{"id":4850,"date":"2018-01-31T07:02:46","date_gmt":"2018-01-31T14:02:46","guid":{"rendered":"https:\/\/blogs.ubc.ca\/stem2018\/?p=4850"},"modified":"2018-01-31T21:53:12","modified_gmt":"2018-02-01T04:53:12","slug":"tpck-and-me","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/stem2018\/2018\/01\/31\/tpck-and-me\/","title":{"rendered":"(T)PCK and Me"},"content":{"rendered":"<p><span style=\"font-weight: 400\">I first encountered the TPCK framework in one of my earliest MET courses yet I still think about it every term, whether it comes up formally in the readings or not. At the risk of sounding like every classic educational reading, I credit the persistence of my reference to TPACK due to its simplicity as a framework, one that elegantly encompasses so many key ideas that lie at the heart of education.<\/span><\/p>\n<p><span style=\"font-weight: 400\">The clearest description I encountered of the original PCK framework came from Shulman (1987), who describes it as the \u201cblending of <\/span><b>c<\/b><span style=\"font-weight: 400\">ontent and <\/span><b>p<\/b><span style=\"font-weight: 400\">edagogy into an understanding of how particular topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and presented for instruction.\u201d Although first written in 1987, the statement resonates strongly over three decades later and continues to inspire (well, to inspire me, at least). I always viewed PCK as a practical application of the classic expression \u201cgreater than sum of its parts\u201d; while <\/span><b>p<\/b><span style=\"font-weight: 400\">edagogical <strong>k<\/strong>nowledge and <\/span><b>c<\/b><span style=\"font-weight: 400\">ontent <strong>k<\/strong>nowledge are essential, the greatest lessons are created using both at once.<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><span style=\"font-weight: 400\">Not to leave the most relevant knowledge type (to ETEC533) out to dry, Mishra &amp; Koehler (2006, p. 1029) extended Shulman\u2019s framework to include <\/span><b>technology<\/b><span style=\"font-weight: 400\">, which details TPCK as:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">the basis of good teaching with <\/span><b>t<\/b><span style=\"font-weight: 400\">echnology;<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">requires an understanding of the <\/span><i><span style=\"font-weight: 400\">representation of concepts using technologies<\/span><\/i><span style=\"font-weight: 400\">;<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">pedagogical techniques that <\/span><i><span style=\"font-weight: 400\">use technologies in constructive ways<\/span><\/i> <span style=\"font-weight: 400\">to teach content;<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">knowledge of what makes concepts difficult or easy to learn and <\/span><i><span style=\"font-weight: 400\">how technology can help redress some of the problems <\/span><\/i><span style=\"font-weight: 400\">that students face;<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">knowledge of students\u2019 <\/span><i><span style=\"font-weight: 400\">prior knowledge <\/span><\/i><span style=\"font-weight: 400\">and theories of epistemology; and<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">knowledge of how technologies can be used to <\/span><i><span style=\"font-weight: 400\">build on existing knowledge <\/span><\/i><span style=\"font-weight: 400\">and to <\/span><i><span style=\"font-weight: 400\">develop new epistemologies <\/span><\/i><span style=\"font-weight: 400\">or <\/span><i><span style=\"font-weight: 400\">strengthen old ones<\/span><\/i><span style=\"font-weight: 400\">.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">Mishra &amp; Koehler continue by giving ideas on how to develop lessons using the framework with technology included.<\/span><\/p>\n<hr \/>\n<p><span style=\"font-weight: 400\">As for an example of how I teach a particular concept, I\u2019ve chosen my most recent \u201cversion\u201d of teaching <strong>Integration by Parts<\/strong> in math.<\/span><\/p>\n<p><b>Notes<\/b><\/p>\n<p><span style=\"font-weight: 400\">I start by either handing out notes physically or making sure my students have a copy of the notes through some platform like D2L. If students don\u2019t use a physical copy I encourage them to use a program on their mobiles that allows them to take and save notes.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4851 aligncenter\" src=\"https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-notes.png\" alt=\"some math notes for integration by parts\" width=\"749\" height=\"483\" srcset=\"https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-notes.png 1313w, https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-notes-300x194.png 300w, https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-notes-768x495.png 768w, https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-notes-1024x661.png 1024w, https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-notes-620x400.png 620w\" sizes=\"auto, (max-width: 749px) 100vw, 749px\" \/><\/p>\n<p><b>Mind Map &#8211; Assessing and Building on Prior Knowledge<\/b><\/p>\n<p><span style=\"font-weight: 400\">I\u2019ll write \u201cIntegration by Parts\u201d in a circle on the board and ask a bunch of questions about what students think it means, what topics we\u2019ve covered in Calculus up to this point and so on. I have them \u201cremind me\u201d what integration techniques they know so far. This is a mix of direct questions or passive observations. Depending on what the class comes up with I may assign a few short review questions or solve some quick problems on the board. I\u2019ll usually return to this throughout the class and make connections (literally, with lines) between what they\u2019re learning today to what they (should) already know. Ultimately the whole point on this part is to help them determine that they do not yet have a strategy to solve the types of integration problems they\u2019re seeing today.