For me to improve… September ’17

This is my first blog post in the ‘For me to improve…’ series in which I explain what I’m doing to be a better maths teacher. This blog explains the thought process behind the series.

I’m always looking to use equipment and images to represent concepts, and I like my maths lessons collaborative and open. This makes my classroom management skills important so lessons teeter on the healthy side of organised chaos. My partner Y1 teacher last year was the maestro in seeing a logistical detail that I’d missed. I learnt a lot from her, and I also came across some interesting ideas reading Visible Learning for Mathematics. So here are my five targets for the new term:

Promote a learning action
In each lesson, identify one key ‘learning action’ to promote. My thought process will be ‘Which learning behaviour will improve the outcomes in this particular lesson?’ It could be as simple as turning your body to face your partner; it may be more complex like asking clarifying questions; it might be a maths-specific thing like finding different ways to answer a question.

Prepare individuals for the social demands of lessons
I’m a big fan of small-group pre-teaching to help all children access the big ideas of a lesson, breaking down barriers and predisposing misconceptions. It’s helped me to facilitate mixed-attainment groupings. However, for some children the barriers may be the social demands of a lesson. Perhaps Harry finds it harder to share resources; maybe Jade dominates group discussions. A quick conversation or organisational change beforehand might make a big difference.

Make discussions active
I liked this idea from VL for Mathematics: during a whole-class discussion, put your thumb up on your chest if you agree with the speaker and want to add something; put your fist against your chest if you have a different viewpoint. This encourages children to actively participate in discussions without being intrusive to the speaker.

Exit tickets
I’m going to make a clearer distinction between most questions and tasks, used to generate discussions, and short ‘exit ticket’ tasks that are completed independently and used to give more accurate AfL information. The nature of the marking may also vary depending on the conditions in which the work is completed. I’m hoping that this will help to keep children accountable for their own progress and avoid social loafing in group tasks.

Cognitive load and challenge in calculation
In some lessons, particularly early in a unit, I want the challenge to come from understanding the concept so I will minimise the challenge in the calculation. Consider 14 = 6 + ___ (WR Progress Check, Aut Y1, q4). We can learn the concept ‘= means same as’ using numbers within 5. Once that concept has been secured (a concept which tends to need more than a little reinforcement), the challenge within the calculation can be set at an age-appropriate level.

And as ever this year, I make the same vow to the children in my care:
‘I promise to learn alongside you.’


Training and Resources for Summer ’17

I set up I See Maths to help time-limited teachers create powerful learning experiences in maths, engaging children intellectually and emotionally. To that end, here’s what I’m offering this summer:

I’m delighted to announce four new conference dates this summer: full conference details can be found here. Early Number Sense: Beyond Counting  will give a clear Nursery-Y2 vision for how children build a strong feel for number and learn to calculate using non-counting strategies. We will explore how mathematical play can be extended and how reasoning can be embedded. Reasoning and Depth in KS2 Maths will give an exciting and practical vision for deepening mathematical learning, including how images and resources can be used to build understanding.

If you are interested in this training, you may consider arranging a conference event at your school – all that is needed is a spare room. This is a very cost-effective and popular way of running training – for full details click on the top two links on this page.

Resources to Buy
I’m working hard on the I See Reasoning eBook range and hope to write the UKS2, LKS2 and KS1 versions this term (I may be dreaming!). This will give teachers a massive bank of questions and tasks that will open up discussions and encourage reasoning. I’m extremely excited about this project – this blog gives more detail.

The iPad app I See Calculation is also in the final stages of being built. It will show standard written methods for calculation one step at a time. A child could check their answer to a question with a calculator; with I See Calculation they will be able to check each step of their written calculation.

Free Resources
I’m intending to create a series of free ‘flipbook’ dot pattern games that will help children to visualise addition, subtraction and multiplication, opening up discussions about calculation strategies.

Full details about my INSET training and in-school support can be found by clicking the links. I’m a NCETM Charter Standard provider of CPD and, being a class teacher, still very au fait with the realities of teaching in the classroom.

