Math fluency matters: Teach 4 + 5 = 9 before trying to discover 'concepts'

Students must memorize addition and multiplication facts -- quickly and accurately -- in order to understand math, write David Margulies and Rahim Nathwani in EdSource. They're unlikely to be discussing concepts, exploring ideas or solving complex problems if they don't know that 4+5=9 and 7×8=56. Without using a calculator.

As one education analyst Tom Loveless puts it: “Math facts are to math as phonics is to reading.”

Only 37% of California public school students are proficient in math, they write. Senate Bill 1067, which requires screening early elementary grade students for math difficulties, hopes to change that. Margulies, a former IBM researcher, and Nathwani, who works on high-tech startups, argue for testing for math fact fluency.

California’s Math Standards call for students to memorize addition facts by the end of second grade, multiplication by the end of third grade. But many students do not, they write.

In a Monterey County school district where 17 percent of students scored proficient in math, only 25 percent had achieved fluency in math facts by the end of fourth grade, Margulies and Nathwani write. Of those fluent in their math facts, 63% scored at or near grade level in fifth grade; only 7 percent of non-fluent students reached grade-level proficiency.

Working memory is limited, researchers say. If a student who's trying to solve a problem has to stop to recall 7x9 (or look for the answer on a calculator), they often lose their place. Margulies sees this as an elementary classroom volunteer. Knowing math facts fluently "frees working memory for reasoning, explaining, connecting concepts and problem-solving."

The Institute for Educational Sciences’ practice guides and the National Mathematics Advisory Panel’s final report both emphasize the need for “automatic recall” of math facts, they write. Teachers agree. It's very hard to teach math to students who don't know their math facts.

Massachusetts has similar standards and similar problems, comments Maureen Kane. "As a middle school math teacher I find it impossible to teach kids who need to use their fingers to count out 8-6. They’ve wasted all of their mental energy on figuring out something that should be automated."

England, which is rising in international education rankings, screens all students for multiplication fact fluency. This has "mobilized the entire teaching workforce in primary schools around times tables and fact fluency” and had “huge ripple effects” on students’ math conceptual understanding, said Nick Gibb, who served as minister of education.

Fluency interventions take only five to 10 minutes per day, Margulies and Nathwani write. "Think of practicing scales for learning a musical instrument, dribbling drills for basketball, or footwork drills for soccer."

California's sensible Math Standards should guide screenings, they write. The 2023 Framework should not.

The controversial framework "aims to put meaning-making at the center of the math classroom, promoting a focus on problem-solving and applying math knowledge to real-world situations," Sarah Schwartz reported in Education Week. "It also encourages teachers to make math culturally relevant and accessible for all students, especially students of color who have been traditionally marginalized in the subject."

What it doesn't do is tell teachers that students need to memorize addition facts and times tables. Using "trendy buzzwords and false promises of greater equity," the framework misrepresents research, argues one critique. It denigrates the importance of students knowing math facts fluently, says another. The framework falsely "claims that timed tests cause math anxiety," write Margulies and Nathwani. These claims "have been shown to be not based on evidence."

I think not knowing math causes math anxiety.

New York keeps rewriting its math standards without improving student achievement, writes Jennifer Weber for the Manhattan Institute. Screening all students would ensure they get help before they fall too far behind. She also recommends prioritizing foundational math skills to support "long-term achievement and students’ capacity to engage meaningfully in math problem solving." When students don't master the basics in the early grades, she writes, "gaps widen over time and become increasingly difficult to remediate."