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small chunks, revisited - as opposed to cramming
"It is, for example, becoming increasingly clear that using spaced or distributed practice, where knowledge is rehearsed for short periods over a longer period of time, is more effective than so-called massed practice, where we study more intensively for a shorter period of time. It is therefore good practice to block learning and repeat practice over time, as this leads to better long-term retention of knowledge (Rohrer & Taylor, 2006; Rawson & Kintsch, 2005). A related practice is interleaving. Traditionally, most schools use blocking, where practice of particular knowledge happens in blocks (e.g. AAABBBCCC). In interleaving, we instead mix practice of A, B and C (e.g. ABCABCABC). There is growing evidence that this can improve retention, and research in mathematics is particularly promising (Richland et al, 2005; Rohrer et al, 2015)."
- Ofsted 2019 EIF research overview

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knowledge of self, knowledge of strategies, knowledge of task

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Engelman (pdf of book)

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Ask yourselves these questions about your scheme:

Does it ensure the teachers know exactly what content they are responsible for passing on?

Is enough time devoted to establishing the most fundamental skills and representations which underpin successful teaching of the content?

Does it ensure a consistent approach to vocabulary, models and representations so that pupils have a coherent experience when moving between teachers?

Is the sequencing of content logical (mathematically, pedagogically sound)?

Are ideas revisited and developed at intervals that minimise the need to re-teach?

Are review,revision and assessment built in at intervals that encourage and enable learners to develop fluency and embed knowledge and skills in their long-term memory?

Does the scheme demonstrate an expectation that pupils will have learned what they have previously been taught?

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The madness of writing Schemes of Work or how I fell in love with curriculum design

Why do people keep asking us to redo schemes of learning? There's barely enough time to plan and teach and mark, so why does any school bother wasting time just shuffling things around? After all, surely whether you teach plans and elevations in year 8 or year 9 doesn't really make a difference does it? And aren't all schemes basically the same anyway: a glorified re-ordering of the GCSE specification, possibly with references to some resources if you're lucky?

Five years ago I think I might have agreed with these frustrations. My experiences in departments up to that point had been that schemes of learning served little purpose other than to make sure all the prescribed content was covered by the time the exams hit. With this minimal guidance,teachers were largely left responsible for their own medium-term planning, and since my students generally didn't seem to have any coherent sense what they had learned in the preceding years anyway, what the SoW said they had covered up to that point wasn't really all that helpful either.

And in the end it didn't really matter: year 11 was characterised by a mad dash back through all of the material. Gaps needed to be addressed here, there and everywhere, and since different pupils remembered different things and with only finite lesson time left, their success under examination often came down to whether or not they were able to make good use of their revision guides.

In hindsight, I had perhaps dismissed the importance of a scheme of work because I'd never actually known a real one.

Then in 2012 I joined a department that showed me just what a scheme of work really can be.

The discovery that a highly selective private school would pay so much close attention to the sequencing of teaching was something of a surprise to me. I had naively assumed that in an independent school,teachers (some extremely well-qualified mathematicians) would be left to their own devices much more than in the setting I was used to. And given the aptitude of its intake, I'd imagined that there would be much less concern about pupils missing out on bits of content here and there - after all, they would probably be able to put it all together themselves well enough.

What I realised very quickly was quite the opposite. As a teacher in this department, I was entrusted by my colleagues with a great responsibility: to join in the telling of a story.This story was one that all of us were in the process of revealing to our pupils, and it was one that was uncovered for them over the course of their five (or seven) years at the school.

It was a complex novel, with multiple, overlapping themes and carefully constructed characters. The introduction of each strand of the story had been pondered over; the groundwork for each new concept established carefully in earlier chapters, well in advance of its exposition. For every student to be able to follow this story it was therefore essential that each teacher knew exactly what part of the story they were responsible for passing on. The structure of the narrative was communicated to us in great detail, and the pupils really did come to know it well.

This story was not static but as a department we rewrote it, collaboratively, over the years. We enjoyed debates about whether this idea would really fit better here, and whether this theme might be better understood with this other introduction. It was a joy and a privilege to play a small role in the telling and the rewriting of a great story.

This might sound all very flowery, and I suppose it is,but I cannot think of a better analogy for a scheme of learning. Unfortunately,the "story" that is so often passed on to pupils is far from coherent. Learners hear the same sections over and over again, yet they are expected to recall something vaguely mentioned many years earlier in order to make sense of a new theme. Some parts are told without the necessary back story for them to make sense of it, and certain vital sections might just have been missed out entirely. You can hardly blame someone for not following the story if the storyteller is essentially a rambling old uncle!

