Week 5 Reflection

In this weeks class we were responsible for reading chapter 14 in the Making Math Meaningful textbook. This chapter was focused on integers. However, integers are a fairly straightforward topic and we did not actually spend that much time on this topic. Instead of breaking down the intricacies of the mathematical topic of integers, Pat wanted us to move away from just trying to teach integers by teaching rules. Instead of just hammering into the students heads that multiplying or dividing a negative and a positive will equal a negative, or that two negatives multiplied equal a positive, she told us that we need to be able to explain the reasoning and thought process behind these algorithms. She also said that until we are able to fully explain these concepts, we should not be basing our lessons around teaching them; the formula is not as important as the reasoning behind it.

            We actually spent a lot of time revisiting last weeks topic of fractions as Pat said that she realized many of the students in the class, including myself, were having a little bit of trouble understanding fractions from this new perspective of us being the teacher. She began the lesson with an activity called red light green light. I really enjoy the way that Pat teaches and you can see the experience that she has in the way that she runs her lessons. She chooses an activity that gets the class physically involved and then relates it to a lesson. In the green light game you are thinking about fractions in terms of who is closer to the end, without even really knowing that you are, as it is just part of the game. You are fostering a real life connection to the mathematical concepts in the students. I also really enjoyed the Mr. Tan problem involving the broken tile. Again, you can feel Pats experience in the way she leads the class. I hope to one day be that comfortable and smooth in my lessons; she dropped the tiles at just the right moment when explaining the problem and smoothly involved the mathematics into her story telling. I think using stories to teach is a great technique, but for me, the one challenge that I find in that is being able to find an appropriate story for the lesson, and making sure that what you are trying to teach is clear and understood.

Vinayak Hedge. (2011) Porcelain Tile. [Online Image] http://bit.ly/1PaO89z

            We also covered an interesting technique that we were never taught in school. Much like last week, Patricia showed us that the algorithms that we were taught in elementary school might not have been the best way to teach the concept. For example, when dividing fractions, we were taught to flip the fractions and multiply, however, Patricia showed us that if the denominators are easily divisible, you can simple divide across, much like you can just multiply across fractions. Furthermore, if the denominators are not easily divisible, you just have to convert the fraction into one that is easily divisible. This makes the division of fractions much easier in my eyes and is something that I will keep in mind when teaching fractions in my own class. Again, this is evidence that the concept behind why you do things in math is more important than how you do it. I cannot explain why we were taught to flip the fraction and multiply, so why would I teach that to the students. This does not foster a deep understanding of math, but rather it just leads to memorization of algorithms. This style of teaching and learning may work for some students, but you can be sure that it will not work for all; if you are able to explain the concepts fully you have a better chance of making sure that everyone leaves your math lesson feeling like they understand fractions better than they did before class. 
            We also had a good discussion in class about what to do when a child asks you a question, or provides input that you were not prepared to address, or that you don’t know how to respond. Pat told us not to be afraid to ask the class about what they know and for explanations and interpretations of mathematical concepts. She says that as new teachers we will undoubtedly be nervous trying to lead these types of discussions because we are not sure of what a child is going to say. However, she told us that we cannot be rattled, and we have to be ready for a student to say anything. Our job is to try and make sense of it on the go, and to relate it to our lesson if possible. There is no right or wrong when asking students what they know.  We also explored CLIPS [http://oame.on.ca/CLIPS/] which is a great resource for teachers that identifies common gaps in student learning and gives lesson plans/teacher notes and games that students can play to fortify their learning of troublesome concepts. This is great resource and I can see myself consulting it to get lesson ideas and to fortify my own.