My Weekly Report and Reflection 6

          It is hard to believe that almost six weeks have past since I began this course and that in less than two weeks I will be standing in my second classroom, ready to begin teaching a grade 8 class for a seven week period. This unfortunately means that I will be writing my last reflective post, but I am pleased to say that this past week has been the best learning experience that I have had in this course. In the last class my partner and I had the opportunity to deliver a 30 minute presentation, the purpose of which was to facilitate a beneficial learning experience for my peers. The topic that we chose was teaching strategies/math inquiry and by the end of the presentation I think the learning experience was two fold. I wouldn't be surprised if my partner and I learned more from this experience than our peers. We delivered a math inquiry involving place value and the beautiful part about this demonstration was experiencing just how risky inquiry can be. We had hoped that we would have seen a diverse display of strategies being used to solve for the problem but every group decided to figure out the problem in the same way. This meant that we needed to be flexible in our delivery of the lesson and ask questions that guided the students' thinking towards other possible solution strategies. To consolidate we discussed these strategies and then we discussed the other teaching strategies that were being intertwined with the inquiry lesson. Although a struggle to design and facilitate, this learning experience has allowed me to feel just a little more comfortable in my ability to run other inquiry lessons in the future and to be confident in my ability to be a flexible educator who can go with the flow during a lesson. For the purpose of this post I don't want to dive to far into this inquiry lesson and all of the little intricacies that were involved, partly because I have already written a reflection about this experience, but also because there were other great learning experiences for me while participating in the other group members' learning demonstrations.

          As I have mentioned earlier in this blog, fractions and I are not the best of friends. Not because I don't understand them, but because I find them difficult to teach. One of the groups presenting in the last class did an excellent job showing how to differentiate the process of learning and did so under the umbrella of teaching fractions. We participated in learning about fractions through three separate learning stations. One stations used paper plates with various visual displays of fractions and required us to group them into separate fraction categories (e.g., 1/4, 5/8 and 2/16). Another station required us to make up a song about fractions after watching three different video examples modelling our task. The last station allowed participants to use an app on the computer requiring us to make different sized pizzas, each with their own separate fraction of toppings. This app was engaging because the faster and more accurate that you could create the correct pizzas, the more money you made. Each group tried their best to outdo the last group and the competition made everyone put in their best effort. Throughout these stations, the one that I had the most amount of difficulty with was the paper plates station. For some reason the various picture representations involving different fractions was hard for me to discern. The more practice I got with them, however, the better I got at picking the correct paper plate. My partner was a big help during this station and I learned from this that it is important to have a collaborative partner during these stations because we learned from each other and the learning experience was far more useful and engaging. In the future when I run a math lesson such as this I will be sure to make collaborative groups where those who fully understand the problem can help those that are struggling and together they can benefit from the partnership.

          It was interesting to see the contrast between this kind of partnered learning experience to the more independent kind of learning experienced seen in the demonstrations involving financial literacy. Two group shad this same topic and each group decided to take more of an independent approach. One group used the Kahoot! online app to facilitate a questionnaire and I found this app to be very useful in promoting competition but it was also difficult for me to do well because each question is timed and the faster you answer the question, the more points you get. This element to the learning experience didn't allow me to think through the questions enough to really give an honest account of my learning because I was more worried bout my speed. I learned from this experience that this kind of app is very useful as a minds on or icebreaker activity that excites students and encourages them to be interested in the action or core activity portion of the lesson. The other lesson demonstration involving financial literacy was more of a hands-on demonstration where the group gave each individual five hundred monopoly dollars and were asked to spend our money on a variety of items that we would need for the month. Those items ranged from tuition, to rent, to groceries, to games and so on. The list of items essentially ranged from very useful and based on necessity, to least useful and based on want. During this activity we were also allowed to save any money that we thought appropriate. Along with their icebreaker activity that had us reviewing different terms involved with financial literacy, I was influenced to think more about my needs than my wants and was positively thinking about my future spending habits and my financial goals. I believe that with this kind of positive set-up, younger students who often don't think about these kinds of life skills would also be encouraged to incorporate such spending habits into their daily life. Essentially I learned that giving students these kinds of tools early in life will benefit them in the future and help them to be more mindful individuals who are more concerned with their needs than their wants and can become active participants in future change.

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. 

         
         
         

My Weekly Report and Reflection 4

          This week's math class was a beneficial one for me as I learned about interleaving practice and creating rich performance tasks. It is very easy to get caught up in the idea that a math class must be organized into neatly packaged blocks that teach students a concept and then has them performing tasks related to said content. After that information has been ingrained into each student the teacher will give an assessment that relates to that idea. The issue with this approach is that it doesn't leave room for students to make decisions about the strategies they will use to solve the problem. They already know that they will be using a particular set of operations to find the solution. Interleaving practice helps teachers to overcome that stale form of instruction. Interleaving practice involves the instruction of more than one concept at a time and then requires students to decide what kind of strategies need to be used to solve the problem. They will already have all of the tools necessary to address both content areas but will need to take that learning one step further as they ask themselves questions about what is being asked of them and which operations are needed to find a solution. In class I discussed the idea of teaching students the content areas of perimeter and area and having them solve problems that relate to both concepts. Our instructor felt as though this would be an appropriate form of interleaving. As I left the class I continued to think about this issue and was reminded of my past experiences teaching these two concepts to grade 4 students. Perimeter was one that they grasped fairly well, however, area took a lot more finessing to achieve a deeper level of understanding. In this regard I think it is important for educators to perform lots of formative assessments as they teach these two concept areas so that they have enough evidence of learning to determine whether or not their students are ready for an interleaving assessment. Creating rich performance tasks for students in both content areas can give educators the information they need to make that judgment call.

           Rich performance tasks are ones that allow students to ask questions, leads to other problems and has many possibilities. Much like the decision making process involved in interleaving practice, rich performance tasks encourage students to ask themselves questions about what the problem is asking them to do. I experienced this in today's class as we were given two mixed fractions: 3 1/4 and 3 31/9. The question asked us to find three other mixed fractions that fit in-between these two given mixed fractions. Right away I was asking myself what needed to be done here and how was I going to determine which three mixed fractions fit in the middle. I immediately turned to decimals so that I could give myself a range. Once I had that I needed to fool around with some other fractions to find if their decimal equivalents fit within my range. It was interesting to see how this kind of question had other possibilities as well. Some students decided to make common denominators to figure out the improper fractions that would fit in-between the original mixed fractions. These improper fractions could then be turned into mixed fractions and I was again reminded about some of the operations that I had forgotten since high school.

(Dekker, 2016)

          Later we expanded on that idea by using various repeating decimals to figure out what fractions would be their equivalents (without using Google's search engine). These problems had me intrigued and I first struggled with figuring them out. After some trial and error I was able to figure out how to get the correct answer and I started to think about what kinds of real-world applications that could be used to create rich performance tasks that have students asking questions about this kind of content area. Fractions have always been a difficult subject area for me as I have mentioned in previous posts and I'm still wondering and interested about ways that I can incorporate these kinds of problems into my classroom to help students work with fraction problem solving.