After numerous really interesting and thought provoking discussions both online and face to face I’ve come to the conclusion that teaching Maths really is very similar to being a bricklayer. Allow me to explain –
For non-specialists, Maths is a series of interlinked topics that support each other in fundamental ways. There are key building blocks of knowledge, like times tables, that are like a foundation stone. Without a strong knowledge of times tables so much other knowledge in maths cannot be acquired and secured. When building something, if you do not have a good foundation stone the whole structure is at risk of collapse.
All maths teachers will appreciate that maths is a hierarchical subject. You cannot teach topics as complete standalone principles/ideas, because there is always some prior learning that is needed before you can move understanding forward. This is why testing of prior knowledge before embarking on a new topic is vital to establishing a solid understanding of new concepts. If the prior knowledge is not secure, then it is like having a cracked/broken brick in the wall. There is an in-built weakness that needs fixing to ensure a strong wall that will last. Our remedy for this is to establish prior learning tests as a first lesson in all topics so that students are aware of what the need to learn, and teachers what they need to teach. We can then use either ‘therapy’ lessons that consolidate these pre-requisites, or we set catch up tasks on http://www.hegartymaths.com for them to do the work independently.
The next step is what to do if you find a broken or missing brick. The key is timely and focussed intervention. We are establishing an intervention programme built around this model. At the moment we are testing year 7 and 8 on the key knowledge of times tables, and then putting in place focussed intervention using year 10 mentors that develops this key skill. We will then move on to testing other fundamentals and intervene for those that need it once times tables are sorted. This rolling programme will develop over the year, and then we are fixing the broken bricks at the bottom of the wall before we build the wall too high and it falls down.
Our use of post-testing of knowledge in lessons with a simple RAG activity, allows us to test the new bricks for stability, and by planning for one or two ‘therapy’ lessons at the end of a topic, we immediately intervene with students on their new knowledge and secure it before moving on. Again, this is supported with videos and quizzes on http://www.hegartymaths.com that can be individually set depending on the weaknesses of the individual.
On reflection, this model of rapid intervention felt like a pretty good attempt at working the Shanghai Maths model into UK classrooms (you may not agree, and I am certainly no expert on the Shanghai model). We don’t have the luxury of afternoon lessons that catch up those who didn’t get it earlier in the day, but at least we get to them pretty quickly, and while we are still covering the same topic before moving them on.