The Role of Mathematical Tools
This article stressed the importance of the question as a teacher, what do I want my students to understand, instead of what do I want my students to do? This article argues for the use of concrete materials in a more judicious and reflective manner. Because although the use of concrete materials has always been appealing, just using them is not always enough to guarantee success. One thing the article mentioned that stood out to me was the part about the 3/5 circles chart. It talked about all the different ways that at student could look at that chart, or that concrete material, and interpret it. We as teachers, tend to want to encourage them to interpret it in a particular way, or in a few different ways, but there are so many ways that he/she can interpret it and we need to be open to that. The article says, "Mathematics, like beauty, is in the eye of the beholder--and the eye sees what the mind conceives" (pg 52).
"And the Answer is... Symbolic" by Mary Lou Witherspoon
This article talks a lot about the misconceptions that happen in math. One misconception that happens a lot is with the equal sign. Many children think that it can only mean, "and the answer is...." The article goes on to talk about then how to foster the communicative role of mathematical symbols in an elementary school. The way to do this is by communication! When students are communicating, they are talking about how they solved that math problem, using different manipulatives, such as their fingers, the chalkboard, etc.
"Using Math Manipulatives to Aid Learning" by Dottie Oberholzer
The main goal of this article was to create students who were flexible problem solvers who could apply math ideas to all kinds of situations! It talks about when teaching a new math concept, you should always start with a concrete stage (math manipulative), then progress to a semi-concrete stage, then to an abstract stage. This teaching helps the students be active participants in learning.
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