From: Terry Garraffa
To: Teacher2Teacher Public Discussion
Subject: Place value and different bases
I have taught fifth grade for 9 years. This year I am working a district math trainer, along with 6 other teachers. One of our district's initiatives is the implementation of a new math program designed to enhance our district's curriculum. One vital component of the program includes Fair Lands, which consists of manipulatives designed to develop proficiency in the "exchange" process. As teachers, we assume students can conserve the idea of tens, on which our number system is based, and although, some students can parrot back or duplicate on a sheet of paper that there is a one's place, ten's place, etc., most students do not conceptually understand what these places represent. Breakdown in this area of "exchanges" really can have a detrimental effect that feeds through most other threads of the math curriculum. Having grown up in the fifties, I was taught using algorithmic formulas which I could not apply to problem solving and mathmatical thinking, hence, until graduate school I was seriously math phobic for most of my life. Not until I was led to an understanding of what it means to "exchange" did math begin to come together for me. While teaching other bases can facilitate an understanding, it is important to begin with something as simple as base 2, and it is critical that manipulatives be used before any pencil and paper. Move from the concrete (the manipulative) to recording only the outcome of the "exchange", then to recording the outcome of each discreet part of the process, finally to the abstract where no manipulatives are used at at all. Feel free to contact me should you need a more specific explanation, with some samples of the procedures.
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