At the earliest stage, beyond addition facts and rules, memorization involves multiplication table. Is memorizing multiplication table unnecessary, as a Stanford researcher is suggesting? She compares memorization of poetry with that of mathematical facts, emphasizing the anxiety associated with the speed demanded in math. From the admittedly detrimental effect of “timed tests,” she jumps to the wrong conclusion of abandoning the memorization of mathematical facts altogether.

If Andrew Wiles had not started his mathematical training with memorizing multiplication table, Pythagorean theorem, the fundamental theorem of algebra, the principal ideal theorem, and … he would have been incapable of proving Fermat’s Last Theorem.

There is a marked difference between memorization in poetry and in math. Poems are not vertically linked to each other. If a student fails to memorize a poem by Shakespeare, (s)he will not be hampered in his/her learning of a poem by Robert Frost. However, if a student fails to memorize the table and rules of multiplication, (s)he will have problems with fractions and long division. Weakness in these areas hampers learning algebra and beyond. (For those who refuse to accept the obvious without “studies,” here is one; here is another, and another.)

The urgency of learning math stems from the dependence of higher-level topics to the lower-level ones.

Perhaps that’s why teachers want to “speed up” the learning of mathematical facts; definitely not a good solution! The real solution is the allotment of some of the after-school time of students to a relaxed practice and learning of mathematical facts … homework. But since homework interferes with the variety of “plays” that a typical American student is culturally expected to engage in, many parents and teachers are opposed to homework.

And as long as (mostly semi-literate) American parents are in charge of the education of their children, and ill-prepared teachers are awarded teaching certificates (I had a few students in their **junior year** in college, soon to be certified to teach *high school* physics, who thought that ), no solution seems to be in sight, despite all the good intentions of mathematics and physics education researchers!

Good points you have made in this article, professor. I myself had always hated memorisation during my school years. Now, with your classification of types of memorisation, I see that what I hated was actually the bad kind of memorisation. e.g. Why did I have to memorise the agricultural products of neighbouring countries in order to get a full mark on geography? What was the point?!

On the other side, learning the proofs of matyematical theorems or ways to solve a problem in physics did not have the bad feeling of memorisation and was actually quite challenging and enjoyable.

Without your classification, It seems natural for people to try to abandon memorisation altogether.

I guess we have to accept that getting well-educated has no shortcut. We are talking about the accumulation of hudreds of years of evergrowing human knowledge that every child has to start to learn from scratch. This is a formidable task! The new education system tries to make the path easier and more enjoyable, but the truth is that we have to strive for years and years to gain even a small fraction of the whole human knowledge. This cannot be made any easier.