Learning content, developing habits of thinking

I’ve taken a lot from listening to Dylan Wiliam speaking over the years. One of his insights has particularly resonated with me: the idea that the improvement in learning that a child derives from being in the class of a highly effective teacher extends well beyond the time that the child is in that teacher’s class. For example, if a child experiences expert teaching in Y3, they are likely to make more rapid progress in Y4 and beyond too.

It is, therefore, hard to judge the true effectiveness of teaching from end-of-year maths assessments. It might give an indication of progress made in the content goals for that year but it won’t give the full story of the long-term impact of that teaching. The lens is too narrow. If all our efforts are placed on getting children to achieve their ‘content goals’ for the current day/block/year, we may always be limited in our impact. We want out teaching to help children to learn the content and to build children’s capacity to learn other new content.

I have come to think of each maths lesson as an opportunity to develop a child’s content knowledge and their habits of thinking. Of course, surface knowledge is important as reasoning doesn’t happen in a vacuum. However, I generally look at the content of the lesson as the context through which I will build the mathematical habits of mind. This may involve helping children to represent ideas visually, explain misconceptions or spot patterns. Perhaps children will be challenged to create their own examples. Or maybe a task will require an element of perseverance and self-regulation. This approach may have a short-term cost in the speed at which content knowledge is acquired, but this is likely to be a worthwhile investment. It can give the children a richer experience of being a mathematician.

My simple encouragement is to be aware of the need to develop content knowledge and build mathematical habits of mind. To focus on the detail as well as being aware of the bigger picture. Content knowledge is more tangible and it is easier to assess. The habits of thinking that are developed, though, will play a powerful role in children’s long-term mathematical success. We want all children to develop these habits, not just pupils whose attainment is already relatively strong. It will also require us to make thoughtful choices about what we don’t teach. Where time is limited, content is usually prioritised.

A starting point might be to establish What, as a school, do you consider to be your ‘mathematical habits of mind’. What are the characteristics that you want to build within children over time? How are they explicitly taught and made visible? And how do we promote and celebrate children’s progress is developing these habits? My aim, of course, with the I See Reasoning eBooks is to write questions and tasks that help children to develop these habits. Schools generally have a clear plan for how children learn their number bond facts. I want schools to have the same clarity in how children reason mathematically and grow as creative, independent thinkers.

If you have any thoughts on this blog, please share them with me by emailing iseemaths@hotmail.com or commenting below – Gareth.