Category Archives: Maths Ideas

Daily Whole Class Feedback by @Mroberts90Matt

A recent idea shared by @_MissieBee has prompted me to share this. It links very closely to a brilliant idea where the class are given a whole class feedback slide or sheet to stick in their book which highlights good things done and common misconceptions. I shared a very similar idea previously and have updated it over the years. It is different to what was shared as it offers a regular, even daily, model which could fit into most, if not all, subjects which require recording in books.

One of the most frustrating things I  (used to) deal with as a teacher was the amount of time marking takes. It really is one of the biggest causes of workload. The most tiresome aspect was writing the same comments in multiple books. Things such as “Don’t forget to line up your place value,” or “Check you use punctuation at the end of your speech,” or even “Name one impact of exercise on the body.” Yes – not only can this approach address misconceptions, but give a follow up challenge without either the teacher writing it 20-odd times or cutting it out and sticking it in multiple times. This Daily Whole Class Marking allows me mark a set of books within 30 minutes complete with personalised comments on misconceptions and challenges. It hones in on each child with the teacher only writing in two or three symbols into their book.

Some examples are here: Cinquain Poem Writing

12Another one for Suspense Narrative writing:13

Maths this time – with challenge questions:

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And finally a Science:

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The Idea

I would start straight away by emphasising that this is not my original idea. I came across the method in a series of excellent summer blog posts by @LearningSpy who referenced it to Joe Kirby’s blog! The idea is so simple – basically instead of writing comments that is expected by a teacher to praise what the child has done and give constructive steps on how to improve – you write down three symbols. Then, in the very next lesson (as this method allows you to mark books for the very next lesson with ease) children are given 5 mins to copy down the relevant feedback to those symbols. Typically I have numerous various comments that are used across a set of 30 books ranging from correcting common misconceptions to a gentle reminder to underline the date and LO. During this specific 5 mins at the start of the next lesson, I am then able take the time to target individual children I have made a note of to give some extra verbal feedback on what they’ve done and try to progress their understanding further. I personally have labelled this time ‘MAD Time’ (Make A Difference) but the concept is that the children write the personalised comments down, rather than the teacher.

Does it MAD?

Well, I have been using this method in my feedback approach for over three years now. There are issues:
1. It may be more challenging for Phase teachers younger in the school (particularly KS1) to adapt this. Possible, but more challenging
2. The first week is always the most ineffective as the children get used to the method of feedback and are given the opportunity to take responsibility for their learning. It does take focus from them and reminders on how to use the time best but each year I have done this, the most challenging learners I have had have seen the advantage of this and taken it on board.

Despite these potential barriers, there has been clear outcomes. These are listed below:

  1.  My workload has balanced

Before I would spend up to an hour, maybe more, marking a set of class books. After having written repetitive comments in books the children would then barely give them a second glance, despite my attempts at the start of each lesson to get them to read and initial the words painstakingly etched by me. This would become disheartening after time. Now, I find I am spending 20-30mins or so on the same number of books. This means I have more time to prepare engaging follow on lessons from the learning I’ve just assessed. We all know providing written feedback is a huge drain on time and whilst some schools may be moving away from written feedback reliance, many are still expecting this. This approach allows this still to be met, whilst freeing time for the teacher.

2. The feedback has improved

I am not afraid to admit it – after marking 20-23 books, my enthusiasm would deplete and my comments to the children in their books would become more and more generic and rushed. I suppose this is human nature (and why a wonderful piece of writing from a child might get more rushed toward the end!) Because of this technique, the level of personalised feedback is constant for the whole class, not just the children whose books are nearer the top of the pile! One big loss in the later books in my pile would be follow up questions. I would be less likely to write these in later books. Also, if I planned to stick in follow up challenges, I often forget to print these off and take them home. Once I have the books home, I have forgotten them and therefore no challenge question to push my learners further. This way, there will always be opportunity for follow up challenges.

3. The technique gets the children to take the feedback in

Now that the children are, in essence, writing comments on their own work they seem to take it in more. I have seen direct improvement on a child’s work from comments they have written. Would those improvements have been made if I had written them? Maybe, but it is less likely the child would have read them. This way, the feedback is certain to be acknowledged, even if then the child makes no effort to act on it.

We all know the frustration when we spend all this time writing comments then the children just turn the page without taking it in. This approach means the children have to at least read, write and respond to the feedback (in their purple pen) to indicate any difference to their learning.

4. It shows innovative practice which is centred on one thing – learning

This marking approach has been used under two senior leadership teams. Both of them have stated that they feel this is outstanding practice in feedback. The MAD Time was stated as an extremely good way of helping children make a difference in their learning and straight away set a precedent for that lesson that we were there to learn, and they would have the feedback yesterday to work on. The whole reason I have decided to use this is because it has an impact on the children’s learning. This can be seen in session, in the books and in the data. Learning is the centre of this approach.

