That’s an exciting title, but I am having a bit of a break from curriculum thoughts for a bit. After an excellent days at Research Ed Northampton, my head is full of ideas I want to get down – but this is actually just a thought about my own practice.

I know that one of the issues in maths is that we (everyone – not teachers) are too concerned about answers. I know as a teacher I care about the process and the deeper understanding, but ask me a question in a CPD session and I’ll want to get the answer right first. There are loads of great things about this, and lots of correct answers is great for combatting maths anxiety. But – does it test understanding?

Anyway, I’m trying to change my own practice. I’m a good teacher, and I get good results but I am not sure I’m doing things right all the time. On some level hasn’t this bothered me becuase I get good results and the students I teach do well… but I want to do better. Anyway, I’m just writing here so I can record my thoughts – I don’t think anyone actually reads this other than me.

So, let’s take subtracting fractions with different denominators. I would have modelled how to do this and discussed the stages, and the layout I wanted. Asking questions for each step of my working.

What is the lowest common multiple of 3 and 5? 15

What do I multiply 3 by to get to 15? 5

What do I get if I multiply 1 by 5? 5

What do I multiply 5 by to get to 15? 3

What do I get if I multiply 2 by 5? 10

I’ve always done this nicely, with curly arrows between the fractions and layed out clearly. All modelled, with the students all being aware of the processes I use and the questions I ask myself. And it’s generally worked… but every time most students can replicate it – and often most of them can retain it. .. and some can

I want to get rid of the deminishing returns of their learning, and I know that’s how memory works, but if I can change my teaching so they’re not copying my method but they understand the method and can remind themselves then they can do it without being told by me.

Basically, I’ve turned me into an exam factory… and although I get good results I’m not happy with my teaching. I realise I’m opening myself up for judgement – but hey.

The other issue was when I ask students how to do it, they either can or can’t. The more able jump to the answer and any misconceptions (like cross multiplying and simplifying) are not picked up early enough by me. And ones that need the support say a number, or are walked through it and breate a sigh of relief knowing they are safe and can switch off.

Anyway, what I’m trying . (I’m not saying it’s better or perfect, but I’m a lot happier and it’s helpign for now. However, I won’t know if I students will get it into their long term memory more effectively until I give them time to forget. So, the key thing I’m trying is to get them to ask each other the questions as I go through.

So, I am modelling the questions with the first student. They work through it and tell me the answers, and then I do a new question on the board. I ask them to chose another student (or I chose for them if I want to select someone specific) and then I get them to ask the questions. I won’t let the other student say the answer too early, or miss out bits of learning. Once we have done that we chose another student and the new student asks the same questions. The students are gettign the questions right, because it is broken down and scaffolded for them.. but it’s coming from the students.

What I’m finding. The students are less worried about answering questions, because it is being broken down for them. I am focusing on do they know the process, not do they know the answer. The students are able to repeat the process and break down the problems better. Occasionally they get the questions wrong or the process wrong and we can talk about that… but I don’t have to worry about the answers being wrong (because if they are we can correct them but don’t have to discuss it – because we have dissucced the process)