Summary & Synthesis

During the last month we have been talking about fraction concepts, which is definitely not my favorite subject but I feel I have learned a lot through the class activities. I think many children don't like dealing with fractions because of the way they were taught and they don't have the relational understanding as to why it must be done the way it is. This class has shown me a variety of ways to learn and understand fractions, yet our schools are all teaching in the same manner, it doesn't make much sense to me. I really liked using the pattern blocks and cuisenaire rods to complete those worksheets because I could see how the problems made sense instead of just completing the problem in the way I was taught. I think many students enjoy working with manipulatives but teachers need to ensure that that is not the only way students can solve problems, they need to reach the symbolic stage of working. I was a little confused when using the dot paper to solve fraction problems but I can see how it may be beneficial for some students.
I really like the blue CGI book that we are reading because although I have used these types of problems and can teach it, I didn't realize that each strategy has a name. The error patterns book that we did some problems out of was also really neat and gives some great ideas for helping struggling students. It seems like the past month we have been doing a lot more hands-on activities that could easily be used in the classroom and I feel like I get a better understanding of the concepts by doing these activities.

New Insights and Their Implications

What did you learn from your peers, from the instructor, and/or the readings, about elementary school students, and/or about yourself, and the teaching and learning of math and what are their implications to teaching and learning mathematics?

While we have begun our foray into writing the lesson plan for understanding, I have learned a lot about myself. This lesson is very difficult for me to write because I want to fall back into my comfort zone and the way I have always been taught. In writing this lesson, I know it is more beneficial to my students and their learning to use the approach that we have learned thus far in class. While old habits die hard, new and improved ideas are popping out of my head. I am using and adapting the ways that I was taught into my new way of thinking.

Kami and I are working together to create a lesson for the order of operations. I distinctly remember my teacher writing the order on the board, making us copy it, and then telling us we had to memorize it. We were to use what we memorized (Please Excuse My Dear Aunt Sally) to complete different problems in assignments and test now and in the future. She never explained why we had to use them and why specifically in that order. It was just something we were expected to know. In our lesson, we have realized that we need to let students discover the order (Thanks Dr. Reins) on their own and also the importance of knowing why they have to do it. We have looked into a variety of sources and our just now discovering the why's. Hopefully our students will not have to wait ten or more years to discover this.