{"id":2066,"date":"2010-08-08T10:38:22","date_gmt":"2010-08-08T14:38:22","guid":{"rendered":"http:\/\/shermandorn.com\/wordpress\/?p=2066"},"modified":"2010-08-08T10:38:22","modified_gmt":"2010-08-08T14:38:22","slug":"problem-37-with-critical-thinking","status":"publish","type":"post","link":"https:\/\/shermandorn.com\/?p=2066","title":{"rendered":"Problem #37 with critical thinking"},"content":{"rendered":"

The last entry on trends in college-student studying time is a little of what Jonathan Zimmerman calls the historian’s scold (“you didn’t get that right!”), but moreso it’s an attempt to fight a popular availability bias, the thumbnail narrative of declension. As I was trimming my beard this morning (I do that every three years whether I need it or not), my mind ran through the various heuristic fallacies human beings are prone to: fundamental attribution error, confirmation bias, availability bias, and so forth. To some extent, efforts to teach what’s commonly called critical thinking<\/em> is just a series of “Fight your innate biases!” lessons.<\/p>\n

The problem with such an approach is that you can fight only some of those biases without a deeper understanding of a field. You can fight fundamental attribution error by teaching students to disagree agreeably (or whatever anti-ad-hominem homily you pick). But how do you fight confirmation bias? You ask students to identify specific alternative hypotheses and appropriate tests of the competing views of the world. But to do that, students need enough knowledge in a field to know what the competition to their bias would look like. Similarly, to fight availability bias, you ask students to consider a range of possibilities, which can only exist once students are exposed to those possibilities. That sounds mundane, but it’s difficult in practice.<\/p>\n

Maybe the best parallel is ordinary differential equations, which was my favorite part of second-year calculus.* In differential calculus, you learn a fairly general approach with some heuristic shortcuts (e.g., d(xn<\/sup>) = n*xn-1<\/sup>dx), and for the purposes of learning you ignore some of the assumptions and just look at the world of smooth-enough functions. In integral calculus, things get a little more interesting. There are still general techniques, but there are some special tricks (such as changes of variables) that you just have to learn. You extend that with vector calculus, which is very like one-variable calculus in some ways and much cooler in others.** Then you get to ordinary differential equations, which you might think is just like integral calculus—you’ve got an equation with some derivatives and you look for the original function. But it doesn’t quite work that way. The first thing out of my instructor’s mouth was the point that the techniques are not really general, the solutions are often non-unique, and the whole field may feel like a bag of tricks. There are very, very<\/em> cool tricks for things like catenaries and even better tricks that lead to infinite-series estimators for various quantities But to pretend that there are general solutions to ordinary differential equations may be a form of educational malpractice.<\/p>\n

The same is true for “critical thinking.” There may be common fallacies<\/em> we have to fight as human beings, but the counters<\/em> to those fallacies depend on the issue of the moment and require a certain amount of knowledge of that issue and its context. And even the ways we address them are going to vary by the field (which is why interdisciplinary discussions can be great: I learn from your approach to an issue because it’s different<\/em> from mine). <\/p>\n

*My favorite problem: four ants are at the corners of a square. Each ant starts walking directly towards the ant counterclockwise from her, and she keeps heading towards wherever that ant is, even as her target follows the next counterclockwise ant. The task is to derive the equation for the spiral the ants take towards the center of the original square. I wish I could remember the steps of the solution…<\/p>\n

**I’ve deleted the second metaphor layer comparing first-year and vector calculus to most 60s guitarists and Eric Clapton. Aren’t you glad I was restrained?<\/p>\n","protected":false},"excerpt":{"rendered":"

The last entry on trends in college-student studying time is a little of what Jonathan Zimmerman calls the historian’s scold (“you didn’t get that right!”), but moreso it’s an attempt to fight a popular availability bias, the thumbnail narrative of declension. As I was trimming my beard this morning (I do that every three years […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[12,6],"tags":[],"class_list":["post-2066","post","type-post","status-publish","format-standard","hentry","category-higher-education","category-teaching"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/pag0MB-xk","_links":{"self":[{"href":"https:\/\/shermandorn.com\/index.php?rest_route=\/wp\/v2\/posts\/2066","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shermandorn.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/shermandorn.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/shermandorn.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shermandorn.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2066"}],"version-history":[{"count":2,"href":"https:\/\/shermandorn.com\/index.php?rest_route=\/wp\/v2\/posts\/2066\/revisions"}],"predecessor-version":[{"id":2068,"href":"https:\/\/shermandorn.com\/index.php?rest_route=\/wp\/v2\/posts\/2066\/revisions\/2068"}],"wp:attachment":[{"href":"https:\/\/shermandorn.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2066"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/shermandorn.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2066"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/shermandorn.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2066"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}