Rationalizing memorization, Dept.

I thought this article would be in the category of “learning math through interpretive dance” but I’m happy to say, I was wrong. It’s about a math teacher who uses musical chants/rhymes to help students memorize (yes, memorize) particular formulas and procedures.

As she puts it:

“Memorizing basic formulas can make it easier for students to grasp larger, more abstract mathematical concepts because students’ minds aren’t mired in the minutiae, Jorgensen said.

For example, it’s easier to understand the square root of 36 if you already know the answer to 6 multiplied by 6.

Jorgensen’s method has yielded results. In her 8th-grade geometry class from last year, 23 of her 40 students had perfect scores on the Smarter Balanced exam, and in the 7th-grade algebra class, every student exceeded the standards, she said. Seven of those students had perfect scores.

I couldn’t believe I had actually read that and read it several times to make sure I wasn’t dreaming. Most teachers would be hung for saying something like that without mentioning the U word. (“Understanding”).

Oh, but wait.  Here comes an apologist to offer a strawman about understanding and memorization:

Mark Ellis, a math education professor at California State University, Fullerton, said he observed elementary teachers in Japan using songs and chants to successfully teach math to their students and he has used music to help low-performing middle-school students learn their multiplication tables. … But it’s not the end of the story, he said.

“Music itself cannot teach kids to understand mathematics,” he said. “Music can help students improve dramatically, but ultimately math is not about memorization. It’s about reasoning, seeing patterns, making conjectures. It’s about meaning.”

Memorizing formulas will only be effective in the long run if students understand the concepts underlying the formulas, he said.

Anything else, Mr. Ellis? Oh, yes, he does have something more to say:

Ideally, students should be able to come up with formulas on their own, with guidance from the teacher. In some cases, it’s not even necessary to memorize formulas because so many students have calculators on their phones, he said.



6 thoughts on “Rationalizing memorization, Dept.

  1. calculators on their phones…

    I wonder if he’ll feel that way when he encounters a nurse using a phone to calculate the medication dosage before giving it to him.


  2. Two things stuck out for me immediately.

    “In her 8th-grade geometry class…”

    “… and he has used music to help low-performing middle-school students learn their multiplication tables.”

    One group is way ahead and another is way behind. A lot is going on here besides memorization. Memorization (remembering and using) the times table is a third-grade thing at the latest – and that’s not middle school and it’s not memorization as a last resort for low-performers.

    However, my position has always been that mastery of skills at all levels takes a LOT of understanding. Mastery is NOT memorization. At the lowest level, as with multiplication tables, few remember all of the understanding that took place, and it was nothing like just memorizing a list of presidents. You actually had to use the facts you memorized over and over and over on specific problems with real life money and time. We have feet (10) inches (12) minutes (60), days (24 hours), months (various) and more. Do these pedagogues complain about the rhyme: “Thirty days hath…?”

    Remembering is always good, but memorizing too many facts at a time is not effective. However, educational pedagogues make no distinction and go out of their way to create thematic learning situations where facts are supposed to attach themselves to other kinds of conceptual understanding learning. Um, no. In first grade, my son had a thematic unit on the Arctic where they read about an Inuit boy and his life with NO conceptual framework of why it’s so cold there for most of the year or why they live there in the first place. Later that year they had a thematic unit on “Sands From Around the World”, but my son, who loved to study geography and loved to memorize, had to show the student teacher where Kuwait was on a map. His teacher made a point to tell my wife and I that “Yes, he has a lot of superficial knowledge.” This was just one of many preemptive parental attacks we received.

    We run the risk here of spending too much time making detailed cogent arguments when their arguments border on systemic ignorance and B.S. They can’t even explain how those who get into STEM careers got there, or show how that works for ANY pedagogy they propose. Even the College Board can’t explain how “Distinguished” CCSS math students can use their new “Social Justice” Pre-AP algebra class in 9th grade to magically get to AP Calculus as a senior. This comes after they denigrate the real need to get to a proper algebra course by 8th grade. They completely let K-8 off the hook.


  3. “But either way, students with self-confidence and a solid math education in middle school are well positioned to thrive in the more challenging and abstract math classes they’ll encounter in high school and college, he said. Middle school math is the critical juncture where students transition from arithmetic to more complex concepts about proportions, ratios and multiplication, which are the basis of advanced level math courses.”

    “… a solid math education in middle school…”

    So why are some kids allowed to get to middle school before trying to enforce memorization of the times table – finally! – using music or whatever. Do they think that this is not part of a “solid” pre-middle school education or do they think that “kids will learn when they are ready?”


    • Good point. It appears that this teacher realizes they aren’t prepared and is teaching them what they need to know — and should have learned in 3rd grade. What she says is correct; i.e., knowing the times table frees up working memory. She herself probably wonders why they don’t know the multiplication facts by middle school. But she is at least trying to rectify the situation rather than depend on calculators as the person at the end of the article recommends.


      • I don’t disagree at all. I’m all for direct memorization any which way – along with the individual work required to turn that into plain remembering. In that process, a whole lot of understanding is created – much more than parroting back conceptual understanding words – one of your counters to their claim of rote memorization. With “invert and multiply” successfully applied to many different problem variations, one “understands” a lot more than any conceptual parrot understanding words told to a teacher.

        It’s unfortunate that teachers have to fix pass-along age-tracking mastery problems as if that’s how education should be done.


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