Maths — the big ideas

The beauty of maths lies in the interconnectedness of ideas and concepts yet this concept of relationships is often lacking in children who struggle with maths.  Mike Askew, Professor of Education at Monash University, Melbourne, has written about what he calls the big ideas of maths. These help children to connect different areas of mathematical understanding, yet are small enough to understand in their own right.  

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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. 
Read the rest of the article on the Rising Stars website…

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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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How To Get A Four Year Old To Write – EYFS

Mamuna Ahmed

When children start school in Reception, it is not uncommon for them to have significant difficulties in reading and writing.

I’ve had moments where I’ve found it a struggle to decipher a starting point to build upon and enable me to maintain my sanity, but the truth is that it doesn’t matter where you start as long as you do!

Children are wonderful creatures that will do what they are shown but sometimes we forget to do the showing. If we don’t model the expectations, how can we expect children to meet them? Often we become frustrated because a child ‘isn’t listening’ or ‘won’t do as he/she is told’. If we don’t model what good behaviour is, we mustn’t expect it. If we don’t show children what good sitting is, we shouldn’t complain when they don’t do it.

Writing requires the same strategies: model what you want the children to learn.

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Story time in EYFS

Mamuna Ahmed

The Very Hungry Caterpillar? No.

Goldilocks and the Three Bears? No.

Matilda? YES!

Each year, I ask my class to choose a book from the Roald Dahl collection in our classroom  as a way of exposing children to stories beyond what they can read independently.

Children often look forward to story time as it marks the end of the day when they can wind down, listen to  a story, drink their milk, and prepare to go home. You would imagine that the thought of going home would excite them, but often, they would rather stay in school as they are engrossed in what is unfolding in the story and so that we can ‘read just one more chapter’ together! Their groans as a reaction for being told to get their things and to go home as their parents stand glued to the window bring a different kind of satisfaction. We have the luxury of…

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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.’

Read the rest of the article on the Rising Stars Blog.

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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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