1. A bit of history
We previously used a traditional "spiral" curriculum, based on the Collins Frameworking Books. I'll make no secret that I really loathe them - I appreciate how difficult it is to write a good textbook for Key Stage 3, and I think they were one of the best out there, but I felt that my first couple of years of teaching were very bitty. The rough scheme was three chapters per half term, then a test. Most pupils scored fairly low on these, and we moved on without any time to really address what had gone wrong, other than a lesson of "going over the test".
In June/July last year, I started writing a new scheme of work for Key Stage 3 to support the new curriculum. About halfway through this endeavor, we partnered up with a local Maths Hub, who had written their own mastery curriculum (the Mastery Pathway). My first drafts looked very similar to their pathway, so I (sadly) binned what I'd been working on, and we adapted their model from September this year.
2. Starting off
We decided to dive in the deep end, and start all of Year 7, 8 and 9 on the scheme as given. This meant that each year group started with a baseline test on the "Elementary" section of the pathway, which begins with simple multiplication, division, place value and fractions. We assumed that our Year 8s and 9s would be able to do this easily and could progress quickly through the steps, and that we'd only be starting from scratch with Year 7; we were wrong about the former.
When I analysed the test results of my Year 9s (set 3, working at around old NC level 5/6 "apparently"), I was surprised at the number of basic things they got wrong. Some of them didn't have a reliable way to multiply or divide large numbers, and their understanding of fractions seemed to be based on trying to follow methods that they'd obviously only half-understood the first time round. Most of them scored around 30 - 40% on the first section of topics.
Now, I'm not saying that they'd never learned these things. I'm willing to bet that, when they arrived in Year 7, they were fairly competent with basic number work due to drilling for SATs. Unfortunately, with the idea that outstanding progress means ploughing through the curriculum at a rate of knots, we'd spent two years teaching them new topic after new topic, without really giving them any time to cement what they already knew. I'm willing to bet that whoever taught them in Year 7 and Year 8 covered adding and subtracting fractions with them in both years (as I know I did with my groups in the previous years), but they still couldn't actually do it a couple of weeks later, let alone nearly a year later. Three pupils in the group readily confessed to not even knowing their times tables properly.
For our Year 7 cohort, we had carte blanche; they didn't know any different, and we'd usually start off with cementing basics in the first term. However it was a big gamble going right back to square one with Years 8 and 9 - what if the mastery model didn't work, and we ended up with two cohorts way behind where they "should" be, particularly with the added challenge of the new GCSE content to cover? However, when we looked critically at the content in the Elementary stages of the Mastery Pathway, we decided that spending time on these would mean they could access a fair chunk of the number side of the new GCSE syllabus, and we could fix all the extra bits in Years 10 and 11.
3. Using assessment to drive planning
After issuing the baseline tests, we spent a few long, boring hours entering all the data into a spreadsheet. Although this was time-consuming, it was incredibly useful in terms of deciding where to start. We shared this data with pupils in the form of tracker sheets; each unit is broken down into about 10 or 12 closely linked objectives, and we indicated if they had already "mastered" (i.e. scored more than 75%) on those topics. The pupils could clearly see what they could already do, and, more importantly, where we'd be going over then next few weeks.
Every single group in each year started off on the first unit. With the exception of a handful of pupils in top sets, none of them had sufficiently mastered whole number calculations and simple fractions work. This was a real eye-opener for me as a teacher - I'd always assumed I was doing a pretty good job. Whenever I did my progress checks at the end of a lesson, the pupils demonstrated that they'd "learned" what I wanted them to, and that we could move on next lesson. I quickly realised that what I'd been doing was years of surface learning, which is why I spent two weeks this year reteaching ratio to a group of Year 11s, using almost the same material I'd used when teaching them in Year 8.
4. Changing the teaching model
The pathway works on roughly 12 weeks per unit, which gives a week to cover each objective. This gave us plenty of time to address each one in great depth. Luckily, due to our involvement in the previous year with the NCETM's Multiplicative Reasoning project, we had plenty of materials for enhancing understanding of fractions, and I've drawn very heavily on these ideas in my teaching this year.
