Category Archives: Maths Ideas

Observing Shanghai Teaching by @Mroberts90Matt

Since becoming Maths Coordinator, I’ve taken the opportunity to align our school with our local Maths Hub. I feel this is a valuable link as not only does it mean we can learn from other school’s and their good practice but we are given the chance to observe and learn about current advances in Maths education.

 

Two of these unique experiences have taken place in the past couple of weeks. One was an opportunity to observe a lesson from an educator from Shanghai. This was an incredible experience.  Shanghai is one of the top performers in Mathematics according to the Programme for International Student Assessment (PISA) and I was fascinated to see what all the fuss was about!

Me and my colleague entered the school hall and found around 70 chairs set out for teachers to observe and sets of tables set out in a classroom layout. This surprised me already. I had heard of lesson studies and observation opportunities like this but had never seen one. I was very intrigued to see how this would work. As the lesson commenced there were clear differences between this approach and the usual starter-main-plenary approach that we have become used to in the UK, with plenty of differentiation and limited teacher-talk. This is what I noticed:

1)    Use of language and vocabulary
I was particularly pleased to notice this straight away. The Shanghai teacher repeated the key mathematical vocabulary and sentence structures throughout the lesson. Whenever a question was asked, the children were always expected to answer in full sentences and in clear response. The class that I was observing were trained in this style of instruction for almost 4 years so they were very adept at this. However, it does not necessarily take that long to implement. I mentioned I was pleased because we have begun to implement the same value of mathematical talk and vocabulary in our school using our TalkMaths approach. It also encourages staff to use stem sentences, similar to the Shanghai lesson that I saw. Interestingly, the teacher deliberately chose a higher attaining pupil to model the correct use of vocabulary in full sentences. This provided a good role model and other pupils then followed suit. This practice therefore requires a mixed ability class. The practice of setting or streaming Maths classes would frustrate the efficacy of this approach.

2)     Conceptual Understanding 
I was watching a lesson where the objective was to compare fractions with the same numerator to a class of Year 5 children. The progression from previous lessons was laid out for us by the Shanghai teacher and they had been using a fraction wall to enable the children to work through the concepts step by step.

Fractions

Although the children did not move completely into the abstract without the pictorial representation in the majority, they were beginning to solve problems at the end of the lesson without the pictorial aid.

3)     Focus on the objective
In this lesson I observed the objective was to compare fractions with the same numerator. The children had previously learnt about comparing fractions with different denominators but, after a brief review of that objective at the beginning, this wasn’t mentioned again. This was not the only thing though that showed a complete focus on the learning objective. The teacher planned a game at the end where the children had to create the largest fraction when given a numerator. For example, they were given the numerator ‘5’ and had to make the largest fraction. Now, me and my competitive self, wondered how long it would be before some clever child realised all they had to do was write the number ‘1’ as the denominator and win every time. However, one child tried ‘4’ and the teacher simply addressed this by requesting  the denominator be greater than or equal to the numerator to create a proper fraction. Evidently this year group had not yet dealt with improper fractions and they were required to focus on the objective at hand. If any of my children had done this I would have applauded them and said they had indeed found the larger fraction. This made me question which was the better approach.
However, on reflection, I realised the genius behind staying on the objective. If the Shanghai teacher had gone in a different direction to explain the improper fraction concept then some children would have become confused and question their understanding of the concept at hand.

4)     Differentiation and Teacher Talk
This was a stark difference, noticeable instantly as the lesson progressed. The teacher spoke to the class, modelling language and demonstrating concept knowledge, for the majority of the lesson. This is where external watchdogs and validators such as Ofsted have had a real influence on teaching practice. Around 10 years ago it wouldn’t be uncommon to see, where teaching had been graded as less than outstanding, that there may have been too much talk by the teacher. This led to a wave of dislike over too much teacher talk in internal observations and a culture of no teacher talk ensued for many years. However, in the past few years Ofsted have shifted and have stated that they will favour no particular teaching style, so long as there is progress in the lesson. As such, this means that teaching approaches, such as Shanghai Maths, are now becoming more accepted in the classroom.

