N pairs of skis were standing leaning against a wall. Kolobok (spherical gingerbread-man type character of Ukrainian folklore) rolled along and bumped the skis. What's the maximum number of pieces Kolobok got cut into by the skis falling on it? (Skis cut along straight planes.)
#MathsEd
Mathematics Teaching 299 now available online https://atm.org.uk/Mathematics-Teaching-Journal-Archive/177734
Design by me
Five free articles for non-members:
Increasing access for a student teacher with a visual impairment
Zahara Hussain, Emily Thouless, René Hartmann and Helen Thouless explore Zahara’s experiences as a student with a visual impairment on Core Mathematics modules during an undergraduate primary education course.
Computational mathematics
Allen Tsui shares some activities for learners aged 8 to 16 to apply mathematics when learning about programming.
Introducing Multicolour Maths
Brook Tate shares his love of mathematical relationships expressed in colour.
Fixing the mathematics transition from primary to secondary
Tom Manners suggests some ways of improving the transition from Key Stage 2 to 3.
Barbara Jaworski (1944–2025)
Peter Gates, Anne Watson and Dave Hewitt remember Barbara Jaworski’s contribution to mathematics education.
#MathematicsTeaching #iTeachMath #MathEd #MathsEd #Math #Mathematics #teaching #pedagogy #didactics #education #design #GraphicDesign #AMiE #MT #MT299
They care about the score.
You care about the data. This unit solves both.
https://eduhacking.com/how-to-turn-afl-fever-into-maths-english/
#Teaching #MathsEd #AFLLesson
Ian Stewart’s (2005) book Game, Set and Math includes 12 puzzles linked to the 12 days of Christmas. A favourite is Five Gold Rings. The five gold rings are arranged to maximise the overlaps. At every overlap there is a diamond. You have diamonds of 1, 2, 3, 4, 5, 6, ... carats. Arrange the diamonds so the total number of carats on each ring is the same.
Try starting small—just two rings, two overlaps and each ring has a total of three carats (1 + 2). Now three rings, there are six overlaps, arrange diamonds of 1, 2, 3, 4, 5 and 6 carats so each ring has the same total.
#MathematicsTeaching #iTeachMath #MathEd #MathsEd #Math #Mathematics #puzzle #teaching #pedagogy #didactics #education #design #GraphicDesign #atm #MT #MT298 #xmas #christmas
Seasonal Values
Each of the symbols in the grid has a value. From the totals given for each row and each column can you work out what they are?
The eight symbols have values 1 to 8 and each has the same value wherever it appears.
An excerpt from the freely-available https://atm.org.uk/write/MediaUploads/Journals/MT298/08.pdf
#MathematicsTeaching #iTeachMath #MathEd #MathsEd #Math #Mathematics #puzzle #teaching #pedagogy #didactics #education #design #GraphicDesign #atm #MT #MT298
The Association for Mathematics in Education launched on 1 December 2025 https://amie.org.uk/
These articles are also available to non-members
AMET and AMiE https://atm.org.uk/write/MediaUploads/Journals/MT298/11.pdf
Sally Bamber and Ashley Compton, with current AMET committee members reflect on AMET’s legacy and potential contribution to AMiE.
ATM and AMiE https://atm.org.uk/write/MediaUploads/Journals/MT298/12.pdf
Helen Madeley on behalf of General Council reflects on ATM’s legacy and the potential contribution to AMiE.
From the MA to AMiE: celebrating a legacy, forging a stronger future https://atm.org.uk/write/MediaUploads/Journals/MT298/13.pdf
Andy Kemp and current trustees of the MA reflect on the MA’s legacy and potential contribution to AMiE.
NAMA and AMiE https://atm.org.uk/write/MediaUploads/Journals/MT298/14.pdf
Ruth Trundley and the current executive committee of NAMA reflect on NAMA’s legacy and potential contribution to AMiE. Ruth Trundley
NANAMIC and AMiE https://atm.org.uk/write/MediaUploads/Journals/MT298/15.pdf
John Barton and current trustees of NANAMIC reflect on NANAMIC’s legacy and potential contribution to AMiE.
