Q&A #332

Teachers' Lounge Discussion: Place value and different bases

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From: Terry Garraffa

To: Teacher2Teacher Public Discussion
Date: 1999120513:41:24
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

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