Tag Archives: spacing

What I think about…learning

Moving schools and with more than an eye on headship is sure to get you reflecting.  The following posts are what I think about various things, in no particular order.  First was displays.  Next up – learning.

Asking teachers what learning is surely throws up disagreements of varying degree from polite dispute to outright warfare.  What makes sense to me is that learning is a change in long term memory.  Too often, children don’t manage to transfer concepts from working memory to long term memory and without that internalisation, we cannot say that they have learned.  All we can say is that they have done some work.  Now that work might well have been good, but teachers and leaders need to be aware of the difference between short term performance and long term internalisation.

Performance vs learning and the importance of desirable difficulties

The key paradox is that to improve long term retention, learning has to be made more difficult in the short term even to the extent of being unsuccessful.  We remember what we think about and learning happens when we have to think hard about content.  If children are thinking about things other than what we have intended for them to learn (a distracting context, for example) then that’s what they’ll remember.  If they haven’t had to think too hard, they may well produce some decent work but the thinking behind it is less likely to be retained.  So what does this mean?  Units of work and individual lessons need to be planned around what it is that children will be thinking about.  Each decision about what the teacher will do and what the children will do needs to be justified with that question mind and amended accordingly.  We all get better at what we habitually do – we become more efficient – so if we require children to be able to remember knowledge, procedures and concepts, we must give them ample opportunities to practise remembering those things.  The efficacy of the testing effect has robust evidence and seems to work because testing (either yourself or a teacher posing questions) triggers memory retrieval and that retrieval strengthens memories.  Flash cards are a perfect example of this in action.

What’s important is that this testing is low stakes – no grade, no mark at the end of it, just practice in remembering and feedback on responses.  Feedback can take two forms.  Firstly the feedback can be from teacher to child and is as simple as telling the child what they were good at and what they misunderstood, then correcting those misconceptions.  Secondly, feedback can be from child to teacher and involves the teacher using the information to plan what to do next to develop understanding further.

Low stakes testing is a desirable difficulty – one way of making learning difficult (but not too difficult) so that children have to think hard.  Other desirable difficulties apply more to curriculum design:

  • Interleaving (switching between topics)
  • Spacing (leaving some time between sessions on a particular topic)
  • Variation (making things slightly unpredictable to capture attention)

By presenting content to children little and often, with increasingly longer spaces in between, teachers can instill the habit of continual revision rather than only revising when some sort of exam is approaching.  As such, concepts are internalised and retained rather than forgotten.  Robert Bjork’s research on desirable difficulties can be found here:


The idea of knowledge can be divisive.  Recalling knowledge is often described as lower order thinking and many are keen, quite rightly, to get children to do higher order thinking. This can be dangerous because knowledge is necessary but not sufficient.  Higher order thinking skills rely on a sound basis of knowledge and memory so teachers must ensure that these aspects are fully developed before expecting success in higher order thinking.  Knowledge needs to be internalised too.  It’s not enough to be able to Google it.  The more a child knows, the easier it is to assimilate new knowledge because more connections can be made:



Children are more alike than different in how they learn.  Attempting to teach to a child’s perceived learning style is nonsense.  Everyone, no matter what we are learning, requires three things: knowledge, practice, and feedback on how we’re doing.  It is of course true that children come to a lesson with varying levels of prior knowledge and to a certain extent have different needs in order to be successful.  Teachers may have (and many, I’m sure, still do) differentiated tasks three, four or more ways – an unnecessary burden on time and a practice that reinforces inconsistency of expectations, particularly of the perceived ‘lower ability’ children.   For those children that are behind their peers, if they are not supported to keep up with age related expectations, they will be perennially behind and will never catch up:

Keeping up Differentiation

If we only cater for their next small step in development, we’re failing them.  Instead, all children should be expected to think and work at age related expectations.  Teachers should scaffold tasks appropriately so that all can work at that expectation and we do not have a situation where ‘that’ table are doing something completely different.