#MathematicsTeaching #iTeachMath #MathEd #MathsEd #Math #Mathematics #teaching #pedagogy #didactics #education #atm #amie #MT #MT298
Mathematics Teaching 298 now available online https://atm.org.uk/Mathematics-Teaching-Journal-Archive/177733
Design by me
Free articles for non-members:
For the classroom: seasonal mathematics https://atm.org.uk/write/MediaUploads/Journals/MT298/08.pdf
Sue Pope shares some personal favourites.
When can things be added together? Tom Francome and Colin Foster https://atm.org.uk/write/MediaUploads/Journals/MT298/07.pdf
Tom Francome and Colin Foster find that simple addition is not as simple as it might seem.
Remembering Paul Stephenson https://atm.org.uk/write/MediaUploads/Journals/MT298/17.pdf
Sue Pope remembers Paul Stephenson (1947–2025).
Book review: Descent into Infinity Heather Odell https://atm.org.uk/write/MediaUploads/Journals/MT298/18.pdf
Heather Odell reviews an adventure story with some mathematics, Edward Cookson’s ‘Descent into Infinity’.
Book review: Make Your Own Rainbow https://atm.org.uk/write/MediaUploads/Journals/MT298/19.pdf
Alan Cross reviews ‘Make Your Own Rainbow: a colourful approach to all things STEAM’ by Leonie Briggs from Crown House Publishing.
#MathematicsTeaching #iTeachMath #MathEd #MathsEd #Math #Mathematics #teaching #pedagogy #didactics #education #design #GraphicDesign #atm #amie #MT #MT298
@SmartmanApps
Thanks for you insights.
I think the threading on my server means it's easier to view the whole thread directly at https://dotnet.social/@SmartmanApps/115524576264052792
#iTeachMath #Mathematic sEducation #MathEd #MathEdChat #MathsEd #MathsEdChat
#education #mathematics #math #didactics #pedagogy
@SmartmanApps
Skemp was writing about England in the 1970s.
However, even today, are all learners in all the world’s schools taught the reasons for all the rules, and use constructivist learning?
I’m not sure in fact that instrumental cf. relational understanding are direct analogies of rote cf. constructivist learning.
Perhaps a relevant analogy is atomised cf. connectionist learning, e.g. ‘Alternatives to atomisation’ by Colin Foster (2025), Mathematics Teaching 295 https://www.foster77.co.uk/Foster,%20Mathematics%20Teaching,%20Alternatives%20to%20atomisation.pdf and Teaching to Big Ideas https://www.youcubed.org/resource/teaching-to-big-ideas/
#mathematics #education #iTeachMath #MathematicsEducation #MathEd #MathsEd
@SmartmanApps
It's worth read Skemp's articles as he describes the advantages of Instrumental Understanding as well as Relational Understanding.
Here's a link to the version published in The Arithmetic Teacher, 1978 https://teamone.msuurbanstem.org/wp-content/uploads/2014/07/Skemp-Relational-Instrumental-clean-copy-AT-1978.pdf
This work has been built on by others, including Jo Boaler.
#mathematics #ITeachMath #MathematicsEducation #MathEd #MathsEd
@leon_p_smith
A puzzle from Seymour Papert's Mindstorms:
"A monkey and a rock are attached to opposite ends of a rope that is hung over a pulley. The monkey and the rock are of equal weight and balance one another. The monkey begins to climb the rope. What happens to the rock?"
What is your reasoning and what were your assumptions? If you know the answer, what was your first answer?
