From @ThirdSpaceTweet: Ready To Progress? 9 Things You Should Know About The NCETM Mathematics Guidance As You Plan Your Curriculum Prioritisation

 A detailed look at the ready-to-progress criteria and non-statutory mathematics guidance in the context of the KS1 and KS2 maths curriculum and mastery approach to maths.

https://thirdspacelearning.com/blog/ready-to-progress-criteria-mathematics/

If you would like Aidan to work with you on developing maths at your school, please visit his website at https://www.aidansevers.com/services and get in touch via the contact details that can be found there.

From @Matr_org: Understanding Maths Anxiety: A Parents’ Guide On How To Overcome This Primary School Problem

"I remember finding ways to get out of maths lessons as a youngster.

My favourite ruse was to offer to tidy up the teacher’s cupboard – I even clearly remember stacking the maths textbooks neatly on the shelves, feeling inwardly smug that I did not have to open them and attempt the questions inside.

I recall my dad spending what seemed like hours with me trying to help me to understand negative numbers and how to calculate them – unfortunately, his pictures of eggs and egg cups didn’t help at all although I appreciated his efforts!"

https://matr.org/blog/understanding-maths-anxiety-parents-guide/

Times Tables Fluency and the KS2 SATs

This blog post is now available at: https://www.aidansevers.com/post/times-tables-fluency-and-the-ks2-sats

From the @TES Blog: Times Tables Check: What Do I Need To Know?

We’ve known about the proposed key stage 2 multiplication check for a while now, but have so far been waiting for more information about exactly what the check will entail. With the publishing of the 2018 'Key stage 2 multiplication tables check assessment framework' this month, we now have a greater insight into what we can expect of the tests.

Click here to read the rest on the TES site: https://www.tes.com/news/times-tables-check-what-do-i-need-know

Explicitly Teach Metacognition to Boost Maths Skills

Anyone who has ever taught primary maths will, most likely at many points, have asked themselves, ‘Why on earth did they do it like that?’.

You know, when a child completes a full written calculation just for adding 10 to another number or attempts to divide a huge number by reverting to drawing hundreds of little dots.

And it’s an absolute certainty that every primary teacher will have asked the following question, but this time with a little more frustration: ‘Why didn’t they check their answer?’.

Click here to read the rest on the Teach Primary website: https://www.teachwire.net/news/we-need-to-explicitly-teach-metacognition-to-boost-maths-skills

From Teach Primary Magazine: KS2 World Cup Maths Lesson

I wrote a lesson plan for Teach Primary Magazine to go along with their feature on lessons inspired by the World Cup.

This lesson was one I taught during the last World Cup - an event which also coincided with an Ofter inspection at my the school where I was working at the time. The inspectors commented that they hadn't seen much use of ICT so of course being the computing lead I was asked to tweak a lesson for the next day. Whether or not I'd agree with this sort of thing these days is another matter but suffice to say I met the request and this lesson is what I came up with.

If I remember correctly (I do but I'm trying to be modest) the school's maths lead and one of the inspectors couldn't really find any 'next steps' for me when they gave feedback and only had positive things to say. That's not to say that this is a failsafe Ofsted outstanding lesson - there's no such thing, and it's mostly in the delivery - but that hopefully it will provide a good starting point for a lesson for other teachers.

The whole lesson plan/article is available online so you don't have to squint at the photo above.

https://www.teachwire.net/teaching-resources/ks2-lesson-plan-make-predictions-using-real-time-statistics-from-the-2018-football-world-cup

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/

From The @thirdspacetweets Blog: EEF Report Summary: Putting Evidence To Work

My work with Bradford Research School has really turned me on to the work of the EEF. So when they release another a guidance report I'm always keen to read it first to find out what its implications are. The latests one applies to all subjects and all schools but here, in this blog post for Third Space, I outline how I should have used it had it been published in time, and how I will use it in the future to introduce any new changes.

Winds of change blew in the world of primary Maths when the 2014 National Curriculum was introduced. We now had to teach some things sooner, other things later, some things not at all and there were additions too (hello, Roman numerals!). The ‘new’ holy trinity of Maths teaching and learning were introduced: fluency, problem solving and reasoning.

Then the SATs gradually changed. The calculation paper had already been done away with; next to go was the mental Maths test, replaced by the arithmetic test. And the reasoning tests appeared to begin to assess how pupils were doing on the 2014 curriculum ahead of schedule. The two new reasoning papers were perceived by many to be more difficult than before.

And so, up and down the land, Maths leaders and teachers have been making changes to the way the subject is taught in their schools...

Click here to read on: https://thirdspacelearning.com/blog/eef-putting-evidence-work-report-slt-summary/

Teaching Mathematical Problem Solving: What The Research Says

Recently the EEF published their guidance report for KS2 and KS 3 maths. It gives 8 recommendations for improving the teaching of mathematics:

In this blog post for Bradford Research School I focus in on problem solving but touch on the use of manipulatives, developing a network of mathematical knowledge and other areas of the guidance. In the article I outline a maths lesson which follows much of the advice given in the guidance (the cube trees at the centre of the lesson):

https://researchschool.org.uk/bradford/news/teaching-mathematical-problem-solving-what-the-research-says/

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:

• These AET Mathematics plans give ideas for how to represent every single learning objective in the national curriculum from year 1 to year 11.
• My article for Third Space Learning: Maths Tricks or Bad Habits? 5 Bad Habits in Maths We're Still Teaching Our Pupils
• Articles by Mike Askew: KS1 and KS2 Maths – using visual models and Models in Mind
• Mr Bee's article: Fractions? I Love Fractions! 

