Deconstructing Word Questions in UKS2: see the vision, share your views!

I’m passionate about helping all children to become effective problem-solvers. Over the last 3 years, I’ve done a huge amount of work on helping children to deconstruct multi-step word questions using techniques similar to those described here by Brian Bushart or here by The Erikson Institute for Early Math.

The focus is all about getting children to focus on the deep structure of a question by removing the need for children to find the single definitive answer. It’s far too big a topic for me to write about in a blog, but this video gives an insight by showing how a SATS question can be deconstructed:

I’m going to embark on a big project to give teachers the resources to outwork these ideas in the classroom, initially in UKS2, and I’d like to get input/inspiration from as many people as possible before I start work on the resource.

As such, I’m holding two free 30-minute Zoom sessions where I will spend 15 minutes explaining my ideas, then I will provide an open forum for people to give their thoughts and suggestions. And no pressure to contribute! You are very welcome to join in without having to interact. I will also share lots of free resources in the upcoming months to everyone on my mailing list as I create and trial the resource:
Register for the session on Tuesday 25th January, 12:30pm-1:00pm
Register for the session on Wednesday 26th January, 6:30pm-7:00pm

I hope this project will help children to flourish as mathematical problem-solvers. I’d love to see you there!

I See Problem-Solving – Y2 has now been released!


Reflecting the Emotional Experience of Mathematics, Redefining Success

Mathematics can be tremendously rewarding. The experience of making a new connection, understanding an idea or overcoming a seemingly impossible barrier is inherently joy-filled. I love seeing children battling with the various emotions that arise when doing mathematics – including the excitement of a new discovery. However, learning mathematics can also be very uncomfortable. Therefore, I believe that it’s crucial to help children become literate in the emotional experience of mathematics. And I never tell children that ‘maths will be fun today.’ Here’s why…

When we engage in learning, our brain releases a cocktail of stress chemicals to heighten our level of alertness. This is great for learning but it means that, in terms of our brain chemistry, at the start of a learning experience we have to walk through a temporary ‘door of discomfort’. At this point, I don’t want children to think that they should be enjoying themselves. The joy of a new discovery usually comes on the far side of effort, repetitive practice and maybe after some confusion. It involves discomfort. I want children to recognise and value that discomfort. Notice what it feels like and reframe these moments as part of the learning process – a gateway to success. And, of course, enjoy the moments of breakthrough!

For children to enjoy maths, they certainly need to experience success – to know that effort leads to success. For example, my training explores how children can have high initial success in problem-solving. Where children don’t experience success, I try to explain their difficulties, for example ‘When you can easily recall your times tables, you will have more brain space free to think about the question.’ I always try to address ‘mathematical status differences’ in the class, for example recognising a moment when someone perseveres through a moment of challenge. And I try to be careful in what I celebrate, downplaying the importance of an answer and placing the emphasis on the process of the thinking.

Then, I love to give children the chance to express their understanding in ways that are unique to them. In my training, I like to explore how children can extend sequences of Small Difference Questions, create their own Rank by Difficulty examples or tweak How Many Ways? tasks to increase or decrease the number of possible answers. I think we all have a deep-held desire to be unique. This is a wonderful way to express that in mathematics. It’s a skill that takes training. It’s a hugely worthwhile investment to make.

Mathematics brings up a wide range of emotions. In helping children to recognise and understand the full spectrum of these feelings (and to persevere through them) I believe children will have more mathematical success. I also believe it will also help children to grow as emotionally literate people. I’d love to hear your thoughts. Which ideas resonate with you? What do you disagree with? And how do you help children to navigate the emotions of learning mathematics? All views are welcome!

Using lessons from neurobiology to enhance learning

I’ve always been fascinated by cognitive psychology. I remember, perhaps 6 years into my teaching career, thinking that I should really know more about the science of our brains and how we learn. Since then, so much more is known about optimising learning, like the relationship between working memory and long-term memory or the importance of spaced practice.

Over the last few months, I have been listening to a fascinating podcast by Professor Andrew Huberman who works at the Stanford University School of Medicine called The Huberman Lab. A number of things from the podcast have really resonated with me, and I wondered if they could have application in our schools to further enhance learning. Here are just a few of them.

