I’m often rather disturbed by how mathematics is taught in school. Take, for example, the way I was taught the following (important) equation:<\/p>\n
$latex int_a^b f(x) ,mathrm dx = F(b) – F(a)$<\/p>\n
Those of you familiar with calculus will immediately recognize what this means. Those of you who aren’t should know that the above set of squiggly lines means something very important in the upper levels of confusing math.<\/p>\n
When I first was taught the equation I was taught it by being exposed to it exactly as I just exposed it to you: an equation. There were some words with it too, but they made just as much sense as the equation did at the time. A few moments later the teacher explained what the equation means: one can find the definite integral of an equation using its antiderivatives.<\/p>\n
But we were never taught why<\/em> that’s the case.<\/p>\n <\/p>\n With the diabolical mind I have I set out to figure out just why this worked, and with the help of some prior knowledge (I’m nerdy) I figured out just why the antiderivate of an equation might help me find its definite integral. But nobody else in the class got the benefit of my epiphany — I wasn’t the one teaching it.<\/p>\n It has been my fervent belief for a very long time that the understanding<\/em> is as crucial as the knowledge<\/em>. I made it through years of school without studying (at all) through this method: you don’t need to remember how the fundamental theorem of calculus was written if you remember why it works. The rest of it comes naturally when you understand<\/strong> the math. You can solve problems you’ve never seen before if you understand the fundamentals — but if you memorized the equations and how to solve them, you’ll be baffled by new types of problems.<\/p>\n Too often I see students trying to study by memorizing formulas and equations for hours on end — and then failing their exams. Why? Because however readily they may be able to recite $latex x – x_0 = V_0t + frac{1}{2}at^2$, they still don’t know what it means or how to use it.<\/p>\n","protected":false},"excerpt":{"rendered":" I’m often rather disturbed by how mathematics is taught in school. Take, for example, the way I was taught the following (important) equation: $latex int_a^b f(x) ,mathrm dx = F(b) – F(a)$ Those of you familiar with calculus will immediately recognize what this means. Those of you who aren’t should know that the above set…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-16","post","type-post","status-publish","format-standard","hentry","category-education"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/capn\/wp-json\/wp\/v2\/posts\/16","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/capn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/capn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/capn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/capn\/wp-json\/wp\/v2\/comments?post=16"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/capn\/wp-json\/wp\/v2\/posts\/16\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/capn\/wp-json\/wp\/v2\/media?parent=16"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/capn\/wp-json\/wp\/v2\/categories?post=16"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/capn\/wp-json\/wp\/v2\/tags?post=16"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}