I ask my intermediate algebra students to memorize the derivation of the quadratic formula. Some moan and groan but I reply that this is what I expect from an “A” student. I also explain that the act of memorizing the derivation is like the act of memorizing a poem. They will gain insight into the fundamental structure and meaning of both. I had the most successful term yet. Around five students out of fifty wrote the correct steps. One student even commented, “This was exciting.”
This post was prompted by a New York Times Book Review of Joshua Foer’s new book Moonwalking with Einstein: The Art and Science of Remembering Everything. One of his memorization methods is that of the ancient “method of loci” which is mentally placing objects to be memorized into locations in a familar physical space. Recall consists of simply visualizing the space containing the objects. One year I wanted my calculus II students to memorize the formulas for rotated volumes and the like. I told them about the method and then gave my personal rendition which I thought was pretty clever. None of them took up the idea and their test scores on that section were low. However if I ever teach calculus II again, I would require them to memorize the formulas for same reason I require my algebra students to memorize the derivation of the quadratic formula. The act of memorization will help them gain a deeper understanding of the integral methods.