5. FInally…the children GET it!

I did NOT expect this outcome! Quite honestly, I thought my class would hate it to begin with. However, now when I display the 8-10 comments they may find in their work, they actually get excited to see what they receive! Some even utter a ‘yesss’ when they know it’s MAD Time before they then find they have a ~) or a +) which they need to work on. Why? I don’t know. Maybe it’s because it’s a new idea and it’ll lose it’s freshness after a couple of weeks. Maybe it’s because they feel they are actually engaging in something they feel is new and a good way to improve their learning. They actually care that they understand why they’ve received certain feedback and what they can do to achieve that.

Will you try MAD Time in your teaching and learning? How do you get written and verbal feedback across to your class and are there any other ways that have been effective for you? Are you MAD?

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Developing a World-Class Maths Model by @Mroberts90Matt

Previously I wrote about a whole school initiative I was planning to implement into my school called Talk4Maths, a Maths-focused drive on vocabulary and maths talk drawing on ideas from the well-known Literacy initiative Talk4Writing. The research and thinking behind this Talk4Maths can be found here. After some development with a team I was fortunate to work with in school and implementing it, I have refined this strategy into a model which is now at work across my school and has been for almost 5 months. It seems to be going well – some of the impact will be addressed later in this post.

What is Talk4Maths?

Talk4Maths is an approach to teaching and learning Maths which is based on talk and discussion. It asserts that Maths learning is taken in more when children are given the chance to explain their reasoning and describe different skills and processes. There are opportunities for children to internalise mathematic skills and concepts using oral retelling and actions. They then talk. Talk has been shown to develop mathematical understanding significantly:

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As talk is the focus of this initiative, the Talk4Maths strategy then breaks down into three main approaches.

How does Talk4Maths look?

There are three key elements of our Model that we started to implement:

  • 1. Using oral retelling and actions to internalise mathematical terms and skills:
    This is the part of Talk4Maths which draws from Talk4Writing in a similar way. The children are encouraged to internalise mathematical skills and terms using mnemonics and actions to improve their memory of them. As a school we developed universal actions which all staff could use:

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What you see above is the action for ‘multiply’. My Y6 class used this method to memorise terms such as ‘factor’, ‘prime’ and ‘square number’ as well as how to use the four operations on fractions.

  • 2. Creating ‘concept maps’ to show step-by-step understanding:
    The fluency developed from oral retelling and actions is then built on by children developing concept maps to help them break down skills and concepts and visualise them. They can create the concept maps, talk through them with their peers and even create other types of ‘concept maps’ such as tutorials (an example is when we created Long Division tutorials on Explain Everything on the iPads). An example of a written concept map can be seen below:

    Factors

    What you see is ‘Factors multiply together to create a product’. As mentioned in my previous post I had a child working at a low Year 3 level who went home and taught his parents about what a factor was and gave some examples. This was a great example of how creating concept maps could work.

  • 3. Special ‘Talk4Maths’ sessions which involve problem solving, talk and informal recording on sugar paper.
    This is my favourite part (and probably the most important) for what is the purpose of developing fluency in mathematical  skills and concepts if this fluency is not developed in reasoning and problem solving challenges. As such, we set staff the challenge to involve AT LEAST once a fortnight a session dedicated to problem solving and talk. Of course they are expected to incorporate this in most sessions, but this session is special. It is out of books on a more informal style of recording, whatever that may be, and provides ALL the opportunity to discuss and tackle problems using the skills they have developed up until that point.  Some examples below:

To add extra incentive for the children to engage fully, the teacher circulates the groups and picks out through observation one learner who has stood out for their use of mathematical vocabulary. They are crowned in that week’s celebration assembly as (wait for it…) the Ruler of Reasoning!

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And it gets even better – the Ruler of Reasoning from that fortnight receives a personalised RULER OF REASONING (a special ruler with the above logo inside it) which is theirs for the next two weeks until the next winner is crowned. The kids love it!

Why Talk4Maths?

Already, the soft data from the Talk4Maths initiative has been evident. The language used by the children and the staff in discussing who is the Ruler of Reasoning and why they have won that coveted title shows the focus being given to vocabulary, problem solving, determination, talk and mastery – just some of the key words being used in all communications around this strategy.

Hard data – we are just waiting to receive our school’s end-of-year data but a question-level analysis of the KS2 SATs Maths shows that the problem questions were not the vocabulary-based questions or questions that required explanations (of which there were two this year). As well as the improvement in isolated questions, the overall progress of this year’s cohort was greater than last year’s. Also, about 5 classes trialled the Talk4Maths strategy back in Autumn Term – of all the classes in our 2/3 form entry school the top 3 classes that made the most progress were classes that were trialling this strategy. I’ll hope to update it when we can see the impact across the school once that data comes through.