On The Third Space Learning Blog: Maths Tricks or Bad Habits? 5 Mathematical Misconceptions We Still Teach Pupils (And How To AvoidThem)

Whilst I'm sure I've been guilty of all of these 'tricks' during my time as a teacher, undertaking my role as maths lead and learning more about best practice has prompted me to become rather passionate about avoiding trick-based teaching in maths

It is also certain that the root of my desire to eradicate this kind of teaching which does little to support conceptual understanding can be found in my own school experience. I remember asking one question constantly in maths: "Yes, but why?". Teachers expected me to rote learn and regurgitate maths procedures but I struggled to remember them because I didn't understand them.

Whilst the list of tricks I've outlined in my latest blog post for Third Space Learning is by no means comprehensive, it will hopefully serve to provoke thought on this matter and will be a starting point for some who are not yet teaching so that children truly understand the maths:

https://thirdspacelearning.com/blog/maths-tricks-bad-habits-we-teach-pupils/

My Guide To Bar Modelling

My guide to bar modelling, written for Third Space Learning, is now available to download. The guide includes information on different types of bar model, how to use them across the primary phase and in different areas of the maths curriculum.

The download also includes a PDF of PowerPoint slides which can be used for staff training purposes.

https://www.thirdspacelearning.com/resource-ultimate-guide-bar-modelling/

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:

https://www.thirdspacelearning.com/blog/sats-qla-year-6-sats-revision-data-2018/

Poster: Maths Written Feedback Comments

Many teachers will still be operating in schools where feedback policies require a certain amount of written feedback. Some schools have begun to adopt no-marking policies but these are in the minority; most teachers, in order to follow policy, have to provide written feedback: marking.

For primary teachers, this is fairly simple in English but is a little trickier in maths. My team and I sat down and analysed a selection of marking comments which we found in maths books and reduced them to question/statement stems. We tried hard to make them as succinct as possible in order to make the task of perhaps having to mark 30 books a little less onerous.

When I put these maths marking comment stems on Twitter some people pointed out that these comments were things that we should be planning into our daily lessons, and they are right. Many of the ideas are to do with reasoning and problem solving - something we should be giving all children the opportunities to engage with on a very regular basis. So, these comment stems come with a multiple purpose: plan maths activities using them, and if required, use them to provoke thought in children who have finished the work you planned for them.

Of course, I would always advocate that much of this kind of 'feedback' is provided in lesson, so these comment stems aren't just for writing - they're for giving verbal feedback too. I have found that sometimes verbal feedback is forgotten - making a quick note (just a few words) in a book might just be enough to jog a child's memory, meaning they won't have to wait for the teacher to come round again for another explanation of what they need to do. Written feedback during lesson time can be useful for this purpose - the fact that these comments are only a few words long makes this more manageable.

Another point some have made is that it isn't necessary to write one of these in every book - it isn't (although some policies may require it). If all children need the same comment (unlikely), then these comments can be provided whole-class, perhaps by way of writing it on the board.

A final note on the comments themselves: there are quite a variety - some pertain to mistakes made, others are intended to challenge further; all are supposed to make children think and to help them to improve their understanding in maths.

For the record: my own school's feedback policy does not require teachers to provide written comments (although they are allowed) but we recognise instances where they are useful and productive. Our maths policy also states that problem solving and reasoning activities should be part of daily lessons.

Click here to download the poster and the editable Word document of the 30 statements

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

This blog post is now available on my website: 

https://www.aidansevers.com/post/what-does-greater-depth-look-like-in-primary-maths

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.

Click here to read more: https://www.thirdspacelearning.com/blog/2017/9-changes-to-primary-maths-curriculum-and-assessment-slt-guide

The documents referred to throughout are these ones:

Primary Assessment Consultation Response: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/644871/Primary_assessment_consultation_response.pdf

Teacher Assessment Frameworks At The End of Key Stage 2: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/645021/2017_to_2018_teacher_assessment_frameworks_at_the_end_of_key_stage_2_PDFA.pdf

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

Here's one I wrote for Third Space Learning: https://thirdspacelearning.com/blog/reflections-primary-maths-leader-ks2-sats-new-curriculum-blog/

‘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://thirdspacelearning.com/blog/reflections-primary-maths-leader-ks2-sats-new-curriculum-blog/

KS2 Tests 2017 Maths SATs Round-Up

https://www.thirdspacelearning.com/blog/2017/ks2-sats-results-2017-what-they-mean-what-they-ll-never-tell-you-what-to-do-next

I produced a quick response to the KS2 maths SATs results for the Third Space Learning blog.

In it I cover what to do once results are opened: support staff, conduct a marking review, report sensitively to parents and children, learn from the results and look for the positives in the results.

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

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

If you would like Aidan to work with you on developing maths at your school, please visit his website at https://www.aidansevers.com/services and get in touch via the contact details that can be found there.