Tag Archives: low stakes testing

Principles and practices of effective homework

Homework can have quite a negative reputation.  It is often the source of familial tension as parents make sure their little ones have done it, not to mention the effect on teacher workload.  Research organisations like the EEF have not found it to be too effective either.  That said, research can only judge the effectiveness of existing practices so the job of teachers and school leaders is to find better ways of doing it.  When it is done well, homework can undoubtedly have a positive effect on learning.  The EEF states that effective homework is associated with short, focused tasks which relate directly to what is being taught and is built upon in school.  It also recognises the importance of parental involvement.  With these conditions in mind, here is a set of principles and practices for making homework as effective as possible. 
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SATs not as hard as it looks!

One of my favourite responses when working with with children on tricky problems is, ‘Oh is that it?  It looked much more difficult!’ As May draws closer, children in Year 2 and Year 6 up and down the country are preparing for end of key stage SATs. Tests often invoke strong opinions among teachers. As adults who have typically done well in the education system, tests may never have been a worry and we may see them as a chance to shine and something to look forward to. Others may hold the view that testing children is barbaric and sucks the life out of curricula as schools teach to the test. Either viewpoint, or any gradation in between, does not change the reality that schools are accountable for the success of children on tests. Perhaps more important than accountability though is ensuring that all children, particularly those who are disadvantaged, are able to graduate from an education system that provides qualifications through examinations and have access to wider opportunities in the future.

Every school will be familiarising children with the upcoming tests, most likely by using practice papers, with the aim of children knowing what to expect and in turn doing the best that they can when the time comes. In my experience, there are a number of strategies to do this well and there are also some strategies that could well do more damage than good.

SATs are the ultimate summative test for primary school children and it can be tempting to recreate these summative conditions when preparing children for them. Practice tests done in exam conditions where they receive an overall score at the end have some value but could well set children up for failure, creating anxiety as the high stakes take their toll. Removing the test conditions gives children a chance to learn how to take tests. If the stakes are made lower still, for example by removing the importance of the score achieved, then we can go some way to normalising test situations and therefore reducing the likelihood of anxiety.

It is very easy to get hold of past papers and although the examples here are maths questions, the principle applies to reading, spelling and grammar tests too. One important first step in teaching test technique is to model what a successful test taker does and verbalise their thoughts. Displaying certain types of question, saying what you’re thinking and showing what is appropriate to record is crucial to encouraging children to do the same. From this modelling and explanation, teachers can co-construct success criteria for how to go about the test. The criteria will be a selection of tools to choose from depending on the question being tackled. Sure, those who are successful in tests know subject content very well but by explicitly showing what it is that successful test takers do, we can unlock the mystery of how to be successful. Looking at the KS2 sample tests, the success criteria for answering those types of questions might be:

paper-1-sc

sc-2

Over time, advice like this can build up and if children can internalise it, they will be equipped to deal with tricky problems. Of course, strategies like this are no use without good content knowledge but when combined, set children up to succeed.

Once strategies have been modelled, children can be set off practising. Again, it’s tempting to give children their own paper and have them complete it as they would have to during the test. However, it becomes a much more valuable exercise if children talk about what they’re doing so getting pairs to complete papers collaboratively gives them an opportunity to talk and hear how someone else goes about tackling a test. A few guidelines help to keep them focused:

  • Both work on the same question.
  • Agree an answer before moving on.
  • If you disagree with your partner, explain why you think you’re right and listen to their explanation too.

One of the stressors of testing is the time constraint. When children are practising test techniques there is no need for such constraints. Over time, they’ll get quicker and the strategies they work on will become more autonomous. At that point, time restraints can be put in. For example, you might set the target of getting to question 6 in 10 minutes or halfway in 15 minutes.