Any questions – just let me know 🙂 – you heard it here first!

Eradicating Maths Anxiety by @Mroberts90Matt

I recently came across this post bringing up an issue in Mathematics which has an impact on learning across the nation, for adults and children:

http://ukedchat.com/2015/08/31/maths-anxiety-by-mathscraftgame/

The natural reaction to anxiety in Maths is avoidance. Even in members of teaching staff there are some who feel they are ‘no good’ at Maths and therefore they avoid all possible interaction with the subject. Of course, when children are then raised by these parents with anxiety about Maths, this attitude can be passed on.

The biggest challenge we face as teachers in Mathematics is encouraging those children who experienced doubt or anxiety to engage fully – otherwise these children may fall further and further behind. As such it is vital for all Maths practitioners to identify what can cause anxiety in Maths and how they can support learners to either avoid this anxiety or guide them through it. And is anxiety even a bad thing?

1. Parental Influence

Children receive the strongest influence in their early development by experiences in the home. They are moulded and taught there first. Parents teach (actively and passively) behaviours and preferences to their children. This can be magnify feelings about Maths. If parents convey negative messages about Maths (or indeed any other subject), that is more likely to rub off onto the child. Of course, this is not guaranteed but it can be a factor. If a parent also experiences maths anxiety, they are likely to avoid it and therefore not support their child as much.

As teachers and schools, we can support parents and therefore children through this. We can provide experiences for parents where they can begin to understand the way that maths is taught to their children and how they can support their child in simple ways. Events such as subject workshops, Curriculum Meetings and Parents Evenings are vital moments where change can happen in the children’s home. With the support from home, children can then begin to feel supported in all areas of their life and feel less anxiety about maths.

2. Ethos of the Classroom

As a teacher, I still have a lot to learn. I am only in my third year of teaching and I recognise I still need to develop in a number of areas. Something which I feel strongly about though is developing the correct ethos in the classroom. Whilst there are times for high-stakes learning, children need to feel secure in making mistakes. If they make mistakes, these are big steps in their learning journey. For any subject, it is vital for children to feel they can take ownership of their learning without worrying about feeling they will be looked down on (by their peers or staff) for making a mistake.

I think about my ability in Art. If I were to go to an Art workshop today then I would certainly feel anxiety. A scene involving stick men is beyond me. However, I know that if i were placed in a scenario that I would not be belittled or looked down on for my ‘weakness’ then I would be more likely to have a go with the task that I was given.

3. A strict diet of problem solving

This may seem like an odd strategy for tackling anxiety – placing children in situations early on where there may be an increased likelihood of anxiety. However, if children are trained to take on problem solving challenges more, rather than comfortable pages of rote calculations, then they will develop their problem solving toolbox more for later on.

The average score in the 2016 KS2 SATs Arithmetic paper was in the mid 30’s out of 40 (around 80% score) and the average scores on the Reasoning Papers (Paper 2 and 3) were 7 and 10 out of 35 (around 20-30% score). This is telling. Children are not being exposed to enough problem solving challenges. As such, it’s hardly a surprise that children experience anxiety when faced with mathematical challenges.

 

It is no secret that a controlled level of anxiety in the classroom can push children out of their comfort zone and encourage greater learning steps. However, there will be a fine balance for teachers to strike which will mean children feel secure enough in their learning to take risks but also push their learning further.

Introducing…Talk4Maths by @Mroberts90Matt

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So, as part of my NPQML qualification I am required to lead an initiative within my school. This initiative has to be linked to the School Development Plan, have a measurable outcome and require the deployment of a team. As such, with my role as part of the Maths Lead Team, I looked into an article found on nRich which refers to a case study of a school which trialled a way to develop mathematical vocabulary.

In essence, this strategy outlines an approach to learning which includes ideas found in the well-known ‘Talk4Writing’ initiative. Talk4Writing gives the children the opportunity to internalise story and text structures with oral rehearsal and physical actions. Along with this, the strategy uses story maps (or concept maps) to memorise text structures once again. If you haven’t heard of it just go to their website or @Talk4Writing – I have only mentioned a couple of ideas from this strategy. There is much more. It is a very effective method of developing writing as it focuses on enhancing vocabulary and language to improve writing.

As I considered this, it became clear that the Talk4Writing strategy was very successful in our school as it developed vocabulary and text techniques with our children. 80% of our children speak English as an Additional Language which can be a major barrier for writing. However, in the first new-look KS2 Writing assessment last year, 80% our Year 6 children achieved the Expected standard and 23% of three cohort achieved Greater Depth! Now, I know what a few of you may be thinking “well it’s teacher assessed so the data can be questioned.” We were moderated. Now you may be thinking “Oh very good…Still potential for questionable results though.” Our moderators were being moderated at the time by someone from the STA. So if you want reliable writing results you can’t look much further really! (To be honest, that experience may warrant it’s own blog post!) 