<\/span><\/p>\n<p><b>Formal Introduction to Topic<\/b><\/p>\n<p><span style=\"font-weight: 400\">Once the scene is set I\u2019ll work through some examples with them and introduce them to a new formula:<\/span><\/p>\n<p style=\"text-align: center\"><em><span style=\"font-weight: 400\">\u222budv=uv-\u222b<\/span><span style=\"font-weight: 400\">vdu<\/span><\/em><\/p>\n<p><span style=\"font-weight: 400\">I often help students connect this formula to a prior formula (&#8216;Product Rule&#8217; in differentiation) through a short, non-rigorous \u201cproof\u201d. This tends to help them remember it, or at least buy in slightly, as it gives them some context of where it came from.<\/span><\/p>\n<p><b>Piece-by-Piece<\/b><\/p>\n<p><span style=\"font-weight: 400\">Without getting too detailed (in this post), I spent the next few minutes working through an example with students and explaining the philosophy behind how to approach solving problems like this, one step at a time. I began including a mnemonic, LIPET, for students who struggled badly with this, and this tends to help them succeed assessment-wise.<\/span><\/p>\n<p><b>Checking for Misunderstanding<\/b><\/p>\n<p><span style=\"font-weight: 400\">After this I have students break out into groups to work on the first set of practice problems, one designed to iron out misconceptions or misunderstandings of the concept before they have to do any real calculations. I circle the room while they discuss the problems with each other and compare solutions. A student (or a few students &#8211; time depending) is asked to write their solutions on the board &#8211; or cast it using ScreenBeam or AirPlay &#8211; and them we discuss them as a class.<\/span><\/p>\n<p><span style=\"font-weight: 400\">(For those who know the topic of Integration by Parts, this activity asks students to look at a set of expressions to determine 1) which function should be labeled as <\/span><em><span style=\"font-weight: 400\">u<\/span><\/em><span style=\"font-weight: 400\">, which will in turn give <\/span><em><span style=\"font-weight: 400\">du<\/span><\/em><span style=\"font-weight: 400\">, and 2) which function to label as <\/span><em><span style=\"font-weight: 400\">dv<\/span><\/em><span style=\"font-weight: 400\">, which will in turn give <\/span><em><span style=\"font-weight: 400\">v<\/span><\/em><span style=\"font-weight: 400\">).<\/span><\/p>\n<p><b>Practice Time<\/b><\/p>\n<p><span style=\"font-weight: 400\">Once we\u2019ve had a discussion why may range from from pairs, to groups, to the whole class, a set of practice problems is assigned to work on solidfying what they have been working on today. Students may work independently or in groups, while I check in on all students throughout. Eventually students are provided full solutions which may be projected on the board at the front of the class or accessed online through D2L or similar, and they check each other\u2019s work. Issues are flagged and I may choose to review questions either on a per-student basis on for everyone on the board. It depends on how many students had the same issue, and whether or not a student could instead be used to help another student. <\/span><\/p>\n<p><b>Using Technology to Redress Problems<\/b><\/p>\n<p><span style=\"font-weight: 400\">To end the lesson I provide an \u201cIntegration by Parts Exit Card\u201d which is essentially 2 quick multiple choice questions that contain question types students often struggle with. This is either a physical card that they circle an answer on, or more commonly I will have them respond using something like Google Forms. Once they finish the card and submit it they can leave, and I\u2019ll aggregate and review the results prior to the next class. This allows me to ensure that I can focus on specific problems my class is having with the topic before we build on it.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4852 aligncenter\" src=\"https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-exit-card.png\" alt=\"exit cards\" width=\"591\" height=\"399\" srcset=\"https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-exit-card.png 968w, https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-exit-card-300x203.png 300w, https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-exit-card-768x519.png 768w, https:\/\/blogs.ubc.ca\/stem2018\/files\/2018\/01\/ibp-exit-card-620x419.png 620w\" sizes=\"auto, (max-width: 591px) 100vw, 591px\" \/><\/p>\n<hr \/>\n<p><span style=\"font-weight: 400\">And that\u2019s about it! I don&#8217;t leverage tech too much for this lesson because I haven&#8217;t found too much tech that seems like it would actually benefit the students, but I feel that the tech I do use is beneficial.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Do you have any suggestions on how I could improve here? I\u2019d love to get some feedback!<\/span><\/p>\n<p><span style=\"font-weight: 400\">Thanks for reading,<\/span><\/p>\n<p><span style=\"font-weight: 400\">Scott<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>References<\/p>\n<p>Mishra, P., &amp; Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge.\u00a0<i>Teachers college record<\/i>,\u00a0<i>108<\/i>(6), 1017-1054.<br \/>\nShulman, L. (1987). Knowledge and teaching: Foundations of the new reform.\u00a0<i>Harvard educational review<\/i>,\u00a0<i>57<\/i>(1), 1-23.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I first encountered the TPCK framework in one of my earliest MET courses yet I still think about it every term, whether it comes up formally in the readings or not. At the risk of sounding like every classic educational reading, I credit the persistence of my reference to TPACK due to its simplicity as [&hellip;]<\/p>\n","protected":false},"author":44953,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1669398],"tags":[],"class_list":["post-4850","post","type-post","status-publish","format-standard","hentry","category-b-pck"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/4850","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/users\/44953"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/comments?post=4850"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/4850\/revisions"}],"predecessor-version":[{"id":4873,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/4850\/revisions\/4873"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/media?parent=4850"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/categories?post=4850"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/tags?post=4850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}