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Doing maths when you don’t know what you’re doing

August 10, 2012

“I have no idea how to do this.”

How often have we heard this? How often have we said it?

I certainly say it (and even more often think it) when I look at some maths problems. Some, particularly worded questions in upper secondary courses, require quite some thought to see a way forward. At times, I feel like I’m in a very dark room, feeling around, looking for a door handle.

In fact, part of the practice of doing maths is working out what to do when you cannot see the end point, or even how to get there.

But all is not lost – here are some hints on what to do, when you haven’t a clue what to do…

1. Write down what you know

I expand on this below. But write something – anything – down.

You never know what you might see when you look at what you’ve written.

2. Give things names

There will always be variables in the problem – give them names. Especially make sure that you include in these the quantity or quantities that you are asked to find.

Make the names easy to think about: if it’s a length, you might call it d or l or x; if it’s a speed, s or v (for velocity); if it’s a time, t and so on.

Once you have names for the variables, then you can start to write down relationships between them.

3. Draw a diagram

If you have an absolutely clear understanding of the problem and what to do to solve it, ignore this.

If not, draw a diagram. It will help you clarify what information you have been given.

This is a real skill all by itself, and it takes practice to know how big, how detailed, how precise (or not) a diagram should be.

It takes practice, so draw a diagram – please.

4. You know how to do it

That’s right, you do. Or at least the method you need to use has been explained to you, even if it didn’t sink in at the time. This massively limits the number of possibilities.

Research mathematicians frequently work on a problem without knowing if they have the capability – or even the possibility – of solving it.
You are in a different situation – any problem given to you can be solved, and by one of a fairly small number of possible methods.

For example, if it’s a length you have to find, then (almost certainly, you will) put that length into a triangle, and mostly a right-angled triangle at that. If there isn’t one there now, make one.

I’ll say more about these standard approaches another time.

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