Basically, Talk4Writing works (in our school at least).

So, seeing the great success of Talk4Writing I started to question “Can there be a Maths equivalent to this?” Mathematical learning hinges on understanding of vocabulary, mathematical and lexical. As such, someone with poor language skills will struggle to access Reasoning and Problem Solving sides to Maths – and in the KS2 assessment, there’s 2 whole papers for that! What if we could develop language, or talk, in Maths in a similar way to our already successful Talk4Writing scheme?

Enter the Case Study mentioned earlier. I will not decrypt it all here (just follow the link talk-for-maths-case-study) but it basically is an example of a cluster of school trying to prevent the Year 3 dip in Maths. Each Year 3 class teacher utilised this initiative of Talk4Maths – using oral rehearsal and actions to memorise and understand mathematical concepts; using story maps to learn step-by-step processes; breaking down (or ‘boxing-up’) problems to make them easier to solve. The whole basis behind these methods is to develop one thing: talk. One Google search and you will find a vast array of sources and research into the value of ‘talk’ in Maths and Talk4Maths is just a strategy to empower children to do this more.

Some discussions later, and couple of weeks of trialling by me done, a presentation to the SLT carried out and I was off! I formed my team (one teacher from each Phase – being in a 2-3 form every school to get the coverage) and we have begun. Up to this point my team and trialled the strategy and shared their experiences. I have tasked some members with carrying out a Pupil Perception Interview to gather initial info on the general view of Maths in the school currently and hope to see a positive change. I will probably write a post later about the progress and outcomes because this will be the first educational change I have led across a school – exciting times!

What I will do now is explain the actual Talk4Maths strategy in a little bit more detail so anyone reading can see if they can envision this in their classroom:

1. Utilising oral rehearsal and actions 

This is pretty straightforward. For whatever mathematical concept is being distilled, the teacher will break it down into a simple definition of series of steps (depending on the content). 

For example, the very first concept I trialled this with was factors. I came up with the sentence ‘Factors multiply together to create a product.’ Straightaway this brought up discussion. What is a product? Can there only be two factors of a number? Can there ever be one factor? The list went on… Then I invited the children to develop simple actions with me to memorise this definition. These actions offer a great little beginning to a lesson when we are going to quickly revise factors, they also support the children’s knowledge and understanding as they have visual cues to remember the language. 

2. Story Map Concepts 

This follows on naturally after creating visual cues as a further aid to learn concepts and processes but they don’t have to be used together. Talk4Maths Story Maps are a sequence of images (very basic images), sketched by the children to help them remember the skill or concept. We have drawn story maps for remembering factors, prime numbers, square and cubed numbers, long division, adding/subtracting/multiplying/dividing fractions and more. My team have done some for comparing numbers, adding numbers and even presenting word problems to help children break the problem down. All the while, these handy little story maps can be kept in the back of a book or in the classroom somewhere for reference. 

3. Boxing up problems 

This was mentioned in the case study but I am less aware of how this would work and the case study said it was too complex for Year 3-4s. Simply, this means breaking down the problem into steps so it’s easier to solve. We are going to make a decision whether to attempt this or leave Upper Key Stage 2 practitioners to teach children to break down the problems as they are already anyway. 

Then what…?

After having identified what we wanted to implement into the school, we recognised a need to have some sort of ‘celebration’ or ‘reward’ in the school which promotes children who engage more and more in Maths talk as a result of further confidence and opportunities in discussing Maths.

Unlike Writing, it is more difficult to see an ‘end product’ in Maths learning. There is no ‘final piece’ that can be assessed by teachers to determine a ‘T4M Reward Winner’. Thus, we created the ‘Ruler of Reasoning Session. Each fortnight, each class will have at least one (Ruler of Reasoning Session) where they will not use books – only graffiti paper – and the teacher will circulate every group, listening to each group discussion how to solve problems based on their current topic.

The use of graffiti paper in Maths removes barriers of worrying about presentation. It encourages group discussion and therefore, the use of the vocabulary children will develop in a classroom adopting a Talk4Maths approach. The concept of using graffiti paper in a lesson will also guide staff towards using a problem to solve rather than a list of basic calculations.

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Using their observations and the resulting graffiti paper recordings, the teachers will then choose one child that has stood out as their ‘Ruler of Reasoning’. This child, along with the other Rulers, will be celebrated and they receive…wait for it…the special ‘Ruler of Reasoning’ to use for the next two weeks! 

And the outcomes…

Well, considering I’ve trialled for a half term and my team for about 4-5 weeks it is difficult to say for certain. However we have seen quantitative and qualitative results.