With Year 9, I spent a whole week's worth of lessons doing "Which is bigger?" activities; I would have previously covered equivalent fractions in one lesson, then assumed they could do it. The adding and subtracting fractions context work took us three weeks, without even touching a "method" or any basic problems. We did lots of discussion, drawing of bar diagrams and really talking and thinking critically about what we were doing. "Why?" became my favourite question to ask, and pupils began naturally appending their answer with "...because...". We spent a lesson drawing pictures to represent different division problems, with nary a "bus-stop method" in sight.
Once we'd learned something, we revisited it frequently. I actively looked for opportunities to connect more topics. For example, I'd previously never used fraction examples when working out the area of a rectangle, other than as a challenge activity for the "more able" - but why not? If pupils can multiply fractions and find the area of a rectangle, they should all be able to calculate a fractional area.
We went back to basic practice starters, ignoring the received wisdom that this was an Ofsted no-no, as pupils weren't "making progress" in the first ten minutes of the lesson. OK, I'll accept that they weren't making visible progress in terms of "oh look, they've learned this skill that they didn't have five minutes ago", but doing this has made a huge difference to their progress over time.
I've stopped minding if we spend more time on a topic than I'd planned, or if lessons don't fit nicely into a sixty-minute package. I've stopped worrying about "every pupil must make progress every lesson", because unfortunately, all kids don't fit a typical model. Some struggle for two or three lessons, then have a breakthrough, and that's a natural part of learning.
5. Making assessment meaningful to pupils
To start with, we were working on the principle of testing roughly once every 12 weeks. We did our first unit test around Christmas; by this time, my Year 9s had already progressed onto the next unit of work, while some groups were still working on the first few objectives from the first unit. We quickly abandoned this idea for all future assessments, and have now started assessing as and when we feel our groups are ready.
The assessments contain a mixture of basic problems and deeper problem-solving questions. The idea is that pupils need to get over 75% to say they have "mastered" each unit, and that we don't move on until everyone has passed.
After each assessment, we re-enter the data and give pupils another tracker sheet. If they've all passed the unit, we move on, with some targeted work in starters on topics they are still a little weak on. If they've not passed, we then re-teach either select topics or the entire unit. Something we've found incredibly useful is re-teaching for a couple of weeks, then returning the paper for pupils to re-attempt or correct. They have got used to aiming for 100%, and not just going "oh, I'll never get this" and giving up on a particular topic.
I've used a bit of peer-tutoring to work on weaker topics, pairing up a pupil who has mastered that topic with one who is still unsure, for twenty minutes at the start of a lesson. We've experimented with targeted homeworks, and I'm keen to develop this further next year.
6. It's not perfect...yet
We've had several stumbling blocks over the course of this year, and it hasn't been easy. Because all year groups started off at the same place, I feel like I've been teaching fractions, multiplication, division and rounding for the whole year, and it's got a little boring at times. Year 9 are now through the entire set of Elementary units, and I'm looking forward to getting into some more complicated algebra work with them before the end of this year.
We're fiddling around with our setting for next year, and are going to experiment with mixing sets 3, 4 and 5 together. This is going to prove challenging in terms of supporting pupils who come to us at Level 3, and we're looking at how we can provide additional lessons to catch them up to their peers.
Although it's not perfect yet, and we've still got quite a way to go in making sure that every pupil is successful under our new curriculum model, I feel that it's working much better than our previous spiral curriculum. Retention is much better; emphasising the importance of mastery with pupils means that we're also thinking much more carefully about building in interleaved practice of old and new skills, ensuring that they don't forget what they've already learned.
One of the biggest successes for me of this year is the change in how pupils talk about how they are doing in mathematics. At the start of the year, pupils were pestering me when they got their test results for a level: "Am I working at Level 6? Is this Level 7 work?". Now, they are talking about the skills and objectives: "I know I can round to decimal places, but I need to do some more work on significant figures". It will be interesting to see if this translates to improved independent learning when revising for GCSEs in a couple of years time.