ProfSmudge
@profsmudge.bsky.social
School maths should be more than tables and algorithms. I try to write materials that show that. Dietmar Küchemann
2½ heads. How many legs?
November 14, 2025 at 10:39 AM
2½ heads. How many legs?
I bought this wonderful ex-Uni-Leicester-Library book for £1. What was the library thinking of?!
November 13, 2025 at 11:09 AM
I bought this wonderful ex-Uni-Leicester-Library book for £1. What was the library thinking of?!
These authors provide a useful taxonomy of proof schemes:
Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234-283).
Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234-283).
November 9, 2025 at 12:20 PM
These authors provide a useful taxonomy of proof schemes:
Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234-283).
Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234-283).
#NotMyBBC This is Fiona Bruce's typically negative intro to Question Time this week:
"Why is it so hard to keep prisoners in prison?
Rachel Reeves, should she quit if she raises taxes?"
The obvious answer:
"We don't fund the legal system properly. Be brave, Rachel, please raise taxes."
"Why is it so hard to keep prisoners in prison?
Rachel Reeves, should she quit if she raises taxes?"
The obvious answer:
"We don't fund the legal system properly. Be brave, Rachel, please raise taxes."
November 8, 2025 at 11:07 AM
#NotMyBBC This is Fiona Bruce's typically negative intro to Question Time this week:
"Why is it so hard to keep prisoners in prison?
Rachel Reeves, should she quit if she raises taxes?"
The obvious answer:
"We don't fund the legal system properly. Be brave, Rachel, please raise taxes."
"Why is it so hard to keep prisoners in prison?
Rachel Reeves, should she quit if she raises taxes?"
The obvious answer:
"We don't fund the legal system properly. Be brave, Rachel, please raise taxes."
Aims like this are all very well, but the trouble is, though we might be able to impose a coherent order on elements of the school maths curriculum, children's thinking doesn't work that way; their ideas fluctuate and evolve and do so in individual ways.
November 6, 2025 at 5:11 PM
Aims like this are all very well, but the trouble is, though we might be able to impose a coherent order on elements of the school maths curriculum, children's thinking doesn't work that way; their ideas fluctuate and evolve and do so in individual ways.
#MathsUntangle Week13. Using a calculator to enhance the concept of multiplication
mathsuntangle.blogspot.com
mathsuntangle.blogspot.com
November 4, 2025 at 5:57 PM
#MathsUntangle Week13. Using a calculator to enhance the concept of multiplication
mathsuntangle.blogspot.com
mathsuntangle.blogspot.com
Nice item, UKMT, but your stricture of "please don't post an answer" means we don't get the pleasure of other people's methods - only your one, often rather formal solution.
Here's the gist of a method I came up with.
Here's the gist of a method I came up with.
October 31, 2025 at 12:20 PM
Nice item, UKMT, but your stricture of "please don't post an answer" means we don't get the pleasure of other people's methods - only your one, often rather formal solution.
Here's the gist of a method I came up with.
Here's the gist of a method I came up with.
USA making a comeback? But what about the UK?
October 29, 2025 at 9:28 AM
USA making a comeback? But what about the UK?
Circle(s) is the key, I think!
It seems like we don't even need those two angles (a, b) to be equal.
In this diagram, the shaded triangles are congruent (SAS) and so both bases are 5root2.
[Seems too simple - am I missing something??]
It seems like we don't even need those two angles (a, b) to be equal.
In this diagram, the shaded triangles are congruent (SAS) and so both bases are 5root2.
[Seems too simple - am I missing something??]
October 26, 2025 at 5:56 PM
Circle(s) is the key, I think!
It seems like we don't even need those two angles (a, b) to be equal.
In this diagram, the shaded triangles are congruent (SAS) and so both bases are 5root2.
[Seems too simple - am I missing something??]
It seems like we don't even need those two angles (a, b) to be equal.
In this diagram, the shaded triangles are congruent (SAS) and so both bases are 5root2.
[Seems too simple - am I missing something??]
Similar kind of diagram. I'd like angle a to equal b (red dot, orange square)
October 26, 2025 at 4:44 PM
Similar kind of diagram. I'd like angle a to equal b (red dot, orange square)
#MathsUntangle The blog has suddenly been discovered in China. What does it mean? Should I be worried?
October 24, 2025 at 8:54 PM
#MathsUntangle The blog has suddenly been discovered in China. What does it mean? Should I be worried?
Gulp! Beaten 4-nil.
Maybe we do have join up with those other maths associations.
Maybe we do have join up with those other maths associations.
October 22, 2025 at 9:33 AM
Gulp! Beaten 4-nil.
Maybe we do have join up with those other maths associations.
Maybe we do have join up with those other maths associations.
This is from Liping Ma. She found that Chinese teachers were much better at coming up with a story than USA teachers....
October 21, 2025 at 10:54 AM
This is from Liping Ma. She found that Chinese teachers were much better at coming up with a story than USA teachers....
Yes. This really resonates with me - and my younger self!
October 18, 2025 at 10:54 AM
Yes. This really resonates with me - and my younger self!
#MathsUntangle Week 13. Using a calculator to gently move away from the notion of multiplication as repeated addition.
mathsuntangle.blogspot.com
mathsuntangle.blogspot.com
October 17, 2025 at 1:49 PM
#MathsUntangle Week 13. Using a calculator to gently move away from the notion of multiplication as repeated addition.
mathsuntangle.blogspot.com
mathsuntangle.blogspot.com
#MathsUntangle And here's the second best....
October 17, 2025 at 8:43 AM
#MathsUntangle And here's the second best....
#MathsUntangle Probably the best fractions task I've ever written (at least I thought so at 4 am this morning....)
October 16, 2025 at 11:49 AM
#MathsUntangle Probably the best fractions task I've ever written (at least I thought so at 4 am this morning....)
#MathsToday Working with two Y11 students yesterday, we checked to see whether 121 was divisible by 3.
The division 121÷3 gave us 40 r1.
I suggested we could treat the remainder as 1÷3 which proved to be very challenging.
The division 121÷3 gave us 40 r1.
I suggested we could treat the remainder as 1÷3 which proved to be very challenging.
October 15, 2025 at 11:52 AM
#MathsToday Working with two Y11 students yesterday, we checked to see whether 121 was divisible by 3.
The division 121÷3 gave us 40 r1.
I suggested we could treat the remainder as 1÷3 which proved to be very challenging.
The division 121÷3 gave us 40 r1.
I suggested we could treat the remainder as 1÷3 which proved to be very challenging.
They remind me of this ICCAMS lesson, though your tasks seem mindbogglingly more difficult!
October 15, 2025 at 9:18 AM
They remind me of this ICCAMS lesson, though your tasks seem mindbogglingly more difficult!