{"id":44,"date":"2014-11-01T23:25:38","date_gmt":"2014-11-01T23:25:38","guid":{"rendered":"https:\/\/cohort21.com\/andrewruston\/?p=44"},"modified":"2014-11-01T23:25:38","modified_gmt":"2014-11-01T23:25:38","slug":"technology-and-the-enduring-understandings-of-algebra","status":"publish","type":"post","link":"https:\/\/cohort21.com\/andrewruston\/2014\/11\/01\/technology-and-the-enduring-understandings-of-algebra\/","title":{"rendered":"Technology and the Enduring Understandings of Algebra"},"content":{"rendered":"<p><a href=\"https:\/\/cohort21.com\/andrewruston\/wp-content\/blogs.dir\/72\/files\/2014\/11\/PhotoMath.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-45 aligncenter\" src=\"https:\/\/cohort21.com\/andrewruston\/wp-content\/blogs.dir\/72\/files\/2014\/11\/PhotoMath-300x168.jpg\" alt=\"PhotoMath\" width=\"382\" height=\"214\" srcset=\"https:\/\/cohort21.com\/andrewruston\/files\/2014\/11\/PhotoMath-300x168.jpg 300w, https:\/\/cohort21.com\/andrewruston\/files\/2014\/11\/PhotoMath-1024x576.jpg 1024w, https:\/\/cohort21.com\/andrewruston\/files\/2014\/11\/PhotoMath-960x540.jpg 960w, https:\/\/cohort21.com\/andrewruston\/files\/2014\/11\/PhotoMath-100x56.jpg 100w\" sizes=\"auto, (min-width: 960px) 75vw, 100vw\" \/><\/a><\/p>\n<p><a href=\"https:\/\/photomath.net\/\">PhotoMath\u00a0<\/a>came out a few weeks ago and it has given me a lot to think about.\u00a0It&#8217;s funny how a new technology can force you to\u00a0look inward and re-evaluate\u00a0what your role is as a Math teacher.<\/p>\n<p>My\u00a0first\u00a0thought was, of course, &#8220;How cool is this!&#8221;. An app that lets you take a picture of an equation, and it shows you not only the answer, but the step-by-step process to solve it. \u00a0I showed some of my students and they had a similar response. It was also followed by the question &#8220;isn&#8217;t using this cheating?&#8221;. That&#8217;s a great question.\u00a0As I told my students, I don&#8217;t think it is cheating at all.<\/p>\n<p>We have to design our courses and learning goals to be valuable in the context of\u00a0the 21st century. The actual solving\u00a0is more efficiently\u00a0done by computers in the modern world, especially when the equations get more complicated. The next logical question is: What can people do that computers can&#8217;t? This is what I could come up with:<\/p>\n<ul>\n<li>People can think critically and\u00a0interpret solutions to equations in the real world in order to solve real problems.<\/li>\n<li>People can use their understanding of mathematics to program computers to automate processes.<\/li>\n<li>People can use their understanding of mathematics to develop new processes to solve a broader scope of problems.<\/li>\n<\/ul>\n<p>This is what I hope to be training my students to be prepared to do.<\/p>\n<p>I have been planning a project (with a lot of\u00a0help from fellow BSS teachers <a href=\"https:\/\/twitter.com\/J0eMcRae\">Joseph McRae<\/a> and Cassandra Arsenault) with the goal of facilitating\u00a0this type of learning.\u00a0They will use the <a href=\"http:\/\/scratch.mit.edu\/\">Scratch<\/a> environment to write\u00a0a program that allows the user to solve simple equations instantly from a pre-set list. Examples:<\/p>\n<p><a href=\"https:\/\/cohort21.com\/andrewruston\/wp-content\/blogs.dir\/72\/files\/2014\/11\/eq.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-46 aligncenter\" src=\"https:\/\/cohort21.com\/andrewruston\/wp-content\/blogs.dir\/72\/files\/2014\/11\/eq-300x45.png\" alt=\"eq\" width=\"340\" height=\"51\" srcset=\"https:\/\/cohort21.com\/andrewruston\/files\/2014\/11\/eq-300x45.png 300w, https:\/\/cohort21.com\/andrewruston\/files\/2014\/11\/eq-100x15.png 100w, https:\/\/cohort21.com\/andrewruston\/files\/2014\/11\/eq.png 616w\" sizes=\"auto, (min-width: 960px) 75vw, 100vw\" \/><\/a><\/p>\n<p>This can be done fairly easily from a coding perspective. Hopefully the students end the project with not only a better sense of how to work with and rearrange equations without substitution of numbers, but also a better understanding of what the role\u00a0of a 21st century mathematician is.<\/p>\n<p>The computer should be doing the heavy lifting, but people\u00a0should be doing the thinking.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>PhotoMath\u00a0came out a few weeks ago and it has given me a lot to think about.\u00a0It&#8217;s funny how a new technology can force you to\u00a0look inward and re-evaluate\u00a0what your role is as a Math teacher. My\u00a0first\u00a0thought was, of course, &#8220;How cool is this!&#8221;. An app that lets you take a picture of an equation, and &hellip; <a href=\"https:\/\/cohort21.com\/andrewruston\/2014\/11\/01\/technology-and-the-enduring-understandings-of-algebra\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Technology and the Enduring Understandings of Algebra&#8221;<\/span><\/a><\/p>\n","protected":false},"author":78,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"wds_primary_category":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-44","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/cohort21.com\/andrewruston\/wp-json\/wp\/v2\/posts\/44","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cohort21.com\/andrewruston\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cohort21.com\/andrewruston\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cohort21.com\/andrewruston\/wp-json\/wp\/v2\/users\/78"}],"replies":[{"embeddable":true,"href":"https:\/\/cohort21.com\/andrewruston\/wp-json\/wp\/v2\/comments?post=44"}],"version-history":[{"count":0,"href":"https:\/\/cohort21.com\/andrewruston\/wp-json\/wp\/v2\/posts\/44\/revisions"}],"wp:attachment":[{"href":"https:\/\/cohort21.com\/andrewruston\/wp-json\/wp\/v2\/media?parent=44"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cohort21.com\/andrewruston\/wp-json\/wp\/v2\/categories?post=44"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cohort21.com\/andrewruston\/wp-json\/wp\/v2\/tags?post=44"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}