Summary and Synthesize

Over the past month, I have really come to understand what I need to do in order to teach math effectively. First of all, it can be said the the majority of us in this class (not all, but a lot) came into this class with strong dislike of math. I myself have always disliked math and struggled with many concepts. What this class has taught me thus far is that students can NOT continue to come out of math instruction feeling this way. We as educators need to adapt to the new methods of math instruction that we are being taught and implement them into our classrooms even if we are planning on teaching lower grades. The traditional mathmatics approaches that we have been taught are not effective and we (myself included) are all the perfect example of this. I now understand why I struggle with some math concepts, because I was just given a concept and I memorized how to do it (or at least that's what I want to think). I enjoy learning new ways to teach different concepts, and have taught myself to keep an open mind with learning new techniques. I have finally come to terms with the idea that teaching math traditionally is not going to work. I will be cheating my students. The things we have learned about fractions has really helped me with the idea of not teaching traditionally. I honestly can say that I have never thought about fractions this way, and I hope that I will continue to see ways to teach students the right way.

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?

Recently in class, we have been working with a variety of manipulatives to assist in student understanding of various concepts. Prior to our working with manipulatives, we were to read an article by Deborah Ball entitled, Magical Hopes: Manipulatives and the Reform of Math Education. She begins the article by discussion a particular situation in which she has asked educators what they would do in a situation regarding student exploration about even and odd numbers. Many of the educators responded by asking whether or not manipulatives had been used prior to the student presenting their ideas. Educators, on the majority, also suggested that manipulatives be used to help further student discussion. Ball's point in mentioning what educators said is that many have the misconceptions that manipulatives are the answer for EVERYTHING! She continues on to state that the difficulty in educator's relying on manipulatives is in their misinterpretation of the standards. There is a clear discrepancy in what the standards say and what educators say with regard to "concrete objects" as vehicles for teaching and learning.

Due to reading this article and my experience in our class using manipulatives, it has made me much more aware of how educators are actually using them in the classroom. I recently observed a teacher using Base Ten Blocks (ex. shown above in yellow) to help a student understand addition of three digit numbers. As I sat and watched, I wondered whether or not having the student use the manipulatives was really helping to reinforce what the teacher wanted the student to learn. It seemed as though the student was able to understand the concept when using the blocks, but when it came time to solve the problem on paper, the student struggled. I feel that this is a clear example of the disconnect that we have talked about in class between differing understandings.

~Kristin

P.S.) I hope everyone has a wonderful week and safe SPRING BREAK!

Summary and Synthesize

This class has brought forth new ideas for dealing with fractions and the explanation of why certain techniques are used. I knew how to work with fractions but when asked in class I was not sure why I was doing some of the things that I was doing to solve fractions. I even answered some questions with “because they told me to”. Discussions in class helped me to realize that I need to know why certain rules exist and that sometimes you can come up with your own method that will work. I knew to find the LCM when adding and subtracting fractions but I never knew why that was the way to do it. Working the different manipulatives in class helped me to learn why we use that process. I know now that having students work through these different ideas on their own is important because then they will understand a concept better. I do believe that working through these methods has helped to improve my understanding and my belief that I can help others understand. I am worried that I may not be positive of the best methods to teach with the manipulatives.