## Monday, 30 April 2018

### Concepts, Processes and Facts

Recently my department has been doing a lot of work towards our new Year 7 Scheme of Work. At some point (probably over the summer) I will get around to blogging about what we are doing and what has influenced it. Needless to say it is quite a departure from our current practice. The current scheme for Years 7 to 9 has been there since my predecessor was head of department. When I joined the school was only just adding Years 10 and 11 and so the development of schemes and materials rightly focused on those year groups. Now that we have seen a couple of years of GCSE through my attention has turned to Key Stage 3.

I have been doing a lot of development work with the team on some of the approaches and pedagogy behind our new scheme and one of the things we have talked about that I thought would be worth sharing is a recent session we did around the teaching of concepts, processes and facts. This is inspired, at least in part, by some of the excellent work that Kris Boulton has talked about in his mathsconf talks.

The session revolved around the idea that facts, processes and concepts are different forms of  knowledge, and will need to be approached in different ways. Although simplified, the major distinctions were:

Facts: Need to be taught explicitly and then tested repeatedly to support pupils retention in long term memory.

Processes: Need to be modelled, with each step broken down and explained, and then practised.

Concepts: Need to be illustrated and explored, allowing pupils to see the limits of the concept.

The line in quotation marks is taken from the National Curriculum in England as something expected of pupils in key stage 3. We looked at the distinct ideas that allowed pupils to reach the point where they could apply the properties indicated - namely they would need to know the particular given fact, they would need to be able to carry out the process of finding a missing angle on a straight line, and importantly they would need to understand what it meant for angles at a point to form a straight line. The point I made to staff is that very often we would provide pupils with the fact, then model and practice the process, and almost expect pupils to absorb the concept from the other two. Of course, this generally proves to be ineffective; we all know pupils that struggle to identify when angles form a straight line, particularly once they encounter diagrams that exhibit multiple properties. We also talked about the possibility that these were in the wrong order for teaching, and that a better order might actually look like this:

The logic being that once pupils are secure in the concept of what it means for angles at a point to form a straight line, then they learn the fact(s) associated with the concept, before carrying out the process of finding missing angles. This should support pupil learning a lot more because rather than learning a disparate and disconnected fact, they can connect the fact to the concept they have learned. There is copious research out there that suggests that connecting knowledge to other knowledge is important for pupil learning, and so approaching a topic in this way will make it easier for pupils to form those connections.

In terms of illustrating the concept we discussed different approaches - in this case I suggested that a series of examples and non-examples would allow pupils to form a strong understanding of the concept. These would be presented one at a time:
An important point here is the use of positive and negative examples that include diagrams pupils may not see until points in the future, for example the parallel line angle diagrams and circle theorem diagrams. It was pointed out that interior and exterior angles of different polygons would also be good examples to include here.

In our lesson design for the new scheme of work we will be focusing a great deal on the facts, processes and concepts we want pupils to learn, the most effective ways to teach/model/illustrate these and the best order to approach these in. I look forward to blogging about our work on this next year.