# Duh! Ohhh… What?

I often tell students that I’ve made any mistake they make, and usually more often than I care to admit. I know all about mistakes – if you learn by your mistakes, then I’m a genius. In fact, I confess that I’m still getting cleverer.

But there are different types of mistakes, though the boundaries between them can be blurry at times.

The thing is to find the balance where you can both

– recognise what you don’t know

– give yourself credit for what you do know

#### 1. Duh! (“silly” mistakes)

You know, like in the middle of a long calculation, you say that -3 x -4 = -7. Duh!

Of course, from that point on, anything that follows on from this is almost certainly rubbish.

But these are easy to fix, right? Well, not always.

Even if you know that you must have done something silly, you can very easily look for the error 10 times without seeing it.

It’s much better to do things so you make these mistakes as little as possible in the first place.

Try to be aware of where you tend to make these slip-ups and *be on your guard*.

Missed sign changes, faulty algebraic expansions etc etc.

You’ll know what you need to look out for most.

But, having said that, *you do actually understand how to solve the problem*.

You just made a silly mistake.

#### 2. Ohhh… (you’ve lost your way a little)

For example, you say (a+b)^{2} = a^{2} + b^{2}

This might be a silly mistake for some. For others, it may show up a gap in understanding what’s going on.

But if I show how (a+b)^{2} = (a+b)(a+b) = a^{2}+2ab+b^{2}, it’s “Ohhh, now I get it”.

So, you did know it after all – sort of.

#### 3. What? (I don’t get the bit after “The main approach here is…”)

For example, you say (a+b)^{2} = a^{2} + b^{2}, and this is the limit of your understanding.

Well, we (you and your teacher) need to step back and start from somewhere you do understand.

Maybe that 12^{2} =(10+2)^{2} ≠ 10^{2}+2^{2}, for example.

Maybe moving to a visual version of the problem – draw a 12×12 grid and count the squares.

** **

Just remember – you’re not starting from scratch here.

It’s still likely that you understand more than you give yourself credit for.