We’ve all experienced that frustration of seeing children answering a question wrong in a test. This doesn’t have to be the case when they are practising and like in any great lesson, teachers react formatively to the information before them. If everyone is struggling with question 4 about fractions of numbers, then stop them and teach them how to do it, give them a few extra practice questions and make a note to return to it soon. If it is just one pair or a handful of children struggling, then a little scaffolding, followed by some more practice will help. The example below comes from the KS1 sample test:

KS1 Maths SATs.png

Having seen that this pair of children did not know how to approach the question, the teacher explained that division can be seen as sharing and that this is asking to share 35 into 5 groups. The teacher, in blue pen, drew five groups and began sharing one at a time before the pair completed the question. Now evidently that won’t be enough for that pair to have understood completely so it can then be followed up with sufficient practice to internalise the idea.

Once children have completed the practice tests, teachers will be keen to know the score they achieved as well as looking for specific detail about which questions and topics children struggled with. The well-worn phrase ‘Check your work’ will I’m sure be repeated countless more times with varying levels of patience but that means nothing unless children are explicitly taught how to do so effectively. The way that test are marked can encourage the habits of checking. The most structured way would be to mark each question with the number of marks awarded:

Mark the page.png

When scripts are marked this way, children can see which questions they were successful in answering and which they got wrong. When the tests are returned, children can look for the questions they got wrong, and if it was a case of making a mistake, can discuss what happened with their partner and make the necessary corrections.

This may be a sensible place to start but of course it makes children reliant on the marking to see where mistakes have been made. A gradual removal of that scaffold could involve marking the score for each page rather than individual questions:

mark-the-page-2

In this example, out of the 3 marks available for the questions on this page, the pair of children scored 1. It is then down to the pair to re-read questions to first of all determine which are incorrect and secondly to work through it again to see what went wrong.

A third option, to remove the support a little further, would be to count up the total marks, only telling children something along the lines of ‘You scored 33 out of 40. Find and correct the mistakes.’ It goes without saying that these marking strategies push for corrections of mistakes and will do no good if the child never knew the content well enough in the first place.

Test papers are valuable resources to use in the classroom, not least because of the teaching opportunities for test technique that they allow. One subtle but significant benefit is the varied practice they provide too. During maths lessons, the focus may be narrowed to one objective or concept, and rightly so to provide focused support and practice. Tests’ varied questions though provide a great opportunity for revision, to interrupt forgetting and to provide teachers with a wealth of information with which to inform future lessons.

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A place for everything and everything in its place

Place value is very often one of the first units of work for maths in most year groups and is absolutely fundamental to a good understanding of number.  By getting this right and giving children the opportunity for deep conceptual understanding, we can lay solid foundations for the year.

For the purpose of this blog I’m going to assume that children can count reliably and read and write numbers without error. If these things are not yet developed to the appropriate standard then targeted intervention needs to happen without the child missing out on good modelling and explanations of place value.

Children need plenty of practice constructing and deconstructing numbers, first using concrete manipulatives like base ten blocks or Numicon.  This is to show that 10 ones is equivalent to 1 ten etc.  While they’re making these numbers they should be supported to talk articulately about what they are doing, perhaps with speaking frames: ‘This number is 45.  It has 4 tens and 5 ones.  45 is equal to 40 add 5.’

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What I think about…reading

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. Previous posts were about displays, learning generally and maths. Next up – reading.

I’m proposing a model for teaching reading grounded in the various books that I’ve read. The examples will be for a fiction text but I think the principles apply to teaching non fiction too.

Reading model

Some principles

The first principle to be mindful of is that the teaching of reading is not the asking and answering of questions about a text: that’s testing comprehension.  Sure, asking and answering questions is an important part of developing comprehension – it’s one way we get children to think hard about what they have heard or read – but there is much more to it than that.  Any reader constructs a mental model of the content of what they have read – we don’t usually remember text verbatim without rereading many times and deliberately trying to remember it word for word. Poor comprehenders construct weaker, less detailed and perhaps outright inaccurate mental models whereas good comprehenders construct more accurate and elaborate ones.  One goal of teaching reading then is to ensure children construct good mental models of what they have read. I’m making the assumption here that children can decode fluently and focusing solely on the development of language comprehension.