Among the many science-based tools and protocols shared, Professor Huberman describes how important it is after a bout of learning – and ideally immediately after – for deep rest to take place to improve the transfer into long-term memory. After a 90-minute bout of piano practice, for example, learning can be enhanced by having just a few minutes of resting with your eyes closed. I know that this exact protocol won’t apply directly in primary schools. But might another protocol take its place?

He also describes the importance of utilising the visual system, including having at least some periods of time each day for looking into the far distance. As well as being important for eyesight, your brain has significant rest when you are not focusing on things that are close up. Looking into the distance after a lesson could potentially enhance the transfer of learning into long-term memory. This is also why looking at an electronic device is unlikely to give your brain a good break after a bout of learning. A large proportion of our brain activity is generated by the visual system, so knowing how to optimise it to enhance learning is perhaps a less explored aspect of learning.

I was also fascinated by Professor Huberman talking about adult learning. He describes how, before the age of about 25, we are wired for brain plasticity. However, after that age we need to work harder for our brain to adapt. At the start of a bout of learning, our brain releases Epinephhrine – the name given to adrenalin in the brain. This increases alertness but can initially feel uncomfortable. Learning new things is hugely rewarding and joyful. However, in terms of our brain chemistry, it also comes with some discomfort. My current belief is that we need to recognise that learning is both enriching and uncomfortable. This is the biological experience of learning.

One final example. I listened to Professor Tim Spector, on the Feel Better, Live More podcast, questioning how frequently children should be eating snacks. He talked about the benefits that can be gained from stabilising children’s insulin response from them not eating too regularly and how that can improve concentration. He talked about how Italian and French children have different patterns for eating within a day. Do we know the optimal approach in this regard for maximising learning and improving health?

I don’t claim to be an expert on any of these subjects. I don’t suggest that you implement any changes based on this blog post either: I’m not knowledgeable enough on any of these subjects to be a prominent voice. However, I think there is scope for improving learning by listening to the real experts in the respective fields. I’m sure that there will be so many other lessons that we can take away too.

I’d love to hear your opinions on any of these subjects. All comments are welcome: what you agree with, disagree with, other possible areas of interest and other sources of information that I can learn from. I pick up my messages on social media and my email address is I can be slow to respond, but I read every message! I would love to hear your thoughts.

Shape Puzzles in Y2: small numbers, deep challenge

I’m busy writing I See Problem-Solving – Y2, a resource that I’m super-excited about. It will provide sequences of related questions, tasks and open-ended challenges so children can understand and then explore different problem-solving tasks. I will explain the philosophy behind the resource in a series of future blog posts.

For now, have a look at this sequence of tasks, how it builds children’s understanding of additive reasoning and lays the foundation for algebraic thinking.

Part A: Children are introduced to the idea that a shape represents a number.

Part B and C: Children find the value of each shape. They look for lines made using the same shape. Otherwise, they workout how the sum of a line increases when one more shape is added. Notice the top right example: an extra star is added but the sum for the row does not change. This shows that the star is worth zero!

Part D and E: They apply these principles to find the value of the shapes in these grids, where the sum of each column and row is given.

Part F: Then children can make their own examples.

This blog explains how these ideas can be extended using the I See Reasoning resources in KS2. If you want to trial I See Problem-Solving – Y2 as it is being written, click here to join the I See Maths mailing list

For more information about Gareth Metcalfe’s INSET and twilight maths training click here or for CPD sessions about using the I See Reasoning eBooks. My passion and expertise is in developing children’s ability to reason mathematically and building children as mathematical problem-solvers.

Shape Puzzles in KS2: exploring additive reasoning, laying foundations for algebra

I love using shape puzzles to explore some of the principles of algebraic thinking. The examples in this blog post are from I See Reasoning – Y4 (there are shape puzzles in all the KS2 I See Reasoning eBooks) and I often use these questions with older children too. I’ve found children love completing these questions and love creating their own puzzles!

Step 1: These questions help to uncover the key strategies for working out the value of the shapes.

Left example: the second line has one more circle than the first line and its total is 5 more. Therefore one circle = 5.
Right example: a rectangle is 2 more than a diamond. The child answering this question extended the pattern to show that three diamonds have a sum of 12 and therefore one diamond = 4.

