The article shows a confusion between training (committing things to muscle memory, or to visual patterns that can be recognized or executed) and teaching (a deeper understanding of a thing). Training is always more testable than teaching, yet for the most part the things we test people on (e.g. multiplication of small numbers, solving quadratic equations) are only evidence that something like mathematical skill and understanding is building up rather than the desired thing itself.<p>Rote memorization is a skill that's quite useful, but it's only one skill among many others that people should take away from school or university. And just as it's wrong to dismiss certain teaching as "just" rote memorization (e.g. knowing vocabulary in a foreign language) it's also wrong to just omit the teaching part altogether and train people to do well on standardized tests.
Related to Albert Wenger's "attention as the scarce resource" thinking. <a href="https://thoughtshrapnel.com/2018/06/28/attention-scarcity/" rel="nofollow">https://thoughtshrapnel.com/2018/06/28/attention-scarcity/</a>
A perspective from Wozniak from supermemo:<p>The core knowledge of intelligent thinking, in mathematics and beyond, is the rules of mathematical derivation in the most abstract and universally applicable form. Those rules can be applied in a myriad of daily situations. This universal applicability in problem solving makes the basis of what others consider an intelligent person. If properly formulated and represented for learning, these rules can be memorized in a standard way; in other words, memorization can be a way toward intelligence!"<p><a href="https://www.supermemo.com/english/ol/ks.htm" rel="nofollow">https://www.supermemo.com/english/ol/ks.htm</a>
But... you have to know what a derivative is <i>for</i> in order to be motivated to learn how to do it. If it's all just mindless manipulation, how will one know whether to apply this or that mindless manipulation?