I hope that, in some way, my work can help you in the daily challenge of delivering great maths lessons. Enjoy the summer term!

Help! Long Multiplication

So it turns out that I’m not 100% sure how to do long multiplication. I really should be, you probably are. Please help.

I want to make a resource that will support children doing long multiplication so but first I want to make sure I’ve got my method straight. Here’s the issue: when you are multiplying by the tens value in a 2-digit number, where are you supposed to position the digit being carried? Here, I’ve done 80×3=240 and have put down 40. Where should the 2 hundreds go?


A shows where the 2 hundreds will be added to (but it could make the calculation messy). B shows the 2 above the hundreds column, the column that it will be added to (but two places along from the 3 we’ve just multiplied by). puts the 2 above the next number to be multiplied, but in the same column as the 4 tens.

The example on the national curriculum (below) somewhat ducks the issue in that there are no carries from the 20, and the examples in the mark scheme for the 2016 SATS don’t show the position of carried digits.

I inferred from this it’s up to schools to decide which way is best. Is there a ‘right’ way? What do you do? I’d love to know. Just to repeat, this isn’t me trying to make a point, rather I’m in the process of designing a resource that will model this calculation process, but I want to do it right. I’d love to know what you think, or from any ‘higher power’ if they can give a definitive stance.

All input welcome!

Enrichment in mathematics

In the early 20th century, psychologist Lewis Terman carried out a now-famous research project: he aimed to prove that by knowing a person’s IQ at an early age, you are able to accurately predict his or her life success. Using a series of intelligence tests, he identified an elite group of 1,470 children to study. Terman believed that it was these children (and others of extraordinary IQ) that ‘we must look for production of leaders who advance science, art, government, education and social welfare generally.’

Terman carefully monitored the progress of the ‘Termites’ over a period of 35 years to ascertain their life success. The results surprised many, including Terman himself. The group thrived in many ways, most notably being healthier, taller and more socially adept than the average American. However, their achievements were far from remarkable. In fact, a later study concluded that a random sample of people, given the same socio-economic status, would have achieved just as well. Terman himself reluctantly concluded that ‘intellect and achievement are far from perfectly correlated.’

Later studies went on to explore this idea more thoroughly, as explained in Malcolm Gladwell’s book Outliers. Generally speaking, people who achieve great professional success have an above average IQ: usually 115 or above. However, beyond this ‘intelligence threshold’, a person’s success is determined far more powerfully by other skills and attributes rather than the full extent of their IQ. Gladwell argued that it is hard to be highly successful without above average intelligence; however, beyond the intelligence threshold success is determined by other factors, for example the character and inter-personal skills of the individual.

Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content.
National Curriculum, Maths

This led me to think about the nature of the ‘rich and sophisticated problems’ that we should be providing. In order to equip children for long-term success, tasks should help children to develop personal and social skills as well as subject-specific expertise. Easier said than done for a busy and pressurised teacher!

That’s what I’m going to dedicate my working life towards: creating learning experiences in maths that engage children intellectually and emotionally; tasks create curiosity and lead to collaboration. I hope that this characterises First Class Maths, Maths Outside the Box and The Maths Apprenticeship.

I’m convinced that, if the system allows, these are the kinds of learning experiences that we as teachers want to provide for our children.

Personal Skills

Plans for maths, 2016-2017

This is a great time to be involved in maths education: there’s a collective movement towards developing deep, conceptual and varied learning experiences; teachers are being proactive in promoting positive attitudes towards maths; maths hubs are growing in their influence.

I’m excited to play my part in this movement. Put simply, I spend hours thinking about and trialling ways to get children involved in maths tasks that are collaborative, open and (wherever possible) visual. I want children to become engrossed in maths; to experience its agonies and thrills, engaging emotionally as well as intellectually.

Here’s what you can expect from me in 2016-2017:

I can’t wait to release Maths Outside the Box, the natural follow-up to First Class Maths. The 15 tasks (logic puzzles, multi-dimensional tasks and investigations) will give children challenging, quirky contexts in which to apply their learning. The perfect way to end a unit of work – it’s been SO much fun writing and trialling.