The other noticeable difference was the distinct lack of differentiation. All children in the class engaged, all children in the class aimed for the same goal and all children in the class completed the same activities. This again would be condemned by the previous Ofsted regimes. It still would be frowned upon in most schools. However, if the approach is to work this is clear, all must take part in the same language and same learning opportunities. From the staff that I spoke to who had taken this approach on board at the school this observation took place, they felt very strongly that the Shanghai approach had contributed to the gap between the lower ability and the higher ability reducing, whilst still pushing on the higher ability children. This was a question that came up, how are the gifted and talented stretched and challenged if they encounter the same challenges as their peers. There were many responses: peer coaching, finding more methods to solve the problems, creating their own similar problems and explaining their methods in numerous ways.

Next Step

For me, the week later I was able to network with a number of schools that had implemented the Singapore Maths approach to their schools through the ‘Maths – No Problem!’ textbook and principles. These principles of the Singapore Maths I found to be very similar to Shanghai – teacher-led, no differentiation, subject knowledge focused, focus on small steps and specific learning objectives. And of course, the ‘Maths – No Problem!’ textbook is the only textbook approved by the DfE. All of this has definitely caught my interest…

As Maths Lead my focus is the well-being of Maths at the school and so far I see two issues to be addressed: subject knowledge of staff and the workload on our staff to plan sessions. We follow the White Rose scheme which breaks down the content well and has good questions to use with the children but not really enough activities to deepen understanding fully. As such, staff are required to look in different places such as nRich, NCETM and other sites. These are sufficient however it is a huge drain on staff time when they could be sharpening up subject knowledge on what they will be teaching instead.

There is a long way to go but all of this is food for thought for the weeks, months and years to come…

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Times Tables Rock Stars by @Mroberts90Matt

It’s been a few years now that a mandatory times tables assessment as been banded about. Snap general elections, changes in Education Secretaries and basically the fact that other more important things had to be sorted meant that this took a while to come into force. However, the time has come and we have an answer. From the 2019-2020 academic year, every Year 4 child across the country will undertake a mandatory, online assessment of their times tables.​​​​​​ Whether this is required or not is another debate – however I am personally pleased with the way in which the format and timing of the assessment was decided – namely through an open online consultation for education professionals. It’s a shame that just under a thousand teachers responded (if we want decision-makers in education to listen to teaching staff then we need to take the chance to have our voice heard) but it is still a positive step I feel.

One thing that this announcement has done for me as a new Maths Coordinator is take action – I suppose if that’s the case for others then the new times tables assessment may already be successful?…

Anyway, as a school we decided to improve our mastery of our children’s times tables by investing in Times Tables Rock Stars. And was it worth every penny! What I will aim to do here is explain how we have trialled this programme in my Year 6 class, how the school is buzzing about it and the impact we are already seeing from our two-prong approach:

Paper Challenges

One feature of TTRS is the worksheet challenges they offer. In the past our school would do times tables mental starters every now and then, followed by a main times tables challenge at the end of the week. These would take the form of times tables grids with randomised numbers. Older year groups would take on a big grid and the younger year groups some smaller ones. However, we wanted to integrate times tables challenges more throughout the week and drive more purpose into the challenges. Times Tables Rock Stars does this very effectively with a number of banks of challenges. Teachers can personalise these schedules of challenges to certain times tables, whether they do 3, 4 or 5 challenges a week and whether they include division.