First, a child who was assessed as working at a Year 2/3 level on entrance to Year 6, asked me one day before our lesson if we were doing the ‘actions’ again in Maths today. I said, of course. He voiced he was a little unwilling (being a cool Year 6 boy and all) and I asked ‘What’s a factor?’ and he reeled off the definition (this was about 3-4 days after learning about factors). Then, to prove the point even further, I asked him ‘What is a factor of 21?’ He said ‘3’…If you want further evidence then go away and do it yourself!

Now, for further evidence, at Parents Evening, I learnt that this same child (who really does struggle in Maths) taught his Mum what factors were as she had forgotten!

Quantitative data – we have just received our internal analysis of our Autumn Assessments and being on the Maths Lead Team I received the Maths data for the whole school. The 3 classes who showed the greatest rate of progress in Maths? Those three classes are in my Talk4Maths team who have been trialling our new Talk4Maths strategy.

What about you? Will you be looking into Talk4Maths? How do you develop talk in your Maths sessions?

photo credit: –Sam– <a href=”http://www.flickr.com/photos/52061252@N00/31108362865″>Let’s Talk</a> via <a href=”http://photopin.com”>photopin</a&gt; <a href=”https://creativecommons.org/licenses/by/2.0/”>(license)</a&gt;

Mathematical Fluency Part Three by @Mroberts90Matt

This is the third in a three part series around developing Mathematical Fluency (which has been highlighted as a key aim in the National Curriculum) in teaching and learning. The previous posts have dealt with using technology to enhance pedagogy and allow children to take on the mantle of the expert. The other discussed developing children’s conceptual understanding which would allow children to apply those principles with greater authority.

3. Problem Solving

One of the most potent forms of developing mathematical fluency is giving children the opportunity to apply basic skills in as many problem solving activities as possible. As a profession, I think we have a tendency to go through the basic concept first and then (and only then) introduce the idea of applying these skills into problems that relate. However, recently I planned out a few sessions focus on teaching volume to my Year 6 (a brand new concept for the vast majority of my class). The results have been really pleasing – not because they can just apply a formula I’ve given them, but because they really have grasped the concept.

The Golden Cube

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With a variety of Maths resources in front of them, I asked my class to close their eyes and picture the following problem as I verbally told it to them:

The Golden Cube Problem

“You create a larger cube from a number of smaller cubes. You decide to paint the outside of this larger cube all gold, every face. You go to put this golden cube on the windowsill to dry but you trip and drop the cube. When it hits the floor, it breaks into all the original smaller cubes. How many cubes have 3 faces painted gold, how many cubes have 2 faces painted gold, how many cubes have 1 face painted gold and how many cubes have no faces painted gold?”

I gave them no more guidance on how to solve the problem – and of they went. Little did the children know that they were not only developing their understanding of 3D Shape, but they were beginning to become aware of volume. As can be seen below, different strategies were used and we discussed that learning moment too:

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So, with the problem solved and some challenges completed along with that, the next session I asked the children how many base 10 cubes (because that was the main resource that was used) made up the cube. 64 cubes. What were the dimensions of the cube? 4x4x4 – what do you notice? The number of cubes used can be calculated by the dimensions of the cube. Visualiser up, we tested that hypothesis with a couple more cuboids. It worked. The children then went into pairs and worked on created cuboids which the partner had to calculate how many cubes were used to create the cuboid by just being given the dimensions by the pair creating the cuboid. I would include photos but they contain children focusing intently on their learning!

Finally, after discovering that we could create different cuboids with the same volume, the children then moved on to calculating the volume (and also a missing dimension when given the volume) on a cuboid given to them not to scale. The children, because of the problem solving activities that had gone before, were so fluent in applying the formula and working with it to suit their needs. These questions also involved converting measurements in the question and subtracting chunks of the cuboids that had been taken out. However, because of their grounding in the concept of volume, their fluency in applying the knowledge to a formula, these did not raise a problem.

Of course, after this three part series, I’m sure others to add ideas to getting children to teach, developing conceptual understanding and using problem solving. Please, if you have done anything in the classroom that has developed mathematical fluency really well, please don’t keep it to yourself, share it!

Mathematical Fluency Part Two by @Mroberts90Matt

This is the second in a three-part series that I have developed when I have been thinking about Mathematical Fluency. Fluency in Maths has been highlighted as an aim in the National Curriculum and it is down to us as educators to ensure children are equipped with the tools needed to access such fluency. Last week I posted about the power in children teaching others to develop their fluency. This week I will focus on building their understanding of concepts and in the final week I will unpick problem solving.

