Tag Archives: the law of the vital few

Spacing, Interleaving and Retrieval Practice in Primary Maths

In the last few weeks there has been a flurry of posts written on spacing, interleaving and retrieval practice. It seems that this flurry has in part been triggered by @miss_mcinerney’s Touchpaper problems. Two that stand out are Joe Kirby’s and Mark Miller’s. Both digest the research before summarising with great clarity what seems to be optimal conditions for learning. I first came across the ideas reading David Didau’s blog, and have been working on Year 6 maths planning to benefit from the effects of spacing, interleaving and retrieval practice. It’s split into 2 parts: longer term curriculum design and shorter term lesson planning.

Curriculum Design


This screenshot is a section of the Year 6 Spring Term overview. The overview is split into units of work which consist of two topics. Sometimes, these topics compliment each other in order to show children links between areas of maths: working walls depict these links and they are referred to often. Other times, there is no link between them. This is a first draft of a curriculum overview and although there are probably more meaningful combinations of topics, it will take some time to reflect and switch things around. In this instance, I’m not sure how significant the benefit would be to deliberate too much over this.

The superiority of spaced rather than blocked practice is well known, and this overview plans for spacing in two ways. Some topics are repeated regularly as additional teaching blocks. The Pareto Principle, or the ‘law of the vital few’ describes the imbalance of effects of different causes. The theory applied to this situation would suggest that twenty percent of the content of the curriculum provides eighty percent of the value: there are certain topics that have much greater value than others. Knowing number facts such as times tables as well as being able to calculate quickly and reliably would certainly be within that twenty percent. As such, these vital few topics are repeated often.

Day to Day Planning

The other way that spacing is set up is through the switching between the two topics in each unit of work. Deciding when to switch is contextual – a natural break in one topic is the switching point.  For example, a few days on converting betweeen fractions and decimals before switching to working on calculating unknown angles would provide a few potentially fruitful opportunities.  It gives the teacher a bit of time to assign any extra practice (perhaps for homework) to help some children to be ready for ordering fractions and decimals.  It also gives the teacher a chance to delay feedback for a couple of days, which could be well worth experimenting with, as David Didau suggests here.

But what of the topics that are not in the vital few? These need to be spaced too if they are to be encoded into long term memory. A relic from the National Strategies is the oral / mental starter which could be tweaked to provide spacing and retrieval practice. Each lesson, an old topic is selected to work on where children use a model or image to practise recalling a concept, before working through a series of questions to practise recalling procedural knowledge. This not only spaces out learning but gives the teacher the opportunity to see what children can still do or what they have forgotten; to give feedback on known and likely misconceptions; and plan for revision sessions.  In the example below, children had, within the last few weeks, been working on calculating the area of compound shapes.  The success criteria that we developed at the time was shown on the screen and children used the images to recall the steps needed.  After that, they had the opportunity to practise.  The questions got progressively more difficult from left to right and children either chose to start from ‘column 1 or 2’ or were directed to the appropriate questions:

 MM PerimeterMM PErimeter 2

Factual recall is crucial in order to think with clarity about a concept. For example, if children are to be able to compare fractions, decimals and percentages, they have to be able to quickly recall conversion facts. For situations like these, the mental maths session would include individual use of flash cards, like these.



Children look at the prompt then say the decimal and percentage conversion. They turn the card over to check and make two piles. One pile of facts that they can reliably recall accurately, and one pile of facts that they have not yet internalised. When putting the cards away, the ‘wrong’ pile gets put on top to practise first next time. Often, having practised an area of maths, a short problem solving task is presented for children to work through, like in the screen shot below.


What next?

My organisation of the spacing is still fairly arbitrary. Whether there are optimal spacing times is not yet clear and certainly, trying to engineer optimum times would be difficult and perhaps not worth the opportunity cost, especially if it turns out to be non linear.


Filed under Maths

Improving teacher quality – With vision must come action

In terms of securing the best outcomes for the children that we teach, you’ll have to travel pretty far to find someone who disagrees that teacher quality is key.


Every teacher needs to improve, not because we are not good enough, but because we can be even better. Dylan William

In order to address the ‘Ok plateau’, which describes the apparent halt in improvement after teachers’ first few years, a relentless focus on improving teacher quality through CPD must be a priority for schools, regardless of their circumstances. I have read a lot over the last few weeks, including books and blog posts, which included a lot of wisdom. With vision must come action and this post is my attempt to turn the many ideas I have read about into something tangible – the first steps into applying my reading into a great CPD program in my school. I don’t claim this to be in any way a polished plan, but I hope that by writing it that I find further clarity.


