Are we sometimes making maths harder to learn than it needs to be?

In this episode of AfterMaths, Jon and Becky explore cognitive load theory and what it means for teaching primary maths. From trying to remember a recipe to learning a musical theatre routine, they consider why our working memory can become overwhelmed — and what that tells us about the demands we place on children in the classroom.

They revisit some of their own spectacularly overcomplicated lessons, question whether elaborate activities can distract from the mathematics, and explore why knowledge and experience make even difficult calculations feel easier.

Then, inspired by Oliver Burkeman's Four Thousand Weeks, Jon raises another question: are we so focused on preparing children for the maths they'll need in the future that we're forgetting to celebrate what they can do with it right now?

Along the way, they discuss problem-solving, mathematical puzzles, the importance of noticing and why making maths enjoyable doesn't have to mean adding more bells and whistles.

Resources and events

• PlanIt Maths: Explore Twinkl's flexible primary maths scheme – https://www.twinkl.co.uk/l/1djqmc
• Primary Maths Problem-Solving Resources: Discover the latest resources, including Changing the Process – https://www.twinkl.co.uk/l/1djqmc
• FREE Live Professional Development – Informal Approaches to Multiplication: Join Becky for practical ideas and strategies for the classroom – https://www.twinkl.co.uk/l/w7xeg

Also mentioned:

• John Sweller's cognitive load theory
• Richard Mayer's coherence principle
• Oliver Burkeman's Four Thousand Weeks
• Episode 30, featuring Phil Hurd

We'd love to hear from you! How do you help children enjoy and use the mathematics they're learning right now? Email us at primarymathspodcast@twinkl.co.uk.

Subtraction isn't always about taking something away. So why do we so often teach it that way?

Before we get into that, check out our free upcoming CPD sessions:

Informal Multiplication: https://www.twinkl.co.uk/l/w7xeg

Practical Techniques to Reduce Cognitive Load in Primary Maths: https://www.twinkl.co.uk/l/ij2cs

In this episode of The Primary Maths Podcast: Aftermaths, Jon and Becky explore the different meanings of subtraction, why children might find it harder than addition, and how we can help pupils become more flexible and confident mathematicians.

From taking away and finding missing parts to comparing quantities, they unpack the three structures of subtraction and explain why understanding the context of a problem matters far more than spotting keywords.

Along the way, they explore the difference between inverse and opposite, discover the history of the minus sign, revisit the shopkeeper's method of counting change, and even find out why computers often use addition to perform subtraction.

In this episode:

• Why subtraction might be harder than addition
• The three structures: reduction, partitioning and comparison
• Why 'more' doesn't always mean add
• The importance of representations and conceptual understanding
• Counting on as an efficient subtraction strategy
• Why choosing the right method matters more than mastering one procedure
• The surprising history of subtraction and its symbols

Because sometimes, the best way to solve a subtraction problem is not to subtract at all.

PlanIt Maths Scheme: https://www.twinkl.co.uk/l/1djqmc

Problem Solving: https://www.twinkl.co.uk/l/65mp5

The Primary Maths Podcast: Aftermaths — with Jon Cripwell and Becky Brown.

Why do some pupils seem to thrive in maths while others struggle to access the same lesson?

Jon and Becky discuss the latest PISA findings and the widening gap between higher and lower attainers, before exploring what that looks like in real primary classrooms. They talk about teaching for mastery, adaptive teaching, pre-teaching, the pressures of a packed timetable and why taking time to simply observe pupils can be so valuable.

With place value being taught in classrooms everywhere at this point in the year, they also look at why it can reveal so much about what children genuinely understand, rather than what they’ve simply memorised.

Plus, there’s maths in the wild involving an ultra-running teacher, a critically endangered parrot and around 70,000 pints of stolen Guinness.

How can the universe be 13.8 billion years old but the observable universe be around 93 billion light years across?

In this AfterMaths Summer Special, Jon is joined by primary science specialist Sarah Hutson to tackle some of the wonderfully ridiculous numbers involved in trying to understand the universe.

They talk solar eclipses, meteor showers, shooting stars, the speed of light, the size of the Sun and Moon, and why looking into space is really looking back in time.

There is also Sarah's highly scientific game What on Earth Have I Drawn?, a surprising rise in colander sales, the reason total solar eclipses are possible, and an attempt to explain the expansion of the universe using an ant on an elastic band.

By the end, Jon needs a lie down.

Which is probably the correct response to cosmology.

Can maths help you win at games?

In this AfterMaths Summer Special, Jon and Becky explore the line between luck and strategy — and whether understanding the maths behind a game can actually give you an advantage.

They take in Rock Paper Scissors, Noughts & Crosses, chess, a deceptively simple counting game, the chessboard-and-rice problem, expected value, roulette and the mathematics hiding inside Monopoly.

Along the way: why some apparently random games aren’t quite random, why exponential growth gets ridiculous remarkably quickly, why the house tends to win at casinos, and how a little probability might improve your chances during family game night.

Maths can’t guarantee that you’ll win every game.

But it might make people considerably less keen to play Monopoly with you.

Can maths really predict the future?

We can predict the return of a comet decades in advance, but tomorrow's weather can still catch us completely by surprise. In this AfterMaths Summer Special, Jon and Becky explore why some futures are easier to calculate than others.

From probability, forecasts and projections to Halley’s Comet, the phantom planet Vulcan and Edward Lorenz's discovery of chaos theory, they ask how much mathematics can genuinely tell us about what happens next.

There's also the butterfly effect, an unexpectedly important rounding error, the difference between chaos and randomness — and the small problem that human beings refuse to behave like nice, predictable mathematical models.

Especially children.

So, can maths predict the future?

Sort of. Which is perhaps the most mathematically appropriate answer possible.

Podcast Show Notes

What makes a route the best route? The shortest distance? The quickest journey? The cheapest option? Or simply whichever one Google tells you to take?

In this AfterMaths Summer Special, Jon and Becky explore the maths of getting away — from Google Maps and traffic predictions to queues, theme parks and an 18th-century puzzle that helped create an entirely new area of mathematics.

Along the way, they discuss the Seven Bridges of Königsberg, Euler's ingenious solution and what it can teach us about problem solving: representing problems, working systematically, spotting patterns, simplifying and knowing when there might not actually be a solution at all.

Plus: why the other supermarket queue is always faster, whether you should ever switch queues, 99 smartphones causing a fake traffic jam in Berlin, and the deeply troubling emergence of people forming orderly queues at pub bars.

It's maths. It's holidays. It's considerably more Euler than your average trip to Orlando.