Saturday, 11 May 2013

The Value of N

I've been thinking a lot lately about the way math is visually presented to young students. Looking at equations and the meaning of equal signs, as written about in this recent post, I also began to wonder about the use of answer blanks, such as can be found in questions like this one:

5-3=___

There are reasons to write it like this, most obviously to give the student a place to put the "answer" or, better put, to complete the equation. However, following the equal sign with a blank might also be the cause of some confusion when students reach introductory algebra. They may have learned to associate the = sign, and/or the blank with "this is where the answer goes" rather than understand that this is an equation in which the value of each side must balance.

Consider the following way of representing the same question:
5-3= n
which could be followed with:
n = ___

or simply the words, "What does n equal?" or perhaps better still, "What is the value of n?".
(I chose the letter "n" because it can stand for the word "number", but any letter would work as well)

While there is still that problem of the equal sign followed by the blank, the way the first part is represented manages to help convey some information that is missing in the first example, such as "what are we looking for?" and "how can we represent the unknown number that will balance the equation?".

Maybe a picture would help get the idea across better (please forgive my crude drawings!):


Of course, if you have a balance and unit weights handy, you could always use those to help solve the problem.

I wonder if presenting simple arithmetic with a variable rather than a blank from the outset would help students better understand the concept of equation and equality better, and also predispose them to accept variable notation when it becomes more crucial in algebra.

If you choose to use this idea with your students, I'd be very grateful if you would let me know how it goes.

No comments:

Post a Comment