From: Claire (for Teacher2Teacher Service)
Date: Jan 28, 2008 at 10:59:41
Subject: Re: Making algebra concrete

Hi, Colleen --

Thanks for writing to T2T. There is a lot of discussion about introducing
algebraic thinking earlier in the curriculum, so that by the time children
reach middle school, they have a conceptual foundation on with to build the
formal operations of algebra. In your case, you'll need to provide that
underpinning, if algebra is going to be meaningful to your students. Even
algebra tiles are an intermediate step between the concrete and the abstract,
and only a representation of something real.

I believe the best way to develop algebraic thinking is through real (word)
problems that put the ideas in a context. Our Problems of the Week are just
the thing! :-)

If you don't already have a subscription, you can get a 21-day free trial at
http://mathforum.org/products/trial.html

Here are a few problems from our Library that develop concepts that are
critical to algebraic thinking:
Eating Grapes
http://mathforum.org/librarypow/puzzles/index2.ehtml?puzzle=3247
Growing Worms
http://mathforum.org/librarypow/puzzles/index2.ehtml?puzzle=3283
Sports Weigh In
http://mathforum.org/librarypow/puzzles/index2.ehtml?puzzle=3643
They are solvable by means other than algebra as well, which gives students a
way to judge the reasonableness of their answers.

With your trial subscription you can have students submit their solutions to
any current PoW.

Another way to make good use of technology is by using interactive online
applets. Our Math Tools project helps you find them.
http://mathforum.org/mathtools/
Here's one I found there that might help you:
Balance Beam Activity
http://www.mste.uiuc.edu/pavel/java/balance/index.html
Also check out the applets for gr 6-8 at
http://standards.nctm.org/document/eexamples/#6-8

I hope this is helpful. Please write again if you have more questions.

 -Claire, for the T2T service

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