What makes a good maths scheme of work?
In June 2013, my Head of Department, another member of our team and I, sat down to write a brand-new maths scheme of work. I documented this process from start to finish in an epic series of nineteen blog posts, containing examples of all the resources we used, which can be read here (http://www.mrbartonmaths.com/blog/category/writing-a-new-scheme-of-work/). My posts proved popular, with many other maths departments around the country seemingly in a similar position to ours, with changes to the National Curriculum followed by a new GCSE being sat for the first time in 2017, prompting people to make changes. Indeed, one lady wrote to me to say that having finished the 50 Shades of Grey trilogy, these blog posts were her new favourite bed-time read – which is somewhat ironic as any mention of our new scheme of work seems to have quite the opposite of an aphrodisiac effect on my wife.
Anyway, with our scheme of work officially one year old, I thought it was a good time to reflect upon why we built what we did, what worked and what didn’t, and where we go from here.
What was there before?
The scheme of work that existed in our school before we made the changes shared its main features with schemes I have seen in the many schools and maths departments I have been fortunate to visit over the last few years. There were objectives, ideas for enrichment, assessments, and homeworks were combination of MyMaths and worksheets. Crucially, the Year 7 and Year 8 schemes of work looked rather similar – two weeks for fractions in Year 7, and then another two weeks on Fractions on Year 8. It was the same with ratio, probability, angles and many other topics.
Things ticked along nicely, results were fine, but I wasn’t happy. Sure, we were doing fractions in Year 7 and Year 8, but we were also covering it in Years 9 and 10, and then we still had countless numbers of Year 11s who would act as if they had never seen a fraction before in their lives. In addition, I was fed up with some students getting a different deal to other students, in terms of the richness of their learning experience, depending on which teacher taught them. I call this the “Lesson Lottery”, and it simply had to go.
Fortunately, my Head of Department agreed with me, so we set about making some simple, but key changes.
Content and Structure
We started off by halving the content covered in Years 7 and 8, so topics would only be covered once across those two years. The time we saved would be used going into each topic in more detail, and on the compulsory rich tasks that I will talk about in the next section.
“But what if a child was off when you covered ratio in Year 7, or what if he didn’t fully understand it? Are you really saying that they will not meet that topic again for another two years?”
This perfectly reasonable question was one of the main ones we had to deal with. I have three responses. Firstly, all the evidence suggests that if students do not get a particularly topic first time around, there is no guarantee they will understand it any better second time around, especially – and I find this is often the case – if it is presented in exactly the same way. Secondly, and more importantly, topics would appear again, in fairly regular intervals, via the compulsory rich tasks and the new homeworks we devised. Finally, by spending more time on each topic, I believe there is more chance of it sinking in as the teacher is able to adapt the extra lessons to better suit the needs of their students.
A final key point to note is that every class moves onto the next topic at the same time. No-one jumps ahead, no-one falls behind. There are enough lessons to ensure all the content is covered, and enough supporting materials and activities to ensure that lessons can be filled in a meaningful way after the key content has been taught. All staff moving on at the same time makes things like assessment schedules, homeworks and joint-planning far easier.
Compulsory Rich Tasks
How many schemes of work have you seen that have links to lovely NRICH activities for each topic, often tucked away in the final column of the scheme of work spreadsheet? More importantly, how many times are these lovely, important activities used?
In my experience, the answer is not a lot. And why? Well, sometimes it is because there is simply not enough time to do rich activities when you only have one or two weeks to whizz through a topic. Secondly – and this is going to sound a bit harsh, but I have seen it many times – these rich activities are harder to plan and deliver, so some teachers opt to take the easy way out and deliver the same old lessons they have always delivered. So we have the “Lesson Lottery”, where one class is doing a rich, challenging task that is stretching and engaging them, whilst in the adjacent classroom we have dull, passive learning going on. It is simply not fair.
Now, I want to be very clear about this next point – I am in no way saying that all teachers should be forced to teach in the same way, using the same resources. That is no good for anyone. Just as we need to cater for the fact that all students learn differently, it is also true that all teachers teach differently, and diversity in a maths department is a very good thing.
So, what we settled upon was that topics could be taught however teachers chose, using whatever resources they liked. But at some point during the topic (it could be at the start, middle or end, depending on the task itself or the teacher’s preference), all classes would do a compulsory rich task. These tasks were planned and devised by me, and all followed a similar structure. Each contains an easily accessible starting point (the low barrier), followed by a series of suggested prompts, questions and lines of inquiry that they teacher can use to allow their students to make as much progress as possible, demonstrating their creativity, problem solving skills and powers of communication. The prompts also contain ideas for support to simplify the task if needed. All students in all classes across a year group do the same task, but all access it at different levels. This for me is proper differentiation.
As a department, we have a quick run through the forthcoming set of compulsory rich tasks in departmental meetings thinking as students, with teachers suggesting ways we might modify, simplify or extend them to make them suitable for their classes, all the time adding to the bundle of prompts, questions and lines of inquiry.
I have shared the vast majority of the rich tasks we use on TES, and they can be accessed here: http://www.mrbartonmaths.com/blog/links-best-maths-websites-world/#rich
We wanted to ensure two things with our homeworks: they were consistent across the department, so we knew they were quality and allowed meaningful comparisons between classes and students to be made; and they enabled students to practise not just the current topic, but topics from earlier in the year and previous years.
So, we rewrote all our homeworks. It took flipping ages, with all members of the department getting involved, but it has certainly been worth it.
Our students are set across four bands of ability, so we needed a fortnightly homework for each band in each year group. Homeworks are paper based and consist of 30 marks – the first 10 are revision of prior topics, and the next 20 are based on the current topic(s) being taught. There are a mixture of skill-based and more problem solving questions.
Homeworks are given out on A4 sheets, which are then stuck on the left-hand side of students’ exercise books (we use blue A4 books with our students). The students do their working on the right-hand blank page, and then fill their answers in on the sheet. This makes the marking of them quick, encourages working out, and gives the teacher plenty of space to write corrections, model answers, and engage in written feedback and dialogue.
On that final point, we have devised a simple system that every teacher and student uses. The students answer in blue or black, the teacher marks in red, students then correct in purple, the teacher remarks in green. In order to make this process as formal and meaningful as possible, we dedicate one lesson a fortnight purely to reflecting on the homework just gone, which is where the purple pends get handed out!
We have one formal assessment every half term for each student. In the past, these have been compiled by our department and made up for past SAT paper questions. The problem we have found with these are that they style of the questions can be a bit weird, and as soon as you start compiling assessments, then levelling or grading them in any manful, consistent, objective way becomes very tricky. At times we found ourselves deciding on level/grade boundaries after we had all the data in, trying to ensure we had evidence our students were making progress, which is never a good way of doing things.
So, from September we are trialling using current specification GCSE Foundation papers as our half termly assessment with Years 7 to 9. We each have our own reservations about this, not least about the unavoidable assessing of topics not taught. But the advantages of good questions and existing, objective grade boundaries, offset our concerns.
The plan is that we (and our students) can track progress over five years as we work towards the GCSE.
Our scheme of work is not revolutionary, neither is it a variation of the Mastery approach that a lot of schools are opting for. It is based on a few very simple features that we wanted to ensure were consistent across teachers and students, so everyone knew what to expected, and everyone could be supported.
Like with any kind of change, there have been highs and lows. But I think I am safe in saying that all our department are behind the core principals of what we are trying to achieve, and nothing makes me happier than hearing both teachers and students discussing ideas and spin-offs for the latest rich task they are working on. You don’t get that kind of satisfaction from 50 Shades of Grey.