2. Conceptual Understanding
When we teach children methods in Maths, there is a danger that we overlook teaching them why we do certain things. A classic example is teaching a written method for addition. When children are eventually taught the standardised column method (as in the Appendix of the National Curriculum, following on from non-formal methods such as the number line) they are taught to ‘carry over the one’ or some other vague comment meaning we carry a remainder over from the previous place value. Do all children understand that ‘one’ is actually a hundred being carried over from the addition in the ten column? Maybe, maybe not. It is such conceptual understanding that is vital in developing the mathematical fluency in a child’s knowledge of working with number.

Recently, as mentioned last week, our school had an Ofsted inspection. In a discussion with Year 5 pupils, the understanding of this sign was brought up ‘=’. The children were fine with this (x+5=9, what is x?) but there was slight confusion when this problem was shown (x+5=6+y – what is the value of x and y?). These children, according to National Assessments, were competent mathematicians. The problem was not in being able to ‘do’ Maths but in ‘understanding’ – that ‘=’ doesn’t just mean ‘makes’ or ‘comes to’ but literally means ‘is equal to’. Our school has an extremely high proportion of children who speak English as an Additional Language so it may come as no surprise that the most challenging area in Maths might be in language and terminology rather than in ‘doing’ the Maths.

How do we help develop children’s conceptional understanding rather than just training them in the ability to go through the mechanics of methods? There will be a number of ways. Recently, my wife became an Usborne Independent Organiser. Basically she promotes a love of reading through organising parties based around the Usborne Book Publisher and tries to generate interest. In the Beginner Pack she received, there was a ‘First Illustrated Maths Dictionary’. See link below:

First illustrated maths dictionary

http://www.usborne.com/catalogue/catalogue.aspx?area=MTH&subcat=MD&id=5913

This was the first I had heard of a ‘Maths Dictionary’ (and this post is not to sell the book to you, I’m sure many other Maths Dictionaries are available – although if you would like a copy then let me know ;P)

Having had a look through it, I thought it was a brilliant book! Very colourful, engaging and goes through concepts found in the National Curriculum. There is also a 7+ version and 11+ version. These publications go through the language used in Maths (including the ‘=’ sign mentioned before) as well as many other mathematical concepts. I think this is another medium through which we can try to develop children’s mathematical fluency by consolidating their conceptual understanding.

Are there any other publications that you are aware of that could support children’s Maths understanding? It is pretty clear that if we develop children’s conceptual understanding then this will improve their fluency – but do you have any ideas or techniques that have worked in the classroom?

Mathematical Fluency Part One by @Mroberts90Matt

As I write this I am sat in the lovely evening sun at a lovely, quiet B&B in the countryside near Alton Towers… Yes the Alton Towers which had been shut today and will be tomorrow, the first two days of the 4 day getaway my wife and I are having from the kids we’ve had planned for months… Typical. Fortunately we have other plans with the Tree Top Challenge, Water Park and Spa the next couple of days, which are open, so hopefully we can do the main Theme Park on Saturday… Wish us luck!
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In the National Curriculum, one of the aims in the Maths area states:

“become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.”

In my school we recently had Ofsted. However, this was not a usual whole school Ofsted inspection. It was a Maths Subject Inspection. Reception, Year 2 and Year 4 were observed in Maths sessions and books from Year 1, Year 3 and Year 5 were scrutinised. A learning walk also took place throughout the whole school. The feedback was generally positive, areas to work on of course, but good.

One thing that seemed to be a buzz word, or a focus on the inspection was this ‘fluency’. The definition of fluent online is ‘smoothly graceful and effortless’. In looking at the aim in the National Curriculum, it seems to refer to bring able to understand why methods work in Maths (not just go through the motion of doing the method) and apply the method to appropriate questions and problems. So how do we develop Mathematical fluency in children? Do we give them a list of calculations? I hope all educators reading educational blogs, even my lowly blog, would know this is not sufficient (although maybe occasionally required). Over the next few weeks i will post an entry that offers a way to develop mathematical fluency in the classroom. These ideas are only a few that I have tried or come across that have potential. If you have others I would love to hear them.

1. Tutorial
It is well documented that we learn 20% of what we hear, 30% of what we see and so on… But we learn 95% of what we teach others. So the question was for me then ‘How could I get my class to teach others in a way that will include all?’ Of course I could go down the route of whole class presentation… But if I were a10 year old child I would struggle to stand up and teach my peers the basics of long division. Teaching to groups is always fun, less intimidating. The question that method throws up is how could I accurately assess if each individual child had met the LO when different groups are teaching each other at once? To have each group teach other one by one so I could listen to every child would be too time consuming. So what?

I was led to an app called Explain Everything which was perfect.

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An example of the app in use

The app allows the user to create a video whilst using a drawing tool or a highlighting tool and images. This gave the perfect opportunity for the children to ‘teach’ someone how to use skills in Maths. In doing this, the children themselves become increasingly competent, developing their fluency.

