Monday, 25 September 2017

What Does 'Greater Depth' Look Like In Primary Maths?


What do we mean by 'Greater Depth' in maths? What would a child working at greater depth be doing? How can we support children to work at greater depth? With a little detective work we can piece together a good idea of what we might be talking about.

At first, we might think that to be working at greater depth in maths children should be fluent in their mathematical ability, and that they should be able to solve problems and reason well. But that can't be it as the National Curriculum states that those are the aims for ALL pupils:


So whilst children working at greater depth will be fluent and will solve problems and reason mathematically, we can't use those indicators to define 'Greater Depth' in maths. The National Curriculum document does give us another clue, however:

We might define children who work at greater depth as still working within the expected standard but at a deeper level; this is how the Interim Teacher Assessment Framework (ITAF) classifies them. These children will most likely be children who 'grasp concepts rapidly' - let's assume the two are synonymous. For these children, the ones working at greater depth, we should provide 'rich and sophisticated problems' and we shouldn't just be getting them to move on to the next year group's work - this is made clear in the NC document and the language of the ITAF: working within the expected standard. So, as an indicator, those working at greater depth should be able to access 'rich and sophisticated problems'.

But what about 'mastery'? A word mentioned only twice in the National Curriculum document (in relation only to English and Art) but one which has been bandied about a lot since its publication. If a child demonstrates mastery, could they be considered to be working at greater depth? In a word: no. The NCETM have this to say: "Mastery of mathematics is something that we want pupils - all pupils - to acquire, or rather to continue acquiring throughout their school lives, and beyond." Again we see that word 'all'. The NCETM say that "at any one point in a pupil’s journey through school, achieving mastery is taken to mean acquiring a solid enough understanding of the maths that’s been taught to enable him/her move on to more advanced material" - mastery is something which allows children to move on to be taught new content (c.f. to the NC) whereas working at greater depth pertains to working on current content, but at a deeper level. Notice those words 'solid enough' - a child working at greater depth won't just have 'solid enough' understanding - they'll have something more than that.

The Key Stage 2 ITAF does not contain any information about what a children working at greater depth should look like by the end of year 6 so we have to look to the Key Stage 1 ITAF for more clues. Thankfully Rachel Rayner, a Mathematics Adviser at Herts for Learning, has done a great piece of work on this already. Her article 'Greater Depth at KS1 is Elementary My Dear Teacher' identifies three key differences between the statements and exemplification material for working at the expected standard and working at greater depth within the expected standard: she says that for pupils to be working at greater depth they should confidently and independently be able to deal with increases in complexity, deduction and reasoning. Please do read her article for more information about, and examples of, these three areas.

Complexity

Complexity is not about giving children bigger numbers, nor is it necessarily giving them more numbers (for example, giving children more numbers to add together, or order). Complexity needs to be something more as, based on curriculum objectives, giving bigger numbers is just a case of moving children onto the content of a following year group.

So, how do we provide more complex work which will challenge those children identified as working at greater depth? One consultant advises that "in order to provide greater challenge we should keep the concept intact while changing the context." And, anyone who has witnessed a year 6 class doing their SATs will know that if there's one thing that throws them more than anything, it's the context of the questions. The test writers come up with endless ways of presenting maths problems but children working at greater depth are very rarely phased by these, whereas children working at the expected standard will come up against a few that they cannot answer.

The best bet for increasing the complexity of the maths but continuing to work within the expectations for the year group is to present the problems differently, and in as many ways as is possible. The more children are exposed to problems presented in new ways, the more confidently they will approach maths problems in generally - gradually, nothing will phase them and they will have the determination to apply their maths skills to anything they come across.

The NCETM Teaching for Mastery documents, although designed for assessment purposes, contain a wide range of complex problems under the heading 'Mastery with Greater Depth'. Organised under the curriculum objectives, these provide a great starting point for teachers to begin thinking outside the box with their maths questioning. Here's an example from the Year 1 document:


A working group from the London South West Maths Hub have also begun putting together some similar documents, focusing initially on number, place value, addition and subtraction and again categorised under NC objectives - those documents can be downloaded here. Here's an example of one of those, taken from the year 3 documents:


It's also worth looking at the KS1 and KS2 tests to get an idea of the question variety. The mark schemes will help you to decide which year group's content is covered in each question. When picking a question from the tests, decide whether or not it could be considered as an example of greater depth, rather than just mastery. Here's an example (from last year's year 6 test) of how different the questions can look:


Reasoning

Reasoning is defined in the NC document as "following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language." 