@leon_p_smith
‘Mindstorms’ is full of quotable text, here’s just one:
“Imagine that children were forced to spend an hour a day drawing dance steps on squared paper and had to pass tests in these ‘dance facts’ before they were allowed to dance physically. Would we not expect the world to be full of ‘dancophobes’?Would we say that those who made it to the dance floor and music had the greatest ‘aptitude for dance’? In my view, it is no more appropriate to draw conclusions about mathematical aptitude from children’s unwillingness to spend many hundreds of hours doing sums.” — Seymour Papert (p. 43)
#mathematics #ITeachMath #MathematicsEducation #MathEd #MathsEd #SeymourPapert #Mindstorms
@leon_p_smith
Yes, I think programming can be a good way to learn mathematics (and more).
Seymour Papert wrote about this in Mindstorms (1980).
I was fortunate to learn Logo and turtle programming on a modest home computer in my early teens. I don't know which was cause and which was effect, but I still like geometry and programming today.
For those not familiar with Mindstorms, a good summary is at
https://medium.com/bits-and-behavior/mindstorms-what-did-papert-argue-and-what-does-it-mean-for-learning-and-education-c8324b58aca4
#mathematics #programming #Logo #TurtleGraphics #ITeachMath #MathematicsEducation #MathEd #MathsEd #SeymourPapert #Mindstorms
Now suggestions for curious and interesting ‘Mathematics’. This means strange facts, anecdotes, paradoxes, portraits of eccentric mathematicians, mathematical philosophy, quotes and mathematics education.
“The only way to learn mathematics is to do mathematics.” – Paul R. Halmos
“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” – William Paul Thurston
“The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’ but ‘That’s funny…’” — Isaac Asimov
“I used to think that maths teachers were all teaching the same subject, some doing it better than others. I now believe that there are *two effectively different subjects being taught under the same name, ‘mathematics’.*’
...‘relational understanding’ [means]… knowing both what to do and why. Instrumental understanding I would until recently not have regarded as understanding at all. It is what I have in the past described as ‘rules without reasons’, without realising that for many pupils *and their teachers* the possession of such a rule, and ability to use it, was what they meant by ‘understanding’.” Richard Skemp (https://atm.org.uk/write/MediaUploads/Journals/MT077/Relational_Understanding_and_Instrumental_Understanding_–_Richard_R._Skemp.pdf)
#mathematics #MathEd #MathsEd #iTeachMath #iTeachMaths #education #AskFedi #books #quote #quotes
The first two episodes of MT Talk discuss articles from Mathematics Teaching 296 https://atm.org.uk/MT-Talk
Episode 1
Elizabeth Bridgett, Lisa Coe and Jay Timotheus compare and contrast Mike Askew's 1999 article, ‘Teaching numeracy: will we ever learn?’ from MT168 with Jane Hawkins' much more recent, 2025 article, ‘Why purposeful talk in mathematics lessons matters’ in MT296.
Also mentioned in this episode is the 1999 paper ‘Arbitrary and Necessary Part 1: A Way of Viewing the Mathematics Curriculum’, Dave Hewitt's first in a three-part series in For the Learning of Mathematics, as well as Mike Askew’s book, ‘Transforming Primary Mathematics’, published by Routledge in 2011.
Episode 2
Lisa Coe, Fin McLaughlin and Jay Timotheus talk about John Mason's 1987 article, ‘Only awareness is educable’ from MT120, alongside Tom Francome's 2025 article, ‘Everyone can think mathematically’ from MT296.
Fin recommended two books: ‘Thinking Mathematically’, by John Mason, Leone Burton and Kaye Stacey (Pearson, 1982, and 2010) and ‘Researching Your Own Practice: The Discipline of Noticing’, by John Mason (Routledge, 2001).
https://podcasts.apple.com/us/podcast/mt-talk/id1838379708
https://open.spotify.com/show/3cJF2EXKyIe1FTNrRO8xm5
#podcast #ITeachMath #MathematicsEducation #MathEd #MathEdChat #MathsEd #MathsEdChat
#education #mathematics #math #didactics #pedagogy
For people who like to explain maths:
Suppose you have a struggling student, and you need to explain why:
"Probability of one in five"
... is the same as ...
