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!