There seems to be a current surge from Heads of Maths and KS3 Maths Coordinators looking to adopt more of a mastery approach to teaching maths. This post is a quick run through of the journey the curriculum at King Solomon Academy has gone through and concludes with some advice for designing a maths mastery curriculum of your own.
Confession: We got it wrong to start with
The first maths curriculum we designed at King Solomon Academy didn’t work – at the end of year 7 our students hadn’t learned what we’d taught them.
That summer (2010), we went away wondering what we’d done wrong and came to appreciate the following flaws in the original curriculum:
- Flaw #1 – There’s so much to learn that we have to keep moving on. It turns out you don’t have to keep moving on – not at the expense of pupils actually learning what you’re trying to teach them. Yes, there’s plenty for them to learn but we don’t need to cram so many concepts into one year.
- Flaw #2 – They might not get it now but we’ll come back and teach it again in year 8 and 9 and *then* they’ll get it. We falsely reassure ourselves that they’ll understand it next time, however, the chances are they won’t. Why? Because if they didn’t understand it this time round, they probably don’t have the underlying skills they need to access what you’re teaching them and you probably don’t have time now to re-teach this for very long before you have to move on to the next topic. The tragedy is that year on year we keep piling on more things and we get to year 11 with a massive maths deficit.
- Flaw #3 – This is the way most other maths departments and publishers organise their curriculum so they *must* be right, with all their years of experience. Obviously a broken argument if they’re not right after all.
In short, we were moving the topic on too quickly (roughly every two weeks) and we were teaching “over” an insecure understanding of place value and poor recall of the basic number facts. We didn’t give our pupils a fair chance at learning when these factors were stacked against them.
With the experience the last 4 years has given us, these are our observations:
- No real time is given to the 4 operations or place value. It’s critical to spend 7-13 weeks on place value and the 4 operations unless you’re teaching a whole yeargroup of level 5s and above.
- Not enough time is spent on fractions (needs 6 weeks) or on algebra basics (needs 5 weeks)
- Area and perimeter are being taught together (should be as separate as possible)
- Mean, median and mode are being taught together (should be as separate as possible)
- Reflection, rotation and translation are being taught together (should be as separate as possible)
- The following don’t need to be taught at all – tessellations, function mapping
- The following don’t need to be taught in year 7: ratio, probability, transformations, functions and graphs, sequences, units of measurement, describing data, comparing sets of data
- Algebra comes up too soon in the year – save it until half-term 5
- Generally it’s trying to cover too much in too little time or in the wrong order (e.g. probability comes before fractions, although we’ve suggested probability doesn’t even need to appear in year 7) or together with concepts that are minimally different and likely to get confused (area/perimeter, mean/median/mode, reflection/rotation/translation).
- Too much chopping and changing doesn’t allow the pupils to get a footing in any of the topics before they’ve moved on, especially in schools that only have 3 hours a week of maths.
(Note: We were also sent a detailed breakdown of the curriculum, which is why we’re able to refer to things like tessellation and transformation that don’t appear on the overview.)
You should notice that more time is given to number work at the beginning of year 7 (especially times tables), we spend one half-term at a time teaching a topic rather than 2 weeks, some things are ‘missing’ (because they’re taught in KS4), we’ve tried to separate minimally different concepts and we’ve thought carefully about the order things are taught in so that all the while we’re building on top of prior learning.
Something to suggest it’s working
The graph shows the mean maths grade of our first three yreargroups over the last few years.
Notes: Exams were written by AQA especially for ARK schools using the Mathematics Mastery curriculum and the KS4 exams are past papers from AQA. We’ve ‘converted’ NC levels into GCSE grades. The conversion was crude but was applied to all datapoints in the same way and seems to have produced a reasonably smooth trajectory between the end of year 9 and beginning of year 10, which is obviously when the switch from NC levels to GCSE grades happens.
The simple messages from this are:
- The Class of 2016 (current year 11s) and the Class of 2017 (current year 10s) started from the same baseline. The Class of 2017 have had a higher average grade since the end of year 7, which could be attributed to the introduction of daily times tables practice and a switch to a mastery curriculum.
- Of the three yeargroups, the Class of 2018 had the lowest KS2 average but closed the gap by the end of year 7.
For the ResearchEd crowd, we realise the sample size is small, there is no control group and that we have no external results to validate any of this.
Six tips for creating your own maths mastery curriculum
- Don’t be afraid to go back to basics for 12 weeks in year 7 – more place value, more number bonds and single digit addition, more explicit teaching of mental arithmetic, more times tables, more written algorithms.
- Don’t be afraid to do *lots* of practice no matter what the discovery brigade tell you.
- Separate minimally different concepts so that things like mean, median and mode are not taught at the same time.
- Keep skills ticking along by dropping things from earlier in the year into starters, homework, flash tests and end of term exams.
- Don’t teach things until the pupils are ready to learn them, so, for example, don’t teach fractions until they can find factors and multiples, don’t teach factors and multiples (at the same time, ever) until they know the times tables.
- Spend more time teaching fewer things. For example, algebra can wait until the end of year 7, ratio can wait until year 8, probability and transformations can until KS4.
Far from building the curriculum in isolation, my wonderful colleagues at King Solomon Academy, at Mathematics Mastery (Helen Drury, especially) and from other schools in the ARK network have refined, contributed and altered different parts of the curriculum over the years. The snapshot presented above is something that many people have worked on and credit goes to them.
School contexts are different, we get that. So while what we’ve said has suited our school, we’m not saying it suits everyone else’s.
We didn’t set out to call it a mastery curriculum or Singapore maths but somehow over the years the labels have stuck.