This video not only gives the children an opportunity to engage in a meaningful and purposeful activity, but it can also serve as a future stimulus to remember previous learning. An example of this in action is when we learnt about long division. Fluency begins in internalising the basics and the children had not yet learnt this skill. So, after teacher input and practise with feedback, the children created their ‘Long Division Tutorials’ – these are some examples:

http://www.kingsroadschool.com/year-6-long-division-tutorials/

This was successful because, months later, just before the SATs, I taught a lesson where the children had to opportunity to revisit this skill by applying it to a problem solving activity. After recognising the problem required long division, one child said “Oh, I looked at our videos recently to make sure I remembered this!” She then proceeded to solve the problem. Fluency.

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photo credit: Explain Everything for iPad Screen via photopin (license)

Anyone for Long Division? by @Mroberts90Matt

Calculation methods in Maths form a core skill set that students need to acquire in order to progress and attain. A child who can master the skills of written methods in Maths week most likely go on to be very successful in future Maths problems as they will have that basic skill set to build upon.

Therefore, when it came to teaching my Year 6 children how to tackle long division, a skull which they had not yet come across, I knew that it would require something really engaging to make sure they got it (as with every area of learning in my classroom really)!

The Idea
I had recently been in a staff meeting led by @ICT_MrP who showed the staff an app which I’d come across recently – Explain Everything. This app allowed you to easily create videos with voice recording and annotating images. What this does is allow the user to create short tutorials with visual aids on the screen.

Linking this to the long division need, I remembered the saying where people learn only a small amount of what they listen to/are shown but they learn a higher proportion of things that they teach others. Suddenly, the way became clear, children could use this Explain Everything tool to encouraged use of language and internalisation when acquiring this long division skill. From what I understand this is a strategy called something like ‘Role of the Mantle/Expert’.

The Method
After teaching the chn the method suggested by the Maths Coordinator in our school, I decided this would be a good time to implement making a Long Division Tutorial to consolidate their learning so they could apply the calculation.
The result can be found on the school website here: http://www.kingsroadschool.com/year-6/

(We would have posted them onto our class blog but we’re with Primary Site and I’m personally hoping we get off it!)
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[Level] Six of the Best? by @Mroberts90Matt

I recently went on my first course that wasn’t for NQT’s – Achieving Level 6 in Reading and Writing. Expecting to go with my mind blown with what would be expected of 10-11 year old children to reach Level 6 in those areas I was not disappointed. When we discussed the poem Dulce Et Decorum Est as a possible text for a Guided Reading session with Year 6 I was amazed. Not to mention, when looking through the ‘anthology’ that was provided as possible stimuli there were texts in there that I distinctly remembered looking at in my GCSE studies! I quickly realised it was little wonder why nationally the chasm between children achieving Maths Level 6 is consistently larger than those children who achieve Level 6 in Reading or Writing. As I left the course, wide-eyed, it became clear to me that we had work to do.

Level 6 – Why the sudden interest now?

When I was in Year 6 (2000-2001) I was almost put forward for the Level 6 Maths paper – I’ll point out that not being selected for that test has not hindered my life opportunities but more on that later – but I didn’t realise until recently that Level 6 was discontinued until fairly recently. I haven’t had the chance to do research into why Level 6 was brought back but I am fully aware of the arguments to suggest why it shouldn’t have been provided for in Primary Schools. These include:

1. The children going into Secondary with a Level 6 are NOT at a Level 6

Simply put, the children who are trained to jump through the hoops of Level 6 – reading, writing or Maths – do not have the breadth of knowledge of a Level 6 learner…they have just been taught the techniques and heavily-weighted in marks topics that come up in the Level 6 paper they sit. I am of the understanding this is the complaint that secondary educators had and rightly so.

2. It adds more workload/stress to the Primary staff involved

Speaking as a Year 6 teacher, I have some experience in this. Not only are primary school teachers expected to have children reach a Level 4/5, which in itself is a task that is no mean feat for ALL children, but also to then push the other end up to heights that some children don’t reach until the end of Year 9 is taking it (quite literally) to another level. Now, before the comments flow, I am ALL for pushing children to succeed to their potential and setting high expectations for learning – but Level 6 has now become a process where children who would not naturally achieve this ‘level’ (remembering that they aren’t REALLY a Level 6) are being pushed to reach that level…which brings me succinctly onto the final point…

3. It adds more stress to the child

This is what everything in education SHOULD be about – the child. I have a child in my Year 6 class who is working at a low Level 5 currently in Maths. She’ll be a solid Level 5, no doubt. However, the Level 6 culture has taken hold. At home, she is expected to have a tutor group each week and 2-3 hours of school work EVERY night. Whilst I praise children to the high heavens when they take their learning outside of the classroom, beyond homework and our class blog, this is too much. It is not healthy. These are children. The sad thing is, despite all this extra pressure at home to attain a Level 6…this child is making the amount of progress expected, not an accelerated rate. I am aware that this is not a sole example, but many other children are put under this pressure, particularly in their final year in primary school, which they should be savouring. Would this pressure be as intense if there was no Level 6, or at least less of an emphasis from the top-down about Level 6 attainers…I doubt it!

