{"id":32,"date":"2004-06-16T16:23:55","date_gmt":"2004-06-16T16:23:55","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=32"},"modified":"2004-06-16T16:23:55","modified_gmt":"2004-06-16T16:23:55","slug":"misunderstanding","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=32","title":{"rendered":"Misunderstanding"},"content":{"rendered":"<p>When teaching maths that you are familiar with, it is not easy to see why students struggle with it &#8211; indeed once the student has understood the problem, they can&#8217;t see why they had difficulty before! This means that you have to be very careful what you say in case an attentive student takes it literally.<\/p>\n<p>How many times has a lecturer said &#8220;<i>the integral of e is itself <\/i>&#8221; ? So this happens:<\/p>\n<ul>Q. Find the value of <img src='\/maths\/latexrender\/pictures\/d84bbe5f89c2d944166e075cdaae3257.gif' title='\\displaystyle \\int_e^{e^2}\\left(\\frac{5}{x}+e\\right)\\ dx' alt='\\displaystyle \\int_e^{e^2}\\left(\\frac{5}{x}+e\\right)\\ dx' align=absmiddle><\/p>\n<p>A. <img src='\/maths\/latexrender\/pictures\/e846d6c1a3346703ff51cd012cc2f2bb.gif' title='\\displaystyle \\int_e^{e^2}\\left(\\frac{5}{x}+e\\right)\\ dx=\\left[5\\ln |x| + e\\right]_e^{e^2}=\\dots=5' alt='\\displaystyle \\int_e^{e^2}\\left(\\frac{5}{x}+e\\right)\\ dx=\\left[5\\ln |x| + e\\right]_e^{e^2}=\\dots=5' align=absmiddle><\/ul>\n<p> When the error was pointed out to the student, they responded with <\/p>\n<ul><i>Why does <img src='\/maths\/latexrender\/pictures\/e1671797c52e15f763380b45e841ec32.gif' title='e' alt='e' align=absmiddle> integrate to <img src='\/maths\/latexrender\/pictures\/29ee2832b7e11359861acaeb2e696f82.gif' title='ex\\;' alt='ex\\;' align=absmiddle>? <img src='\/maths\/latexrender\/pictures\/ff2d26be6b0b506663911208302f91b3.gif' title='e^x' alt='e^x' align=absmiddle> integrates to <img src='\/maths\/latexrender\/pictures\/ff2d26be6b0b506663911208302f91b3.gif' title='e^x' alt='e^x' align=absmiddle> and as <img src='\/maths\/latexrender\/pictures\/1d8e50a2e68d4a40e8b947d6b5552ec5.gif' title='e=e^1' alt='e=e^1' align=absmiddle> surely the integral of <img src='\/maths\/latexrender\/pictures\/e1671797c52e15f763380b45e841ec32.gif' title='e' alt='e' align=absmiddle> is also <img src='\/maths\/latexrender\/pictures\/92d8c35669b056b40d192750ad8239b4.gif' title='e\\;' alt='e\\;' align=absmiddle><\/i>?<\/ul>\n<p>How would you respond to this?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When teaching maths that you are familiar with, it is not easy to see why students struggle with it &#8211; indeed once the student has understood the problem, they can&#8217;t see why they had difficulty before! This means that you have to be very careful what you say in case an attentive student takes it [&hellip;]<\/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-32","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/32","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=32"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/32\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=32"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=32"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}