So when I say I have fallen in love with curriculum design, what I am talking about is the careful construction of a coherent narrative: one which respects the limitations of learners' working memories;one which accounts for the inevitability of forgetting; one which establishes high expectations of the learner's ability to think logically and make connections for themselves without leaving to chance whether they have all the necessary skills and background knowledge to do so.

When teachers say "stop re-inventing the wheel" I want to point at this:

First stone wheel

This is apparently what we got the first time we invented a wheel, around 3500BC. It's a damn good thing it was "re-invented", and that it continues to be re-invented because there are always better wheels to be made and different things that need wheels. You can't put that block of stone on a Ferrari or a skateboard or a chair. Luckily there are people who like re-inventing wheels, they are really good at it, and as technology develops they are doing it all the time and in all sorts of contexts.

Cognitive research has come on leaps and bounds in recent years. Educators and psychologists alike have a much better understanding of what we can do to help our students to remember and understand what we want them to learn. If this knowledge isn't embedded in the structure of our schemes of work- if it doesn't define (or even inform) the narrative we tell them - then our schemes of work are not fit for purpose.

Ask yourselves these questions about your scheme:

Does it ensure the teachers know exactly what content they are responsible for passing on?

Is enough time devoted to establishing the most fundamental skills and representations which underpin successful teaching of the content?

Does it ensure a consistent approach to vocabulary, models and representations so that pupils have a coherent experience when moving between teachers?

Is the sequencing of content logical (mathematically, pedagogically sound)?

Are ideas revisited and developed at intervals that minimise the need to re-teach?

Are review,revision and assessment built in at intervals that encourage and enable learners to develop fluency and embed knowledge and skills in their long-term memory?

Does the scheme demonstrate an expectation that pupils will have learned what they have previously been taught?

What we teach and how we teach cannot be separated.The starting point for successful teaching has to be the understanding of where students are now and where we are trying to get to. It's imperative not only that schools have the best scheme of work they can, but that teachers engage with it critically. A colleague of mine at the independent school said "I get so frustrated by how schemes just degrade over time". I think she's right, they do, but I know there are teachers like me who find the challenge of re-imagining, tweaking and improving a scheme one of the most interesting and satisfying aspects of teaching.

It takes great subject expertise and many years of iteration to go from nothing to a successful scheme of learning which really does satisfy the criteria above. But now that I am running a department, I consider this to be one of the single most important things I can establish in my role, and I am excited and daunted by the challenge. However, I know it can be done because I have seen it, and I'm not starting from scratch.
Jen Brewin, Subject Leader of Mathematics, Huntington School

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The madness of writing Schemes of Work or how I fell in love with curriculum design

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Why do people keep asking us to redo schemes of learning? There's barely enough time to plan and teach and mark, so why does any school bother wasting time just shuffling things around? After all, surely whether you teach plans and elevations in year 8 or year 9 doesn't really make a difference does it?

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Ben Gordon - Cognitive Load Theory Training.pptx

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-procedural and conceptual variation
-focus attention on the mathematical constructs
e.g. minimally different questions

e.g. MrBarton
Variation theory website

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This website is my attempt to assemble a collection of high-quality, sequences of questions and examples using key principles from Variation Theory. By holding key features between questions and examples constant, together with the mathematical behaviour that I call Reflect, Expect, Check, Explain and the supporting role of the teacher, I believe we can help students better understand key mathematical ideas.

You can find out more about the site and the different types of sequences available by visiting the Introduction.

You can access all the sequences of questions and examples from the Topics menu above.

My 2020 book, Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom, goes into detail about making the most of these activities in the classroom. You can order the book from Amazon, John Catt, or wherever you get your books.

My 2023 book, Tips for Teachers: 400+ ideas to improve your teaching, details my most recent thoughts on using these sequences effectively. You can order the book from Amazon, John Catt, or wherever you get your books.

I have an online course store which offers low-cost, high-quality CPD on-demand. Each course contains short videos, resources, research, activities and questions to reflect upon. The courses most suited to the sequencers on the Variation Theory website are:

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Sequences and behaviour to enable mathematical thinking in the classroom - by Craig Barton @mrbartonmaths

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https://www.tes.com/teaching-resources/blog/tes-maths-pedagogy-place-interleaving