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Thinking deeply about what we teach

We are reviewing our year 7 curriculum currently and refining it in preparation for students to come to secondary school a lot weaker than in previous years because of the sheer amount of school time students have missed out on.As part of this I have looked at how we feed forward some of the representations and teaching that we advocate, linking the current topic to future ideas. Talking about why we are promoting using a method or representation and where that then goes on to in their future maths career. 

Not only can this benefit students but it also shows teachers the many ways that we can make links within maths and that something that we may show when teaching place value is also relevant when we look at scales on a graph or explaining why we want to push the use of number partitioning so that when we look at multiplication it can make things easier for us to calculate. These have to be carefuly selected and incorporated though, using a particular representation/method has to serve a purpose. I feel there is no need in doing something if there isnt a particular reason for it and doesn't help me, as a teacher or a student, in the future. 

Below is an example of some of the ideas I had. 

- Number partitioning - to be used to make addition and subtraction calculstions easier. Also used with methods of multiplication.
-Gattegno Charts - can be used to link to standard form and index laws
- Completing Number lines and intervals - can be used with scales on a graph, averages, moves nicely into rounding
- Rounding - links to estimating calculations and checking answers

This is by no means an exhaustive list but as I was writing it it made me realise that a topic like place value can have so much depth to it and we can potentially teach it for weeks if not months exploring lots of concepts around it. When I first started teaching Place Value, it was a 1 or 2 lesson thing that I would get through before I got on to the 'cool', 'tough' maths. But now my eyes are wide open to the endless possibilities and avenues that I could go down with my students. What i will say though is that, we as teachers need to upskill ourselves so that we can better enrich our students with these topics that, when you truly think about it, make such a huge difference to future understanding. 

Place value was a classic that I thought was just for bottom set students and the higher attaining students just needed to answer 1 or 2 questions on it to show me they knew what it was. Thats not mastering a topic though, I've looked at using different number base systems, going into number partitioning, using gattegno charts etc to ensure I am stretching the concept for high attaining students. This continues to be a development for me but one that I am looking forward to adding to my repertoire. 
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