<story><title>You never did math in high school</title><url>http://j2kun.svbtle.com/you-never-did-math-in-high-school/?_nospa=true</url></story><parent_chain><item><author>sfrank2147</author><text>I&amp;#x27;m a former math teacher, now a programmer.  I think he leaves out a few considerations:&lt;p&gt;1) You need to be able to do basic calculations before you can do advanced proofs.  I taught a lot of high school seniors, and I had a ton of students who were smart enough to handle abstract concepts, but couldn&amp;#x27;t follow along when I showed them cool proofs because they got caught up on the basic calculations (because they hadn&amp;#x27;t learned them well in middle&amp;#x2F;high school).&lt;p&gt;2)  Good high school teachers DO do a lot of pattern recognition&amp;#x2F;abstract reasoning.  That&amp;#x27;s the entire idea behind a discovery lesson and constructivist teaching - having students learn formulas by discovering patterns and reasoning about them.&lt;p&gt;3) Again, as he points out, American high schools do do proofs in Geometry.  He thinks they&amp;#x27;re really pedantic, but there are  good reasons why 2-column proofs are so tedious.  For one, students seeing proofs for the first time freak out, so giving them structure helps.  For another, if the students write out every single step, it&amp;#x27;s easier to identify who really knows his&amp;#x2F;her stuff and who&amp;#x27;s BSing.</text></item></parent_chain><comment><author>j2kun</author><text>I have taught enough lectures to high school students (presenting &amp;quot;advanced proofs&amp;quot;) and talked to enough geometry teachers who abandoned the two-column geometry proof to know that 1) is not true and 3) is not worth it. The problem is that people build up proofs like they&amp;#x27;re something to freak out about, or that the proofs that are presented are inherently mechanical because that&amp;#x27;s what students are taught. You can&amp;#x27;t expect someone learning to write proofs to be perfect any more than you can expect a first-time drawer to color within the lines. It&amp;#x27;s okay and should be embraced as an opportunity to reflect and improve. A proof is not complete just because you &amp;quot;got to the answer.&amp;quot; It&amp;#x27;s complete when it&amp;#x27;s simple, elegant, and easy to explain to others.&lt;p&gt;I can and have explained beautiful proofs without the need for mechanical proficiency to ten year olds and mathphobes alike. Here are a few examples:&lt;p&gt;[1]: &lt;a href=&quot;http://jeremykun.com/2011/06/26/teaching-mathematics-graph-theory/&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;jeremykun.com&amp;#x2F;2011&amp;#x2F;06&amp;#x2F;26&amp;#x2F;teaching-mathematics-graph-t...&lt;/a&gt;
[2]: &lt;a href=&quot;http://j2kun.svbtle.com/things-mathematicians-know-proofs-are-beautiful&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;j2kun.svbtle.com&amp;#x2F;things-mathematicians-know-proofs-ar...&lt;/a&gt;
[3]: &lt;a href=&quot;http://j2kun.svbtle.com/things-mathematicians-know-more-than-one-infinity&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;j2kun.svbtle.com&amp;#x2F;things-mathematicians-know-more-than...&lt;/a&gt;
[4]: &lt;a href=&quot;http://jeremykun.com/2011/06/26/tiling-a-chessboard/&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;jeremykun.com&amp;#x2F;2011&amp;#x2F;06&amp;#x2F;26&amp;#x2F;tiling-a-chessboard&amp;#x2F;&lt;/a&gt;&lt;p&gt;The world is full of these cool problems and proofs. I could literally teach an entire course and do nothing but puzzles involving chessboards. That many teachers ignore these great topics is a problem, but it&amp;#x27;s certainly for a good reason (the myriad of other problems with high school education).</text></comment>
<story><title>You never did math in high school</title><url>http://j2kun.svbtle.com/you-never-did-math-in-high-school/?_nospa=true</url></story><parent_chain><item><author>sfrank2147</author><text>I&amp;#x27;m a former math teacher, now a programmer.  I think he leaves out a few considerations:&lt;p&gt;1) You need to be able to do basic calculations before you can do advanced proofs.  I taught a lot of high school seniors, and I had a ton of students who were smart enough to handle abstract concepts, but couldn&amp;#x27;t follow along when I showed them cool proofs because they got caught up on the basic calculations (because they hadn&amp;#x27;t learned them well in middle&amp;#x2F;high school).&lt;p&gt;2)  Good high school teachers DO do a lot of pattern recognition&amp;#x2F;abstract reasoning.  That&amp;#x27;s the entire idea behind a discovery lesson and constructivist teaching - having students learn formulas by discovering patterns and reasoning about them.&lt;p&gt;3) Again, as he points out, American high schools do do proofs in Geometry.  He thinks they&amp;#x27;re really pedantic, but there are  good reasons why 2-column proofs are so tedious.  For one, students seeing proofs for the first time freak out, so giving them structure helps.  For another, if the students write out every single step, it&amp;#x27;s easier to identify who really knows his&amp;#x2F;her stuff and who&amp;#x27;s BSing.</text></item></parent_chain><comment><author>vkjv</author><text>1. This. And many of the smarter students also gravitate towards these things.
2. It&amp;#x27;s easier for many students to grasp things when they are not abstract.
3. Yes, it still rattles my brain that Algebra teachers force students to memorize the quadratic formula. It&amp;#x27;s ridiculous. The method of completing the square is straight forward, more applicable in other situations, and can even derive that verbose formula. It only fosters the, &amp;quot;memorize every possible form of the question that could be on the exam&amp;quot; type of learning.</text></comment>