For children that grasp concepts quickly (not our ‘most able’ children – heavy lies the crown…), teachers provide opportunities to deepen their understanding before acceleration into subsequent year groups’ content.  Undoubtedly, there are a small number of exceptions to this.  There are some children that have a lot of catching up to do before we can even think of getting them to keep up with age related expectations.  But if they are removed from lessons to carry out this catch up work, then everything will always be new to them – they’ll miss seeing and hearing how children are expected to think and work.  It is much better to precisely teach, and get them to practise, the basics that are not yet internalised in short bursts and often so that they remain with their peers as much as possible, experiencing what they experience but having the support needed to catch up.  This could be basics such as handwriting and number bonds, for example, and teachers should work closely with parents where there is a need to catch up to set short term, focused homework until the basics internalised.


When children misunderstand something, when the work in their books is not to the standard expected, is a crucial time.  Paramedics talk of the golden hour – one hour after an accident – where if the right treatment is given, the chances of recovery are significantly higher.  With children’s learning, if we leave misconceptions to embed or even thrive, we’re failing them.  Even if we mark their books and write some wonderful advice for them to look at and act upon the next day or the day after, we leave holes, holes which children can slip through.  When there is a need, we should intervene on the day so that children are ready for the next day’s lesson and are keeping up.  This of course requires flexible and creative used of TAs and non-class based staff but from experience, it works. Interventions focus on the work done that day.  For some children, pre-teaching may be more beneficial.  Before the school day starts, they are shown the main content of the day’s lesson and carry out a couple of practice examples so that when it comes to the lesson later on, they have some prior knowledge which will improve their chances of success in that lesson.  This concept is in contrast to pre-planned, twelve week intervention programmes where children are removed from other lessons for significant periods of time.

Learning is complex and relies on many interrelating and often unpredictable conditions.  That said, there is much that we can control and doing so greatly increases the likelihood that what we intend to learn is learned – really learned.


Filed under Memory

Language acquisition and reading comprehension

Understanding the spoken and written word relies on, amongst other things, word knowledge.  Language aquisition then is part of English teaching that we cannot afford to get wrong.  My thinking in this post is a reflection on reading Time to Talk by Gross; Bringing Words to Life by Beck, McKeown and Kucan; Developing Reading Comprehension by Clarke, Truelove, Hulme and Snowling and Teacing Literacy by Wray.

Getting the explanation of the text right

It is undoubtedly sound advice to analyse a text meant for children to study with the following question in mind: Which bits are children likely to find difficult to understand?’ In any text, the background knowledge of the reader contributes significantly to comprehension, so extracting the required knowledge to understand the references is a must. In the text I’m using (Kensuke’s Kingdom extract (Gibbons) – T4W), children need to know the following schemas to make sense of the main events:

  • The ‘deserted on an island, waiting for rescue’ schema
  • The ‘hunting wild animals’ schema

The explanation of these concepts will come first in a simple explanation of the story structure.


This way, children will have some prior knowledge with which aspects of the story can fit in with. Further knowledge will of course be needed. They’ll need to know what an orang-utan is!

There’ll be some words that children will not know the meaning of which will become the focus on the language acquisition section of the unit. Here, I’m looking for ‘tier 2’ words; words that are tricky but functional.  Words that are unfamilar but the concept is one that children can understand and talk about.  Tier 1 words are common words that most children come across early in learning English, while tier 3 words are domain specific words. More on language acquisition later.


After words that may hinder comprehension of the text, I’ll look for phrases that may do so. Idiomatic phrases that children may have never come across before can be tricky for native English speakers let alone those with English as a second language. In the story I’m using, the narrator says ‘I had my work cut out at the back.’ I’ll need to show children the clues around that sentence and use them to explain the meaning.

Once the tricky phrases have been identified, I’ll be looking for examples of the writers’ decision making that create particular effects. The effect of this short story is that we feel worried for the characters. Before we read this story together, I’ll want to have a good idea of which bits do that best and which bits don’t work so well.

Finally, I’ll want to draw attention to the bits that the writer includes because they are crucial to the development of the plot. Certain objects or places are mentioned which may seem, to the inexperienced reader, to be irrelevant at the time but as skilled readers, we know that the writer has woven these things into story on purpose and that they must be important. The same goes for the characters’ actions. The writer, with supreme puppetry, has full control over the characters for the development of the plot and children need to know this and what it looks like.