Simple view of reading

Good readers combine word recognition with language comprehension to be able to decode the print and understand the language it yields. Once fluent in decoding, it is depth and breadth of vocabulary and general knowledge that contribute to comprehension and so the teaching of reading must develop vocabulary and background knowledge.

Developing reading comprehension

Poor comprehenders share many similar characteristics which we need to understand and use to drive the teaching of reading.  Poor comprehenders:

  • have limited general knowledge
  • have a limited knowledge of story structure or don’t relate events in a story to its general structure
  • have a narrow vocabulary and don’t know the meaning of important words
  • read too slowly, without fluency or enough prosody to understand the content
  • focus on word reading without focusing on content
  • make incorrect pronoun references
  • don’t make links between events in the text
  • don’t monitor their own understanding of what they’ve read
  • don’t see the wider context in which the text is set
  • don’t build up a secure understanding of the main events in a story
  • misunderstand figurative language

When it comes to vocabulary, we can’t teach every word or phrase that children might not know and neither should we. If we do, not only would it be incredibly time consuming but we’d also greatly reduce the experience that children have of deciphering meaning from contextual cues. Some words and phrases need to be taught explicitly before or during reading while others can be learned implicitly during reading.  Either way, if children are to master the language, they must think hard over time about its use.  Put the dictionaries away and don’t start off with ‘Who knows what x means?’  These are both particularly inefficient uses of time and are ineffective.  Instead:

  • Model the use of the word in its most common form
  • Use an image (this post from Phil Stock is excellent)
  • Act it out
  • Model other common uses
  • Explain word partners (for example, if teaching the word announce you often see make an announcement together)
  • Show various forms of words including prefixes and suffixes
  • Show words that are similar to and different from the focus word

Lemov (Reading Reconsidered)

That last bullet point is not the same as using the synonym model for teaching word meaning.  Telling  a child that melancholy means sad robs them of the beauty of shades of meaning because it is similar to, not the same as sad.

Memory is key. We remember what we think about, so part of teaching reading needs to be giving children plenty of spaced practice in remembering word meanings, general knowledge, events from the text and details of the characters that are crucial to developing a sufficient mental model of the text. It could well be the case that a child who has shown poor understanding of a text is not unable to comprehend it, they just can’t remember what’s necessary to comprehend. Regular low stakes testing of key knowledge from the text is a strategy to ensure this retention and readiness to mind.  Joe Kirby’s knowledge organisers are very useful for this and here’s one I made for Philip Pullman’s Northern Lights. 


Stage 1 – oral comprehension

Prepared reading, or providing a brief structural overview, ensures that no child hears the story without some prior knowledge.  In the first instance, read aloud or tell children the story. Capture their interest. Retell it, perhaps in different ways.   Lemov, in Reading Reconsideredidentifies different types of reading and here I’d go for what he calls contiguous reading – reading without interruption from start to finish, experiencing the text as a whole.  It may be sensible to teach the meaning of some words that are crucial for overall understanding of the text but not too many at this stage.  I’ve compiled some thoughts on introducing texts and teaching vocabulary here.

What have children understood?

Clearly it is tricky for teachers to know what children have understood and by asking questions all we really know is whether they are capable of comprehending, not whether they actually comprehend independent of us. Before any specific questioning, it would be useful to get an idea of what they have understood by asking them to tell you about what they’ve just read. The decisions they make about what they say (or write)  reveal what they think is important and you can also judge the accuracy of their literal and inferential comprehension. Aidan Chambers’ Tell me gives advice on developing this in a slightly more structured way whilst still retaining the importance of open questioning.

