Latest on the California Math Wars

For the last couple of years, the California educational community–teachers, administrators, parents of students, STEM academicians–has been embroiled in a controversy over K-12 math curricula. Concerned that many underrepresented minorities (URMs) run into major obstacles in high school math, a proposed new plan has been developed, the California Mathematics Framework (CMF), spearheaded by Stanford education professor Jo Boaler. The State Board of Education is due to decide on the fate of the CMF next month.

A major theme of the CMF is to develop “alternative math curricula” in Data Science (DS). The CMF proposes that students be allowed to take DS in lieu of Algebra 2.

Advocates of CMF-style curricula have already convinced the UC and CSU systems to add DS to the list of Advanced Mathematics courses that count for UC/CSU admissions eligibility.

But while improving conditions for URMs is a laudable, indeed imperative goal, blindly approving drastic policy changes without due diligence in considering the consequences is extremely irresponsible. Actually, thousands of STEM professors and professionals have signed petitions in opposition to the CMF. As I have written here earlier, I am one of those critics.

My current post is in response to an article by Pamela Burdman (PB), a former education writer for the San Francisco Chronicle, who argues that the “alternatives to classical math” notion is beneficial to students in general, not just URMs.

Let’s take a look…

“First, Do No Harm”

As noted, thousands of STEM professors and professionals have signed petitions in opposition to the CMF. What are they worried about?

Data Science is a buzzword that boils down to drawing some histograms, telling some stories and learning a bit of statistics. The proponents of this alternative approach cite the booming role DS is now playing in technology, and claim that adding a DS alternative would enable students to participate in that boom. But though the boom is real, those expectations are sadly false. A college degree in DS requires lots of math–calculus, linear algebra, calculus-based statistics and so on. DS jobs, or jobs making heavy use of DS, are not open the people who didn’t even take Algebra 2.

As I have written earlier, the CMF would hurt the very students it purports to help, the URMs. Not only would it make false promises to the students regarding their employability, but also their mastery of math basics would suffer.

The latter is no idle speculation. The San Francisco Unified School District (SFUSD) has basically been implementing the CMF in the last few years, with disastrous results in the statewide math tests: Scores for low-socioeconomic status (low-SES) children declined after the new curriculum was implemented, while scores for low-SES California kids statewide were rising. Such tragic consequences should give pause to anyone inclined to support the CMF.

The Burdman View

I am a longtime admirer of PB, both as a Chronicle reader and as one of her interviewees some years back. However, I feel she has missed the mark in this case.

Ever the journalist, PB does not bury her lead. She makes her goals clear from the outset:

The recent debate over California’s proposed math framework is missing the forest for the trees. In its myopic focus on which advanced math courses best prepare high school students for their futures, it glosses over a glaring fact: More than half of California seniors take no advanced math course at all…

[In 2018] [m]ore than 200,000 students left high school without the benefit of any advanced math. These students were more likely to be Black, Latino and low income than students taking advanced math…

California educators can ill afford to disagree over the value of a more traditional precalculus or calculus course versus a rigorous course in statistics, data science or mathematical modeling. Both are valuable — the former as preparation for the fields of science, technology, engineering and math, or STEM, with the others aligning well with an interest in fields such as psychology, law or political science. Rather than prejudge students’ choices — or preclude them from making choices — educators should focus on making multiple rigorous options available.

That Elusive Word, “Rigor”

There are major problems here from the git-go. The proposed DS curricula are anti-rigor. They water down the material.

For example, the CMF proposal’s coverage in statistics omits many key topics in the existing high school statistics course, such as binomial distributions and Bayes’ Rule. These topics are not in the much-praised DS curriculum designed by UCLA for the LA Unified School District either.

These are not frills. For instance, the binomial distribution is the basis for the Margin of Error reported in presidential and other pre-election polls, numbers that every informed citizen must understand. And Bayes is the basic principle underlying predictive analytics, the reason for today’s DS boom.

The UCLA/LAUSD curriculum is much shallower than even the level of its intended audience (students without Algebra 2) would imply. For instance, consider the material on histograms. It makes a big issue of observations that happen to fall on the boundary between two bins–but it says nothing about the much more fundamental issue of why the width of the bins matters.

In other words, the proposed DS curricula do not meet PB’s calls for rigor at all. The curricula are in fact deliberately watered down, based on the implicit–and egregiously insulting–assumption that URMs are incapable of doing Algebra 2 and so on.

To be sure, I do not ascribe such an attitude to PB. As seen in her opening above, for PB it is an issue of personal preferences and aspirations. Not every high school wants to become a physicist, so why make them take calculus, or even trigonometry (trig is part of the Precalculus course)? Why not a rigorous course in DS, for instance?

The problem is, again, that the DS courses are not rigorous. A DS course cannot be rigorous without some serious math. That math need not involve calculus, but it at least requires precise statements of the principles, goals and methods, and extensive use of algebra. The CMF, by omitting the binomial distribution from its statistics coverage, won’t even allow math as basic as a summation.

One major problem with teaching DS in high school is that most DS teachers would lack a degree in DS or Statistics. DS is a very subtle, highly-nuanced field, one in which it is easy to make serious, highly consequential errors. This has been exemplified repeatedly during the Covid pandemic. So it’s not enough to merely train DS teachers with a special short course, for instance.