"Odds of one to four".
How would you do that?
#MathEd #MathEdChat #MTBoS
#MathsEd #MathsEdChat
Other HashTags?
Mathematics Teaching 297 now available online https://atm.org.uk/Mathematics-Teaching-Journal-Archive/177732
Design by me
Six free articles for non-members:
For the classroom: fractions
Tom Francome offers activities from LUMEN (Loughborough University Mathematics Education Network https://www.lboro.ac.uk/lumen).
https://atm.org.uk/write/MediaUploads/Journals/MT297/08.pdf
Critical mathematics education student teachers’ perspectives
Manjinder K. Jagdev and her student teachers reflect on their experiences of developing critical mathematics education and social justice themes in initial teacher education courses
https://atm.org.uk/write/MediaUploads/Journals/MT297/10.pdf
Awareness of the division of fractions keep your flipping change to yourself!
Sam Brace describes a unit of work that uses learners’ powers of the mind to understand the division of fractions.
https://atm.org.uk/write/MediaUploads/Journals/MT297/11.pdf
Jan Potworowski the quest to humanise mathematics education
George Knights and Lyndon Baker have prepared this tribute to Jan Potworowski.
https://atm.org.uk/write/MediaUploads/Journals/MT297/13.pdf
Julian Williams teacher researcher theorist. 1954–2025
Geoff Wake and Laura Black celebrate Julian Williams’s contribution to mathematics Education.
https://atm.org.uk/write/MediaUploads/Journals/MT297/14.pdf
I want to remember...
In memory of Julian Williams by Laya Hooshyari.
https://atm.org.uk/write/MediaUploads/Journals/MT297/15.pdf
#MathematicsTeaching #iTeachMath #MathEd #MathsEd #Math #Mathematics #teaching #pedagogy #didactics #education #design #GraphicDesign #atm #MT #MT297
Mathematics Teaching 296 now available online https://atm.org.uk/Mathematics-Teaching-Journal-Archive/177731
Design and cover photographs by me
Four free articles for non-members:
Everyone can think mathematically by Tom Francome
Tom Francome explores ways of developing the mathematical thinking of all students, including low attainers.
https://atm.org.uk/write/MediaUploads/Journals/MT296/02.pdf
Book review Learning with AI by Ian Benson
Ian Benson reviews 'Learning with AI' by Joan Monahan Watson published by Johns Hopkins University Press (296 pages, $24.95)
https://atm.org.uk/write/MediaUploads/Journals/MT296/14.pdf
Book review Breaking images by Pete Wright
Pete Wright reviews ‘Breaking images: Iconoclastic analyses of mathematics and its education’, edited by Brian Greer, David Kollosche, and Ole Skovsmose.
https://atm.org.uk/write/MediaUploads/Journals/MT296/15.pdf
Ole Skovsmose—the man who put the critique in critical mathematics education by Peter Gates
Peter Gates has collated this obituary for Ole Skovmose.
https://atm.org.uk/write/MediaUploads/Journals/MT296/16.pdf
#MathematicsTeaching #iTeachMath #MathEd #MathsEd #Math #Mathematics #education #design #GraphicDesign #atm #MT #MT296 #photography
Happy New Year! Enjoy the January #ProblemSolving Calendar! Share your process here or on post.
Also: BONUS article-teaching strategies for success in #math class.
Sign up to get an email for new posts ✅
#MTBoS #iTeachMath #ClassroomMath #RecreationalMath #MathEd #MathsEd
https://karendcampe.wordpress.com/2025/01/01/january-calendar-problems-3/
The solutions are posted for the December Calendar of Problems! If you've done some #ProblemSolving tell us your favorite solution methods here or in blog comments.
January Calendar coming soon!
#MTBoS #iTeachMath #ClassroomMath #RecreationalMath #MathEd #MathsEd
https://karendcampe.wordpress.com/2024/12/01/december-calendar-problems-3/
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