{"id":58,"date":"2018-10-14T21:36:54","date_gmt":"2018-10-14T21:36:54","guid":{"rendered":"https:\/\/borovik.net\/selecta\/?p=58"},"modified":"2025-12-13T21:47:35","modified_gmt":"2025-12-13T21:47:35","slug":"confident-students-do-not-cheat","status":"publish","type":"post","link":"https:\/\/borovik.net\/selecta\/2018\/10\/14\/confident-students-do-not-cheat\/","title":{"rendered":"Confident students do not cheat"},"content":{"rendered":"<p>This is the abstract of a talk given by me at the Meeting &#8220;<em>Mathematical Academic Malpractice in the Modern Age<\/em>&#8220;, Manchester, Monday 21st May 2018, with the title<\/p>\n<blockquote><p><strong>Confident students do not cheat: how to build mathematical confidence in our students<\/strong><\/p><\/blockquote>\n<p>I think it could be useful to address the question which, in my experience, is almost never asked: what pushes problem students to cheat by plagiarising work from their peers and, increasingly, from the Internet? Some answer can be found in Denizhan (2014):<\/p>\n<blockquote><p>&#8220;These students exhibit an inability to evaluate their own performances independent of external measurements.&#8221;<\/p><\/blockquote>\n<p>Plagiarism is one of the psychological defences of a student who does not otherwise know whether his\/her solution \/ answer is correct. Mathematics provides a simple remedy: systematically teach students how they can check their solutions. This will boost their confidence in their answers &#8211; and in themselves. I teach linear algebra; I have at least two dozen undergraduate linear algebra textbooks in my office &#8212; none of them provides systematic advice on these matters. The same applies, I think, to any other undergraduate subject. In my view, the most efficient methods for checking answers in a particular class of problems usually provided by a more advanced point of view. For example,<\/p>\n<ul>\n<li>all these elementary problems about systems of linear equations can be effectively checked if the concepts of the rank of a matrix is used;<\/li>\n<li>the correctness of eigenvalues of a matrix can be checked by using the fact that the sum of eigenvalues is the trace of the matrix, and the product is its determinant, etc.<\/li>\n<\/ul>\n<p>This retrospective reassessment of previous material can give students a chance to see how actually simple it is &#8212; and boost their mathematical confidence. In my talk, I&#8217;ll discuss how to incorporate error-correcting aspects of mathematics into course design.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is the abstract of a talk given by me at the Meeting &#8220;Mathematical Academic Malpractice in the Modern Age&#8220;, Manchester, Monday 21st May 2018, with the title Confident students do not cheat: how to build mathematical confidence in our students I think it could be useful to address the question which, in my experience, [&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-58","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/posts\/58","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/comments?post=58"}],"version-history":[{"count":1,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/posts\/58\/revisions"}],"predecessor-version":[{"id":59,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/posts\/58\/revisions\/59"}],"wp:attachment":[{"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/media?parent=58"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/categories?post=58"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/borovik.net\/selecta\/wp-json\/wp\/v2\/tags?post=58"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}