&gt; Far better to show them the most effective technique, let them practice it, and move on.<p>This can work for the base levels of what most folks think as mathematics, namely arithmetic and algebra. But it starts falling apart as students get to more advanced algebra and mathematical topics. Memorizing a particular algorithm does <i>not</i> lend to understanding mathematics. In particular, the parallels between algebra (and some arithmetic) and geometry are non-obvious and not easily conveyed via a series of exercises and then jumping to the next topic. See the visualization examples of `18x5` in the linked article. Letting students see the correlation between the numbers and the objects (squares and rectangles) greatly helps their understanding of the subject. <i>Discussing</i> it reinforces this experience and gets them to see it beyond the exercises they&#x27;ve been doing, abstracting the concept beyond a handful of cases and to the general case.<p>&gt; Riding bikes and mathematics were never evolutionarily selected for, so we have to learn them by, well, learning them.<p>There are many ways to learn and to teach. Teacher-tell, student-regurgitate is one method. And it works for some (many) subjects, at least in getting facts and figures into students heads. Teacher-tell, student-explain gets the students past thinking about facts and thinking about whys and hows of the world. (You can expand tell beyond spoken word to shown, demonstrated, etc.) Teachers can take it further by starting on a mathematical topic, and directing the student conversation and discussion towards understanding (I think this is the example I&#x27;m looking for, graph theory for eight-ear olds: <a href="http:&#x2F;&#x2F;jdh.hamkins.org&#x2F;math-for-eight-year-olds&#x2F;" rel="nofollow">http:&#x2F;&#x2F;jdh.hamkins.org&#x2F;math-for-eight-year-olds&#x2F;</a>).