{"id":696,"date":"2011-10-02T20:17:11","date_gmt":"2011-10-02T20:17:11","guid":{"rendered":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/?p=696"},"modified":"2012-01-18T09:16:23","modified_gmt":"2012-01-18T09:16:23","slug":"errors-in-finding-the-gradient-of-a-graph","status":"publish","type":"post","link":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/?p=696","title":{"rendered":"Errors in finding the gradient of a graph"},"content":{"rendered":"<p>Consider the simple question shown below:<\/p>\n<p><a href=\"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-697\" title=\"Figure 1\" src=\"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-1.png\" alt=\"\" width=\"293\" height=\"381\" srcset=\"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-1.png 293w, https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-1-230x300.png 230w\" sizes=\"auto, (max-width: 293px) 100vw, 293px\" \/><\/a><\/p>\n<p>This question is generally well answered, but when students make a mistake, what do\u00a0they do wrong?<!--more--><\/p>\n<p>The most common mistake (5.7% of non-blank responses) is to calculate the gradient as if the line went through the origin. After that, the problem is units again &#8211; 5.3% of responses contain incorrect units whilst 2.5% contain no units at all. And 4.0% of non-blank responses are incorrect because they are not given to two significant figures.<\/p>\n<p>Now consider a question (below) that is more difficult in one regard only. Suddenly we have 16.4% of responses that have failed to take the &#8216;\/10<sup>5 <\/sup>Pa&#8217; into account.<\/p>\n<p><a href=\"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-21.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-699\" title=\"Figure 2\" src=\"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-21.png\" alt=\"\" width=\"373\" height=\"444\" srcset=\"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-21.png 373w, https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-21-252x300.png 252w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><\/a><\/p>\n<p>And finally, in the question shown below, things really get interesting. The graph is plotted for negative values of temperature, but the gradient is positive\u00a0 &#8211; you can see this by looking at it. However, 16.8% of responses\u00a0give the negative of the correct answer. And for some reason students start getting the answer upside down too\u00a0&#8211; 2.7% are the reciprocal of the correct answer and 2.0% are the negative reciprocal of the correct answer.<\/p>\n<p><a href=\"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-701\" title=\"Figure 3\" src=\"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-3.png\" alt=\"\" width=\"371\" height=\"412\" srcset=\"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-3.png 371w, https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/wp-content\/uploads\/2011\/10\/Figure-3-270x300.png 270w\" sizes=\"auto, (max-width: 371px) 100vw, 371px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider the simple question shown below: This question is generally well answered, but when students make a mistake, what do\u00a0they do wrong?<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[167,166,111,110],"tags":[384,383,369,368,367],"class_list":["post-696","post","type-post","status-publish","format-standard","hentry","category-gradient","category-graphs","category-mathematical-misunderstandings","category-question-analysis","tag-gradient","tag-graphs","tag-mathematical-misunderstandings","tag-question-analysis","tag-units"],"_links":{"self":[{"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=\/wp\/v2\/posts\/696","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=696"}],"version-history":[{"count":5,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=\/wp\/v2\/posts\/696\/revisions"}],"predecessor-version":[{"id":804,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=\/wp\/v2\/posts\/696\/revisions\/804"}],"wp:attachment":[{"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=696"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=696"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}