Poor Guidance From Influential Math Educators Is Impairing Students

COMMENTARY

Could it be that the nation’s large fraction of students lacking math proficiency is caused by significant numbers of students not having their multiplication tables memorized?

In a California K-12 district with 15% of students proficient in math, according to state testing, only about 25% of fourth graders were found to have their multiplication facts memorized at the grade’s end. This situation exists despite the California Math Content Standards, the math students are expected to learn, stating explicitly that students are to “by the end of grade three, know from memory all products of two one-digit numbers.”

Should multiplication fact memorization be viewed as a minor standard, only one of many, perhaps de-emphasized in a busy school year, or is it a major foundational skill, like phonics is to reading, the lack of which is causing students’ struggles in this district?

The correlation between student multiplication fact memorization and their CAASPP performance was analyzed for one elementary school in the district. The criteria for having multiplication facts memorized, or multiplication fact fluency, is established by research as meaning students can answer multiplication fact questions faster than three seconds per problem. On the CAASPP, students receive numerical scores, and achievement levels are defined using ranges of scores. These levels, from low to high, are: “Standard Not Met,” “Standard Nearly Met,” “Standard Met” and “Standard Exceeded.”  

In the elementary school studied, of the fifth-grade students who did not have their multiplication facts memorized (68% of students), only 7% had scores that fell in the top half of the “Standard Nearly Met” level or higher. In contrast, for the students who did have their multiplication facts memorized, 63% scored in the top half of the “Standard Nearly Met” level or higher. 

Furthermore, for the students with their multiplication facts memorized and achieved “Standard Nearly Met” or better on the English Language Arts/Literacy state test, 85% of these student’s scores fell in the top half of the “Standard Nearly Met” level or higher on the Math CAASPP.

This data indicates that if students have their multiplication facts memorized and can read well enough to understand the math problem, then they achieve reasonable success on the Math CAASPP at a high rate. 

This is not arguing that math fact memorization is all the student needs, but that by acquiring this skill, broader success in math becomes more accessible.

Why?

Oklahoma State University professor Dr. Brian Poncy describes five reasons why math fact fluency positively impacts learning rates: 

1. Fluency increases response rates, producing more efficient learning with increased practice rates, and “practice makes perfect.”
2. Successful problem solving is positive reinforcement for students, builds confidence, and fluency enables higher rates of reinforcement. This is beneficial because students are more likely to start, engage, persevere through and finish reinforcing tasks.
3. For fluent students, limited working memory is not occupied calculating basic math facts; cognitive load is focused on learning the new skill and problem solving. Non-fluent students use procedures to figure out prerequisite skills; this occupies their working memory, inhibiting problem solving.
4. Fluent students, more likely, maintain skills.
5. Fluency enables skill generalization, i.e. the ability to apply knowledge of learned skills to learning new related skills.

In short, math fact memorization is a vital foundational skill. 

Why, then, aren’t well-established evidence-based programs scaffolding students to math fact fluency, with benchmarks and assessments, already an integral part of education?

The answer is misguidance from influential educators.

The National Council of Teachers of Mathematics, “the world’s largest mathematics education organization,” recommends that instead of memorizing basic multiplication facts, students use “reasoning strategies” to figure them out.

The California Mathematics Framework, a document which, according to the California Department of Education, should “offer guidance for implementing content standards,” but instead is infamous for its misguidance, removes “know from memory” when it quotes the standards. Not mentioned once in its 1,000 pages is that students should know from memory their multiplication facts, or their addition/subtraction facts. Furthermore, by constantly disparaging memorization, the framework’s guidance appears a “deliberate attempt to obfuscate know from memory from the standard.”

This comes as no surprise when you learn that one of the co-authors of the CMF was an educator who stated, “I never memorized my times tables. … It’s never held me back.” This opinion is now California’s math guidance.

Moreover, the CMF claims that timed tests, a highly recommended practice for enabling math fact memorization, cause students “mathematics anxiety.”

Researchers have thoroughly examined this claim and concluded it’s not evidence-based. Ignoring this, the NCTM similarly claims, “timed tests … can negatively affect students.”

The CMF, which describes state-sanctioned curriculum, instruction and professional development, doesn’t acknowledge the critical role and need for math fact fluency.

California’s massive investment in math teacher training, invariably framework-aligned, will not be recommending programs enabling students to achieve the standard calling for fact fluency. Without sufficient focus, math fact fluency is not learned. The result? Many students are subjected to the difficult task of trying to learn math without math fact fluency.

If the relationship between math fact fluency and student achievement observed in the district described here represents a microcosm of struggling districts or students everywhere (something readily measurable, as assessing math fact fluency requires only 10 minutes of class time), then California’s plan for students achieving math proficiency without math fact fluency has failed before it’s started.

Listening to education thought leaders denying the role math fact memorization plays in student learning could be causing significant numbers of students to not have their math facts memorized. Students relying completely on public schools for education, more likely lower socioeconomic-status students, are those most impacted.

A solution may be legislatures overriding this misguidance, as they’ve done with reading instruction. Requiring student fact fluency assessments, like mandated universal screening for reading, may enable data-driven solutions.

As it stands, the nation’s huge financial investment in math education, if directed by educators dismissing math fact memorization, guides students to a path of unlikely success — it is pouring money into a pot with holes.

David Margulies has a Ph.D. from UCSD in Materials 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.