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Six for Success?

Now, of course, after my little rant of Level 6 and the downfalls I see about it – I do see the benefits. It does remove a glass ceiling for (natural) high achievers in primary school, it does provide an outlet for AGT children to be challenged and, if the children truly are Level 6, it can provide a springboard to mastery in that subject later on in their secondary school life. These points cannot be ignored – but in my humble, NQT opinion, something HAS to change.

 

Next Steps for Six?

I wonder if there is some way to reduce the pressure (particularly on Headteachers) to boost the number of Level 6 attainers in schools. I do NOT think we should abolish Level 6 completely, yet I do think that there should be a much smaller emphasis placed upon it. Perhaps if children enter Year 6 as a solid Level 5 then maybe they should be guided toward that Level 6, rather than have children who are just behind being pushed up to make the numbers.

 

(Having said all this, levels are going out the window after this year so who knows what point this thought will have after 4 months time anyway…)!

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Set ‘Em Up! by @Mroberts90Matt

Well, was able to finally sit with the other teacher in my year group today and get some planning done! Was a great relief, partly because it was good to get something down on paper and partly because we got along so well! As stated before in my post on collaboration, I think this working relationship will be key to, quite frankly, my sanity and happiness in my NQT year!

One discussion point we had was group setting in English and Maths. The school’s policy is to group children by ability in these areas. An idea was generated for Maths. In my final placement, I had seen an interesting trend. I was teaching the lowest ability across a Year 3-6 band in a 1 form entry school. Thus, my class were about 60% Year 3s, 30% Year 4s and 10% Year 5s. I couldn’t help feel there were a number of issues with this:

1.Children’s self esteem
How would you feel if you were one of those Year 5 children in a class of children who would be 2 years younger than you? It would be a serious barrier to a child’s learning if they were made to feel that inferior that they were sent 2 years below most of their peers.
On the opposite side, there were a couple of Year 4s in the highest ability class with mainly Year 6s. There are serious fundamental issues here as well as self-esteem. Complacency may creep in. If those children are working at the level of Year 6s, why put effort in until they are Year 6? However, the more serious problem I think is the problem of knowledge and understanding. Children’s learning is scaffolded, principle building upon principle. How can this occur when a big chunk of content is skipped? Those Year 4 children would need to develop their understanding in more basic areas of Maths before they step up to more advanced concepts.

2. Logistics
Schools are busy places. If a school is not busy it is not doing something right. This can be to the detriment of learning occasionally but that is the natural way of the institutions. On top of that, sung the need to move children across 4 classrooms for one lesson adds to that. What if one year group is on a trip. Those children miss an ongoing lesson of input and the absent class teacher can’t teach their pupils so those children are left hovering in a session that isn’t suited to their ability. It can just get messy, but this can be avoided I suppose. Ofsted (2000) even found timetabling when setting groups in subjects to be an issue, and as Ofsted say it, it must be true…(insert cheeky wink)

3. Mathematical Concepts
This, to me, was the biggest sticking point. When I received the Maths group list, I noticed that the children were grouped using an overview Maths level given at an end of year assessment. So, here before me were children labeled with a best fit level. The first concept I had to cover was Shape. Some children excelled far beyond what I expected from the level given me, others struggled. Later, we moved to Number. Different children excelled. Others, some of whom had excelled in Shape, struggled with the Number learning activities. An issue started to materialise – this general level wasn’t sufficient to make informed decisions in planning children’s learning, which is one of the points of setting in groups.
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As we discussed this, we came to a joint decision… Our aim is to still group by ability, however, do so by area of Maths rather than a general Maths assessment. So Number, Calculations, Shape, Measure etc. will be preceded by a short assessment which, alongside previous data, will form our groups for each concept area. I think our biggest challenge will, again, be logistics. For example, where is my book? I can see that happening a lot – but with some good planning hopefully we’ll see some results. It should, however, overcome some of the regular challenges of setting, mainly the self-esteem (because generally most children have one area in Maths they are stronger in and will want to be challenged in more) and also the building of conceptual blocks for each individual child.

Maybe you feel strongly against setting in groups for certain subjects? I know in the past I have been cautious about considering setting in groups but this idea had ticked a lot of boxes for me. Do you group by ability? How does that work in your school/year group?

References
Ofsted, 2000. The National Numeracy Strategy: the first year. London: Ofsted.

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