Step 2: We complete shape puzzles using the thought processes from step 1. There are prompts (which can be used or can be hidden) to suggest possible starting points.

Step 3: Children complete different puzzles, explaining their starting points.

Step 4: Time for children to design their own puzzles! I specify two things: there can’t be any rows/columns that are made using only one shape; and the designer of the puzzle must be able to explain a possible starting point.

This webpage, designed by the brilliant Jonathan Hall, enables you to automatically generate these puzzles. And this blog explains how I’ve introduced shape puzzles to children in Y2. A fantastic way to explore some of the big ideas of algebra!

For more information about Gareth Metcalfe’s INSET and twilight maths training click here or for CPD sessions about using the I See Reasoning eBooks. My passion and expertise is in developing children’s ability to reason mathematically and building children as mathematical problem-solvers.

Click here to join the I See Maths mailing list and receive the latest new resources to trial.

Mathematical Reasoning Routines

We all have a very limited attention: as you might be aware, children can’t think about many different things at once! So establishing routines that promote mathematical reasoning – routines that children become familiar with – will allow children’s attention to be focused on the key learning in the lesson. Thinking about these routines in advance can therefore be very important.

And so much better if these routines are consistent throughout the school. In Thinking Deeply About Primary Mathematics by Kieran Mackle, I loved Matt Swain’s routine for how children hold up their whiteboards. The children always hold their whiteboards to their chests; the teacher tells the children to put their boards down one table at a time. When children are familiar with routines like this, their attention isn’t wandering to ‘will Mr Swain see my answer?’ but is held on the content of the lesson.

Here are four routines that I think support learning in a primary maths classroom:

Pair work: short independent thinking slots
In pair work, I often ask children to start by working on a task individually before discussing with their partner. This promotes different methods/thought processes and lessens the risk of one partner becoming too dominant in a conversation. The length of time that I would expect children to work independently will increase as they get older, but it’s something I try to establish with all children. In most contexts, I’d have periods of silence when working independently – children find it more difficult to block out background noise than adults. I have found that these short periods of individual thinking make children value their collaboration time more.

Re-state the views of others
In group or whole class discussions, I generally try to spend longer drawing out the detailed thinking of a child or a small number of children. It’s important, though, that all children are actively thinking about what is being discussed. As a result, I routinely ask children to re-state the opinion of the person that has been speaking. This helps children to follow a conversation rather than just thinking about what they would like to say or to give their opinion. It also opens children up to different ways of thinking or different methods.

Doubt at the point of answer
I want children to focus on the process of their thinking and encourage them to reason. I don’t want children overly focused on whether answers are right or wrong. As a result, I tend to react with indifference when children give an answer. This gives children a reason to explain their thinking and it shows them that the thing I value is their thought process. Also, where a child has answered some questions and has made a few mistakes (but doesn’t hold a clear misconception) I often tell them how many questions they have got correctly/incorrect and ask them to find their mistakes. This gives the child more thinking to do than when the questions are marked and they simply correct their mistakes.

Consistency in question types
I like to have a consistent bank of question types, using common headings, throughout the maths curriculum. These common question types are woven throughout my I See Reasoning eBooks (this blog explains some of the Y3 & Y4 techniques and this blog explains about some of the Y5 & Y6 techniques). So when building understanding, children are used to being given an Explain the Mistakes task; they know that they will be asked to explain links between questions when answering Small Difference Questions and they have become used to working systematically when given a How Many Ways? challenge. By establishing these norms, we can focus more of the children’s attention to the maths content of the task, rather than having to explain how to approach each new technique. I hope the eBooks are super-useful for this!

I’m happy to host training events on Building Reasoning Routines and Building Problem-Solvers for the 2021-2022 school year and I’m working alongside teachers to implement these ideas in the classroom. Please get in touch by emailing if you are interested in receiving support in these areas. I will also keep sharing new resources for people to trial for those people signed up to my mailing list.

Also, please share your favourite school or classroom routines, however big or small. How do they create a positive learning culture? How do they help to direct children’s limited attention in a productive way? I’d love to pick up and share new ideas!

Join the Discussion: How Expert Teachers will Rebuild Mathematical Understanding

It’s session 2 of the free Heartbeat of Education series this Thursday (11th March, 6pm-7pm) and it’s going to be a really significant one: how, as Primary teachers, can we ensure that children continue to thrive as mathematicians? And how should our maths lessons be different in this new season?

