<story><title>How to Teach Math?</title><url>https://rjlipton.wpcomstaging.com/2021/05/05/how-to-teach-math/</url></story><parent_chain><item><author>enriquto</author><text>&amp;gt; Why use X and Y when you could carSpeed and carAcceleration? (...) People can&amp;#x27;t relate at all to math when all the examples use generic terms without context.&lt;p&gt;Couldn&amp;#x27;t disagree more.&lt;p&gt;The whole point is that you &lt;i&gt;don&amp;#x27;t&lt;/i&gt; care about the meaning of the numbers.  They are just numbers.  A big part of math is learning to strip numbers of their context and look at them bare.&lt;p&gt;Besides, variables with several letters in them are extremely ugly.  They look like products.  (They should be banished from programming languages also, but I realize that this is a controversial idea.)</text></item><item><author>adam_arthur</author><text>Teaching in general is best done by &amp;quot;peeling the onion&amp;quot;.&lt;p&gt;By that I mean, start with the highest level explanation first, form an understanding of that, and then repeat the same lesson but at a lower level of abstraction. You have to be able to walk before you can run.&lt;p&gt;First, explain the concept like I&amp;#x27;m 5. Use examples that provide real world context for why the concept is useful. Demonstrate examples of using the concept to solve a problem.&lt;p&gt;Then explain the concept again, with an added layer of complexity. Go through the same examples with this layer of complexity.&lt;p&gt;And so on. The more levels, the easier it will be for people to ease into learning the concept. When confronted with something that&amp;#x27;s too foreign, many people just shut off their brains, and convince themselves they&amp;#x27;re &amp;quot;bad at math&amp;quot; etc.&lt;p&gt;The hardest part about learning is really breaking through the wall of initial understanding. Once you know the language, everything becomes a bit easier to learn.&lt;p&gt;I honestly think math education can be hugely improved with this approach. This could even be done in a &amp;quot;high tech&amp;quot; way, by having an e-textbook with a slider. Adjusting the slider changes the level of abstraction and granularity that it teaches the concepts at.&lt;p&gt;Final note.&lt;p&gt;Math should be taught with well named variables and contextual examples. Why use X and Y when you could carSpeed and carAcceleration? Or whatever, you get the point. People can&amp;#x27;t relate at all to math when all the examples use generic terms without context. At that point it just becomes rote repetition. Obviously this commentary applies moreso to earlier math education.</text></item></parent_chain><comment><author>hnedeotes</author><text>That&amp;#x27;s all fine and dandy when you&amp;#x27;re teaching maths to someone interested in pursuing or studying maths, if your point is to teach someone who hasn&amp;#x27;t yet made the connection between the abstractions and their meaning then you should use relatable things - and as their knowledge increases move to remove the familiar labels and show what is the underlying abstraction.&lt;p&gt;I would think that by now that shouldn&amp;#x27;t even be up for discussion - much less for programming where your objectives, besides achieving a calculation or a side-effect, are also that your code be intelligible to other human beings. Even in assembly you have symbols for move, jump, etc.&lt;p&gt;And no, different people have different ways of thinking, not everyone has the same combination of nature and nurture to be completely comfortable with pure abstract mathematical notation - and for most part they don&amp;#x27;t need to. When you assign fancy greek letters as symbols you&amp;#x27;re also labelling them, so why not label them with something that a person learning might recognise.&lt;p&gt;Outside of teaching people that aren&amp;#x27;t familiar with it, yeah, sure, use all the numerical elegance you can muster (and I would still argue that even there it&amp;#x27;s still detrimental if the objective is sharing knowledge as widely as possible).</text></comment>
<story><title>How to Teach Math?</title><url>https://rjlipton.wpcomstaging.com/2021/05/05/how-to-teach-math/</url></story><parent_chain><item><author>enriquto</author><text>&amp;gt; Why use X and Y when you could carSpeed and carAcceleration? (...) People can&amp;#x27;t relate at all to math when all the examples use generic terms without context.&lt;p&gt;Couldn&amp;#x27;t disagree more.&lt;p&gt;The whole point is that you &lt;i&gt;don&amp;#x27;t&lt;/i&gt; care about the meaning of the numbers.  They are just numbers.  A big part of math is learning to strip numbers of their context and look at them bare.&lt;p&gt;Besides, variables with several letters in them are extremely ugly.  They look like products.  (They should be banished from programming languages also, but I realize that this is a controversial idea.)</text></item><item><author>adam_arthur</author><text>Teaching in general is best done by &amp;quot;peeling the onion&amp;quot;.&lt;p&gt;By that I mean, start with the highest level explanation first, form an understanding of that, and then repeat the same lesson but at a lower level of abstraction. You have to be able to walk before you can run.&lt;p&gt;First, explain the concept like I&amp;#x27;m 5. Use examples that provide real world context for why the concept is useful. Demonstrate examples of using the concept to solve a problem.&lt;p&gt;Then explain the concept again, with an added layer of complexity. Go through the same examples with this layer of complexity.&lt;p&gt;And so on. The more levels, the easier it will be for people to ease into learning the concept. When confronted with something that&amp;#x27;s too foreign, many people just shut off their brains, and convince themselves they&amp;#x27;re &amp;quot;bad at math&amp;quot; etc.&lt;p&gt;The hardest part about learning is really breaking through the wall of initial understanding. Once you know the language, everything becomes a bit easier to learn.&lt;p&gt;I honestly think math education can be hugely improved with this approach. This could even be done in a &amp;quot;high tech&amp;quot; way, by having an e-textbook with a slider. Adjusting the slider changes the level of abstraction and granularity that it teaches the concepts at.&lt;p&gt;Final note.&lt;p&gt;Math should be taught with well named variables and contextual examples. Why use X and Y when you could carSpeed and carAcceleration? Or whatever, you get the point. People can&amp;#x27;t relate at all to math when all the examples use generic terms without context. At that point it just becomes rote repetition. Obviously this commentary applies moreso to earlier math education.</text></item></parent_chain><comment><author>adam_arthur</author><text>Ah, sounds like the common trend in the hard sciences of putting &amp;quot;difficulty&amp;quot; on a pedestal. Can&amp;#x27;t make it too easy to learn, need to make things generic and obtuse so only the most dedicated can master the material!&lt;p&gt;You can apply context to any generic abstraction&amp;#x2F;formula, otherwise the math is useless, by definition.&lt;p&gt;Teaching people effectively requires context.&lt;p&gt;I hope I don&amp;#x27;t have to read your code with single letter variables everywhere then! There&amp;#x27;s a reason that&amp;#x27;s considered a bad practice. Math gets a pass, why?</text></comment>