California’s Very Flawed K-12 Math Framework

Six major flaws in the current draft of the K-12 mathematics instructional framework should lead the California State Board of Education to reject it and start over. The board is having a final hearing on the framework on Wednesday, July 12.

1. Unscientific Teaching Methods

Just as there is a science of reading instruction, there is a science of math instruction. The scientific way of teaching math includes:

• having students memorize math facts (like multiplication tables and addition and subtraction facts) and standard algorithms (time-tested math procedures);
• teaching computational procedures and conceptual understanding together (and not as progressives would have it, concepts before procedures);
• stressing that getting answers to problems right and doing so quickly are components of math fluency; and
• bearing in mind that committing math facts and procedures to long-term memory frees the student’s mind to handle novel problems.

Instead, the progressive-education authors of the math framework want students to learn through their own inquiry and self-discovery. The authors give little emphasis to mastery of facts and standard algorithms. The authors want to organize math instruction not in the architectonic system of increasing abstraction in which it has traditionally been taught, but instead in accordance with vague, billowy “big ideas.”

Educational researcher Tom Loveless (retired from the Brookings Institution) says: “The previous framework was very clear that math fluency involves speed and accuracy. The proposed framework rejects speed as being even part of fluency, and that’s a problem.” 

The newly revised framework delays fluency in multiplication and division tables until late in elementary school. This delay will spill over into subsequent math learning, and Loveless believes that many students will be unprepared for Algebra I even by ninth grade.

As I have written before (with my co-author, the late Ze’ev Wurman): 

The framework promotes only the progressive-education approach to teaching math, calling it “student-led” instruction, “active learning,” “active inquiry,” and “collaborative” instruction. But evidence from the 1950s through recent times shows that this way of teaching math is ineffective. That evidence comes from scrutinizing carefully designed studies featuring randomized control and what are called quasi-experiments, which approximate the effect of a randomized assignment of students to different groups. Quasi-experiments look at cases, for example, where two adjoining districts with similar populations or two adjoining similar schools adopt different policies. Both sorts of studies are much stronger evidence than the case studies that progressive educators rely on.

In the spring 2012 issue of American Educator, the magazine of the American Federation of Teachers, top educational psychologists Richard E. Clark, Paul A. Kirschner, and John Sweller summarized “decades of research” that “clearly demonstrates” that for almost all students, “direct, explicit instruction” is “more effective” than inquiry-based progressive education in math.

Clark, Kirschner, and Sweller conclude that after “a half century” of progressive educators advocating inquiry-based teaching of math, “no body of sound research” can be found that supports using that approach with “anyone other than the most expert students.” Evidence from the best studies, they emphasize, “almost uniformly” supports “full and explicit” instruction rather than an inquiry-based approach.

2. Misrepresentation of Research 

Brian Conrad of Stanford’s math department points out that the revised math framework contains much in the way of “false or misleading” descriptions of research on math instruction. It also cites “unpublished papers with design flaws,” instead of relying solely on peer-reviewed published work. Conrad asks: Why does the framework “still not adhere to the level of research quality” called for by the What Works Clearinghouse?

Conrad says that the framework is invoking neuroscience literature “in misleading ways” to promote “pseudo-scientific claims” about progressive-education math instruction improving pathways in the brain.

The framework wrongly cites a paper to promote the general use of “invented strategies” (that is, students devising their own strategies) as a proven approach to learning standard algorithms.

Conrad finds that the framework distorts citations in a way that indicates “an ideological (rather than evidence-based) opposition to acceleration.” He points out that “there is extensive literature with conclusions opposite” that cited in the framework, “but these are barely ever mentioned.” 

As Wurman and I have written before:

State-adopted education programs and recommendations are supposed to be “research-based.” This does not just mean an article or two in a peer-reviewed journal. It means there is a consensus or strong evidence of effectiveness in the published research. If no strong evidence exists, a practice should not be broadly recommended. ...