The key to this stage of reading is the focus on oral language comprehension.  Difficulty decoding should not be a barrier to children experiencing and understanding age appropriate texts.  Lemov puts this beautifully:

Low readers are often balkanised to reading only lower level texts, fed on a diet of only what’s accessbile to them – they’re consigned to lower standards from the outset by our very efforts to help them.

Lemov (Reading Reconsidered)

This is one of the reasons why I’m in favour of the whole class teaching of reading and not the carousel type ‘guided reading’.  Listening to texts and using open questions to prompt discussions ensures that the focus in on language development in a way that is not restricted by poor decoding.  Having said that, those children who are not decoding to the standard expected will still need some sort of intervention running concurrently to this so that they catch up.  The benefits of focusing on oral language comprehension have been shown in the results of the York Reading for Meaning Project, written about in Developing Reading Comprehension by Clarke, Truelove, Hulme and Snowling and here.


Stage 2 – modelling the reader’s thought processes and shared reading 

The information that teachers can gather from the open questioning in stage 1 then focuses modelled and shared reading on specific parts of the text. The teacher can model the reader’s thought processes, and get children thinking about the tricky bits. This isn’t simply reading the text from beginning to end; reading will be interspersed with commentary, explanation or making links to general knowledge.  Lemov calls this line by line reading, with frequent pauses for analysis and allowing the teacher to show children that good readers think while they read in order to achieve an acceptable standard of coherence.  As children get older and texts get longer, teachers can’t lead shared reading of the whole text, so by initially earmarking sections that children are likely to misunderstand and by using information gathered from stage 1, shared reading can be focused on addressing misconceptions.  Again, Lemov puts it succinctly:

Shared reading mitigates the risk of misreading.

Lemov (Reading Reconsidered)

I’d expect children to then read the text independently, drawing on what they’ve heard from the teacher’s modelling and all the oral language work. Children should have the opportunities for multiple readings of at least the tricky bits.  These bouts of reading become iterative: children build layers of understating with each reading.  For those children whose decoding is weak, they can be directed to smaller extracts, practising decoding and fluency with a text that they should have a decent understanding of following all of the language work.  It’s important to continue to get children thinking about new words that were taught in stage 1.  If that vocabulary is to be reliably internalised, they’ll need multiple interactions.

This is also an ideal point to make some links to non-fiction that can supplement understanding of the fiction. Questioning that involves deliberate comparison between the fiction and non fiction complements understanding of both.  For example, if reading Robert Louis Stevenson’s Treasure Island, spending some time on books or extracts such as below will significantly aid comprehension.

Non fiction links

Written responses

Writing is thinking, and to paraphrase Lemov in Reading Reconsidered, not being able to record their thoughts about what they’ve read on paper does not make them invalid, but children are at a significant disadvantage if they are unable to craft an articulate, effective sentence explaining what they have understood.  To this end, returning to those original open questions and working with children to refine their responses and write them effectively is a valuable use of time.  The teacher can model scanning the text for the part needed to refine an idea, or to check a detail, and then children should also be expected to behave in that way.  This post by Lemov makes very interesting reading on that topic.


Stage 3 – targeted questioning

It’s standard practice to ask questions of a text after it’s been read but a great deal of care needs to be taken in choosing or discarding already written questions, or in writing them ourselves. Questions need to be text dependent, otherwise what we’re really doing is getting children to activate general knowledge. An example of this, from Understanding and teaching reading comprehension by Oakhill, Cain and Elbro, is:

Where does Linda’s pet hamster live?

  1. In a bed
  2. In a cage
  3. In a bag
  4. In a hat

The possibility of guessing the right answer here would tell the teacher very little of the child’s ability to comprehend text and so asking questions where understanding is dependent on what’s written or what must be inferred from the text is a must. Doug Lemov espouses the importance of text dependent questions in Reading Reconsidered.

When designing questions, teachers must also use knowledge of the characteristics of poor comprehenders in order to model corrective thought processes and to ensure children think in a way that helps them to comprehend more reliably.  For example, we should give them plenty of practice in working out to what or whom pronouns refer.

