Q&A #724

Functions in middle school

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From: Marielouise (for Teacher2Teacher Service)
Date: Oct 30, 1998 at 12:47:33
Subject: Re: Functions in middle school

Hi, Jeff,

I think that you have asked a very powerful question. I teach functions to
students prior to taking calculus. While we spend our time on the symbolic
manipulations and understanding much of which we discuss could be part of the
upper elementary mathematics program.

I see the role of functions as a group of rules that are applied to numbers.
What makes the rules very special is that whenever you apply the rule to a
number there is always a single answer. This is very important.

The second property of functions is that these rules follow certain patterns.
There is the doubling rule:  "choose a number and then double it!", the
halving rule: "choose a number and then take one-half of it."  the constant
adding rule:  "choose a number and add 2!"

If students were given pairs of numbers that all were obtained by the same
rule, students need to find the rule.

Even on the college level we discuss the idea of "Remember Mrs. Smith in 4th
grade who asked you what number she was thinking of?" "I'm thinking of a
number. I double the number and subtract 6. The answer is 15.  What's the
number?" Students have to find the reverse order in order to find the
original number. This type of thinking is planting the seeds for inverse

What do I think about functions in grades 5-7? I say plant some seeds.

-Marielouise, for the Teacher2Teacher service

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