This is post 2 in a series. In post 1 I discussed why we’re beginning a mastery scheme of work, some of my initial objections, and a brief description of “mastery” in its current incarnation.
In this post I will describe the process that produced my scheme of work, and share the working draft of the scheme itself.
Some Background Reading & Underlying Principles
It is really very hard to find specific, day-to-day details on mastery, but here are the most useful things I found.
- Spend longer on the most important topics (those that form the foundations of most of the rest).
- Keep minimally different topics apart on first teaching to avoid confusion (HCF/LCM, area/perimeter, mean/mode/median, etc).
- Every class moves on at the same time (which makes group changes much easier).
- Don’t chop and change too quickly.
- Provide challenge through depth and problem solving, not moving on to the next topic.
Will Emeny’s Sankey diagram, below, was a key tool for demonstrating the need for a curriculum where a significant proportion of time is spent getting to grips with the aspects of number that form the bedrock of the rest of mathematical understanding:
By far and away, the most important prerequisite for success in school maths is a firm grounding in number (which includes proportional reasoning). It was very important to me that we focussed on these topics straight away and spent sufficient time on them in year 7 and 8 to ensure our students had a very firm grasp on them. Topics like place value, operations (on integers, decimals and fractions), equivalence of fractions, decimals and percentages, and proportional reasoning (including working with percentages) are essential and easily forgotten when we chop and change topics. Other topics may be particularly easy for most students (take scatter graphs, for instance), so it’s tempting to put them early on in year 7, but they’re so much less important in the grand scheme of things (I always use scatter graphs as my example of a relatively unimportant topic, I’m starting to feel sorry for them).
So, having decided what must come first I began to look at what other schools are doing. I arranged a visit to Michaela Community School where the very kind Dani Quinn (@danicquinn) spent a long time talking me through how they approach maths: sequencing of topics, knowledge organisers, testing and marking. There is plenty of information on the general school approach to these things in the blog of their assistant headteacher, Joe Kirby, but I wanted to see it from a maths perspective. What is particularly interesting is their sequencing – year 7 is all number, year 8 is all algebra and year 9 is all geometry. I spent a while thinking about this as a model, considering the increasing complexity of topics in one year, and decided not to do it this way. I wanted more of a mix of curriculum areas, and there were certain topics in say, geometry, that I wanted students to meet before others in, say, algebra.
Other reading that informed the initial curriculum design came from an article on UKEdChat and the rather non-specific (and primary-heavy) NCETM materials. There is more information on task design and lesson style, but that’s for another post.
Three of the most useful sources of information have been episodes of Craig Barton’s Podcast, specifically episodes 7, 10 and 12 (I listen to the maths podcast on long runs, love it!) – I highly recommend these to anyone considering a mastery approach, they provide more useful information in one place than I have found anywhere else.
The biggest issue for me, when considering spending longer chunks of time on topics, was the potential of meeting something in the early years and not covering it again until year 11, which is not an acceptable situation. Cognitive science has demonstrated the importance of distributing practice to improve retention and interleaving topics and those of us who have been teaching a while just know that you need to revisit things a lot if you want your students to remember them. This was the biggest plus of our old scheme of work, there was plenty of opportunity for revisiting topics. For instance, on one unit students would learn to plot linear graphs, about a year later they would learn about y = mx + c and would have to revisit their prior learning. I’ve tried to keep elements of this, so in the first unit on graphs students don’t learn everything they need to know about graphs, they come back to them throughout their years. I have built in when I think tasks should be set that revisit previous topics (the odd “pop” quiz here and there, a homework, a starter, etc) and when previous topics should be incorporated into a current one (like fractions when we learn about substitution, so the students get chance to revisit operations on fractions).
So I didn’t completely reject the core idea of our old scheme of work, but instead ended up with a purposeful and considered re-sequencing which aimed to prioritise the most important topics in mathematics and which allowed for much more time to be spent on each topic.
To actually design the units I sat down with the National Curriculum learning objectives, the Edexcel specifications, and a handful of other non-examinable bit and pieces I wanted my students to know (take the sets of numbers – natural, integer, rational, real and their associated symbols, for instance) and started to group them into units/blocks based on similar ideas and where they might come in a curriculum sequence. I did this for number and proportion, algebra, geometry, and statistics and probability until I had a complete set of units.
I then had to think about sequencing the units. We have had a five-year scheme of work for a long time and I wasn’t going to change this. I wrote out the units in a long line in the order I wanted them to be taught, considering what is prerequisite for other areas, kind of like putting together a single-line jigsaw. Some parts of the sequence are obvious, others are down to personal preference. Finally, I allocated blocks of time until I had a picture of what each year will look like, from year 7 to year 11. I worked on a total of 37 weeks per year, to allow for assessments, end-of-term shenanigans, missed days here and there. Any surplus time that occurs in actuality can easily be filled with revisiting and practice of earlier work or further extension of current work. The time allocations don’t fit neatly into half-termly blocks, but that’s because I didn’t want to shoehorn things into, say, two weeks, when they really need three.
The current scheme of work is not a final piece, it is a working document. As a team we will be adapting and improving it as the years go on, so consider it still in beta. I am sharing it here for two reasons: if you are interested in the mastery approach, please use it to start your thinking or as a basis for your own scheme of work, and if you do read it/use it/reject it/adapt it or do anything else with it, I’m hoping for some useful discussion on this blog.
UPDATE: June 2018: You will find the latest version here.