The education system we work within requires examinations to be passed which then provides opportunities.  Preparing children for success is morally imperative. Write questions in the style of SATs questions about the text, model the thinking process behind successful responses and give children practice doing just that.


Stage 4 – fluency and prosody

Don’t misunderstand – children should be supported continually to read fluently with appropriate intonation and expression. It’s just that to do that well, a reader needs to understand the text. At this stage, that should be the case. Reading for fluency and intonation using a text that children know very well should yield great results and not only that, it provides another opportunity to glean previously missed understanding.

So there it is. A model for teaching a text that moves from oral to printed comprehension; general to specific questioning; and oral to written responses, all the while practising fluency and developing language.

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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:

Knowledge

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:

Knowledge

Scaffolding

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.

Scaffolding

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.

Intervening

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.

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What I think about…displays

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 up – displays.

Displays can take up vast areas of wall space and many hours of adults’ time, therefore teachers and leaders must be sure of the impact that they are having on learning so that what is on display is justified and not simply a waste of time and space.  Put simply, before a display goes up, we must ask: What will this display do to improve outcomes for children?  For this to be answered with any sort of reliability, the question must be framed within a sound knowledge of how children learn and what learning is – a change in long term memory.

Recognition vs retrieval

Information displayed in a classroom can lead children to recognise rather than retrieve the knowledge and concepts that they have been learning. Recognising information that they have spent some time thinking about is much easier than recalling it from memory and can give the illusion of understanding both for the child (‘Oh I know this…’) and for the teacher (‘Hurrah – she knows this!’).  Classrooms with lots of information displayed can become a trap, a trap where both children and teachers come to believe that children have learned what we wanted them to learn.  Research by Robert Bjork into desirable difficulties differentiates between short term performance and long term retention.  Children can quite easily ‘perform’ if they know where to look in a classroom to find information that they can recognise and use to show their teacher that they know something.  However, it is the act of retrieving that strengthens memories – after all if we deliberately practise remembering things, we get better at remembering them.  If we practise looking for things when we need to know something, we get better at looking for those things.  Some would argue little difference between those two scenarios but the difference is subtle.  If children have knowledge and concepts to mind almost immediately, that means that finite working memory capacity is freed up to focus on other things such as paying attention to solving more complex problems.

Key principles

Displays should serve three functions.  Firstly, they should act as memory prompts for the knowledge, concepts and ways of communicating and thinking that children are currently learning or have been learning.  Images, symbols and words should be used to trigger memories and scaffold thinking and talking, with children being given regular opportunities to use displays in this way.  For example, rather than displaying definitions of sentence types, display something like this:

IMG_4095

Then, get children to regularly use it to think and talk about the concept.

Secondly, displays should set a standard for the extent of knowledge and the quality of work expected of children.  When displays are beautifully set out and are talked about with care by teachers and leaders, it shows that we value the quality with which work is produced.  This is why neat borders, carefully spaced work and pride in what’s on display are important – it’s one way of setting standards of children’s work in their books.  If we allow irrelevant content, or not enough depth of content, or display boards to become tatty, then we’re hypocritical when we expect the those same things in children’s books.

Thirdly, they should make the classroom an inviting place that stimulates interest in the subject content to be learned.  They should trigger enthusiasm for learning – one of many hooks so that the teacher can work with receptive minds.

Pitfalls to avoid

Displays should not be used in an attempt to prove that a particular initiative is embedded.  Posters about mindset or school rules, for example, if displayed on a wall, do not mean that those aspects are established as part of the school culture.  Displays like that mean nothing unless the ideas behind them can be articulated by children, teachers and leaders.  It is important here to return the first idea of recognition vs retrieval: displays about mindset and school rules (to name just two – there are, I’m sure, many other applicable projects) can be useful as long as they are thought about carefully.  Use images, symbols and words and give children regular opportunities to think about and express their meaning.

