How can we reform mathematics education so that ideas are central and rote memorization and calculation is only one but not the principal goal? Is this occurring already? Where?

Here’s the deal: some students still have to memorize the times-tables in the second half of elementary school. All the way to 12 x 12. Their teachers give them problem sheets with fifteen or twenty simple multiplications, and the students race to see who can finish first without a mistake.

This not only requires memorization, it etches the times-tables into their little brains. Add-subtract tables are good ideas too, by the way. What happens as a result?* As adults, those same individuals have a lot fewer problems with and a lot fewer fears of arithmetic. They turn out better-adjusted, if you will.

Memorization is not an either – or, it’s a both-and. The one shibboleth regarding el-hi education that sets my teeth on edge, like fingernails on a blackboard, is “Which would you rather do, cram them with facts or teach them to think?”

Tell me, please, how on earth anyone can contrive a reasonable argument with nothing factual to found it on? Words make language possible. Facts and words are both necessary to make thought possible. Constructing a real-world debate on any issue you want to name is going to require definitions, and those are also called (drum-roll, please) data. A.k.a. facts. Own  them or die.

Here’s a real example; there’s a movement afoot in University circles promoting the idea that the sciences are inherently racist and genderized (white males, bubbula) because they exclude “other ways of knowing.” Please form a line; all those who step forward will be permitted to fly in an airplane engineered using “other ways of knowing.”

Soapbox off.

Ah, not just rote memorization but rote methods. Soapbox on again. For a time it was gospel that math was a language skill, tested by returning rules of operation in whole sentences. Don’t just sit there and make columns of numbers that slant back to the left as you multiply two large numbers because THAT IS ROTE KNOWLEDGE and WE WANT YOU TO UNDERSTAND WHY.

This is like conducting Driver’s Ed from behind a desk, and expecting the student to know what happens when you step on one of the pedals in front of the driver, because that student is proudly verbal, in full sentences, about what is supposed to happen. And we wonder why the rest of the world turns out kids who do math with intuitive understanding. Their kids get real pedals to push.