{"id":753,"date":"2011-12-23T09:02:32","date_gmt":"2011-12-23T09:02:32","guid":{"rendered":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/?p=753"},"modified":"2012-01-18T09:14:44","modified_gmt":"2012-01-18T09:14:44","slug":"estimating-gradient-of-curves-when-variants-behave-differently","status":"publish","type":"post","link":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/?p=753","title":{"rendered":"Estimating the gradient of curves – variants behaving differently"},"content":{"rendered":"

The screenshots below show two variants of the same question. I should start by emphasising that the question is only used formatively – it’s on the Maths for Science<\/em> Practice Assignment.<\/p>\n

\"\"<\/a><\/p>\n

The two variants behave very differently and the reason for this has very little to do with student’s understanding. 63% of responses to the variant on the right-hand side\u00a0selected the correct response but only\u00a049% of responses to the variant on the left-hand side selected the correct response . The difference can be explained by the relatively large proportion of responses (12% just below and 14% just above)\u00a0to the left-hand side variant which gave responses adjacent to the correct one. Students who\u00a0calculate a value close to the correct one are likely to find their ‘almost right’ answer amongst the available options. In contrast, for the right-hand side variant, the incorrect options are more different from the correct one, so students whose calculated answer is a little way off are\u00a0more likely to select the correct option as the nearest.<\/p>\n

I can remember why I asked this question as a multiple choice question (to do with the difficulty in drawing a tangent and estimating the gradient of a curve) however I don’t think I made the right decision and this is not a question of which I’m proud! I should have asked students to estimate the gradient and give their answer as free-text number. I could then have\u00a0accepted a range of values, \u00a0monitored the actual values given and adjusted the range accepted.<\/p>\n

There are of\u00a0 some lessons here about the design of multiple-choice questions and about question design in general.<\/p>\n","protected":false},"excerpt":{"rendered":"

The screenshots below show two variants of the same question. I should start by emphasising that the question is only used formatively – it’s on the Maths for Science Practice Assignment. The two variants behave very differently and the reason … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[167,111,110],"tags":[384,369,356],"class_list":["post-753","post","type-post","status-publish","format-standard","hentry","category-gradient","category-mathematical-misunderstandings","category-question-analysis","tag-gradient","tag-mathematical-misunderstandings","tag-multiple-choice-questions"],"_links":{"self":[{"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=\/wp\/v2\/posts\/753","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=753"}],"version-history":[{"count":6,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=\/wp\/v2\/posts\/753\/revisions"}],"predecessor-version":[{"id":759,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=\/wp\/v2\/posts\/753\/revisions\/759"}],"wp:attachment":[{"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/SallyJordan\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}