nimthiriel (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
nimthiriel) wrote2011-12-14 12:41 pm
nimthiriel) wrote2011-12-14 12:41 pm
Dear Primary School Teachers
I have heard from some of you (and from many of my students) that, in maths, horizontal working out is encouraged. By this I mean the following layout:
3x + 7 + 4x + 1 = 7x +8
PLEASE STOP TEACHING THEM TO DO THIS.
I have seen SO MANY school students try to fit 4 or 5 lines of working out onto just one line of the page. It is messy, they run out of room, and I'll be damned if anyone can follow their working out and tell where they made a mistake if they make one! Furthermore, if you add a substitution in, they end up expressing in a way that is completely wrong! We get things like this:
3x + 7 + 4x + 1 = 7x +8 x = 3 = 29
THIS IS TOTALLY AND COMPLETELY WRONG.
The most obvious wrong thing that expression tells me is that 3 and 29 are the same thing!
Working out should look like this:
3x + 7 + 4x + 1
= 7x +8
x = 3
7x +8
= 29
That is much clearer. I can follow exactly what they did, each step of the way. It also paves the way for when they are doing far more complicated expansions factorisations. They can require as many as 10 lines of working, and ALL of those lines are necessary to keep track of what they are doing!
If they can't show correct working for these simple expressions, they have no hope of showing it for more complex ones. Furthermore, when we get to middle secondary school, we care far less about the answer and far more about the PROCESS. The answer is worth 1 mark, the working can be worth 4 or more.
So please, if you are teaching your students anything other than vertical working out, STOP DOING IT. It is a complete pain trying to teach kids how to do it properly from scratch.
3x + 7 + 4x + 1 = 7x +8
PLEASE STOP TEACHING THEM TO DO THIS.
I have seen SO MANY school students try to fit 4 or 5 lines of working out onto just one line of the page. It is messy, they run out of room, and I'll be damned if anyone can follow their working out and tell where they made a mistake if they make one! Furthermore, if you add a substitution in, they end up expressing in a way that is completely wrong! We get things like this:
3x + 7 + 4x + 1 = 7x +8 x = 3 = 29
THIS IS TOTALLY AND COMPLETELY WRONG.
The most obvious wrong thing that expression tells me is that 3 and 29 are the same thing!
Working out should look like this:
3x + 7 + 4x + 1
= 7x +8
x = 3
7x +8
= 29
That is much clearer. I can follow exactly what they did, each step of the way. It also paves the way for when they are doing far more complicated expansions factorisations. They can require as many as 10 lines of working, and ALL of those lines are necessary to keep track of what they are doing!
If they can't show correct working for these simple expressions, they have no hope of showing it for more complex ones. Furthermore, when we get to middle secondary school, we care far less about the answer and far more about the PROCESS. The answer is worth 1 mark, the working can be worth 4 or more.
So please, if you are teaching your students anything other than vertical working out, STOP DOING IT. It is a complete pain trying to teach kids how to do it properly from scratch.