An INSET schedule for the academic year will have various foci, but it seems prudent to have a consistent thread throughout the school year on the fundamentals for all subjects and all age ranges. Alex Quigley (@huntingenglish) proposes explanations, questioning and feedback as the ‘holy trinity’ of teaching. Doug Lemov, in his book ‘Practice Perfect’ refers to this as the 80/20 rule, or the ‘law of the vital few’. That is, identifying the 20% of things that we do that deliver 80% of the value. There are certainly other aspects of teaching that require status in this 20%, including behaviour management, and individual schools will have their own priorities that they would add to this. For example, there may be targets on the school improvement plan or from rounds of lesson observations that would need to be a part of the 20%. Schools that perceive explanations, questioning and or feedback to be a strength of their teaching profile may be tempted to leave these aspects out of their CPD schedule in order to work on perceived weaknesses. Although weaknesses do need addressing, this may be a mistake. Failure to keep the profile of important aspects of teaching practice high could lead to complacency. With good advanced planning, this could all be linked to individual performance management. How often around the country are performance management targets not effectively worked on? Identification of the 20% needs to happen first, and then be referred to constantly, including as part of performance management targets, observation foci and so on.

Then there is the issue of how CPD is presented. Traditionally, the lecture style by SLT or an external consultant or expert has been the norm. There is nothing necessarily wrong with this, but to expect teachers to apply ideas to their practice will not work for the majority. There needs to be a carefully planned follow up to CPD sessions of this nature. The action research model is an example of this, where teachers ‘act their way into thinking’, after a brief input from an expert. Just like in lesson design for our pupils, we should plan for variation, a ‘desirable difficulty’ as Robert Bjork puts it (see this post by David Didau @learningspy). However it is presented, the CPD that we provide for staff should reflect the importance attached to improving teacher quality. Perhaps the most underused method of CPD that we are not taking advantage of though, is deliberate practice.

Deliberate Practice

Practise the highest priority things more than everything else combined.

The old maxim ‘practice makes perfect’ is not strictly true. Practice makes permanent . Simply doing something regularly does not necessarily lead to improvement. I play football every week, yet I see no discernible improvement (much to the dismay of my fellow footballers). Similarly, just teaching every day, with the exception of in the first few years, will not lead to improvement, hence the ‘Ok plateau’.

So deliberate practice is required in order to improve. Once the ‘law of the vital few’ has been thought about and the 20% most valuable teacher behaviours identified, deliberate practice needs planning for. Lemov cites the need to set up drills where the specific skills related to explanation etc can be isolated and practised. For example, this could be the fluency of the explanation or the use of analogy. It could be the modelling of a formal written method for division to include the generation of success criteria. I wonder how many school leaders are developing these kind of drills? Twitter’s value for teachers is in the collaboration it inspires. Perhaps there is a niche developing here – #deliberatepracticedrills .

Before expecting teachers to practise, they would need to see it done effectively first through an expert demonstration, live teaching of children, or perhaps a video clip. Then they would practise. Feedback is important here. When the teacher demonstrates effectiveness, other observers tell them so. Then they do that bit again. This repetition should help to internalise desired behaviours and skills. When the teacher demonstrates ineffectiveness, the other observers tell them so. They offer advice: “Try saying it like this.” Then they do that bit again. They get an immediate chance to act on the feedback given and internalise effectiveness. This drilling will ideally create a foundation on which individuals can innovate and free up working memory in order to react to the variable classroom environment.

Once embedded, we could aim for really efficient use of INSET time. When staff have internalised the requirements for being effective at a certain aspect of teaching, and have in the past practised a drill, named, the first 5-10 minutes of an INSET session could be as straight forward as: Let’s run the ‘success criteria drill’. Or Let’s run the ‘low level disruption drill’. By regularly returning to well thought out drills, we could also reap the benefits of another of Bjork’s desirable difficulties, spacing.

Deliberate practice drills seems good for working on skills in isolation. But they cannot recreate the fluidity and unpredictability of the classroom. Lemov uses the sports coaching analogy of moving from drills to scrimmages – small sided games – to assess the readiness for performance. Scrimmage for teachers could take the form of coaching in the classroom, which deserves a blog post of its own. After we have deliberately practised and been coached in a more realistic situation, we should be ready for performance. For us teachers, the performance that matters includes every lesson every day with the children we teach. The analogy does not quite work unless we consider performance in this sense to mean some sort of formal observation. Not ideal, I know, but hear me out. Consider a situation where a culmination of the deliberate practice and coaching leaves every teacher ready for a (necessary due to issues of accountability etc) formal observation. The focus for the observation was determined before the CPD cycle began so everyone knows the purpose. The teacher can then request the observation at the time of their choosing, effectively stating: I’ve been working on this, come and see. Clearly some sort of time frame is necessary, say within a term. How’s that for professional trust?

There is much to grapple with in terms of improving teacher quality, and to make it as effective as possible will require some brave decisions. Of course, as with any intervention it will need to be scrutinised every step of the way. But, if we do what we’ve always done, we’ll get what we’ve always got.

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