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All challenges within these banks give the children three minutes to complete sixty questions. The children can then add up their scores and time over the entire week of challenges. This is where the magic really begins to happen…

There is a place on the website where you can fairly easily input this data onto the website. When each child’s score is put into the week (we do this on a Friday) the children can see their individual rock speed. They take great delight in trying to reach our target speed and trying to be the best class in the school (more on that in a minute). You can then see your classes progress on the website also:

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(Ignore week 5 – we have not yet added our fastest group’s time to the class average)

What we have done with this as a school is created a Weekly Times Tables Trophy and the class that does the best with their target speed wins this. This is calculated by the number of children who reach the target time for that class divided by the number of children. Of course, the target time is differentiated by year group and class as can be seen here:

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We have done this twice now and something very interesting has happened. Because the school challenge is far more fair as each class teacher is using their professional judgement to focus their times table challenges on what their class needs and the target speed is differentiated, the award is much more open. And who doesn’t love filling in a quick times tables challenge whilst listening to Living On a Prayer or We Built This City on Rock and Roll? 😉

However, this is not even the most exciting part of using Times Tables Rock Stars…

Online Challenges

On the website there are four engaging and exciting modes to play:

Festival – This mode allows all children across the world to play one minute challenges against each other with random times tables up to 12×12. This is the default mode that appears but must be used with care for younger children as it does include all times tables.
Studio – This is a single player mode that again includes all 12x tables. However, this is a particularly important mode. It allows you (once you’ve completed a minimum of 10 games) to set an online rock speed which you can compete against others in your school on a leaderboard to get the best rock speed. This really brings in a competitive edge to the online version and our children love looking at our class leaderboard in our room to see who’s moved up! You can even compare average rock speeds with other local schools! A must-use method!
Garage – Another vital mode. This is a single player mode where the children receive 10 coins for each correct answer (whereas the other modes reward a correct answer with only once coin). This encourages more children to try this mode which is important as it is the main mode where the teacher can set the times tables questioned. There are even 5 groups that you can put the children in and differentiate the questions that they will receive. This is what I would encourage most younger year groups to use before they have a firmer grasp on all times tables.
Rock Arena – Basically the same as the Garage but it is a multiplayer version for just the children in your class to compete against each other (with their differentiated tables). A good mode to use if you’re going online as a class.

We encourage our children across school to go on the website at home and we have purchased the app add-on which allows them to access it on our school iPads and most devices at home. We incentivise it using ‘Most Improved’ awards and ‘Highest Earner’ awards which are posted in each classroom and can be easily downloaded off the resource-rich website.

Impact

One half-term is usually too soon to note significant impacts on times table progress. However, two pieces of evidence seem to indicate with my two Year 6 groups that this two prong approach using Times Tables Rock Stars is already making a difference.

First, the percentage calculated in both our higher ability and lower ability maths sets has steadily increased each week. This is not a generalisation. I have recorded the percentage each week and (apart from one week right at the start for both groups) each group’s percentage of children reaching their target speed has increased steadily! Evidence that the paper challenges have had an impact in the Year 6 trial!

Secondly, within Year 6 there is a difference between the two classes. One class have a 0.75 quicker average rock speed than the other. This is might not sound like a lot but it is significant. Interestingly this gap has slightly increased over time. What is the difference between the two? The class with more minutes played online on Times Tables Rock Stars are the class with the fastest average speed which has steadily gained a faster speed than the other.

I would encourage all schools to seriously take this programme on. Not only will it help prepare their current Year 2s and future children for the new times tables assessments (which by the way will be typed online, which Times Tables Rock Stars will also prepare them for) but it will help the children gain a quicker ability on the recall of their times tables. Also, it is very affordably priced in a world where schools have to make more and more cuts.

Right – off I go to try and overtake that pesky Year 6 who has once again beaten my rock speed – this time with a 0.77 answers per second!

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Developing Deeper Understanding of Calculation Methods by @Mroberts90Matt

A word that seemed to be a buzz word when the new National Curriculum was published was ‘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? Or is there more required?

Recently our Year 6 began that wonderful journey of dividing by two digit numbers. Why doing this with an extra digit is such a great jump I’m not sure – maybe another focus for a future blog…

Anyway, as many Year 6 teachers will know – along with the teachers who introduce any formal methods of calculation, helping the children understand why they use these methods and the maths behind them is much harder than just getting the children to work on the mechanics of the calculation. Thus, scores and scores of children are taught the method without necessarily understanding the maths behind them. Since the introduction of a mastery approach to teaching maths, this has been improving.

