{"id":753,"date":"2013-08-30T01:15:40","date_gmt":"2013-08-30T01:15:40","guid":{"rendered":"http:\/\/blog.chrislusto.com\/?p=753"},"modified":"2013-08-30T01:15:40","modified_gmt":"2013-08-30T01:15:40","slug":"pretty-big-ideas","status":"publish","type":"post","link":"http:\/\/blog.chrislusto.com\/?p=753","title":{"rendered":"Pretty Big Ideas"},"content":{"rendered":"

So Grant Wiggins threw down the gauntlet<\/a>. \u00a0And Patrick Honner, as Patrick Honner is wont to do, picked it up<\/a>. \u00a0And then Grant Wiggins -- \u00a0I'm not totally sure what traditionally happens to a gauntlet at this point -- did some other gauntlet-related thing in reply<\/a>. \u00a0It was fast and furious. \u00a0Actually, it was incredibly civil and well considered, which spirit I will try to preserve here.<\/p>\n

For the tl;dr<\/a> crowd, Wiggins posted a celebratory 100th-blog-post rant against Algebra (the course, not the content). \u00a0In that post he challenged Algebra teachers to name Four Big Ideas contained in the curriculum. \u00a0And Honner responded with some pretty solid candidates:<\/p>\n

    \n
  1. Algebraic Structure<\/li>\n
  2. Binary Relations<\/li>\n
  3. The Cartesian Plane<\/li>\n
  4. Function<\/li>\n<\/ol>\n

    Wiggins quasi-stipulates to a couple (binary relation, Cartesian Plane) -- with much qualification -- and more or less dismisses the others (quite politely). \u00a0It seems that Wiggins agrees all those ideas are\u00a0important<\/em>, but he has a very particular notion of what makes for a Big Idea:<\/p>\n

    So, I wish to up the ante. To me a big idea is big for both: I am looking for those ideas that are big \u2013 powerful and fecund \u2013 for both novice and expert.<\/p>\n

    I always return to this simple example from soccer:\u00a0Create dangerous space on offense; collapse dangerous space on defense<\/i>\u00a0is a big idea at\u00a0every level<\/span> of the game, from kid to pro. And it is transferrable to all space-conquest sports like lacrosse, hockey, and basketball. Truly big. \u00a0[emphasis in original]<\/p><\/blockquote>\n

    I'm not interested in debating the general lifelessness of high school Algebra, which strikes me as largely uncontroversial at this point in the conversation. \u00a0In fact, the same rant could just as easily be applied to mathematical instruction at almost any level (Wiggins even includes the obligatory quotation from\u00a0A Mathematician's Lament<\/em><\/a>). \u00a0I'm also not interested in trying to produce more convincing examples. \u00a0Nope, I'm interested in talking about soccer.<\/p>\n

    I think the soccer analogy is on the verge of making it impossible to have a meaningful discussion about math education. \u00a0Not just Algebra, but mathematics.<\/em>\u00a0 And here's why: the creating and collapsing of dangerous space might be the\u00a0only<\/strong>\u00a0Big Idea in soccer. \u00a0I submit that, if\u00a0that's<\/em> the standard for bigness, then there just aren't four Big Ideas to be had.
    \n<\/em><\/p>\n

    If soccer were taught like math, then you might take a course called Moving Without the Ball I as a freshman. \u00a0And in that class there would be a unit about Overlapping Runs. \u00a0And you would probably hate it, because it would be an awful lot of running, and you wouldn't ever be sure why you were doing<\/em> all this goddamn running, because maybe your coach isn't overly concerned about unveiling to you the beautiful truth that a good, long overlapping run pulls a defender way down into the corner and stretches the whole defense and creates some dangerous space for a midfielder to run into. \u00a0And you would moan and check the calendar for when you were starting the Passing Into Space unit, because you heard it was totally easy -- mostly just standing around and pushing nice, easy passes toward cones. \u00a0But that really says more about your coach's ability\/willingness to keep your eye on the Truly Big Idea (because hey, he's pretty much coaching the way\u00a0he<\/em> was coached in the first place, back when kids just shut up and did their Backwards Jogging homework without complaint) than it does about the bigness of the Pretty Big Ideas that you're working your way through, because the Truly Big Idea is just too ungodly huge to be useful in making you a better soccer player. \u00a0After all, there's just the one.<\/p>\n

    In an attempt at analogic involution, I'm going to try to come up with a mathematical analogy for the soccer analogy for math:<\/p>\n

    I always return to this simple example from mathematics: Create structure when you're building; look for structure when you're exploring\u00a0<\/em>is a big idea at\u00a0every level<\/span> of the subject, from kid to professional mathematician. \u00a0\u00a0And it is transferrable to all structure-having systems like language, chemistry, and logic. \u00a0Truly big.<\/p><\/blockquote>\n

    Maybe structure is the only big idea in math. \u00a0At least the only one Wiggins might agree to. \u00a0And that's just too big. \u00a0What we really need in Algebra are some Pretty Big Ideas. \u00a0So here's\u00a0my\u00a0<\/em>gauntlet, which is admittedly significantly lighter than the one that's currently being kicked around: what are four Pretty Big Ideas in Algebra? \u00a0Honner got you started.<\/p>\n","protected":false},"excerpt":{"rendered":"

    So Grant Wiggins threw down the gauntlet. \u00a0And Patrick Honner, as Patrick Honner is wont to do, picked it up. \u00a0And then Grant Wiggins -- \u00a0I'm not totally sure what traditionally happens to a gauntlet at this point -- did some other gauntlet-related thing in reply. \u00a0It was fast and furious. \u00a0Actually, it was incredibly […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-753","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/posts\/753","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=753"}],"version-history":[{"count":3,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/posts\/753\/revisions"}],"predecessor-version":[{"id":756,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/posts\/753\/revisions\/756"}],"wp:attachment":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=753"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}