{"id":77,"date":"2022-05-07T05:35:22","date_gmt":"2022-05-07T05:35:22","guid":{"rendered":"https:\/\/src.cikeys.com\/2022\/?page_id=77"},"modified":"2023-02-15T05:24:58","modified_gmt":"2023-02-15T05:24:58","slug":"analyzing-student-understanding-of-mathematical-induction","status":"publish","type":"page","link":"https:\/\/src.cikeys.com\/2022\/analyzing-student-understanding-of-mathematical-induction\/","title":{"rendered":"Analyzing Student Understanding of Mathematical Induction"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Citlalli Villegas and Dr. Ivona Grzegorczyk<\/h3>\n\n\n\n<!--more-->\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h2 class=\"wp-block-heading\">Abstract<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Many undergraduates have difficulty with the principle of mathematical induction (PMI). This project seeks to understand the common struggles associated with this topic and how it relates to students\u2019 overall performance in their course. Additionally, it explores how educators can transform their standard approach to teaching mathematical induction in a way that builds on students\u2019 prior knowledge to create a strong foundation for this type of proof writing. This project gathered data from 80 students, a majority of whom were freshmen. We analyze their response to a midterm question on mathematical induction requiring knowledge of series. We also gathered data from a group of 20 seniors to analyze their performance on a similar induction question and compare their results to the freshmen. Our data explored several correlations between student understanding of checking for small numbers, formulating k + 1 correctly, identifying the induction hypothesis, performing the induction step and arriving at correct conclusions.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h2 class=\"wp-block-heading\">Presentation<\/h2>\n\n\n<iframe loading=\"lazy\"  id=\"_ytid_41030\"  width=\"720\" height=\"405\"  data-origwidth=\"720\" data-origheight=\"405\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/RHvPM3oc8jI?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;disablekb=0&#038;\" class=\"__youtube_prefs__  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe>\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-8997713f-9a6e-4bd7-a5d8-a09017a46afb\" href=\"https:\/\/src.cikeys.com\/2022\/wp-content\/uploads\/2022\/05\/Citlalli-Villegas-Analyzing-Student-Understanding-of-Mathematical-Induction.pdf\">Presentation File<\/a><a href=\"https:\/\/src.cikeys.com\/2022\/wp-content\/uploads\/2022\/05\/Citlalli-Villegas-Analyzing-Student-Understanding-of-Mathematical-Induction.pdf\" class=\"wp-block-file__button\" download aria-describedby=\"wp-block-file--media-8997713f-9a6e-4bd7-a5d8-a09017a46afb\">Download<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<iframe src=\"http:\/\/docs.google.com\/gview?url=https:\/\/src.cikeys.com\/2022\/wp-content\/uploads\/2022\/05\/Citlalli-Villegas-Analyzing-Student-Understanding-of-Mathematical-Induction.pdf&amp;embedded=true\" style=\"width:100%; height:600px;\" frameborder=\"0\"><\/iframe>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Citlalli Villegas and Dr. Ivona Grzegorczyk<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[4],"tags":[7],"class_list":["post-77","page","type-page","status-publish","hentry","category-poster","tag-mathematics","post"],"_links":{"self":[{"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/pages\/77","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/comments?post=77"}],"version-history":[{"count":4,"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/pages\/77\/revisions"}],"predecessor-version":[{"id":602,"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/pages\/77\/revisions\/602"}],"wp:attachment":[{"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/media?parent=77"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/categories?post=77"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/src.cikeys.com\/2022\/wp-json\/wp\/v2\/tags?post=77"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}