Category: Maths ideas

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!

It’s been a wonderful start to the home learning project, the vision for which is described in this short video. During the school closures, I want children to experience rich, emotionally engaging maths learning. I also wanted them to feel as if they are part of a vibrant, real community of children.

Each day, I post a video lesson for Y3/4 children (all Y3/4 lessons here), and a separate video lesson for Y5/6 children (all Y5/6 lessons here). Each video explores a big mathematical idea in small steps and a range of independent tasks are set for children to complete. Everything is free. In the first six weeks, the videos have had 335k views!

Here’s the outline plan for the rest of the school year. I will continue making the videos for the duration of the UK school closures (however long that lasts):
18th – 22nd May: Measures: Money and Time
1st June – 5th June: Data Handing
8th June – 19th June: Fractions
22nd June – 3rd July: Flexible Calculation
6th July – 17th July: Mathematical Puzzles

It’s been thrilling to hear how much the children have loved the lessons and how it’s helped time-pressured parents too:

I want as many teachers and parents to find out about this project as possible. Tell friends, share with colleagues! Lessons can be uploaded onto school websites; many schools retweet my evening tweets each day from their Twitter feeds. Also, if you like the videos it really helps if you give them a thumbs up on YouTube! Here’s the first Y3/4 lesson and here’s the first Y5/6 lesson – they will give a taste of what the lessons are like!

I have also compiled maths games to play with KS1 and KS2 children and I have been running a series of online training sessions for teachers.

I hope you are all keeping well,
Gareth

Here’s a multiplication investigation that I used with a mixed-age Y5/6 class. Before the task we recapped on the grid method (it will become apparent why the grid method was used). Then, the main task was introduced:

Immediately, the children positioned 8 in one of the tens columns and 0 in one of the ones columns. Some children tried 85 x 40, but then we established that the larger digits (8 and 5) need to be placed in the tens columns and the smaller digits (4 and 0) in the ones columns. But where, then, should the digits 4 and 0 be positioned? Which gives the larger product: 84 x 50 or 80 x 54? Will these two calculations give the same answer? This was explored:

We compared these two calculations and asked ‘What’s the same? What’s different?’ The grid method helps to show that multiplying the tens values gives 4000 in both calculations. However, the TO x O parts of the calculation are different. We saw that 80 x 54 gives the largest product. One child even said ‘The short method for multiplying is quicker, but the grid method is better for showing what’s the same and what’s different.’ I show the children an area model to help them to understand the difference between 84 x 50 and 80 x 54:

In the image above, we see the TO x TO part of the calculation. We ask the children to visualise how each image will be changed when the TO x O part of the calculation is also shown (see below):

Of the two calculations, 80 x 54 gives the larger product because we are multiplying a larger tens value by the 4. I also commented that the pair of numbers that are relatively closer together gave the larger product. Then we look at the examples below, comparing pairs of numbers with the same sum that are multiplied:

We see that the pairs of numbers which are closer together have the greater product.

I have run a very similar investigation using a TOxO calculation. Here’s an opening prompt:

And it led into the I See Problem-Solving investigation below. It’s one of the free sample tasks that can be found here:

If you have a go at these investigations or something similar, I’d love to hear about how you get on!

I See Problem-Solving – UKS2 and I See Problem-Solving – LKS2 give a huge bank of rich tasks. There are Worked Examples and Support, Explain and Extend features that help to deepen children’s understanding.

Information can be found here about INSET/Twilight training on developing reasoning and problem-solving. Bookings are currently being taken from late February onwards. For very cost-effective training, you may consider hosting a training event, or running example lessons in your school.