I believe that this is a time of great opportunity. It gives us the chance to reflect on children’s experience of mathematics and think about the skills and attributes that we truly value and want to build within our mathematicians. What can we do, as teachers, to lay the groundwork for children to have long-term success in mathematics? And how is this more than just helping children to ‘catch up’ on end-of-year targets? We will discuss what should be prioritised and how our teaching might be different in the upcoming weeks and months.

Register here to join the discussion live and to receive the recording of the session. I will be joined by award-winning Infant teacher Toby Tyler, leading teacher and teacher trainer Alison Hogben and the outstanding maths specialist Vicki Giffard. I want our discussion to explore YOUR questions. Here are some of the things that people have asked so far:
How do schools go about getting the balance right between focusing on the ‘Ready to Progress’ criteria as well as fully covering the National Curriculum?
How much weight should be given for retrieval practice if there are clear gaps in learning?
How should I differentiate now there are such gaps between children’s knowledge/experience in maths?

I’d love you to join in and please spread the word. Also, add your questions to the debate. Either post them on social media or email me at I’m looking forward to a lively, thought-provoking and important debate!

Heartbeat of Education Webinar Series

I’m delighted to announce the launch of the Heartbeat of Education Webinar Series. In these free webinar sessions, held fortnightly on Thursdays at 6-7pm via Zoom, I will host discussions between a panel of experts on some of the most pressing issues in Primary education.

There’s a specific agenda for each session and the four panellists will hold discussions that that will be relevant for teachers, school leaders and parents alike.

I can’t wait to introduce you to the panellists: they are people I have been challenged and inspired by in my 15 years in Primary education. Whilst we are being joined by top authors and esteemed professors, panellists also include some of the UNSUNG HERO teachers, headteachers and home-school mothers that I have learnt so much from. They are wonderful people, the kind of people who you want by your side in the middle of a challenge! And they all bring very different skills and experiences.

More than anything, we want to interact with YOU. We want to understand your challenges, respond to your needs and engage in a personal, practical way. We want our exchanges to be honest and meaningful. You are very welcome to join the sessions and observe in the background. But you are invited to become an active partner as we work through these issues. That’s why I’m so excited about this format!

Click on the links below to register for the free sessions:
Heartbeat of Education: Leading Emotionally Healthy Schools and Homes in a Pandemic, Thursday 25th February, 6pm-7pm
In this webinar, a panel of leading thinkers, school leaders and parents talk about how we can best support the emotional wellbeing of the children and staff in our care. We will have a 360 degree look at the different challenges that children have faced during the pandemic and how, as educators, we can respond in 2021. With author, educational researcher and leader Emma Turner, headteacher of two schools Mandy Jones and inspirational home-school mother of six children Katy Nyman.

Heartbeat of Education: How Expert Teachers Will Rebuild Mathematical Understanding, Thursday 11th March, 6pm-7pm
In this webinar we will consider how primary teachers can best rebuild children’s mathematical understanding when schools reopen to lay the foundations for long-term success. We will discuss how lesson design, planning and teaching pedagogy may be different post-lockdown as well as a range of other issues including subject leadership, accountability systems and differentiation. I’m delighted to be joined by Y6 teacher and STEM professional development leader Alison Hogben, expert maths consultant Vicki Giffard and Infant School leader and award-winning teacher Toby Tyler.

Heartbeat of Education: Building Children as Mathematical Problem-Solvers, Thursday 25th March, 6pm-7pm
In this webinar we will explore how we can enable all children to flourish as mathematical problem-solvers. We will consider the challenges children face in learning to problem-solve and how, as teachers, we can help to deconstruct and build these crucial skills. The panellists will share their various experiences in building mathematical problem-solving skills and developing problem-solving in other contexts. We will try to offer some light on how schools can support all children to become skilful, resilient, logical thinkers! With London SW maths hub lead and teacher Kate Mole, former school advisor and Deputy Headteacher teaching in Y1/2 James Jones and teacher of 38 years, teaching Headteacher of 23 years, former maths consultant and current Camden maths leader Kate Frood OBE.

