It came up in conversation today that each math program seems to have it's own preferred tool that it uses to teach concepts (fraction circle, tape diagram, number line, area model, etc). When children are taught using a program's preferred method, this actually becomes a rote way of learning how to do something. It reduces it to nothing more than a procedure to be followed and does nothing for the student who truly does not understand the concept. That led to a discussion on flexible thinking. Students should be introduced to topics through pictoral representations using different tools/language to help them gain the conceptual understanding. In the end, it should not matter how they model their knowledge of a math concept as long as they can show they understand.
Think of it like this.... If you ALWAYS show students how to compute fractions using a tape diagram but then they are presented with a problem that asks them to think about serving a pie at Thanksgiving or not having the right measuring cup and trying to figure out what they can use instead to get the correct measurement- will they be able to figure it out?
Lets make sure that no matter what "program" we use, we keep in mind that we need to make sure we are helping to create flexible thinkers (even if that means stepping outside of the program to show students other tools they can use to solve the same problems).
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