daylight drug dealing and use, prostitution etc., again viewed as due in part to the DA.

Meanwhile, there is an exodus of major tech firms from the San Francisco Bay Area, e.g. with Oracle moving its headquarters to Austin, Texas. Why stay in California with poor schools and declining quality of life?

California is indeed at a crossroads. As a lifelong liberal and a mathematician, I call on the state government to reject the proposed math curriculum, and reverse the coming further decline of the state.