The building blocks of understanding are memorization and repetition
The author is arguing that &#x27;the latest wave of educational reform in mathematics&#x27; (in the U.S.) is overemphasizing conceptual understanding, and that doing so will be damaging to students.<p>The author advocates instead using a memorization and repetition based approach.<p>I can see where she&#x27;s coming from, but the argument she is making is flawed. She describes a process for developing fluency both in foreign language and mathematics, wherein she experiments and plays with the constructs being learned—this is a great suggestion, but it&#x27;s not in <i>opposition</i> to understanding: the two complement each other.<p>I think the error arises from making an overly strong identification between learning a foreign language and learning mathematics. If you take the representation of Euler&#x27;s equation, for instance, and consider how much conceptual depth underlies it, versus a string of 20 Cyrillic characters meaning &quot;I went to the store,&quot; or whatever—you can see the difference. You&#x27;d be wasting your time trying to get a deep understanding of the Russian phrase, but there&#x27;s a reason to do it with the mathematical phrase.