Week 8 reflection

This week in math class we were responsible for reading chapter 15 and 16 in the Making Math Meaningful textbook. The two chapters were about 3-d and 2-d shapes and Location and movement. One of the things that I found interesting in the textbook is the different levels of classification in chapter 15. Firstly, the ability to conceptualize shapes classified by Pierre van Hiele and Dina van Hiele-Geldof was interesting to me because it reminded me of theories that we have learned in Cognition and the Exceptional Learner. I had never really thought of math, and more specifically, the ability to recognize and think of shapes, in terms of stages. First the student is able to recognize shapes just by sight, then the student is able to recognize properties of shapes, then the student is able to apply ‘if-then’ reasoning. This is similar to the conversation that we had in class regarding what makes up certain shapes, ill touch on this more later. Lastly, the student is able to identify and classify, as well as deduce properties of shapes. Similar to this theory is Clements stages that young children go through as they combine shapes. In his theory he talks about how children are learning shapes as they play and combine shapes. By playing, students are learning about essential properties of shapes.

Chapter 15 also goes into detail about misconceptions regarding shapes. This is something that we talked about in class that I found pretty interesting as well. Patricia handed us out a sheet with some polygons on it and asked us to classify each shape and give our reasoning. When I looked at the sheet and began working on it, I realized that I don’t actually know all of the rules and properties that every shape must have, other than the obvious ones like triangles, squares, and rectangles. Instead, I think I have just been conditioned to recognize them by sight, much like stage 1 in van Hiele’s stages. Patricia explained to us that the classification of polygons was probably not taught to us very well because our teachers probably did not have a great grasp on the concepts either. This is much like our unit on fractions; we were not taught everything about the concepts because our teachers did not fully understand the intricacies within the concepts themselves. Patricia explained that there is a ton of overlap in the classification of shapes such, as squares are always parallelograms. This made me think that when I have to teach shapes and polygons I will make sure to inform the students of this overlap so they can begin to understand what makes up different polygons, and so they can advance in Hiele’s stages.

            The learning activity presentations this week were also very good. I really liked Shannon’s activity on patterning. I thought that the actual math part of the activity was effective at showing patterns and was not so difficult that students would not be able to figure it out. In addition, her use of the cardboard bridge and the cutout climbers was a great idea. I really think that something like that would engage the kids and really get them into learning the concept. The cutout bridge and hikers could also be used in later lessons to demonstrate other ideas and play math or learning games with students. Eva’s lesson was also really fun. I loved when she played the Mario music as we were using the Miras, as well as when she asked us to come up to the board to draw out the Mario level.

Sean and Steph Mayo. (2015) Mario Mini [Online Image] http://bit.ly/1WD0EDt