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A Mathematician's Lament [pdf]

23 pointsby cauliflower9910 months ago

1 comment

warrenm10 months ago
Any time someone who does not understand the practical outworkings of a given topic tries to &quot;teach&quot; it, you end up with a &quot;presentation&quot; - mostly in the form of propositional statements (dogs are mammals; barges are boats), or key-value pairs (in 1492, Columbus sailed the ocean blue; Caracas is the capital of Venezuela)<p>Propositional statements and key-value pairs are absolutely vital <i>aspects</i> of learning and understanding - but seeing how those ideas, facts, and statements will work themselves out in <i>practical application</i> is absolutely mandatory for proper understanding of the topic<p>If you never learn how you might <i>use</i> these facts, you are going to have an incredibly difficult time &quot;learning&quot; them<p>This is the fundamental problem of why &quot;teaching to the test&quot; (or, for that matter, relying too heavily on multiple-choice, true|false, matching, etc type &quot;tests&quot; to evaluate &quot;learning&quot; or &quot;knowledge&quot;) is problematic: I can teach pretty much <i>anyone</i> how to pass a multiple-choice test with zero knowledge of the subject material (did it myself years ago when I passed the first-tier amateur radio licensing exam without ever looking at any study guide)<p>When you &quot;teach to the test&quot; (which is what, fundamentally, exclusive reliance on propositional statements (and drills over them) and key-value pairs <i>are</i>), you create people who may (or may not) end up being good at trivia challenges ... but have no mental framework for connecting all those dots into anything coherent - iow, you create human-based data lakes: it is all sitting there, but no connective lines have been drawn<p>To get someone to <i>want</i> to learn, you have to show they <i>why</i> it &quot;matters&quot; - you have to get them to develop intrinsic motivation to learn (vs the purely extrinsic &quot;you have to to pass&quot;)<p>To develop that intrinsic motivation, you need to <i>show</i> the &#x27;why&#x27; and the &#x27;where&#x27; of the &#x27;what&#x27;<p>And to do <i>that</i> you have to understand it yourself
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