ProfSmudge
@profsmudge.bsky.social
School maths should be more than tables and algorithms. I try to write materials that show that. Dietmar Küchemann
Would you choose the same diagram or different diagrams for the two tasks?
December 2, 2025 at 1:33 PM
Would you choose the same diagram or different diagrams for the two tasks?
Actually, this makes A and B more equivalent
December 1, 2025 at 10:32 AM
Actually, this makes A and B more equivalent
Which diagram do you prefer here?
December 1, 2025 at 10:19 AM
Which diagram do you prefer here?
Opinions welcome!
November 29, 2025 at 12:47 PM
Opinions welcome!
And we could use Heron's shortest path problem:
November 28, 2025 at 4:56 PM
And we could use Heron's shortest path problem:
If we slide the top vertex of the triangle on the right leftwards to form the triangle on the left, then the length of the red side increases by more than the length of the green side decreases....
[Because of the angles in the two small triangles sharing the 1 unit horizontal base....]
[Because of the angles in the two small triangles sharing the 1 unit horizontal base....]
November 28, 2025 at 11:36 AM
If we slide the top vertex of the triangle on the right leftwards to form the triangle on the left, then the length of the red side increases by more than the length of the green side decreases....
[Because of the angles in the two small triangles sharing the 1 unit horizontal base....]
[Because of the angles in the two small triangles sharing the 1 unit horizontal base....]
- and other possible arrangements of the smaller shape:
November 24, 2025 at 11:19 AM
- and other possible arrangements of the smaller shape:
Wow, thanks. Here's its cousin
November 23, 2025 at 1:25 PM
Wow, thanks. Here's its cousin
It's nice that NCETM is using our ICCAMS task to clarify their thinking on oracy. But how far should one push the use of formal maths language? Is there not a danger that pushing formal language will work against inclusion?
November 21, 2025 at 1:06 PM
It's nice that NCETM is using our ICCAMS task to clarify their thinking on oracy. But how far should one push the use of formal maths language? Is there not a danger that pushing formal language will work against inclusion?
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)