With the sheer amount of content that children are expected to learn, it can be tempting to plaster every inch of wall space with some sort of display.  This is a mistake.  Children can only attend to so much from the environment around them before working memory is overloaded.  A result of this is that some displays barely even get looked at and if that is the case, why are they there?

Displays, if done well, can have a significant impact on children’s learning or they can be a colourful yet ignored decoration.  If we take into account what is necessary for children to learn and use those principles when planning displays, we’re more likely to create an environment that has a greater chance of contributing to long term learning rather than short term performance.

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How can a child catch up to learn times tables in one term?

Children should know all times tables by the end of year 4, but there are children that slip through the net, taking much longer to learn them.  There are also children that may seem to have learned times tables by the end of year 4, but forget and have to work into upper key stage 2 to relearn.

This post describes a plan to get children who are in year 3 and 4 and who are not on track to understand times tables by the end of year 4.  The plan is also for children in year 5 and 6 who still do not know their times tables.

A fact a day for a term

The basic structure of the plan is to work on one fact per day.  Working with commutative facts such as 3 x 4 and 4 x 3 together, and taking into account that familiarity with tasks should accelerate the work the longer it goes, a term is a sensible time frame to work in.  This will be systematic, working from x10 to x5, then x2, x4 and x8, then x3, x6 and x9, finishing with x7, x11 and x12.  This is to enable links to be made between times tables.  Within each times tables, we’ll work in increasing order of times tables (i.e., 10 x 1, 10 x 2, 10 x 3 etc.).  Of course, different children will have different starting points, not all starting with 10 x 1.  As days pass, children will consolidate their understanding of a times tables through repetition, multiple representations, counting and low stakes testing.

Multiple representations

For times tables to stick and to be useful in other areas of maths, they need to be rooted in secure understanding.  To allow this to happen, each fact will be represented in different ways, in the first instance by the teacher but increasingly by the child.  The first representation is Numicon, using the example of 4 x 5:

TT numicon

Using this we can explain that 4 x 5 means 5 lots of 4 and that by counting in multiples, we can find out that 4 x 5 = 20.  Children will have done this for 4 x 1, 4 x 2, 4 x 3 and 4 x 4 in the preceding days so they should be able to count in 4s.  However, they may need to do some skip counting, where they whisper or say in their head each number except for the last on each Numicon piece (1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12…).  The Numicon also helps to lead into other representations:

Repeated addition: 4 + 4 + 4 + 4 + 4 = 20

Bar model:

TT bars

Number line:

TT number line

All the while, the child is practising counting in 4s, and thinking about how 4 x 5 = 20.

Commutativity

One more representation can lead the child into working on the related commutative fact.  An array gives a little further practice seeing how 4 x 5 =20:

TT Array 1

Rotating the array shows how 5 x 4 has the same product:

TT Array 2

This can lead into counting in 5s to get to 20 and showing that 5 + 5 + 5 + 5 = 20.  Then, repeating the representations of Numicon, a bar model and a number line will help to internalise the commutative fact.

Low stakes testing

Having worked on this new fact (and its commutative relative), the child can then work on remembering facts that have been previously worked on in days gone by.  Practising recalling times tables is of course a great way of ensuring that they come to mind immediately when needed.  Quick, effortless recall means that little cognitive effort is required to summon the knowledge, thereby keeping as much working memory as possible freed up to solve a problem that needs the times table fact in the first place.

There are two ways of working on quick recall of times tables.  The first is if the child has a reliably secure understanding of multiplication.  In this case, simple testing such as asking ‘What is 3 x 5?’ or the use of individual flash cards will be fine.  However, if a child is still not quite there with conceptual understanding, testing by using objects or images can help to get them to think mathematically instead of guessing.  The teacher shows any of the pictorial representations already described to prompt thinking about the number of groups, the size of each group and ultimately quick recall of the whole.

 

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