# Reflection on Shanghai Maths experience:

On Wednesday the 25^{th} November 2015, I was lucky enough to attend a professional development workshop to observe lessons that were being led by two experienced teachers from Shanghai. This was part of a project that is aimed at helping English secondary school teachers to understand and implement some of the key elements of Shanghai Maths teaching.

We started the day by looking at some of the elements that had been identified by two English maths teachers who were given the opportunity to go to Shanghai to observe the teaching of mathematics in two schools. Four key components were highlighted to us:

- Conceptual Variation –
*Multiple perspectives and experiences of mathematical concepts* - Procedural Variation –
*Formations of concepts (ability to form step by step methods)* - Intelligent Practice –
*A way to avoid mechanical repetition* - Concept and non-concept –
*eg. What is an angle? What is not an angle?*

One element that stood out for me was the idea of concept vs non concept. It was really interesting to think about how we present maths to our students in the UK. In my opinion, too much emphasis is put on showing students mathematical concepts in the right way. If we are to take on the idea of ‘mastery’ in mathematics then we need our students to be able to recognise that just because something looks similar to the mathematical concept, it doesn’t necessarily mean that it represents it. By not exposing our students to non-conceptual examples, we are potentially unknowingly filling our young people’s minds with countless misconceptions. If we can encourage students to ask questions of the examples (with a mix of conceptual and non-conceptual representations) that they are given. Then this would aid the young person’s mastery of mathematics.

It was highlighted to us that in Shanghai, there is a big focus on the commutative, associative and distributive laws. When I thought about this more, I considered how I knew these laws and it came to me that I had picked them up intuitively over my years of exposure to mathematics. I certainly wasn’t ever taught them explicitly. There is a massive crossover between mathematical concepts when you consider these laws and I think it’s important that we consider whether we should explicitly be teaching our students these laws. After all, it would be a good foundation of knowledge for them to secure!

I was really intrigued and maybe a little bit shocked when it was stated that there was no difference in ability in Shanghai. They make sure that no student is left behind (through immediate intervention) and the whole class move forward together. I would be interested in knowing more about how provision is made for SEND students. It was mentioned that if a student in Shanghai has a specific learning difficulty, then they go to a separate school however it would be useful to know more about this. I also do wonder if the cultural difference has a big part to play in all this, there are obvious differences when looking at western cultures. I think it would be quite intriguing to see how the performance of Shanghai students would change if they implemented our educational system. Would there be any change in their performance? Or would it remain the same because of their cultural background?

I feel there is so much that I can take away from this experience. A couple of elements that I would like to include in my teaching when I am qualified is firstly the idea of concept and non-concept, as I feel that this would be a way in which I could combat misconceptions within the classroom. Also, I’d like to have more of a consideration of the commutative, associative and distributive laws as I think that these are very important parts of knowledge that our students should be exposed to. I am looking forward to seeing how our educational system may change as a result of this national project.

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