As already discussed, reasoning is a skill that we want every child to have. But the greater depth exemplification makes more of reasoning than the expected standard exemplification so we need to be able to differentiate between those who are reasoning at the expected standard and those who are reasoning at greater depth. When it comes to assessing children on their level of depth in reasoning, NRICH have a very useful progression of reasoning:


I would suggest that those working at greater depth would be able to work at at least step 4: justifying. The NRICH article gives excellent examples and analysis of children's reasoning work so it is a must read to become more familiar with recognising reasoning at these five different levels.

For further discussion of reasoning skills, please read this article, also on NRICH, which discusses when we need to reason and what we do when we reason.

Deduction (and asking mathematical questions)

Making deductions, a key part of reasoning, is similar to making inferences when reading and is all about looking for clues, patterns and relationships in maths. Once they have found clues they need to make conclusions based on them, and to then test them out. To be able to make conjectures, generalisations and to follow a line of enquiry, children need to ask their own questions. They need to look a sequence of numbers and ask themselves, 'Does the difference between each number in the sequence is the same?' - this is all about wonder: 'I wonder if...'.

In order for children to ask questions about maths, so that they can begin to deduce things such as patterns and rules they need to be provided with activities that encourage them to do this. But even more importantly, initially they need to have these questioning skills modelled to them by an adult. They need to be taught and shown that maths can be questioned because many children think that every maths problem just has one set answer to be found.

NRICH is the go-to place for such activities, but don't just give children a problem and expect them to be able to get on with it on their own - they need to have had much practice in questioning mathematically. Only when children are asking questions about maths, testing out their hypotheses and following lines of enquiry that they themselves have set, will they be able to reason at those higher levels set out by NRICH.

Confidence and Independence

In order for children to be working at greater depth we would expect to see a certain confidence not seen in all children. We would also want to see that they were working independently on the three areas outlined above. As already mentioned, children may need plenty of modelling before they become confident and independent - especially those children who are currently working at the expected standard who could work at greater depth with some extra help. A key indicator of whether or not children are working at greater depth will be their levels of confidence and independence (especially the latter, as some children are of a more nervous disposition yet are still highly capable).

In Summary

To answer our original questions we would hope to see that children who are working at greater depth would confidently and independently:

  • access maths problems presented in a wide range of different, complex ways;
  • be able to justify and prove their conjectures when reasoning;
  • ask their own mathematical questions and follow their own lines of enquiry when exploring an open-ended maths problem.
In order to make provision for children working at greater depth we must:
  • model higher-level reasoning skills (justification and proving) and encourage children to use them;
  • model mathematical questioning during open-ended maths problems and encourage children to ask them;
  • provide complex maths problems (open and closed) with a variety of contexts and support children initially to access these, until they can do them independently;
  • motivate children to be confident and resilient enough to do the above.

Sunday, 24 September 2017

From the @TES Blog: Why teaching classic literature too early is a 'recipe for ruining great books' for children

Recipe for ruining great books:

Step one: Take a bona fide classic, fresh or preserved.

Step two: Hack out palatable chunks (never use the whole book).

Step three: Add a liberal sprinkle of received interpretation.

Step four: Supplement the text with a movie version.

You are now ready to force-feed this to children who are not old enough to digest such a diet – this is incredibly important to the ruining of great books. You will need to ensure that children endure sitting after sitting of the above. Of course, they should add tasting notes to their texts, but be careful to make sure they never have original thoughts about what they are consuming.

If you follow these very simple steps, you can be sure that the majority of children will be put off reading good literature for a significant portion of their lives.

Continue reading here: https://www.tes.com/news/school-news/breaking-views/why-teaching-classic-literature-too-early-a-recipe-ruining-great

Thursday, 21 September 2017

Book Review: 'The Grotlyn' by Benji Davies

Before you even get to the text in this book, there is much to feast the eyes and mind on. The cover (including the one hidden under the dust jacket) and the double-page spread preceding the title page are gloriously illustrated in smokey muted hues which evoke a particular sense of place and time. The backstreets of a Victorian city are brought to life by a cast of intriguing characters. Children will linger over these pages providing adults a chance to question and discuss what can be seen - a perfect opportunity to explain exactly what a barrel organ is and does.

The title page itself furthers the intrigue with its snatch of song - what is The Grotlyn? Benji Davies does a sterling job of reeling in the reader, child and adult alike.

The first page of text sees the book set out its stall in terms of vocabulary - this is going to be rich in language: 'But what at first we think to be, The eye does blindly make us see.' Pick that apart with an 11 year old, or leave it be with a littler one - the story works on many levels. Every new page brings another beautiful turn of phrase - perfect for the budding logophile.

Once you've read this captivating rhyming text and pored over the images, you'll find yourself working your way back through it, picking up on the clues that the author skilfully weaves through both words and pictures and making sense of them in light of the uplifting (literally) ending. As the mystery unravels, children will delight in the antics of the book's protagonist, and by the end, they will be rooting for the once-frightening Grotlyn.

Every inch of the book is awash with clever and deliberate authorial choices and decisions that make several re-reads an absolute must. The illustrations alone could spark lengthy discussions when presented in or out of context - for teachers, there is so much material to use here.

For those wanting to go a little deeper, the concept of freedom is a main theme here. Should animals be kept in captivity? Why do people want to escape certain aspects of their life? What causes humans to go to great lengths, sometimes even breaking laws to attain freedom?

However this book is read, it is certain to become a favourite for all those who are fortunate enough to experience it. Benji Davies has delivered another thought-provoking, multi-layered picture book that is sure to be enjoyed by readers of all ages. 

For an interview with Benji Davies click here.


Friday, 15 September 2017

9 Important Changes to the Primary Maths Curriculum and Assessment

In response to the DfE's latest documents, I wrote this for Third Space Learning. It's a summary of the key changes in the way primary maths will be assessed over the next few years:

On 14th September, just as we were all getting settled into the new school year, the DfE published not one, but two documents of considerable importance: ‘Primary assessment in England: Government consultation response’ and the 2017/2018 ‘Teacher assessment frameworks at the end of KS2’. Both documents reveal changes that will no doubt affect our approach as teachers and leaders.

Whilst the most imminent and significant changes involve writing and reading, there are also some interesting developments in Maths.

Wednesday, 13 September 2017

Meeting The Needs of Lower Attainers In Whole Class Reading Sessions

Perhaps the biggest worry for teachers when considering the switch from the guided reading carousel to whole class reading is how children of different 'abilities' will manage in the lessons. There are, however, various strategies a teacher can employ to support learners with different needs.

You'll have noticed that above I enclosed the word abilities with inverted commas. The first strategy is for a teacher to alter their way of thinking about ability. One possible problem with the guided reading carousel is that children aren't challenged and are only given books and reading activities which are aimed at their perceived ability. This is probably particularly true on the days when that 'low ability' group doesn't have an adult to work with. As many before me have pointed out (including Bart Simpson: "Let me get this straight. We're behind the rest of our class and we're going to catch up to them by going slower than they are?") by taking this approach we run the risk of children never reaching whatever might be considered to be age related expectations - there just won't be time! These children will need to make accelerated progress in order to reach, or become closer to, the expected level. In order to make this progress in reading they will need to be supported as they attempt to access the text that has been selected for the whole class. It might be better to refer to these children in terms of their current levels of attainment or achievement, rather than in terms of a more fixed ability.

With high expectations, plenty of targeted support and a whole load of positive encouragement, most children who are currently working below age related expectations will have the chance to make accelerated progress whilst taking part in whole class reading sessions.

By teaching reading whole class last year we noticed that it was the children who had arrived in year 6 below age related expectations (ARE) who benefited most from the lessons. Whilst these children didn't achieve a score of 100 or over on the KS2 reading test, progress was evident in a number of ways:
  • Teacher assessment against the national curriculum objectives (and the interim objectives) showed vast improvements in reading achievement for these children.
  • When comparing both number of marks gained and scaled score achieved between the 2016 test taken in December and the 2017 test in May, children arriving well below ARE had, on the whole, made the most improvements. (I am happy to share some more specific data on this.)
  • Confidence and enjoyment are immeasurable but it was obvious to the adults working with these children that whole class reading really made an impact in these ways.
There are, however, some children in your class who may be working so far below expectations, perhaps due to a special educational need, who won't be able to access whole class reading even with the suggestions outlined below. Teachers have a responsibility to provide meaningful learning opportunities for all and as such you should use your assessment and discretion when deciding who should and shouldn't take part in whole class reading.

So, how can you support children currently working below ARE during whole class reading sessions?

Read Aloud

Although the point of a whole class session is to challenge - and as such you'd expect children to tackle most things independently during some parts of the lesson - children should have all aspects of the lesson modelled to them too. This applies to the actual reading itself.

As I wrote in this TES article:

"Reading aloud allows children to access high level texts, enables them to hear how unfamiliar language and sentence structures should sound and is proven to aid comprehension of a text; teachers should regularly read aloud to children. The Teachers as Readers project also found that hearing books read aloud gave children a model for their own independent reading. Children also benefit from opportunities to read aloud themselves."


Even if the text is difficult for them to read (decode) independently, by having it read aloud to them they have the opportunity to show that they understand (or comprehend) it, just as they might understand anything that is spoken to them. Repeated exposure to a text will aid with their increasing understanding of what is written.

Although this technique supports children who are currently lower attainers, it is worthwhile providing this opportunity to all children.

Group Work

Here we are essentially looking at a traditional guided reading session: teacher working with a group whilst the rest of the class are working independently.

What that 'working' looks like might differ. It could be any of the following:
  • discussion about answers to questions leading to writing a group answer which the children can record.
  • further shared reading (aloud) and more general discussion, possibly focusing on word meanings and ensuring a general understanding of the text before they then attempt to answer any comprehension questions.
  • working with children on modified activities and/or with modified versions of the text (see below for more).
  • allowing the children to work in pairs or as a group to collaboratively answer the questions without an adult present.
This approach means that, if you have an additional adult in class, there is the possibility of having two such groups on the go at any one time. Alternatively, the additional adult could attend to any needs that those working independently have, leaving the teacher to concentrate on the group. If you're lucky, your additional adult might even get on with giving feedback (written or verbal) to those children.

Alternative Response

This is the closest thing to traditional differentiation that we get - providing children with a modified activity but one which still helps them to achieve the same objective as the rest of the class.

To modify an activity, a few ideas:
  • provide children with an extra glossary or vocabulary list with meanings - this should be specific to the excerpt and pre-prepared by the teacher. If the focus of the lesson was on finding the meanings of words using contextual or morphemic analysis then you might not do this, instead you could focus on the meanings of easier words.
  • use a structure such as this one designed to help children for whom English is an additional language. It involves encouraging children to ask questions of the text, to summarise the text and to order main points of the text, answering true or false questions as well as answering questions about the text. It's important that the final outcome of the activity matches the whole class objective.
  • provide scaffolded structures for answers, for example: I know that the character is _______ because in the text it says _______________.
  • If the focus of the lesson is inference, create an activity that helps to scaffold children's inferences. This can be done by guiding children to consider vocabulary and information that can be retrieved before making inferences - more about this here in my blog post about Scaffolding Inference. Higher attainers may not need these structures as they will have a similar internal, subconscious approach.
In addition to having a modified activity they might also have a modified text - it could be a shorter excerpt of what has been read as a whole class, or it could be a modified version made easier in some way to help them achieve the whole class objective. Any of above modified activities could be used in conjunction with a modified text.

Modelled Answers


Even if children have all worked on exactly the same written response activity, with no support from adults or peers, they can be very well supported if answers to the questions they have been working on are modelled.

The key here is that once answers have been modelled, either by other children or the teacher, whether verbally or in writing, that children edit their existing answers to include the main points of the modelled answers. With a regular, consistent approach to this children will grow in their ability to give written answers to questions. This modelling may take place whole class or with group time.

Intervention

Whole class reading does not replace the need for intervention. Whilst whole class sessions can be focused on the children achieving a whole class objective, interventions can focus on children's individual and specific needs. 

It might be the case that assessment of achievement in whole class reading sessions decides the content of interventions, or that interventions are a continuation of the work done in whole class sessions. On the other hand the interventions could focus on something as basic as phonics (if this is the case, it will be important that in whole class sessions that they hear the text read aloud and that perhaps they are given a shorter or modified excerpt to work with independently).

This is part 1 of a blog series on meeting different needs in whole class reading; now read: Whole Class Reading: Providing Challenge For Children Working At Greater Depth

Monday, 11 September 2017

KS2 Maths SATs On Reflection: Why We Teach For Mastery In Maths

Here's one I wrote for Third Space Learning: https://www.thirdspacelearning.com/blog/2017/ks2-maths-sats-on-reflection-teaching-for-mastery

‘Without reflection, we go blindly on our way, creating more unintended consequences, and failing to achieve anything useful.’ - Margaret J. Wheatley

Perhaps that’s a little over the top, but there’s something in it. As a teacher it’s always worth reflecting on a year just gone, looking back at what went well and what might need changing for the next year. I spent the year as Maths and UKS2 lead whilst teaching in Year 6.

As such I have the privilege of being up to date with the changes taking place in primary education, especially with regards to the expected standards in assessment. Now that I’ve got a few weeks of holiday under my belt, my mind is a little fresher. It's on natural then, that I begin to look back upon KS2 Maths SATs 2017. Read on for my reflections on the end of July and the ever-present changes to how Maths is assessed in UK primary schools...

https://www.thirdspacelearning.com/blog/2017/ks2-maths-sats-on-reflection-teaching-for-mastery

Translating Research Into Practical Advice (Reflections On ResearchED)

At the weekend (sounds like a year 3 recount, I know) I went to my first researchED event - the national conference, which was held at Chobham Academy in some part of London or other where you can almost see the money pouring into it (but as a Northerner, that's a rant I'll avoid now). With a whole host of speakers it wasn't easy to pick which sessions to attend - a good proportion of the train journey down was spent poring over the workshop descriptions and in some slots I had up to 5 possible choices. There was a definite air of excitement as teachers and other professionals poured into the school's largest hall; it felt good to be part of something which, compared to other conferences I've attended, seemed so big.

Almost immediately I spotted the familiar face of Mark Enser, a wonderful teacher (I'm sure) and writer whose articles I always find myself nodding along to vehemently (in truth, he writes the stuff I most wish I'd written). It was great to meet him in person albeit briefly and I had the pleasure of meeting for the first time some other people who I had previously 'known' online: Dr Emma Kell (who may live to regret a subsequent proposal to co-present something one day), Justin Gray, Karen Wespieser and Kieran Dhunna Halliwell as well as a second time meeting with Martin Galway. Making those face-to-face connections was a real highlight although in each case I wish I'd had longer to chat, but it was always onto the next workshop.

Allow me to give you some of the context behind why I was so keen to attend researchED. My MAT recently won the bid to be one of the EEF's research schools as we are situated in one of the 'opportunity areas'. I will be working on the team to develop the research school's role in our area and, although I have recently attempted to be more evidence-informed in my approach, I felt this a good opportunity to sharpen my understanding and skills with regards to educational research.

The main role of the research school is actually to disseminate research to the schools and teachers in our area - a city where social mobility is low. Also, as leaders in a primary school, my colleagues and I had reflected that although lots of what we ask our staff do is evidence-based, they often don't know it as we have distilled the findings into practical steps for them to take - they are  teaching using evidence-informed methods without knowing it. This is something we'd like to change so that:

  • they become more autonomous in seeking research and using it themselves;
  • they know we aren't just plucking ideas out of nowhere;
  • they understand that when they are asked to do something it's because there's a good chance it'll work.
Because of all this I chose some sessions to help me begin to think about how to help teachers who have no knowledge of or interest in educational research to begin to take notice of its possible benefits. Dr Gary Jones led a session on being efficient when it comes to evidence-based practice and Nick Rose spoke on helping new teachers to use research in their teaching. Both speakers were incredibly knowledgeable and I found much of what they had to say to be very interesting but I struggled to come away with much down-to-earth, practical advice for how to help teachers to make their practice more evidence-based.

And that would be my overall observation of the day. Speakers presented knowledgeably but left me with very few concrete ideas as to what to do with the information. Now, I don't claim to be at all academically-minded in the way that many of the presenters are, but then, neither are many teachers - the ones who we'd like to use evidence or research to inform their teaching. Upon reflection, it is very clear that there is much work to be done to bridge the gap between research and classroom practice.

For example, Nick Rose discussed in great detail that which hinders new teachers (and other teachers) from reading research and using it to inform their teaching but in amongst that he mentioned that the best way is to use case studies. If that's the case, I'd have liked the session to focus on how to access case studies, how to write case studies, how to help teachers see the potential and limitations of being inspired by case studies. Dr Gary Jones provided a wide range of ideas but I would have benefited more from spending more time on just one or two of them.

Dr Gary Jones helpfully pointed out that research is only one of the strands which informs evidence-based practice and that data is one of the other pieces of evidence we have to help us make decisions about teaching. Mike Treadaway shared some fascinating national data on pupil premium children but again, there was very little suggestion as to how teachers might use this information to inform their teaching, only a suggestion that the funding formula needs changing - something none of us have a say in.

When blogging and writing articles I often get to the part where I've made my point, discussed the theory or presented the research (or finished my rant) and there I want to stop. But increasingly I've forced myself to go further to do the hard bit: provide some practical advice relating to the subject of the blog post or article. It's not easy and I suspect the ability to do it it relies on teacher expertise and experience, not just research. Much of the advice I've ever been given has not been borne out of research, but out of teachers' own experience. One point discussed in Rachel Lawrence's session on 'What should a research leader in education do?' was whether or not someone leading in research needs to be a teacher: the discussion seemed to conclude that they would be listened to better if they were a respected teacher who colleagues knew could walk the walk. Perhaps the divide between research and practical advice arises because those involved in research aren't always teachers, and vice versa? I can't be sure.

Having said that, I am aware that there are many resources out there which marry research with good practical advice. The EEF reports for example, and Dominic Salles' book 'The Slightly Awesome Teacher'. I also noticed that Robin Macpherson (whose session I didn't manage to get to) has a book in the pipeline called 'What Does This Look Like In The Classroom? Bridging The Gap Between Research And Practice' which does sound very promising. There are clearly also many books written on many subjects which seek to translate research into practical advice and it's this approach that more teachers would benefit from.

Martin Galway gave me food for thought when it comes to disseminating research by pointing out that often we don't read the original source of the research but instead read blog posts, news articles and meta-studies of the published research. Often we read secondary or tertiary accounts of the research and much can be lost in translation resulting in practice which doesn't do what it is supposed to do. This will be a real challenge for the research school and something that needs navigating carefully. Again, some practical information on how to do this would be really helpful - this may have happened  in some of the other seminars.

I managed to take in a wide variety of seminars, including a panel discussion, and whilst the short sessions meant that interest never dipped, it did mean that some presenters were pushed for time. It's totally out of the organisers' hands but it may have been more beneficial to narrow the focus of some sessions in order to get one point across well and include some time for questions and discussion. Again, this reflection is important for how the research school carries out any CPD - a honed down, precise objective needs to be stuck to when presenting crucial information about research and how it might impact on practice.

Now obviously I only attended a very small percentage of the available workshops and so my reflections may not be an accurate overall picture - I'm very aware of this. In fact, this blog post from Jessica Fear just goes to show that some will have left the researchED brimming with practical advice to follow. Hopefully it's clear that I've framed my thoughts by thinking not about how researchED might change (I'm under no illusions - I don't have that influence) but by thinking about how my limited experiences at the conference will form how I think about how to engage teachers in the use of research over the coming year.

To finish, I would reiterate that the conference gave me much to think through and made me aware of research that has already taken place, research techniques that I knew nothing of before  and gave me a better overall idea about the world of educational research. There are things that I will go on to explore further and there are other seemingly small titbits of information that will actually hugely influence my own practice once I've spent more time thinking through how to apply them practically.

Would I recommend a researchED event? Yes, to anyone. I'd say go with an open mind, even if you think research isn't the be all and end all. After all, Tom Bennett himself in his opening speech reminded us all that "the craft of teaching is enormously important" and Nick Rose made it clear that "evidence-based practice is not a recipe to dictate what a teacher does, nor is it to undermine professional judgement, rather it is to inform and refine it".

researchED links:

Livestreams: https://livestream.com/L4L/rED17?t=1504937237924
Mike Treadaway's blog series for Education Data Lab exploring long-term disadvantage: http://educationdatalab.org.uk/tag/long-term-disadvantage/