The result of this thinking is an annotated version of the story which clarifies my thinking on the most important bits, the bits that are most likely to hinder children’s reading comprehension. Thinking clarified, this can be shared with colleagues teaching the same text as well as used when a cover teacher is teaching a lesson in the unit.


Language acquisition

Before the unit of work will have begun, the tier 2 words (tricky yet functional) will have been identified. Mastery of a language takes years but we aim for marginal improvements and as such, must set up multiple encounters with new words and phrases, where children think hard about their meanings and applications.

Word meanings are best learned in context – asking children to look up words in a dictionary should not be the cornerstone of language acquisition! There is a trade-off though. Language is best acquired in context, say a story, but comprehension of that story relies on, amongst other things, word knowledge. So here’s my idea

1. Summarise the text with a general structure supported by images.  This summary, referred to at the beginning of this post, will do nicely.


2. Provide the focus word in a sentence from the text.  Children may need a little help allocating the sentence into the appropriate place in the summary, but through summary and sentence, I’m providing a context for the new word.

3. Provide an image and explanation.  Now’s the time to explain the meaning of the word using the image, which will later become a memory prompt for recalling the meaning. It’s important to have a fluid explanation so that children don’t form an incomplete, context specific understanding of the meaning of the word. This is helped by step 4…

4. Show examples from different contexts.  This will help to highlight shades of meaning.

5. Processing of the vocabulary. At this point, having heard a clear explanation of the word, its meaning and its application, children are to think hard about it, for otherwise, it won’t stick. Two ideas are:

  • Relate it to words they already know. For example, ‘When you’re exhausted, you’re really tired. Tell your partner how it feels…’
  • Suggest situations in their lives that relate to the new word. For example, ‘When you’ve just finished PE, you could say that you’re exhausted. When else could you say that you’re exhausted?’

My thinking is that this is necessary before children work on comprehending the text at a deeper level. This preparation, followed by modelled and shared reading, re-reading and retelling, ‘book talk’, annotations and text marking, responding to questions etc will prime children to comprehend the text. When children do all these things, they’ll be using all those focus words, but more will be necessary in order for children to internalise it.

Remembering the vocabulary

If children are to be able to recall the meaning of a word and use it accurately when speaking or writing, then they need to deliberately practise those things. A lot. Here are six ‘low stakes testing’ question styles, taken from ‘Bringing Words to Life’ (Beck, McKeown and Kucan), to get children remembering and thinking about the language:

Review meaning with a question

The quality of the question is in the detail. Asking whether a word means this or that can cause some hard thinking if those two meanings are very similar or centre around known misconceptions.

Does scrambling mean ‘struggling to stay on your feet’ or ‘moving quickly’?

Cloze sentences

This is self explanatory, but the quality is in the subtle shifting of context. When explaining the word ‘gather’, I would not have used the context of gathering up some drawings so this may cause some deliberation within a selection of other sentences

After a few minutes, I decided to _______ up my drawings and head home.  (Children would have a number of sentences and all of the a focus words to choose from.)

Example or non-example?

Again, the quality comes from the minimally different scenarios which zero in on the possible misconception. Children choose which sentence is an example of the word in action and which is not.


Mel broke Zac’s toy so she screamed and threw herself to floor.

Mel broke Zac’s toy so she stared at him and marched towards him with her fists clenched.

Word replacement

Quite simply, a sentence where one of the words can be replaced with one of the focus words.

She seemed troubled and Mrs Ricker wanted to help. (The focus word is ‘agitated’, but children will have to select from all of the focus words)

Word association

Which focus word does this make you think of?

The horse looked agitated so the rider patted it on the back and whispered to it. (Reassurance)

Finish the sentence

The beginning of a sentence is given, including the focus word, and children should finish the sentence in a way that demonstrates understanding of the words meaning.

To give her son reassurance, she….

