While many people complain about the ideological biases in the California Department of Education’s proposal to revolutionize the state mathematics curriculum, that’s not the main problem. This plan has fundamental issues of concern and will do no child any good.
It is irresponsible to make the entire state a laboratory for very controversial educational theories, and to do this without any review by the mathematics community. Public education should equip all students with logic and abstract-thinking skills. Even if you don’t remember the quadratic formula, the process of learning it made you a clearer thinker. That’s how the entire world teaches math.
Most countries, from Singapore to Zimbabwe, require three or more years of algebra-based classes, five for students seeking careers in science, technology, engineering and mathematics. Yet the proposed California Math Framework deprives students of opportunities to take deep algebra-based classes, and worse, is based on teaching materials that can only confuse a child’s emerging skills in logic and abstract thinking.
Proponents claim California schools’ persistent achievement gap — the demographic discrepancies in educational achievement — requires a revolution in math teaching. The proposal, which could be adopted next year for use in California public schools serving 6 million students, emphasizes exploration at the expense of skills development. This ignores a mountain of evidence that similar ideas have consistently failed when implemented at scale, and a rigorous approach — teaching students to back up answers with logic — is the only method known to decrease the gap. The 1997 California Math Standards, which required teaching algebra in eighth grade, led to a six-fold increase in the number of algebra-proficient low-income students.
Even more worrisome is the plan to replace an algebra-centered curriculum with one emphasizing data science, described as “21st century math.” While this might sound promising, the proposal’s data science pathway minimizes algebraic training so much that it leaves students unprepared for most science-related undergraduate degrees.
The worst issue, however, is that the actual math problems proposed do not withstand mathematical scrutiny.
Take the example of a geometry problem in Chapter Two:
“A farmer has 36 individual fences, each measuring one meter in length … the farmer wants to put them together to make the biggest possible area.”
This problem is completely inappropriate: It cannot be solved without very sophisticated math, rarely studied even in college.
The goal of geometry ought to be to develop logic and the idea of proof — that is, presenting statements to show a mathematical argument is true. Here, however, an answer is declared without even discussing the necessity of a proof; it introduces a wrong idea of what it means to solve a problem — something that college professors struggle to undo.
Another example is a 5th-grade lesson, where a problem with Ms. Hernandez knitting a scarf for her grandson is labeled noninclusive and then modified to one where Mr. Hernandez is knitting a scarf because “guys can knit too.” Unless the authors intend to imply that women should never knit, it is a crime against fundamental logic.
Even if you don’t have children in public schools, are not a professor who has to teach unprepared students or an IT manager struggling to find qualified U.S. citizen employees, this curriculum affects you.
The world as we know it crucially depends on math. Until now, the United States has gotten by because we’ve been able to attract a steady supply of foreigners to do the jobs for which we don’t have mathematically qualified Americans.
But as other countries overtake us in science and technology, and as the world realizes how poorly we educate our young, California weather will not be enough to lure the best people here. We need a mathematics curriculum capable of teaching all students to think clearly and of producing the STEM workforce of the future.
Social justice, while desirable and necessary, will not come about by abandoning mathematical rigor. California taxpayers must demand that people responsible for public math education be trained in real math.