The Primary Maths Podcast

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 [email protected].

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.

Addition is one of the first mathematical operations children meet, but that doesn’t mean it’s simple.

In this episode of AfterMaths, Jon and Becky take a closer look at what it really means to understand addition. They explore why knowing lots of different strategies matters, why column addition should be a tool rather than the destination, and why Jon has, somewhat inexplicably, developed a favourite addition calculation.

There’s also some Wordle mathematics, new research into the importance of spatial reasoning and partitioning, and a trip through the surprisingly long history of the humble + symbol.

01:16 – Can mathematics help you beat Wordle?

Researchers at Binghamton University have used Shannon entropy and information theory to develop a Wordle strategy that solved more than 99% of puzzles in simulations.

05:50 – What’s your favourite addition?

Jon nominates 8 + 7, and uses it to explore number bonds, partitioning, near doubles, compensation and the different ways children might see the same calculation.

10:58 – The structures of addition

What is the difference between aggregation and augmentation, and do children actually need to know those words?

15:00 – Column addition: servant or master?

Written algorithms are incredibly useful, but they aren’t automatically the most efficient or sophisticated strategy. Jon and Becky discuss why children need a repertoire of approaches and the freedom to choose between them.

20:54 – Research: partitioning is spatial as well as numerical

New research from Chelsea Cutting explores how spatial visualisation, spatial structuring and proportional reasoning can support young children’s understanding of partitioning and fractions.

26:33 – Where did the + symbol come from?

Becky heads down a mathematical-history rabbit hole, from ancient Egyptian walking legs to medieval shorthand and the emergence of the modern plus sign.

34:30 – Free primary maths CPD

Jon and Becky look ahead to Twinkl’s programme of free live primary maths sessions, including subtraction, problem solving, cognitive load and mathematical talk.

And next week: subtraction.

Binghamton University: researchers use maths to crack Wordle

Research paper: Solving Wordle Using Information Theory

Play Wordle

Play Nerdle

Chelsea Cutting: Exploring the critical role spatial reasoning plays in young children’s early partitioning development

Further reading:

Wilson, Myers, Edgington & Confrey: Fair Shares, Matey, or Walk the Plank

MacTutor: Earliest Uses of Symbols of Operation

Explore Twinkl’s upcoming TeachMeet events

Twinkl Primary Maths CPD collection

John Dewey, Logic: The Theory of Inquiry (1938):

The Primary Maths Podcast: AfterMaths

With Jon Cripwell and Becky Brown.

New episodes exploring the ideas, research and slightly unexpected tangents behind primary mathematics.

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.

Who decided how long a metre should be? Why is a mile 1,760 yards? And what connects the French Revolution, an expedition from Dunkirk to Barcelona and the speed of light?

In this AfterMaths Summer Special, Jon and Becky explore the messy, surprising and occasionally bewildering history of measurement.

They begin in a world before standard units, when lengths were measured using hands, feet, cubits, spans and paces. These methods were convenient and widely understood, but rather less useful when accuracy mattered and everybody’s body produced a different answer.

From there, they investigate the historical accumulation that gave us imperial units, including the supposed connections between inches and barleycorns, feet and actual human feet, and miles and Roman paces.

The story then moves to revolutionary France, where mathematicians and astronomers attempted to create a universal decimal system based on the dimensions of the Earth. Their effort to establish the metre involved years of surveying, triangulation, political upheaval, arrests and the inconvenient discovery that neither the Earth nor their measurements were quite as perfect as hoped.

The metre was later represented by a platinum-iridium bar, then by a wavelength of light and, finally, by the distance light travels through a vacuum in a precisely defined fraction of a second.

It is a journey from body parts to universal constants, with plenty of mathematical history, questionable conversions and the inevitable disagreement about whether a pace and a “dolly step” are the same thing.

Explore The Primary Maths Podcast and more from Twinkl:

https://www.twinkl.co.uk/resources/twinkl-podcasts/primary-maths-education-podcast-twinkl-podcasts

We always love hearing from listeners. Send your questions, episode ideas and examples of maths hiding in everyday life to:

[email protected]

Subscribe to the podcast newsletter on Substack:

https://primarymathspodcast.substack.com/

Connect with Jon on LinkedIn:

https://www.linkedin.com/in/joncripwell/

If you enjoyed the episode, please follow the podcast, leave a rating or review, or share it with a colleague. It really helps more teachers discover the show.

Thanks for listening, and as ever, keep doing the maths.

Probability often feels as though it should be intuitive, right up until the mathematics tells us that our instincts are completely wrong.

In this AfterMaths Summer Special, Jon and Becky explore the strange mathematics of chance. From rainy-day board games and rolling two dice to coin-toss streaks, lottery numbers and casino myths, they investigate why humans are so determined to find patterns in genuinely random events.

Why is seven the most likely total when rolling two dice? How can just 23 people produce a better-than-even chance of two sharing a birthday? Are 1, 2, 3, 4, 5 and 6 genuinely bad lottery numbers? And after choosing between three mysterious doors, why should you abandon your original choice?

The episode concludes with the famously counterintuitive Monty Hall problem: three doors, two goats, one car and a very good mathematical reason to switch.

Expect hidden maths, questionable gambling strategies and several probability problems capable of making your brain hurt.

Explore The Primary Maths Podcast and more from Twinkl:

https://www.twinkl.co.uk/resources/twinkl-podcasts/primary-maths-education-podcast-twinkl-podcasts

We always love hearing from listeners. Send your questions, episode ideas and examples of maths hiding in everyday life to:

[email protected]

Subscribe to the podcast newsletter on Substack:

https://primarymathspodcast.substack.com/

Connect with Jon on LinkedIn:

https://www.linkedin.com/in/joncripwell/

If you enjoyed the episode, please follow the podcast, leave a rating or review, or share it with a colleague. It really helps more teachers discover the show.

Thanks for listening, and as ever, keep doing the maths.