Here’s an example for just one word:

Low stakes testing

Having a variety of questions for each of the focus words, spaced out through the entire unit (and beyond) provides short, focused practise of manipulating the language and mastering the application of those tricky yet functional words that children need in order to comprehend text and communicate clearly and effectively.



Filed under Memory, Reading

Mastering maths curriculum design

Recently, Bruno Reddy and Michael Tidd have written about their experiences in designing a mastery maths curriculum. It seems that there are lots of us designing overviews for year groups with the same goals in mind: long term retention of knowledge and concepts with problem solving at the heart.

It is fascinating to see what others have come up with working on the same project, and also a little reassuring. Bruno provides six tips for creating a mastery curriculum, some of which I’d agree with wholeheartedly and some I’d adapt slightly for a primary curriculum. He advocates lots of practice, separating minimally different concepts, teaching concepts in a sensible order, and spending more time teaching fewer things. All of which sound like good advice to me.

Whereas Bruno suggests going back to basics in the first part of Year 7, I’d say that for a primary curriculum, the spotlight on place value, number facts, mental arithmetic and written algorithms needs to be relentless; spaced out and returned to many times over each year. In lower key stage 2, I’d have these units of work at least termly and more likely half termly. Each time the topic is revised, the expectations can be upped, with more and more time devoted to solving problems. This would enable the teacher to spend the time on good modelling and practice, while gradually increasing the expectation in that topic over the year and introducing different styles of problem. I’d say that this is preferable to organising revision through starters, homework etc alone.

Like Michael, I started with the mathematics mastery example overview.


Those arrows denoting the continued study of a concept over the year do not provide enough guidance for a teacher as to when and what to specifically revise. For the draft that I’m working on, I wanted to change that. While Michael describes spending a whole half term on fractions, I’d suggest splitting fractions into different units and linking back each time, like in the draft year 4 example below:


I thought that Children would move from comparing pictorial representations of fractions, to looking at comparing fractions and decimals, to finding fractions of quantities throughout year 4. Each time there’s a unit of work related to fractions, the teacher would check up on prior knowledge (with some sort of test – see benefit number 3 on test potentiated learning) and spend an appropriate time remodelling and getting children to practise previous content before linking to the main work in the topic.

A maths overview like this would be fine for maths specialists but for some, and indeed NQTs and teachers new to a year group, a little more guidance might be necessary. To supplement the overview, I’d have some more detail on the topics themselves including the core knowledge that children must have and be able to recall in order to master the topic and a brief idea of what children should be expected to do:


This pair of topics will be one unit of work within autumn term 1. These topics will be repeated over the year, so that practice will be distributed or spaced, but another layer of spacing can be introduced by switching between these two topics: a couple of days on place value, a couple of days on mental addition and subtraction. See Robert Bjork on desirable difficulties and a recent post of mine on the same ideas.

All of this, of course, is still a draft. The order of concepts could do with a review, as could the expectations for what children should be able to do in each unit. Also, the overview needs to emphasise flexibility. Although topics are arranged to be revised as shown, there will be occasions when some topics don’t need as much revision while others will need more.


Filed under Curriculum, Maths

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

Hassan’s internal number line

Hassan is a wonderful boy. He’s polite and has a great group of friends. But Hassan started Year 6 working significantly below his peers. His school history is of sustained underachievement with very little progress. He did not have an internalised number line with which to think about numbers, to the point where he could not reliably say which number out of two was biggest.


This post is an account of an intervention carried out by a teaching assistant. It is one of the most successful interventions I have seen and has resulted in vast improvements in Hassan’s ability to think about numbers. Here’s what happened:

These number cards were prepared: 53, 67, 54, 35, 76, 45

Two of the cards were presented to Hassan and, with the use of Numicon or dienes blocks or arrow cards, the teaching assistant modelled explaining which was the bigger number. Hassan picked this up fairly quickly, but to help him to retain this procedural knowledge, it was repeated little and often over the course of a few days.