I See Multiplication and Division for iPad is also coming soon. It allows teachers to create a range of visual images to represent calculations, including proportionally sized bar models, area models, dot patterns and arrays. It’s the natural follow-on to ‘I See Addition and Subtraction’.

I hope to write a range of open, visual questions that allow children to explore maths ideas in depth. Questions a bit like this:

I’m also planning on sharing lots of free resources, including (time permitting) videos for improving the quality of parent interaction in maths. Watch this space.

It’s a privilege being able to visit schools to share this passion. Here is the information about my training.

Conference events are scheduled for Manchester and Dudley with a KS2 focus. Expect future dates for bith KS2 and EYFS/KS1 training in the Spring and Summer terms. I am also soon to announce a 2-day training event in London (mid-November) and my first half-day TA training event in South Manchester.

I’m totally committed to my 2 days teaching my amazing Y1 class this year: I hope they can learn as much from me as I will from them. I’m always happy to promote the good work of other people & look for ways to collaborate, so be in touch.

I’ve got more plans than time, and more ambition than realism, but hopefully in one way or another I can play my part in enriching primary maths. I will also keep posting as many bits as possible on my social media feeds in the distant hope that it will inspire someone somewhere.

Have a great 2016-2017 school year!

Questions and Images for Deepening, part 4

Each half-term I’ve been blogging questions and images used to deepen learning in maths (hope they’ve been useful). Next year I’m going to write a resource for each year group made up of lots of these types of questions. I hope they’ll be the ultimate ‘go to’ tool for building deep mathematical thinking into daily lessons, enabling teachers to stretch children’s thinking in all areas of the curriculum.

This half-term I’ve been mainly based in my class, so the questions here are primarily from year 6.  To begin with, finding the fraction of the shape that is blue where the shape is divided into differently sized pieces:
fraction shape

Then a question structure, used in two ways, that allows children to explore the size of fractions:
fractions qs

With negative numbers, we used spatial reasoning to estimate the size of the covered numbers:
-ve 1

Here is a simple negative number question structure:
-18 difference 1

And a visual representation to provide a scaffold where necessary:
-18 difference 2

Looking at rounding numbers, here’s a simple statement that children can explore and exemplify:
Rounding 7

And another that leads to exploring patterns in rounding (adjust the number under the orange box):
Rounding 4

To deepen, a question drawing together an understanding of rounding and finding the area of a right-angled triangle:
Rounding 9

Finally, a question used in year 4 where spatial reasoning is used to identify a coordinate point:

This link gives information about the INSET training and school support that I can offer.

Improving reasoning at the point of answer

Here’s a simple, cost-free, whole-school idea for improving mathematical reasoning – when children give an answer to a question, don’t tell them (or infer to them) in that moment whether the answer right or wrong.

The basic principle is that the moment that a person answers a question, they are likely to go through an intense mental process to check that their calculation is correct. When probed, a child will justify, draw, explain, generalise and reason. The moment after the point of answer is precious, potentially very powerful and too often I have taken it away from the children in my class.

This will also demonstrate to the children that what you really value is their thinking, their justification, their strategy; not whether they have the correct answer. In doing so, especially when it is a collective approach, we will reduce the children’s anxiety about whether or not their answers are correct.

I was struck by the importance of valuing process over answers again this week. A child in my class was struggling with the calculation 1-0.003, so we had a conversation that went something like this:

Me: Ok, so what’s 1000-3?
Child: 997.
Me: How do you know?
Child: (silence, looks at me like I’m daft) Because it is.
Me: I know. But how did you know that? How did you work it out?
Child: It just is.

And so the conversation continued, with me trying to make a link between the two questions. What screamed out at me was that in order to facilitate a true understanding of maths, and understanding that can be built on, strategy must be the thing that is discussed, promoted and celebrated.

We know that, as teachers, our words have great power. I hope, in future, to use mine with ever more precision.