Heartbeat of Education: Adapting School Life Post-Lockdown, Thursday 22nd April, 6pm-7pm
In this webinar we discuss how school life can best meet the needs of children post-lockdown. We will consider the different challenges, both academically and personally, that children have experienced and how we can respond to meet the needs of every individual. We are joined by Professor in Child Mental Health Jess Deighton, the phenomenal Salford-based Headteacher Jane Garner and Dr Lynne Bianchi who is the Director of the Science & Engineering Education Research and Innovation Hub (SEERIH) at The University of Manchester who specialises in primary science and engineering education.

Please sign up, join in and please spread the word by telling your friends and sharing this post on any relevant pages. Thanks, Gareth

If you are unable to attend live, a recording of each session will be shared with people registered for the session only. This recording will be available for 4 days after the event. Details of how to access the recording will be shared via a Zoom email the day after the event.

I See Reasoning for Y3 and Y4: the big vision for deepening mathematical thinking!

I’m delighted to have released the eBooks I See Reasoning Y3 and I See Reasoning Y4. They are breakthrough resources for building conceptual understanding; for helping children to notice patterns and relationships; and for deepening challenges. They are comprehensive and user-friendly.

Free Sample: I See Reasoning Y3 Division and Multiplication and Division

Free Sample: I See Reasoning Y4 Division and Multiplication and Division

These eBooks are a big upgrade on I See Reasoning – LKS2. First of all, between them there are 872 questions in the two eBooks, compared to the 240 tasks in the original eBook, I See Reasoning – LKS2. In each section of the new eBooks, mathematical concepts are shown using different images and representations:

Common misconceptions are highlighted and addressed:

Then there are a range of questions for highlighting patterns, generating discussion and digging deeper. Can children see the relationships between the Small Difference Questions? And find all answers to How Many Ways tasks?

Each eBook costs £24.98 and only one copy is needed per school. I believe that this represents amazing value – hopefully it means that my resources can impact many children. In-depth online or in-person CPD on embedding reasoning within sequences of lessons can also be arranged. To receive updates on all future events and to receive free resources, join the I See Maths mailing list community. Also, here are the links for I See Reasoning Y5 and I See Reasoning Y6.

I hope the eBooks will inspire many children to enjoy deep, rich mathematical experiences and that they will give you many great classroom moments!

Why I See Reasoning – Y5 and Y6 is new and unique!

I’m delighted to have  released the eBooks I See Reasoning – Y5 and I See Reasoning – Y6. They are an exciting development from anything I’ve done before and will enrich all children’s mathematical thinking. Here’s what makes them unique:

Detailed breakdown of small steps
For children to understand the individual parts of mathematical processes, I’ve introduced lots of new questions for breaking down learning into small pieces, focusing children’s thinking on specific points. For example, Next Step questions get children to analyse specific parts within calculations and Part-Complete Examples support children as they first learn to use methods. As ever, a range of misconceptions are addressed with Explain the Mistakes examples.

Opening up patterns and developing flexible thinking
There are lots of sequences of Small Difference Questions which highlight key mathematical relationships and give children surprises. For example, when children realise that different questions give the same answer, we can explore why. There are so many other patterns to uncover! There’s also a massive range of tasks that promote flexible thinking and using different strategies:

Explores big mathematical ideas (including word questions!) and allows children to create
Each topic is explored from a wide range of different angles. We look at different contexts for rounding; algebraic ideas are explored through shape puzzles; concepts are interleaved as children calculate angles between the hands of a clock at different times. There are ‘numberless’ word questions, where children explore different question structures without numbers, tasks where children are invited to create their own questions or extend sequences and How Many Ways? tasks to open up investigations!

I See Reasoning – Y5 has 362 tasks and I See Reasoning – Y6 has 396 tasks, compared to the 176 tasks of the predecessor, I See Reasoning – UKS2. The tasks cover every area of the curriculum and they incorporate the ideas from the latest DfE Mathematical Guidance. And answers are given for every question!

The eBooks cost £24.98 each and only one copy of each eBook is needed per school. I believe this represents amazing value!

Click here to order I See Reasoning – Y5 and click here to order I See Reasoning – Y6.

I hope I See Reasoning makes a huge impact on your teaching and helps all children to think mathematically. Please spread the word!

My very best wishes to everyone for the new term,