California Removes Memorizing Times Tables

COMMENTARY

Did you know that a generation of students may not be told to memorize their times tables?

Welcome to the new California Mathematics Curriculum Framework, a State Board of Education-approved document providing guidance to teachers, districts and textbook publishers on how to teach math to California’s nearly 6 million public school students.

The California Common Core State Mathematics Standards describe the officially approved math content students are expected to learn, and the framework is supposed to cover how to teach these standards. The standards have not changed, the framework has.

This framework was adopted in 2023 despite significant public opposition. Public comment was three to one against it, and multiple open letters signed by over 1,000 college STEM faculty pointed out its many harmful flaws. Strikingly, this framework removes all mention and guidance that students should memorize their times tables.

Since California sets trends for education across the country, this is of national concern.

Is memorizing multiplication tables important for students?

Nationally convened expert panels assessing requirements for high school math readiness, in particular algebra, say it is. The National Mathematics Advisory Panel’s final report concluded: “Computational facility with whole number operations rests on the automatic recall of … multiplication and related division facts.”

Secondly, the federal Institute of Education Sciences discusses that without quick retrieval of math facts “students will struggle to follow their teachers’ explanations of new mathematical ideas,” while “automatic retrieval gives students more mental energy to … execute multi-step mathematical procedures.” They conclude, “Building automatic fact retrieval in students is one (of many) important goals of intervention.”

The reasons for this advice become clear watching fourth-grade students solve problems like 52÷7. These are a snap for students with their times tables memorized, but become skip-counting exercises, or yet again perusing written-out times tables, for students who don’t.

Cognitive load theory describes how working memory, where information is manipulated and processed, is limited and easily overloaded. Students without multiplication tables memorized will be “stopped cold” when attempting multi-step problems requiring deduction, because their working memory is occupied calculating simple math facts. In contrast, students who readily retrieve these facts nearly instantaneously from long-term memory have freed up their working memory, better positioning themselves for successful problem-solving.

California’s State Standards recognize all the above, making times tables memorization unequivocal. Standard 3.OA.7 explicitly requires that third-grade students should be able to “fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division … or properties of operations. By the end of Grade three, know from memory all products of two one-digit numbers.”

Legitimate framework guidance on teaching 3.OA.7 is found in the previous framework from 2013. It included the full standard, verbatim. It spent considerable time explaining how teachers can help students achieve the standard, with repeated emphasis on the second sentence, directing students to memorize multiplication facts.

In stark contrast, when the 2023 framework writes out standard 3.OA.7, it omits the second sentence. To repeat, the sentence stating third-grade students must memorize multiplication facts is gone. 

The framework makes it perfectly clear this omission is intentional and not a space limitation of its 1,000-page document. When the framework mentions memorization, these sentences include phrases disparaging it, like “unproductive beliefs,” “facts devoid of meaning,” “low cognitive demand,” “arbitrary laws,” “not ‘blind’ memorization of number facts,” “unproductive notions,” etc. Not even once does the framework state students should memorize their multiplication tables. 

The framework has, de facto, changed the standard, something frameworks do not have the authority to do. 

Along with removing memorization, the framework also changes the meaning of student “fluency.”

For a useful definition of fluency, the 2013 framework states, “the word fluent is used in the standards to mean ‘reasonably fast and accurate’” and that students should be able to use such fact knowledge “with enough facility” that it “does not slow down or derail the problem solver as he or she works on more complex problems.”

The 2023 framework removes all such language. Instead, we’re told, “Avoid any temptation to conflate fluency and speed.” If it takes a minute to calculate 7×9, what happens to that student when learning algebra?

You may be wondering, “Why is the framework guiding this?” 

The origin appears to be a framework author’s claim that “for about one-third of students, the onset of timed testing is the beginning of math anxiety.” Researchers examined this claim in detail and concluded it’s nonevidence-based. The framework perpetuates this false and misleading belief stating, “A particularly damaging assessment practice to avoid is the use of timed tests to assess speed of mathematical fact retention, as such tests have been found to prompt mathematics anxiety.”

Brian Conrad, Stanford University mathematics professor and director of undergraduate studies in math, has extensively reviewed the framework in his published public comments. Of the framework claim relating timed tests to math anxiety he concludes, “None of the cited references support the key claim made about timed tests causing math anxiety, so this entire paragraph must be removed,” adding, “the passage is ideology in search of citations.” 

The framework writers ignored this, retaining the passage.

If students are taught from kindergarten to avoid timed tests because they’re harmful, will they be prepared for life challenges like license or credential exams? Or college final exams? Or when given one hour to finalize a quote? Or three minutes to explain to a CEO their math-related idea?

This framework is the result of choosing as its most influential author an educator with the opinion, “I never memorized my times tables. … It’s never held me back.” 

The framework’s solution to students struggling to learn the standards is to simply cease teaching them. Students relying completely on public schools for education will not be taught essential skills listed in the standards, while students with greater resources can learn these skills elsewhere. Disparities will worsen.

Legislatures found it necessary to override harmful nonevidence-based reading curricula. Now they will have to do the same with math. Meanwhile, districts should resist adopting the framework’s detrimental nonevidence-based guidance.

David Margulies has a Ph.D. from UCSD in material science and is a former IBM research staff member. He has numerous publications in scientific journals and has co-authored 34 U.S. patents. He can be reached by email.

Michael Malione is a parent and independent STEM enrichment tutor to students in California’s Piedmont Unified School District. He founded SaveMath.net to spread awareness of the new California Math Framework. An alumnus of San Francisco’s Lowell High School, he has a B.A. in physics from Harvard and an M.S.E.E. from Stanford. He can be reached on X.

Sugi Sorensen is a senior systems engineer and a math enrichment instructor.