Why the Need for Advanced Math?

In decrying the fact that so many California students do not take advanced math, PB does not really address the more fundamental issue of why advanced math is important. Let’s do so here. I would cite several points:

1. Everyone needs a solid understanding of math, as responsible citizens and informed consumers. Actually, a GOOD data science course, making extensive use of algebra rather than replacing it as a requirement, would be quite impactful in this regard. I gave the election poll example above, but it’s much more than that. Policy issues, say Universal Basic Income, are inherently data-driven, and understanding them relies much more of a grasp of, say, the slope of a line than on the ability to draw a histogram. Purchasing insurance is, at its core, an issue of probabilities and expected values; should I buy earthquake insurance, given my personal situation? The same holds in the medical realm, whether it be understanding a disease survival prognosis, comprehending the analysis of genetic counseling, etc.
2. The value of mathematics goes beyond mere “usefulness.” Math builds one’s reasoning skills, an extremely important goal. The “alternative math” crowd asks, e.g., “Why learn how to solve quadratic equations? Most students will never use it in the future.” Actually, the quadratic formula rarely if ever comes up even in courses for college math majors. But that’s not the point. The quadratic formula shows how one can apply reasoning to solve a particular type of problem; it is a testament to human ingenuity, inspiration for solving today’s problems, even the nonquantitative ones.
3. One does not develop true skill in math course n until one takes math course n+1, or even n+2. Learning math is all about reinforcement. One learns Algebra 1 by taking Algebra 2.
4. As shown by the late Jaime Escalante, it’s possible to inspire URMs to do well in advanced math, even scoring highly nationwide. Instilling such confidence is the best way to help URMs.

Again, the Elusive Matter of Rigor

Well, then, isn’t the notion of “alternative advanced math” tenable as long as rigorous standards are upheld? Frankly, this is naive. This is just not the way educational institutions work.

Those who set curricula care only about topical content, not the level at which the content is taught, and who can blame them? Requirements of rigor are difficult if not impossible to enforce, and unpopular with students. And, just as water naturally seeks its lowest level, the same is true for the level of intellectual involvement one expects of the students. The harsh truth is that it’s a Race to the Bottom.

Even the thoughtfully crafted UCLA/LAUSD DS plan (linked to above) will at best not have anywhere near the intellectual content of existing advanced math curricula. It already omits important topics, a couple of which I mentioned, and it will inevitably succumb to the Race to the Bottom syndrome. And again, it will not be taught by teachers who have the necessary background.

The Reprehensible Bottom Line

And DS will not be the respectable alternative that PB describes. It will inevitably be viewed by students as the WEAK alternative. And tragically , the DS student population will be predominantly URMs, just as planned by the CMF people. DS will be viewed as “Math for URMs.” Ironically, given the CMF crowd’s opposition to tracking (I agree with them), DS will be the New Tracking.

EdSource interviewed Shirley Guzman, Assistant Principal of Phineas Banning HS in Los Angeles. The Banning student body is 94% Latino, and nearly 90% qualify for government subsidized lunch. Guzman explained, “We have to step away from thinking that there’s only one way [to get into college]. Now we can tell students they can take statistics or computer science [instead of Algebra 2].” Again, sadly that “second way” will be viewed as “the URM way.”

And this is no accident. The head of the UCLA/LAUSD data science program cited earlier has stated clearly that DS is intended to be “Math for URMs”:

It should be noted that IDS is not intended as a curriculum for elite schools or elite students. It was developed in close cooperation with LAUSD teachers and administrators to enhance education in a school district in which 80% of the students are below the poverty level and 20% are English learners.

Worst of all, CMF would merely mask the root causes for the poor math performance of URMs. The URMs will not only be the underclass, but also the permanent underclass. Is that we want?

Is this the best we can do for URMs–shunt them off into the “stupid class”? Wouldn’t it be far better to find inspiring teachers who can uplift the URMs? Escalante poured his life into the class, ranging from friendly Spanish-language insults (“You burros“) to intensive interaction with the students’ parents.

In reading PB’s comments about tailoring course requirements to student aspirations, please read this profile of Escalante and his former student Erika Camacho. Her original aspiration in high school was to become a cashier; instead, Escalante’s class completely changed her world view. She went on to earn a PhD in math, and is now a math professor at Arizona State University.

The choice is clear: We need more Jaime Escalantes, not more Jo Boalers.

My Background

What informs my views in this post?

DS is often described as a blend between statistics and computer science. I have taught both, and in fact was a founding member of both the Statistics and Computer Science Departments in my university, UC Davis. I am the author of an award-winning book in the DS field, and am a recipient of my university’s Distinguished Teaching Award. My current research interests are machine learning and data security. I have served in an editorial capacity in two data science journals, including as Editor-in-Chief of the R Journal.

And, related to the CMF’s professed goal of improved education for children of color, immigrants and so on, I wish to point to my lifelong passion for social justice.  I have participated in a number of university programs to increase our minority population, and have served as chair of our university Affirmative Action Commmittee.  I was humbled to be selected for my university’s Distinguished Public Service Award. I am a former English As a Second Language teacher, and have even taught a brief volunteer course in probability for 6th-graders.