A third card was added and the teaching assistant again modelled, using appropriate concrete equipment, how to order them. When he could consistently order three numbers, a further card was added until he could deal with ordering six cards. Using those six cards, the teaching assistant made seven different sequences:

53, 67, 54, 35, 76, 45

67, 35, 76, 54, 53, 45

76, 35, 67, 53, 45, 54

45, 53, 35, 76, 67, 54

54, 45, 76, 53, 35, 67

53, 54, 35, 76, 45, 67

45, 76, 54, 67, 53, 35

The cards were presented to Hassan in these orders, one set at a time, and Hassan was asked to order them. At first, with this slight change in task, he would place the numbers in fairly random order for each sequence. After completing each sequence, the teaching assistant ordered them with him, using concrete models when necessary. When Hassan was asked to read out the order, if he was incorrect, he often didn’t notice. However, when the sequence was read aloud to him, he could hear the error and would correct it.

This was repeated over several days for short periods of time. Sometimes this was in maths lessons and at other times it was not. The seven different sequences would be laid out in a straight line and he would pull the cards out and order them. As the days progressed, he could very quickly pick out card 35 and put it furthest left and also card 76 and put that furthest right – the smallest and greatest numbers. However the other cards in between were never placed consistently in order.

After a week of doing these sequences once or twice a day, he could order every sequence in the correct order. A new set of numbers was introduced: 12, 27, 45, 54, 59, 72

Hassan was very good at picking out the biggest and smallest numbers. The numbers in between were still more difficult for him. The teaching assistant modelled looking at the tens and units columns and this prompted him to order them correctly.

The cards were then mixed up, with more numbers being added one at a time to see if he could order them again. His confidence was growing and once he was happy with the order he had put them in, he was asked to read the numbers out to see if he could spot any errors himself. He often did and corrected them without the teaching assistant needing to intervene.

After a few days starting with six or more cards, he could reliably order them correctly every time. Next, some three digit numbers were added to make twelve cards overall. He was quickly able to deal with this progression. He was then given cards with multiples of ten to see if he could slot them into the correct places. He struggled a little with cards 10 and 20 but he placed multiples of ten more than twenty in the right places every time. If he needed to, he referred to a tape measure to check.

Once he was confident in ordering these numbers and could do it correctly every time, two numbers from the sequence were chosen. He was asked: ‘What are the smallest and biggest numbers that could go in the gap?’ This proved to be quite tricky for him and he would often say the number before the smallest card. This took him around a minute to process each time, and many answers were guesses. The teaching assistant modelled looking at a tape measure to find the two numbers (53 & 59). He then could see, using the tape, which numbers would come after 53 and before 59, and therefore the biggest and smallest that could go in the gap.

From here, Hassan is now working on adding and subtracting one digit numbers and multiples of ten from numbers in his card sets, with increasing success. Soon, the goal is that he can add and subtract any two digit number from any other.

Why this intervention worked, when other have failed

Spacing and interleaving

Regular short sessions, interspersed with other topics in maths lessons, with varied lengths of time in between those sessions has given Hassan time to internalise patterns of numbers and procedural knowledge for dealing with them.

Building knowledge of the number system

The more he practised recalling facts about numbers and procedures for how to think about them, the more successful he became. Each nugget of internalised knowledge enabled further memory development until he had internalised the basic number system.

Deliberate practice to mastery

The moment that Hassan understood and was successful did not signal the end of the intervention. It will continue until he never makes a mistake, even when tasks are altered.

Making links between ideas

Any new concepts were introduced alongside concepts that Hassan was familiar with.

Detailed dialogue between teacher and teaching assistant

Using video and observing ‘live’, the teacher and assistant talked about the nuances of the decisions that Hassan made to tweak tasks and feedback. This precise tailoring resulted in explanations, tasks and feedback which were accurately matched to Hassan’s needs.

This intervention was put in place because Hassan was working significantly below his peers at number. It was clear that he had not internalised a number line at the beginning of the year, but this shows that he now has. He will need more practice to cement his understanding but the progress that he has made has been good. We did not work on this with him for a week before the Christmas holiday. He had just over two weeks off school over Christmas and when he returned to school after the holiday, he could still deal with the number tasks accurately. Next, we are looking to see if the results are replicable with other children.

Details about the child have been changed to preserve anonymity.


Filed under Maths