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

I See Multiplication and Division

I See Multiplication and Division, the follow-up to I See Addition and Subtraction,  allows teachers to make a range of visual representations, allowing children to see the underlying structure of these calculations.

I got the idea for I See Multiplication and Division whilst watching an NCETM demonstration lesson. In the lesson, a year 3 class were writing multiplication number sentences based on different repeated addition images. My immediate thought was ‘how can a teacher create these visual representations?’ For many, probably by spending an age on Publisher or PowerPoint. So the concept for the I See apps was born: making it easier to create visual representations.

Here’s what you can expect from I See Multiplication and DivisionThe Singapore Bar section allows you to create proportionately sized bar models for both operations. Enter the number of bars, the size of each bar and for division the remainder:
Making Singapore Bar

Then the image is created. The calculation shown can be rearranged and the numbers displayed can be hidden as appropriate:

The Dot Pattern feature allows the user to create repeated addition images. How do children calculate the total number of dots?

UxUxU calculations can also be made visual: again, how many dots, and how did you work it out?

Multiplication can be shown as an area model, with the sections appropriately sized:
Area Model

And arrays can be created and adapted in a range of ways. For example, columns and rows can be re-coloured, for example showing 6×12 as double 6×6:

My hope is that I See Multiplication and Division can deepen learning for children and make lesson preparation easier for teachers. It will be available for iPad in the first week in October.

Again, huge credit to Alan Peat ltd for running with the idea and Doug Stitcher for his extraordinary effort coding the app. You are legends!

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!

Telling parents about The Celebrating Maths Project

I’m delighted to announce that The Celebrating Maths Project has been launched! This blog explains a few ways in which teachers can share the project with parents.

Put the page on the school website
1. Copy the following address: http://www.iseemaths.com/celebrating-maths-project/

2. Go into the menu on your school website. Select ‘Custom Links’ and paste the above address. Add the title that you want to display on your site. Click ‘Add to Menu’.
Web page

3. Position the link where you want it to appear on your website.

Send out the letter to parents
I’ve written a letter explaining the aims of the project. It’s posted on the page with all the tasks. It can be printed and sent to parents.
Letter pic

RT tweets from @gareth_metcalfe from school accounts
I have sent out a range of tweets about the project designed to by retweeted from school accounts.

I hope the project helps you to engage parents in the maths learning process!

The Celebrating Maths Project

This is a blog from the summer 2016 when I first launched The Celebrating Maths Project. This is an AMAZING, FREE resource for showing parents how to enjoy doing maths with their children. I’m hoping to release a new set of videos each year – I’ve just been too busy in 2017!

Click here for The Celebrating Maths Project

How to share the Celebrating Maths Project

Premise 1: Given the right task, parents and children can enjoy doing maths together. This communicates to children that you can get a buzz from doing maths – and its valued.

Premise 2: There are many parents who would like to help their children to enjoy and excel in maths; they just want ideas for how.

The Celebrating Maths Project is a series of 3 short videos written to give parents a range of mathematical games and puzzles to play with their children. The first video, for parents of children aged 4-5, gives suggestions for how to draw out maths in everyday situations. The second video, for ages 6-7, shows some basic strategy games that can be played using dice and dominoes. The third video, for ages 8-10, shares ideas for strategy games and puzzles – some of which have been played for hundreds of years!

I trialled the project at my school last Nimyear. I’ll never forget one of the outcomes: a girl aged 6 coming to me with her solutions for how to win at the strategy game Nim. She had practised over the summer with her Dad, and was able to beat me hands-down! They had obviously thought very deeply about the task and enjoyed the challenge.

The videos will be released soon. I’m hoping that schools with post the videos on their website, direct parents to the links on http://www.iseemaths.com or RT tweets from @gareth_metcalfe to share the idea.

It’s not ‘summer homework’ – rather a great way to spend half an hour of a holiday. And it’s free. Please spread the word!

Alternative Uses for I See Addition & Subtraction

I’m delighted to have released iPad app I See Addition and Subtraction with Alan Peat ltd. The app allows teachers to make a range of high quality visual images with a few clicks. Below are three of my favourite alternative uses for the app.

1. What’s the whole? Estimating with the Singapore Bar
The sections of the Singapore Bar are proportionately spaced. If, therefore, I show one of the parts the size of the whole can be estimated with spatial reasoning:
FullSizeRender[3]By clicking on the number boxes, the numbers are revealed:

Alternatively, the whole can be shown and the parts (2 and 4) then revealed:
2. Missing values on 100-square
By clicking on the boxes on the 100-square, the numbers are hidden. Then, with a quick edit on Explain Everything I have made this image – children work out the value of the red boxes:

3. Reasoning with the 100-square
Hide the numbers on the 100-square as below. How many numbers are hidden? And how many different ways can you work it out?
FullSizeRenderDo children add four equally sized blocks? Two pairs of different sized blocks? Or subtract the number of boxes in the middle from the whole?

I’d love to see how you’ve used I See Addition and Subtraction!

For a written explanation (http://www.iseemaths.com/i-see/) or a video demonstration (https://t.co/ZhZAijtxZH) of the app click on the links.


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.

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