If the framework writers had wanted solid evidence, they would have relied on the final report and subgroup reports of the 2008 federal National Mathematics Advisory Panel. They would have made even more use of the federal Institute of Education Sciences practice guides, which are designed for teachers and curriculum writers.

3. Rejection of Algebra I in 8th Grade

The revised framework rejects (as did its earlier iterations) the time-honored aim of preparing students to take Algebra I in eighth grade. Eighth-grade algebra is the policy in high-performing foreign countries whose inhabitants will compete with America’s children in the future—and that eighth-grade goal was expressly part of the 1999 and 2006 California math frameworks. This current framework recommends ninth grade as when almost all students should take Algebra I. 

Students who plan to go to selective colleges and universities or who plan to major in STEM fields in college need to pass calculus in high school. Taking algebra in eighth grade allows them to do so. 

Education journalist John Fensterwald points out that: 

To discourage widespread enrollment in eighth-grade algebra, the framework’s diagram laying out STEM and non-STEM course pathways omits eighth-grade algebra as an option. 

There are possible (but laborious and bureaucratically troublesome) workarounds for STEM-inclined students, like double-booking math classes in one year. But the system is not friendly to the workarounds, and they are discouraging to students. As Conrad points out, the framework authors (who are ideologically opposed to acceleration) had three years to come up with a way to accommodate those who need to take calculus in high school, but they didn’t do it. 

The recent effort in San Francisco Unified to make all students take Algebra I in ninth grade, was, as Conrad points out, “a total failure, exacerbating the very inequities it aimed to prevent.”

4. Substitution of Weak Data Science for Rigorous Algebra II

The framework promotes the idea of students taking math-lite data science courses instead of Algebra II. Students who take such math-lite courses will be ill-prepared for math and other STEM courses when they get to college.

In his report on an earlier draft of the math framework, Conrad says of the promotion of these data science classes: “Whatever author is responsible for such a myopic view of mathematics should never again be involved in the setting of public policy guidance on math education.”

5. Knee-jerk Opposition to Tracking and Acceleration

I have previously mentioned the framework’s opposition to acceleration. It also opposes tracking. As Conrad points out, the framework uses “citation misrepresentations” to promote its “anti-tracking narrative” of “heterogeneously-grouped classrooms at all levels.”

Homogeneously-grouped classrooms allow teachers to work more effectively without the need to teach students who are at widely different levels. Students can be evaluated on their achievements in different subjects and placed in accelerated classes only in the subjects where they excel. This avoids the misplacements inherent in across-the-board multi-subject tracking. The framework displays an ideological rather than empirical opposition to ability grouping.

6. Classes in Wokeness Instead of Math

In Chapter 2, the framework pushes teaching methods in math class that emphasize radically egalitarian “social justice” goals. Not only is radical egalitarianism ethically dubious, but math class should be for math, not for political indoctrination. 

For example, the current framework contends that mathematics is to be used to “both understand and impact the world.” It argues that math teachers should hold the political position that “mathematics plays a role in the power structures and privileges that exist within our society and can support action and positive change.”

Furthermore, according to this official California framework, teachers should use mathematics politically “to analyze and discuss issues of fairness and justice.” In an elementary school classroom, teachers would, for example, have students “studying counting and comparing to understand fairness” in the context of current and historical events.

The framework recommends the fringy methods of “trauma-informed pedagogy,” which encourage students to suggest “recommendations and taking action.” Teachers should also, it says, provide “curricular examples” that provide students with a mathematical toolkit and mindset “to identify and combat inequities.” According to the framework, students are “to use mathematics to highlight inequities.” Then they should learn to use mathematics to transform the world – a rather inappropriate task for math class.

Conclusion 

There are close to 6 million students in California. What is done in California public schools influences practices in the rest of the country. Parents and taxpayers want math to be taught sensibly. It’s just a scientific reality that children need to learn math facts and standard algorithms. This current California counterproductive math instructional framework will produce a repeat of the Math Wars of the 1990s or a deeper rebellion against public schools and in favor of parental choice.