This is how we tackled this challenge whilst trying to develop a deeper understanding and mastery of the calculation method.

1. Pitch

Naturally in the first session there was already a range of confidence. Some of our Year 6 children were already familiar with and confident with long division whereas some had just about still got a grasp on dividing by a single digit number. Those children were offered the opportunity to either go and attempt a few calculations to make sure there were confident or attempt an estimation challenge involving the long division from nRich: Dicey Operations Game 6

With the rest of the children, initially after a visual representation of the method, a number of demonstrations and a discussion around how the remainders and other aspects of the method worked, the choice was again given to the children where to pitch themselves. Those who felt confident then went to try either of the before mentioned challenges where those that did not stayed in the ‘Long Division Clinic’. The Clinic involves whiteboard work, discussion and targeting from the Teacher and explaining to their peers the process they are working through with careful listening in by the Teacher.

In order to enable the children to practice the calculation and get a real-time assessment on whether they were correct or not whilst I worked with those who still needed to grasp the method we used the website MathsBot which creates instant problems and the chn could quickly uncover the answer on the IWB to check they were correct. If not, they were to analyse, with a partner if needed, to uncover the error.

2. Clinic Continues

Because of the nature of the first session being much more introductory, there is more time given now for those who are less confident to continue working in the Clinic and then try independently. By this stage also, by scrutiny of the previous lesson’s learning, some children may have been discovered who were not as confident as previously thought. These can come into the ‘Clinic’ briefly to check where any misconceptions are.

Meanwhile, those who are more confident have choices on how to push themselves further. Try some more challenging problems set by the Teacher, work on showing their remainders as fractions or decimals and finally some reasoning and problem solving problems set by White Rose Maths which develop understanding on how to apply this method to problems.

3. Tutorials

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. @ICT_MrP was the first to introduce this to me.

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 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. These are some examples:

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

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Not only does this allow the children the opportunity to explain the workings behind the formal method, it encourages them to take it step by step and plan how to break down the calculation for someone that is new to the concept. There is also that extra incentive where they could have their work used for a huge purpose – to have on the school website as part of our calculation policy and teach others who are interested in how to use this formal method.

Considering how to group the children is key in this task. Children should be allowed the opportunity to work independently as some will feel inhibited by not being able to express their explanations with extra discussion. However, some children will not yet be fully confident in their abilities and so mixed-ability pairing is extremely useful here. This is not only enable the children to further internalise the formal method but also make peer coaching another input for all children to get this calculation approach.

4. Take on the Problems!

By this stage – most children should be fairly competent in the method or at least much more closer to grasping it than they were before. This is where the real application, the whole reason why we learn these methods, comes into play. A selection of problems are available of differing levels (strictly no straight calculations) – the children are in mixed ability pairs and take on the challenges they wish to try. This ‘Hot/Spicy/Chilli’ approach means they can start where they feel comfortable and then advance or step back where they feel is necessary.  The challenges can be sourced again from the White Rose Maths documents (they have a lot of sessions when teachers are required to teach a new calculation method) and also many other areas. These challenges are completed on large, graffiti paper so that concerns about presentation or neatness can be put to one side and the maths is the main focus:

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As the session progresses, the children are expected to discuss their thoughts and their answers. This will again develop children’s ability to talk through the calculation. This would be the equivalent of the ‘Ruler of Reasoning’ session in my ‘TalkMaths Approach’ shared in a recent post. The Teacher’s role is to step back and listen in to discussions. From this observation they can address any final or further misconceptions that can be dealt with as a whole class.

No approach is foolproof. There will still be children who won’t have grasped the concept after this approach – however, this will give children a pace to suit them. Faster and more in-depth if needed, slower and more probing if required. Teaching and learning formal methods of calculation is a necessary facet of maths teaching in KS2 Maths and a lynchpin in any child’s mathematical toolkit. A deeper understanding must be developed – hopefully this will help.

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?

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.

photo credit: DSCF0613 via photopin (license)

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