My weekly report and reflection 2

          In this week's math class I found myself doing three important things that really struck home with me. I revisited an old concept that frustrates me and I was performing some creative in class activities. To begin this post I will address the concept that frustrates me the most in mathematics. That concept is fractions. In our last meeting we were discussing the ways of approaching this topic with students and how to help them discern the difference between 5/8 and 6/10. The question was asking students to decide which fraction is bigger. I know it's 5/8, I can completely understand why it's 5/8 but trying to explain this concept in an intelligent and concise way to students is a struggle for me. I even did my best to stand in front of the class and explain how in the fraction 5/8 you have 8 whole parts (I used a pie) with 5 of them coloured in, leaving you with only 3 pieces lefts over. On the other hand, with the fraction 6/10 you have 10 whole pie pieces with 6 of them coloured in, leaving you with 4 pieces left over. Thus, the first fraction (5/8) is bigger because you had less parts left over. Well, by the time I was finished speaking I probably used about 50-75 words too many and had the ugliest looking set of scribbled pies on the board. I learned from that experience that less is more and that I needed to redefine the way that I think about fractions and refine my explanation. Our instructor then showed us the same two fractions represented by squares. For the fraction of 5/8 there were 8 squares with 5 coloured in and for 6/10 there were 10 squares with 6 coloured in. The difference between his diagrams and mine was that both diagrams took up the same amount of overall space, however, the pieces drawn in the fraction 6/10 were smaller. This was because there were more parts that needed to be placed in the same amount of space as 5/8. Visually, it was easy to tell from the very beginning that 6/10 was smaller because the pieces were smaller. He then reminded me of another way to demonstrate the difference between two fractions. Translate them into decimals and use a number line. Personally, I like this way better because it makes more sense to me. Just divide 5 by 8 and 6 by 10 and you get 0.625 and 0.6 respectively. Place those two numbers on a number line and show how 0.625 is closer to 1 than 0.6. In the future I will probably do it this way because it related better to the way that I process information but I won't dismiss the idea of showing the square diagrams because every student thinks differently and what works for me might not work for every student.

          During our in class activities we were asked to look at three separate rotational views of the same picture containing owls on a 4x4 square platform. The question asked us to figure out how many owls were standing on the platform. We were given connecting cubes as manipulatives to help visual/kinetic learners to solve the problem more easily. I chose to not use the connecting cubes but to watch what others were doing and to discuss the problem with one of my classmates. Through community-based learning I was able to better understand the problem and got the correct answer. Just having that one student mention to me which way the one picture was rotating helped me to understand the question much quicker and easier than having to build the entire 4x4 platform. By reading the curriculum document I discovered that this problem relates to the grade 6 specific expectation of "build[ing] three-dimensional models using connecting cubes, given isometric sketches or different views of the structure" within the geometry and spatial sense strand (Ontario Ministry of Education, pg. 92).

          The second in class activity that I really liked and that I will definitely incorporate into one of my classes in the future was a finger counting activity. The task was to count on our fingers from 1 to 1000, starting at the thumb with 1. The catch (and there's always a catch) was that once we reached the pinky finger at 5 we needed to then count in the opposite direction on our hand with the ring finger being 6 and the thumb consequently becoming 9. We then continued counting on our fingers in the same direction that we first started making the pinky 13 once we had returned again. The question asked us what finger we would land on once we reached 1000. What I really liked about this task was seeing the different strategies that people were using to get their answer.

(Dekker, 2016)

          As you can see here in this picture, the diagram on the right shows the group trying to use division to reach a solution and the group on the left was trying to decide which numbers would fall on each finger. Our group started to count each finger to establish which fingers were showing a common pattern.

(Dekker, 2016)

          We discovered that the index finger and the ring finger had a pattern involving groups of ten. At first we thought that those groups of ten were going back and forth from the index finger to the ring finger and back again (i.e., 10 on the index, 20 on the ring, 30 on the index, 40 on the ring). Later we found out that the pattern was a little different were 10 was on the index finger, 20 was on the ring finger and then 30 would also be on the ring finger before placing 40 on the index finger. We finally came to the conclusion that 1000 landed on the index finger and other groups came to the same conclusion after some time and by using various strategies. It would be interesting to see how younger people would try to figure out this problem and would provide some really rich conversations about mathematical strategies and the way that each individual is different and will approach problems in different ways. All in all, this last math class was a really good learning experience and I felt as though I walked away with some good teaching strategies and felt a little more confident in my ability to teach fractions in the future.

Resource Viewed

Ontario Ministry of Education. (2005). The Ontario curriculum grades 1‐8: Mathematics [Program of Studies]. Retrieved September 16, 2016, from http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf.