Showing posts with label KS2. Show all posts
Showing posts with label KS2. Show all posts

Wednesday, 15 May 2019

From The @TES Blog: Five Songs To Get Your After-SATs Party Started


Another bit of fun from me over on the TES site: https://www.tes.com/news/five-songs-get-your-after-sats-party-started

Friday, 8 February 2019

Times Tables Fluency and the KS2 SATs

How important is times tables fluency for the KS2 SATs? I'd say quite important.

When we are fluent in speaking a language, we can speak it without thinking much about it. That kind of fluency will be useful for year 6 children to have when it comes to the tests in May.

I looked through the 2018 SATs papers to see just how many questions required some times tables knowledge.

Here's what I discovered:

  • In Paper 1 (Arithmetic) there are 19 out of 36 questions which definitely require children to have fluent times tables knowledge.
  • In Papers 2 and 3 (Reasoning) there are 18 out of 44 questions which also require children to have fluent times tables knowledge.
But why might fluency be important? Can't children just work out the times tables without knowing them by heart?

Well, yes, they could, but it would cost them time.

For Paper 1 children are given 30 minutes, meaning that they have less than a minute per question. For Papers 2 and 3 there are 40 minutes per question - this means children have about 2 minutes per question.


In a question where 8 different times tables facts must be recalled (see above), it is obvious that this needs to be done quickly so that children can focus on the procedure of answering the question. In the same questions accuracy is essential too: if children are fluent with the times tables facts they are less likely to make mistakes.

If children are spending too much time working out times tables facts they risk going over that l or 2 minute per question; in turn they risk not having time to finish the test.

But, looking at the 2018 tests revealed something else: most of the times tables facts that children needed to use to answer the questions were fairly easy: the sort of times tables that are learned in years 1, 2 and 3. The times tables grid here shows exactly which times tables facts are required. The hardest times tables facts (such as 7 x 8, 9 x 8, 11 x 11) weren't required. The most common facts needed were below 6 x 6 with majority of the additional facts coming from the 2, 3 and 4 times tables.

But children need to be able to do more than recall them quickly; they need to be fluent enough to use and apply them. It's not just about remembering the facts but being able to recognise relationships between numbers. For example, the questions below require children to spot related facts:



I've put together a PowerPoint presentation which contains all the questions that require some times tables knowledge. I've animated the working out and answers for each question too so that these can be used flexibly. The PowerPoint (which the images used above are taken from) can be downloaded here: https://www.tes.com/teaching-resource/powerpoint-to-demonstrate-the-need-for-times-tables-fluency-in-sats-12065667. I used it with year 5 parents who found it useful to know how important times tables were going to be for SATs.

Tuesday, 3 April 2018

From The @TES Blog: 5 Things To Do Instead Of Revising For SATs

From The @TES Blog: 5 Things To Do Instead Of Revising For SATsThis might come across as idealistic or cynical. It might even sound hypocritical to those who’ve taught Year 6 alongside me. But there really is more to Year 6 than Sats revision – even in Sats week.

Regardless of your views on key stage 2 testing, it’s the system with which we’re currently lumbered. And I would always advise that children are prepared for them.

But by preparing, I don’t mean drilled to within an inch of their life: Easter booster classes, daily past papers, hours of homework and the like. There are other ways of helping children to be ready for that week of testing in May – ways that prepare them mentally; ways that ensure they remain emotionally intact.

Here are five suggestions:

Click here to read the whole article: https://www.tes.com/news/school-news/breaking-views/five-things-do-instead-sats-revision

Friday, 16 March 2018

Comprehension Strategies And The KS2 Reading Test - What and How Should We Teach?

Comprehension Strategies And The KS2 Reading Test - What and How Should We Teach?
In my first blog post in this series I explored the difference between reading comprehension strategies and reading skills. I noted that many of the skills that are tested in the KS2 SATs also have a matching reading comprehension strategy. With the conclusion that the deliberate use of strategies develops and embeds skills, I posed a question to myself:

Is there a way to teach comprehension strategies that prepares children well for the KS2 reading test?

In answering my second question I had to consider that which is different about the reading test. Whereas the commonly-used comprehension strategies do not require children to give written answers to questions they ask or generate themselves, the test does. This is the main difference. In addition to this, the year 5/6 National Curriculum objectives mention no requirement for children to provide written answers to questions and many of the objectives aren't tested at all by the SATs. The objectives circled in red aren't tested by SATs; the ones outlined in blue are.
Without having any evidence back this up with, I believe that there are children who, having been taught strategies which have become skills, are able to complete the reading test, confidently giving written answers to the questions it asks. I suspect that these children are also able writers and they have probably had a healthy relationship with literacy in general from an early age. There is a potential argument here for a sole focus on teaching comprehension strategies and never asking children to spend time practising giving written answers to comprehension questions.

But, I also think that there are probably children for whom some explicit instruction about how to give written answers to comprehension questions will be useful and necessary (if they are to have a chance of demonstrating their reading skills in a test, which all year 6 children are). Again, I have no research evidence to back this up, only anecdotal experience. However, there is research evidence to back up the idea that particular written activities do support reading comprehension.

I turned to Steve Graham and Michael Hebert's 'Writing to Read' report which states:

"Writing-about-text activities had a positive impact on struggling students’ understanding of a text. An important key to success in using these activities with lower-achieving students was to provide them with ongoing practice and explicit instruction."

The report recommends that students do write in response to things they have read and outlines a series of recommendations of activities. One of the recommendations is that teachers should have students answer questions about a text in writing, or create and answer written questions about a text:

"Answering questions about a text can be done verbally, but there is greater benefit from performing such activities in writing. Writing answers to text questions makes them more memorable, as writing an answer provides a second form of rehearsal. This practice should further enhance the quality of students’ responses, as written answers are available for review, reevaluation, and reconstruction (Emig, 1977).

For generating or responding to questions in writing, students either answered questions about a text in writing; received practice doing so; wrote their own questions about text read; or learned how to locate main ideas in a text, generated written questions for them, and then answered them in writing. These practices had a small but consistently positive impact on improving the reading comprehension of students in grade 6–12 when compared to reading or reading instruction."

Lemov et al's 'Reading Reconsidered' also provides plenty of classroom evidence that writing supports reading comprehension. They summarise:

"...the strategic use of writing made reading and discussions of reading- the other core activities of English class—more rigorous, focused, productive and engaging- ‘better’ in short.  Writing is a deeply valuable endeavor in its own right, but it is also an endeavor that works in synergy with reading in specific ways."

From 'Writing To Read'
Activities other than answering questions include responding to a text through writing personal reactions or analyses/interpretations of the text, writing summaries of a text, taking notes on a text, and creating and/or answering questions about a text in writing. Actually, all of these activities have a greater effect size than answering questions and therefore should be explored further in the primary classroom - another blog post for another time!

What does come through both the 'Writing To Read' report and Lemov et al's 'Reading Reconsidered' chapter entitled 'Writing For Reading' is an emphasis on explicit teaching: if we want children to be able to write well about the things they read in order to develop a better understanding of what they read, we must explicitly teach these skills - they must be modelled well by the teacher.

What I have found is that evidence from both research and successful classroom practice shows that an approach to teaching reading strategies which includes giving children the opportunities to practise giving written answers to comprehension questions (in order to prepare them well for a test) is not something we should avoid, but is something that, if done right, could be beneficial to the children we teach.
From the IES guide
So, is there a way to teach comprehension strategies that prepares children well for the KS2 reading test? Yes, I think so. As long as there is modelling, discussion (book talk) and time for children to practise, a sequence of learning that will improve reading skills can (and should) focus both on teaching reading comprehension strategies (as outlined in the EEF and IES guidance) and the elements of the National Curriculum (as outlined in the content domain in the KS2 test developers' framework) as they can act reciprocally due to similarities between the skills and the strategies. Reading instruction which includes, amongst other things, teachers, asking children to respond in writing to well-written questions based on a manageable amount of text is a good idea when preparing children for KS2 tests. It shouldn't be the only element of reading instruction but it should help. Where children lack particular skills it will be best to focus modelling and practise on those particular skills.

If children are only given written comprehension activities the comprehension strategies are not likely to be employed or developed. But if the written comprehension activities are backed up with explicit teaching of the supporting strategies (as well as vocabulary, any other necessary background knowledge and how to write answers), then comprehension strategies should be developed. Such explicit teaching (including modelling and discussion) should focus on ensuring that children know what the strategy is, how it is used and why and when to use it. Children can be shown how to use the strategies when completing written comprehension activities.

The York Reading for Meaning Project assessed three reading comprehension interventions delivered by teaching assistants in 20 primary schools. The three interventions were carried out with children who had been identified as having the poor comprehender profile - the three interventions were intended to help children who struggled with reading comprehension to overcome their problems. The three interventions differed:
  • Oral Language Programme: vocabulary, reciprocal teaching with spoken language, figurative language and spoken narrative
  • Text Level Programme: metacognitive strategies, reciprocal teaching with written language, inferencing from text and written narrative
  • Combined Programme: all of the above (vocabulary, reciprocal teaching with spoken language, figurative language, spoken narrative, metacognitive strategies, reciprocal teaching with written language, inferencing from text and written narrative)
Based on the findings, the report concludes that 'the Oral Language intervention overall was the most effective of the three programmes. Theoretically, this finding provides strong support for the theory that the reading comprehension difficulties seen in those who show the poor comprehender profile are a secondary consequence of these children’s oral language weaknesses.'.

Here then is evidence that children who are struggling with reading comprehension, and are falling behind, will benefit from an oral language programme as intervention. In the context of this blog post - which focuses on teaching all children (including those are aren't struggling with comprehension but are still learning new skills and strategies) - it is worth questioning whether these research findings bear relevance - should we scrap writing as part of first teaching of reading and focus solely on an oral approach?
Examples of combined programmes from The York Reading for Meaning Project: An Overview


However, the outcomes of the project also show that 'all three interventions (Text Level, Oral Language and Combined) improved children’s reading comprehension skills'. In this blog post I have been suggesting what is essentially a combined programme for everyday classroom-based reading instruction (see the examples above). The question the research doesn't answer is, where first teaching of reading comprehension is concerned (i.e. not interventions for poor comprehenders), whether or not the benefits of writing discussed above are still outweighed by only focusing on an oral-only approach.

What is potentially telling is that 'the children who received the Combined programme experienced all components but at half the quantity of the other two intervention programmes'. What if children were given a whole quantity of both oral and written approaches? Isn't this something that a reading lesson, with an adequate amount of time given over to it, could offer children that an intervention (in this study set at 30 minutes long) could not?

It would be interesting to know which approach (oral, text or combined) shows the best results for all learners rather than interventions for poor comprehenders . For teachers working on helping children to be prepared for KS2 testing it would be good to see research which focuses on first teaching for all learners where the results are taken from SATs performance. Whether you are in support of year 6 testing or not, they are currently a feature of the UK's education system. In order for children to feel prepared (and hopefully not stressed by uncertainty about the tests) and in order for schools to demonstrate accurately the reading ability of their children, most schools will want to allow children to practise giving written answers to comprehension questions. Would it be too much of a gamble in this case for schools to take an oral-only approach?

Expanding on some of the ideas in this blog post, in previous blog posts I have written about...

From The @thirdspacetweets Blog: What Every KS2 Teacher And Maths Lead Needs To Know About NEW KS1 Maths Assessment Frameworks

From The @thirdspacetweets Blog: What Every KS2 Teacher And Maths Lead Needs To Know About NEW KS1 Maths Assessment Frameworks
Valentine’s Day 14th February 2018 brought KS1 teachers not one but two lovely treats: the teacher assessment frameworks for the 2017/18 academic year and the same document for the 2018/19 academic year.

While there are no changes for the current cohort of Year 2, the current Year 1s will be teacher-assessed on a new and amended framework.

Of course, the biggest question on everyone’s lips is…are the changes to the KS1 assessment framework for Maths an improvement?

To find out more, read on here: https://thirdspacelearning.com/blog/new-ks1-assessment-frameworks-maths-insights-ks2/

Thursday, 14 December 2017

Scaffolding Structures for Reading Comprehension Skills

This is a very different blog post to the sort I normally write; it represents some very hypothetical thinking and the purpose of writing it is to open it up to discussion. My hypothesis is that the reading skills outlined in the English Reading Test Framework for KS2 (and KS1) might be best taught in a particular order. I also hypothesise that when teaching particular skills (represented as being higher up the model pictured) teachers can guide children through how to use other skills (lower down the model) to arrive at a better ability to practice and use the skills that are higher up the model. First of all, here's the model I've put together to which I refer:


Skills (taken from English Reading Test Framework for KS2) are listed in the order that they might best be taught. This suggested order is based on the idea that some reading skills might be required prior to developing others. The most basic skills are towards the bottom.

The inclusion of 2d (inference) may depend on the text type. For example, in many non-fiction texts there is no requirement to infer information, only to retrieve it. In these cases the 2d (inference) step/building block can be skipped.

The only reading skill from the test framework which isn’t included here is 2h (make comparisons within the text). It is possible that texts can be compared at many different levels, for example, the vocabulary used can be compared (2a), summaries of plot can be compared (2c) or structure of the text can be compared (2f). The skill of making comparisons (2h) could be seen as a ‘floating’ skill – one which could be applied in different ways alongside other reading skills.

All of the following symbols and colours refer to the Reading Roles, a system I designed to make the different skills memorable for children and teachers. Read more about the Reading Roles here: http://thatboycanteach.blogspot.co.uk/2016/12/reading-roles-cognitive-domains-made.html


In order for children to begin to make inferences they need to at least be able to retrieve information in the text, and before this they need to be able to understand what the words mean.

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text

2f and 2g are very interlinked as they are both about meaning – one with a focus on word and phrase choice, and one with a focus on content choice. It is possible that 2g and 2f should precede 2d in the teaching sequence but if making inferences is one way in which we take information from a text, then arguably we need that information to make meaning; we can then go on to identify and explain how that meaning is enhanced through word choice and how the content included contributes to the meaning. The fact that these skills are not included in the KS1 test framework might suggest that this is correct, and that these are more advanced skills than making inferences.

2g – Author’s purpose

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text
(2g)       identify/explain how meaning is enhanced through choice of words and phrases

2f – Language structure and choice

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text
(2g)       identify/explain how meaning is enhanced through choice of words and phrases
(2f)        identify/explain how information/narrative content is related and contributes to meaning as a whole

Once children understand word meanings, can find and infer information, explain how language has been used to communicate meaning and, as a result, can understand the meaning of a whole piece of text, then they can begin to summarise the text, or make predictions based on their understanding. It might not be necessary to summarise a text before making a prediction, and the ability to summarise a text should not rely on the ability to make predictions based on it. These two skills are both included in the KS1 test framework, but children at this stage summarise and make predictions based only on word meaning, information retrieval and inference (missing out 2f and 2g) – summaries and predictions at this stage might be at a simpler level. It is probably true that in KS2 similar summaries and predictions could be made, without paying heed to 2g and 2f.

2c - Summarising

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text
(2g)       identify/explain how meaning is enhanced through choice of words and phrases
(2f)        identify/explain how information/narrative content is related and contributes to meaning as a whole
(2c)       summarise main ideas from more than one paragraph

2e – Predicting

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text
(2g)       identify/explain how meaning is enhanced through choice of words and phrases
(2f)        identify/explain how information/narrative content is related and contributes to meaning as a whole
(2e)       predict what might happen from details stated and implied

The model suggests that an understanding of word meaning is core to all reading – this model assumes that children already have the skills of decoding, sight recognition and phonological awareness. The model only includes reading skills outlined by the test framework and does not include factors such as the necessity of activating prior background and literacy knowledge when reading.

The model also suggests that there is a hierarchy of reading skills and that children might benefit from having some reading skills taught before others.

It also suggests that when requiring a child to work on a skill which is ‘higher up’ the model that they work through a sequence of skills usage in order to initially scaffold their ability to exercise the ‘higher’ skill. For example, if requiring a child to summarise a passage, they might first answer questions about the vocabulary used, the information contained within (given both literally and inferentially) and what the authors purpose was with regards to structure and language choices.

This model focuses on the following strands of Scarborough’s reading rope: vocabulary, verbal reasoning and language structures:


I hope I have made my thinking clear in this blog post and I would really appreciate any thoughts about what I have proposed. If you can back any of your comments either with research or with case studies from experience then even better!

Saturday, 2 December 2017

Mathematical Misconceptions And Teaching Tricks: What The Research Says

Imagine a factory. Think of the vast machines clanking away. Think of the whirring, the turning, the raw materials becoming a finished product. Beneath those metallic exteriors cogs, cams, belts and levers are working together to effect that change. But all but the most initiated don't really understand how the machines do what they do, they just know that if they put the right parts in at one end, the machine will produce the desired item.

And this is how many children feel about maths. They know that putting some numbers into a calculation will give the desired answer, but they don't really have a clue what goes on inside the 'machine' of that procedure. This is all well and good until that child has to apply this learning - having no understanding of the mechanics of mathematics makes it very difficult to use procedures in context.

In my blog post for Third Space Learning entitled 'Maths Tricks or Bad Habits? 5 Bad Habits in Maths We're Still Teaching Our Pupils' I make several suggestions for how to use visual representations to teach good conceptual understanding of some tricky aspects of the maths curriculum, such as the ones below:



The recent EEF guidance document on improving maths in KS2 and KS3 backs up the importance of modelling good conceptual understanding in maths lessons, rather than relying on tricks that work but don't help children to have an understanding of the 'why' and the 'how':
Recommendation 4: Enable pupils to develop a rich network of mathematical knowledge 
"Pupils are able to apply procedures most effectively when they understand how the procedures work and in what circumstances they are useful. Fluent recall of a procedure is important, but teachers should ensure that appropriate time is spent on developing understanding. One reason for encouraging understanding is to enable pupils to reconstruct steps in a procedure that they may have forgotten. The recommendations in this guidance on visual representations, misconceptions, and setting problems in real-world contexts are useful here."
In order to teach maths well, and in order for children to succeed in maths, teachers need to make sure children understand what is going on when they carry out a mathematical procedure. A great way of developing this understanding is using manipulatives and representations:
Recommendation 2: Use manipulatives and representations 
"Manipulatives and representations can be powerful tools for supporting pupils to engage with mathematical ideas. However, manipulatives and representations are just tools: how they are used is important. They need to be used purposefully and appropriately in order to have an impact. Teachers should ensure that there is a clear rationale for using a particular manipulative or representation to teach a specific mathematical concept. The aim is to use manipulatives and representations to reveal mathematical structures and enable pupils to understand and use mathematics independently.
Teachers should: Enable pupils to understand the links between the manipulatives and the mathematical ideas they represent. This requires teachers to encourage pupils to link the materials (and the actions performed on or with them) to the mathematics of the situation, to appreciate the limitations of concrete materials, and to develop related mathematical images, representations and symbols."
As I wrote in the guide to Bar Modelling that I produced for Third Space Learning (click to download for free):

If we don't do this, we run the risk of allowing children to proceed in their mathematical education with misconceptions:
Recommendation 1: Use assessment to build on pupils’ existing knowledge and understanding 
"A misconception is an understanding that leads to a ‘systematic pattern of errors’. Often misconceptions are formed when knowledge has been applied outside of the context in which it is useful. For example, the ‘multiplication makes bigger, division makes smaller’ conception applies to positive, whole numbers greater than 1. However, when subsequent mathematical concepts appear (for example, numbers less than or equal to 1), this conception, extended beyond its useful context, becomes a misconception. 
It is important that misconceptions are uncovered and addressed rather than side-stepped or ignored. Pupils will often defend their misconceptions, especially if they are based on sound, albeit limited, ideas. In this situation, teachers could think about how a misconception might have arisen and explore with pupils the ‘partial truth’ that it is built on and the circumstances where it no longer applies. Counterexamples can be effective in challenging pupils’ belief in a misconception. However, pupils may need time and teacher support to develop richer and more robust conceptions."
When we do teach children using appropriate models and images so that they understand the mathematical concepts behind the procedures (or the 'tricks'), we provide children with something that they can actually look at and explain. Explaining something that is concrete is easier than explaining an abstract concept.

In the bar modelling guide (click to download for free) I pointed out that:


By developing children's skills to represent and explain their understanding using a model, we develop their independence and motivation:
Recommendation 5: Develop pupils’ independence and motivation
"Teachers can provide regular opportunities for pupils to develop independent metacognition through:
  • encouraging self-explanation—pupils explaining to themselves how they planned, monitored, and evaluated their completion of a task; and
  • encouraging pupils to explain their metacognitive thinking to the teacher and other pupils."
Next time you plan a maths lesson question how you will ensure that children have a good conceptual understanding of the content you teach. Often, concrete or pictorial representations will be the best way to show children the inner-workings of the concepts you cover. Following Psychologist Jerome Bruner's research-based CPA (Concrete - Pictorial - Abstract) approach means that children (and adults) are more likely to understand what is going on inside the maths machine as calculations and processes take place.

Further Reading and Resources:

Monday, 13 November 2017

On The Third Space Learning Blog: 2017 Maths SATs QLA Analysis

It's often helpful to use data to inform teaching but finding time to sit down and go through it with a fine enough tooth comb isn't easy.

The Question Level Analysis for the ks2 tests now provided on ASP (the RAISE online replacement) contains national and school data which can be useful to key stage 2 teachers to inform their future teaching. It's also useful for year 7 teachers, but they don't often get access to this information.

So, for the benefit of many teachers and children, here's a breakdown of the parts of the 2017 maths tests that children scores the country struggled with the most:

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.

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

Thursday, 24 August 2017

3 Books That Introduce New Vocabulary To Children

Discovering new vocabulary is one of the most exciting parts of reading, but children don't always know what new words mean. Of course, children can be taught methods of finding out what new words mean - morphemic analysis and contextual analysis are the techniques that come in most handy in the primary classroom - but some books do the job for them. Whilst these books are not a substitute for learning the skills needed to decipher new vocabulary, they are a great way to get children into the habit of actually finding out what unfamiliar words mean. Some children are quite happy to skip over unknown vocabulary, which leads to a lack of overall understanding of texts, and one of the most important jobs of a teacher is to enable children to have excellent comprehension skills; if a child can read with understanding they can learn almost anything.

There are several children's books out there which in one way or another creatively and cleverly give definitions for words that children might not already know:

The Great Cat Conspiracy by Katie Davies


This particular book encourages the use of dictionaries - something which some children appear to be allergic to! Perhaps by using this book with children they will catch the passion that the main character has for understanding new and difficult words.

The best way to share examples from this book is to show you some pictures of the book's pages where illustrator Hannah Shaw has done a sterling job of communicating Katie Davis' desire to help children to learn new vocabulary:




Small Change for Stuart by Lissa Evans

'On the second day there was nothing to do. Nothing, nothing, nothing.
Which is why, when his father said, 'Ah there you are. I was just thinking of going for a brief perambulation. Would you like to come too?'
Stuart answered, 'Oh all right, then.'
By 'brief perambulation', his father meant a short walk. That was the way he talked all the time...'

Stuart's father writes crossword puzzles and as such prides himself in the use of words that most people don't use. It's up to the narrator or Stuart's father to explain what the words mean. Here's another example:

''When I was a youngster,' his father told him as they walked, 'there weren't any houses in this part of Beeton at all. This whole area was sylvan.'
'What's sylvan mean?' asked Stuart.
'Wooded. And there was a stream running through the middle of it.''

Stuart appears to be used to the way his dad speaks so sometimes there are no explanations for words such as 'mechanisms' and 'diversified', (although a sentence containing 'conflagrated', 'incediary' and 'armaments' is translated by his father as Stuart has no idea what he is talking about!) meaning that children will also have opportunities to discover some word meanings for themselves.


A Series of Unfortunate Events series by Lemony Snicket

In the most well known of the books here, and representing 13 books in all, the narrator often interjects with definitions of more unusual words. Take this example from the first page of the first book 'The Bad Beginning':

'Their misfortune began one day at Briny Beach. The three Baudelaire children lived with their parents in an enormous mansion at the heart of a dirty and busy city, and occasionally their parents gave them permission to take a rickety trolley - the word “rickety,” you probably know, here means “unsteady” or “likely to collapse” - alone to the seashore, where they would spend the day as a sort of vacation as long as they were home for dinner.'

Another example where one of the characters, rather than the narrator, explains what a word means:

'“‘Perished,’” Mr. Poe said, “means ‘killed.’”
“We know what the word ‘perished’ means,” Klaus said, crossly. He did know what the word “perished” meant, but he was still having trouble understanding exactly what it was that Mr. Poe had said.'


Of course, if you've read any of the Lemony Snicket books, then you'll know they celebrate learning and the reading of books, and the vocabulary used reflects this - there are plenty of other words used that children can discover the meanings of themselves. And hopefully they will be inspired to do so by the way some definitions are included in the text.

All of the books I've chosen are also well-written, exciting and original stories which, apart from their entertainment value, have many other qualities. 'The Great Cat Conspiracy' provides teachers and parents with an opportunity to discuss senile dementia and how we care for the elderly as well as introducing younger readers to the crime/mystery genre. 'Small Change for Stuart' encourages problem solving and could provide great links to books like 'The Invention of Hugo Cabret'. The 'A Series of Unfortunate Events' books contain an alternate view on what it's like to be an orphan when compared to, say, Disney films - there are also opportunities for comparative work between the books and the film adaptation and the Netflix series.

So, if you find your class, or individual children, unwilling to engage with new vocabulary, perhaps one of these excellent books could inspire them to become a vocabulary detective.

This blog post has the potential to be an ever-changing beast with your suggestions - have you come across any books which take a similar approach to the ones mentioned above? Please comment below, or on Twitter or Facebook.

Monday, 31 July 2017

To My Excellent Year Five Teachers

To my excellent year five teachers,

Thank you so much for all your hard work this year - that sounds like such a standard, stock phrase but I really couldn't mean it more.

I couldn't have asked for a better year 5 team - you have been the perfect combination of high standards and nurture and as a result the children have been transformed under your care. You don't really need me to tell you of the amazing changes that have taken place, but by way of celebration I will:

In terms of behaviour, the group of children you've taught this year is unrecognisable. I always believed that together you would make a difference very quickly and you really did - but just because it happened so rapidly that doesn't mean we shouldn't be celebrating it now. I know that the management of their behaviour has been an ongoing task but since you make it look so easy, it can often go unnoticed!

Because of the much-improved conduct the attitude towards learning has sky-rocketed. You both have classes who are so dedicated to learning, who really care about their education. You have modelled to the cohort how important their time in the classroom is and ensured that it has been time well-spent. They are now characterised by being one of the hardest-working cohorts in the school.

As a result, the progress those children have made this year has been so pleasing to see. From very low starting points you have really worked with precision to make sure that individual needs are addressed and worked on. With diligence you have prioritised the education of each child, giving those children the best possible launchpad to their final year with us.

As a result of that grounding, I am confident that these children will write the next chapter in our success story when, next year, results day rolls around. But, as we are all very aware, although it might not always feel like it, it is not all about results, and actually, because of your teaching ('teaching' sounds very crude, because you've done so much more than just teach) these children are well-rounded human beings who appreciate life in so many ways. You have allowed them to be themselves, but have helped and encouraged them to be better versions of themselves.

As for you being members of my team, I couldn't be more grateful. It was one of my main aims this year to lead a team who were a real team - and we have been just that, and that is down to your commitment to our school, our children and your colleagues. It's not going to be easy to leave such a dedicated group of people, but I know that I'm leaving you together and that team spirit won't die with my leaving - I feel very confident of that.

In the summer I wrote a letter to myself which I only re-read lately; in the letter I wrote, aspirationally, that this year would be a year that I would always be proud of, and it has been - it's been a year we should all be proud of. We have achieved so much, but because we are always aiming higher, we don't always just stop to take stock of what we've accomplished. I hope this summer, and perhaps prompted by this letter, you will take time to reflect and congratulate yourselves on all the successes of this year.

Thank you, once again, although I know you don't do it for the accolades - you do it because you care for the children.

Monday, 26 June 2017

From the @TES Blog: Primary and Secondary Teachers Need Each Other — And We Need To Start Viewing Each Other In A More Positive Light

https://www.tes.com/news/school-news/breaking-views/primary-and-secondary-teachers-need-each-other-and-we-need-start

Transition time is fast approaching, and along with it the inevitable discussions about how we can make the move from primary to secondary school smoother for pupils.

Unfortunately, no amount of tutor visits or collaborative projects between key stage 2 and 3 teachers will really bridge the chasm that exists between these two stages.

Attempts to help children cross the threshold are important, and should be continued, but without a more joined-up approach in curriculum and assessment our efforts will never be able to ensure that the learning journey of each child is seamless. For that we need systemic change — something that may not be in our power to effect.

What we do have the power to change, though, is our view of each other.

Click here to read on

Tuesday, 16 May 2017

How To Stay Sane Now The KS2 SATs Are Over


The fourth and final post in my series of blog posts for Third Space Learning focusing on teacher and pupil wellbeing during the key stage 2 SATs testing period:

An almost audible collective sigh of relief rises from Year 6 teachers and KS2 pupils across the realm. Suddenly, the prospect of life beyond SATs becomes tantalisingly real and, at least for now, it is there to be enjoyed.

Feelings during the next few weeks will (though I hate to have to remind you) morph from the relief that the end of the SATs week brings into the impatient wait for results day on July 4th.

Click here to read my five tips for staying sane now that the key stage 2 test are over: https://www.thirdspacelearning.com/blog/2017/sayonara-sats2017-5-golden-rules-for-year-6-teachers-to-make-the-most-of-lessons-after-sats

Thursday, 4 May 2017

Collection of PowerPoints to Introduce the 2019 KS2 SATs Tests (with Emojis!)

I have put together some light-hearted, potentially humorous, but hopefully informative PowerPoints to use with year 6 children either during the run-up to SATs or on the mornings before the tests.

They use questions from the 2016 KS2 test to remind children of test techniques and tips that will help them to do their best on the day.

Reasoning: https://www.tes.com/teaching-resource/powerpoint-to-introduce-the-2017-ks2-sats-mathematics-reasoning-test-papers-2-and-3-with-emojis-11595567

Arithmetic: https://www.tes.com/teaching-resource/powerpoint-to-introduce-the-2017-ks2-sats-arithmetic-test-paper-1-with-emojis-11594343

Spelling, Punctuation and Grammar: https://www.tes.com/teaching-resource/powerpoint-to-introduce-the-2017-ks2-sats-spelling-punctuation-and-grammar-test-with-emojis-11593369

Reading: https://www.tes.com/teaching-resource/powerpoint-to-introduce-the-2017-ks2-sats-reading-test-with-emojis-11589341

Some reviews:

"All the things I say over and over again but with the added bonus of emojis. Maybe this will embed the message just that little more! Fingers crossed. Thanks for sharing."

"Excellent overview of the new SATS - thank you!"

"Thank you its just what I need for the final push."

"Good fun: will make my class smile and remember some of those important things they might forget when exam nerves set in. Thank you for sharing!"

"A wonderfully lighthearted PowerPoint to alleviate the concerns of any Y6 pupils anticipating the reading paper. Straight-to-the-point and precise, with smiley faces to boot. Cheers for pulling it together - may the force be with them."

"Have downloaded all these! Made me chuckle but gets the point across. It's also reassuring to know that all the little niggles I had with these tests, children are doing all over the country! TICK ONE BOX!!!!!!! AARGGH!"

Year 6 Teachers, You've Got This! Your 5-Step Game Plan for SATs Week 2017


The latest in my series of blog posts for Third Space Learning focuses on SATs week itself. The focus is on teacher and pupil wellbeing and provides 5 steps to take to ensure year 6 teachers and pupils aren't too frazzled by the end of it.

So, the time has come. SATs week 2017 is upon us. On Monday morning, after months (hopefully years) of preparation, the nation's Year 6 children will sit down to the first of 2017's Key Stage 2 National Assessments.

Year 6 teachers across the land will be pacing halls and classrooms, catching glimpses of questions and hoping beyond hope that the primary school children in their classes will do their very best.

And I assume you're probably one of those teachers, or a supportive Head or SLT member.

You'll be feeling a heady mix of excitement and nervousness while anticipating the children’s chance to show off all they've learned. You might also be wondering what on earth the test-writers have come up with this time.

Click here to read on over at the Third Space Learning blog: http://thirdspacelearning.com/blog/2017/year-6-teachers-you-ve-got-this-your-5-step-game-plan-for-2017-ks2-sats

Sunday, 2 April 2017

On the TES Blog: The 9 Essential Components of a KS2 Reading Scheme

After the shock results of the key stage 2 reading test last year, there is barely a primary school in the country that hasn't prioritised reading this year. There are many creative ways of encouraging not only a love of reading, but a high level of competence in the subject. You'll have your own, of course, but here’s a reminder of some of the basics that a good reading scheme can’t do without.

To read the 9 essential components head over to the TES blog:

Monday, 20 March 2017

On the TES Blog: Why Every Primary Should Be Using Bar Modelling – And Six Steps To Make It A Success

As a primary maths coordinator, it's been difficult to escape the lure of bar modelling: it's in every new publication, on all the maths blogs and at every coordinator's meeting. And so, when the time was right for my school, I succumbed.

Bar modelling, for the uninitiated, is not a method of calculation. Instead, it is a way of representing problems pictorially: from simple addition, through to finding percentages of amounts, all the way to complex multi-step problems involving ratio and proportion. Bar models can be used to pictorially represent arithmetic problems, as well as reasoning problems written with a context.

For a worked example of bar modelling and 6 steps to ensure introducing bar modelling is successful, read on at the TES blog:

https://www.tes.com/news/school-news/breaking-views/why-every-primary-should-be-using-bar-modelling

Monday, 13 March 2017

Book Review: 'The Night Spinner' by Abi Elphinstone

Ask a child what 'The Night Spinner' by Abi Elphinstone is about and they will speak of magic and monsters, adventure and action. But those are just plot features. Beneath all that, this is a book about far more.

In actual fact, this book is about loyalty, kindness, bravery, resilience - all those things we're attempting to teach our children through well-intentioned school display boards and PSHCE lessons. Where these attempts might not have long-term impact, a book like this, in the right hands, really could.

Aimed at Key Stage Two children, this rip-roaring adventure, where dull moments are banished, is the perfect vehicle for many-a lesson on those personality traits that we all agree are essential for our children to possess. As an adult, it's difficult to see where the reality of the story ends and metaphor begins: one of the book's main villains is a dead ringer for depression as she steadily drains the lead character, Molly, of all hope, leaving her feeling increasingly unable to go on with her quest. Throughout the book Molly, aided by a colourful array of characters, learns how better to deal with her feelings of self-doubt and becomes a case study in how to overcome adversity through perseverance. There is so much for children to learn about themselves as the thrilling story unfolds.

It's becoming increasingly popular for a female protagonist to be associated with action and adventure stories but Abi Elphinstone's trilogy is a welcome addition to the growing canon of books fronted by strong female leads. The fact that Molly Pecksniff - who doesn't flinch at jumping from a bridge onto a moving train with her wildcat - is a girl, certainly does not make this a book for girls. Whilst it is important that girls have such a positive role model, its also crucial that boys are presented with a character who really challenges gender stereotypes. Books like this have the power to change minds and shape thinking.

For all of this, 'The Night Spinner' and its two preceding volumes thoroughly deserve a prominent place on the shelves of our libraries and schools. Not that they will stay on the shelf for long!

Wednesday, 8 March 2017

Using Simple Bar Modelling Techniques To Solve Multi-Step SATs Problems

Bar Modelling is taking the primary maths world by storm. The 2014 curriculum appears, despite initial unhappiness, to be achieving a shift in the way maths is taught. Its three main aims of reasoning, problem solving and fluency have encouraged teachers to seek further ways to encourage conceptual understanding, rather than just teaching tricks or rules. So teachers have looked towards the countries who apparently churn out mastery-level mathematicians by the thousands for inspiration - that or some savvy publishers have decided to capitalise on the desire of teachers to teach the 'why' rather than the 'how'.

Click here to read more about bar modelling and the solution I came up with: https://thirdspacelearning.com/blog/2017/using-simple-bar-modelling-techniques-to-solve-multi-step-sats-problems