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How to Teach Algebra

The way people think about learning is not particularly accurate, I think. Dyslexia, for example, has become fairly well known in recent years, and there are a number of teaching methods for students with that particular learning difference. However, traditional classrooms often make no allowance for learning differences. For that matter, dyslexia is not the only learning difference; everybody learns differently in some way (sometimes in a very small way). What we often consider the "normal" way to learn is really just the way a large number of people learn (maybe not even a majority).

The problem is that teaching towards this majority leaves a whole lot of people out. It would be fairly easy to teach these students as well; "normal" students can also learn from methods traditionally used for dyslexics and dysgraphics. It's just the reverse, which unfortunately is our institutional teaching method, that poses a problem.

So how do we fix this problem? In math, at least, teaching things such as algebra graphically often helps people who can't process the abstract information easily. For example take the equation

4x = 8.

To understand the idea behind the abstract information, let’s write the equation as

x x x x = 1 1 1 1 1 1 1 1;

so essentially four x’s is the same as eight ones. We want to find what one x is, so we divide the left side into groups like this:

x | x | x | x.

Since we did that to the left side, we need to do it to the right side too:

x | x | x | x = 1 1 | 1 1 | 1 1 | 1 1.

Now we look at what we have in each group. On the left side, each group is one x. On the right side each group is two ones. So now we have that one x is the same as two ones, or

x = 2.