My Weekly Report and Reflection 5

          This past week's math class had me thinking about math differently and reflecting upon my previous learning experiences. We were discussing ways in which future educators can step outside of the box to give students learning opportunities that allow them to use their intuition and formulate ideas by drawing and representing mathematical problems. Too often, educators have their students learn a particular formula for calculating a problem and then give them a worksheet of questions that involve applying said formula. The problem with this, is that when it comes time to give a summative assessment to students, they have had a lot of practice with each individual formula but have had no practice making decisions about which formula to apply. Reflecting upon my own mathematical learning experiences, this form of rote formulaic application defines the way that I learned math. Feeling a little cheated about my elementary/secondary education and thinking about my next upcoming teaching block, I have been thinking greatly about ways that I can take students to the next level in their self guided learning experience. How can I present ideas to my students that allow them to ask their own questions, represent mathematical problems in their own ways, use their intuition and be motivated enough to research those ideas through a student-centered educational journey?
       
          One way that I would like to help myself to step outside of this teaching box is by becoming more familiar with the TPACK educational framework. An acronym that stands for Technological Pedagogical Content Knowledge, TPACK presents itself as a trifecta of knowledge that can help future educators to give new and beneficial learning experiences to their students.

Koehler, M. (2016, July 2). "TPACK Image: Reproduced by permission of the publisher, © 2012 by tpack.org" [Online Image]. Retrieved from http://www.matt-koehler.com/tpack/using-the-tpack-image/

          In our course we have learned that the most beneficial forms of learning occur when a student is able to connect new concepts to previous experiences or prior knowledge. Stepping outside of the educator's role for a moment, I feel as though I am a little uncomfortable with this framework because the technological content and concepts being taught to us have no place to connect to my previous education. In class we explored an interesting online resource at geogebra.org and had the chance to play around with creating lines, segments, perpendicular lines, angles, polygons and circles. The one portion of this exploration that resonated most with me was drawing perpendicular lines using two intersecting circles. The question started out by giving us a straight line with two opposing points, one at either end. We were asked if we could draw a perpendicular line by using those two starting points. Instantly, my previous knowledge of using a physical compass to create intersecting circles came back to me and I was able to complete this problem. Reflecting on this experience I think that my previous knowledge came back to me because of the tactile experience of actually using a compass to solve this problem. Part of me wonders if using an online resource such as this one would eliminate one part of learning by removing the physical process of using a compass. Maybe a resource like this one would be beneficial as a form of differentiation after students have had a chance to use a real compass.

          With this in mind, I have already begun to look into ways that I can create mathematical investigations by using tech enhanced instruction to help my students guide their own learning experiences. In my upcoming class demonstration, a partner and I have created a mini math inquiry involving place value by using google slides. Giving the entire class an image prompt, we will be exploring and discussing open inquiry and closed inquiry when approaching this problem. While creating this demonstration we reflected on the best ways to set up an open form of inquiry where our colleagues will make statements about what they notice and ask questions about what they are wondering.  Due to time restrictions we will then switch into a more closed inquiry where we give everyone a piece of information about the same image prompt. Individuals taking part in this investigation will need to draw the image prompt into their notebooks, use their intuition and formulate ideas about how to solve the question. When solving the question they will need to use mathematical conjectures to convince themselves, convince a friend, and convince an enemy to prove whether or not their solution is correct. Although this mini inquiry is not a tech enhanced as I would like, I feel as though it is our best effort at taking the first steps to create an investigation that will have students guiding their own learning. I look forward to receiving some beneficial feedback from our professor that will help us to improve this investigation for a more tech enhanced learning experience.