{"id":248,"date":"2012-02-22T11:38:34","date_gmt":"2012-02-22T17:38:34","guid":{"rendered":"http:\/\/linesoftangency.wordpress.com\/?p=248"},"modified":"2012-02-22T11:38:34","modified_gmt":"2012-02-22T17:38:34","slug":"pretty-little-lies","status":"publish","type":"post","link":"http:\/\/blog.chrislusto.com\/?p=248","title":{"rendered":"Pretty Little Lies"},"content":{"rendered":"

\"\"<\/a><\/p>\n

I find myself lying to my students.\u00a0 A lot.\u00a0 I suppose it doesn't much bother me on a moral level.\u00a0 For one thing, my conscience is perhaps less muscular than it ought to be.\u00a0 For another, I'm generally pretty open with my kids.\u00a0 They know, for instance, that I'm divorced.\u00a0 That I'm quitting smoking for my 30th birthday.\u00a0 That for several years I was professionally violent<\/a>.\u00a0 I go out of my way to let them know that, within reason, I won't shy away from their curiosity.\u00a0 Still, I lie.<\/p>\n

<\/p>\n

Some of the lies are self-serving.\u00a0 (I will <\/em>totally have this graded by tomorrow.<\/em>)\u00a0 Some are self-preserving (Tell your mom it must have ended up in my spam folder.<\/em>)\u00a0 Some of them aren't really even told<\/strong>, more like nurtured<\/strong> from the soil of the teenage imagination.\u00a0 (I have served time in prison.\u00a0 I am the father of the health teacher's new baby.<\/em>)\u00a0 But the lies that keep me up at night are mathematical.\u00a0 (You can't take the square root of a negative number.\u00a0 Functions approach their asymptotes, but never touch them.<\/em>)\u00a0 And, in this last category, I'm not sure what to do about it.<\/p>\n

A while back I wrote a post on the equals sign<\/a> in geometry.\u00a0 One of the difficult concepts for new geometry students is congruence<\/strong>, which looks an awful lot like equality, but isn't quite.\u00a0 Equality can either be used a relation between numbers, or between geometric objects that are identical as sets.\u00a0 Objects with the same fundamental characteristics (e.g. polygons with the same corresponding side lengths and angle measures), on the other hand, are said to be congruent.\u00a0 The standard high-school-level method for keeping the two concepts straight is to say something like, \"Numbers are equal, geometric objects are congruent.\"\u00a0 Full stop.<\/p>\n

But this is a lie.\u00a0 Things are more complicated than that.\u00a0 In fact, congruence is a weaker condition than equality (geometric equality implies congruence, but the converse is not true).\u00a0 So this equality\/congruence lie was one I was just bound and determined not to tell.\u00a0 Of course (and many of you can see this coming), things went disastrously.\u00a0 A few kids internalized the message, but most were so paralyzed by the nuance that they fell back on a self-constructed numbers:equal, objects:congruent shortcut, which is true in all but the pickiest of circumstances.<\/p>\n

Christopher Danielson<\/a> tried to warn me:<\/p>\n

\"What does this expanded version of \"equal to\" ... get you that this simpler distinction doesn't?\"<\/p><\/blockquote>\n

The answer, of course, is nothing.\u00a0 It gets me nothing, really, except the satisfaction of not having heaped one more lie onto the steaming pile of lies that another teacher, in a faraway time and place, is going to have to un-lie.\u00a0 But at what cost?<\/p>\n

So this is my struggle.\u00a0 How do I determine the absolutely necessary lies from the lazy ones?\u00a0 How do I lie with the bare minimum frequency and intensity?\u00a0 My kids are certainly to the point where I can un-lie the domain of the square root function, but they certainly weren't when their first teachers fibbed it with such good intentions.\u00a0 Most of my kids will never obtain the skill set to get at a mathematically rigorous definition of an asymptote, so I'm stuck with: a line that a function approaches, but does not reach, except in certain situations where a function can indeed<\/strong> cross the line, so long as it behaves like an asymptote at some point...eventually<\/em>.\u00a0But for a few of them, this is another lie to be untold as they move toward calculus.<\/p>\n

I have no idea how to avoid<\/strong> lying, but I'm going to try to at least be more explicit<\/strong> about lying.\u00a0 I'm going to try to help kids mentally bookmark my pretty little lies in the hopes that the reptilian parts of their brains will expect to be compensated with genuine truth at some point...eventually.<\/p>\n","protected":false},"excerpt":{"rendered":"

I find myself lying to my students.\u00a0 A lot.\u00a0 I suppose it doesn't much bother me on a moral level.\u00a0 For one thing, my conscience is perhaps less muscular than it ought to be.\u00a0 For another, I'm generally pretty open with my kids.\u00a0 They know, for instance, that I'm divorced.\u00a0 That I'm quitting smoking for […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[30,33],"class_list":["post-248","post","type-post","status-publish","format-standard","hentry","category-math-teaching","tag-lying","tag-math-education"],"_links":{"self":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/posts\/248","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=248"}],"version-history":[{"count":0,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/posts\/248\/revisions"}],"wp:attachment":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=248"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=248"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}