Aaron Paquet-Smith
@ronpaq.bsky.social
Maths teacher based in Paris. Nerdy about pedagogy and task design. Sharing what works (or not!) in my classroom
Professeur de mathématiques à Paris. Passionné par la pédagogie. Je partage ce qui fonctionne (ou ne fonctionne pas !) dans ma classe
he/him
Professeur de mathématiques à Paris. Passionné par la pédagogie. Je partage ce qui fonctionne (ou ne fonctionne pas !) dans ma classe
he/him
Thanks for sharing. I think I'll need to set aside some time to work through this one.
November 13, 2025 at 4:39 PM
Thanks for sharing. I think I'll need to set aside some time to work through this one.
I was also thinking this. But it's not as simple as left and right shifts because the x^0 term disappears when differentiating. So you can't right shift just to undo what you did. But it doesn't feel enough to sufficiently explain the problem because it's not just about the constant.
November 13, 2025 at 4:27 PM
I was also thinking this. But it's not as simple as left and right shifts because the x^0 term disappears when differentiating. So you can't right shift just to undo what you did. But it doesn't feel enough to sufficiently explain the problem because it's not just about the constant.
Reposted by Aaron Paquet-Smith
One of my favourite xkcd's
November 13, 2025 at 3:56 PM
One of my favourite xkcd's
Hmm. I'm a bit stuck thinking about that question, other than that the gradient function won't uniquely determine the function itself. But that's not really an answer. Did you have any intial thoughts?
November 13, 2025 at 3:45 PM
Hmm. I'm a bit stuck thinking about that question, other than that the gradient function won't uniquely determine the function itself. But that's not really an answer. Did you have any intial thoughts?
I like this. This is a very nice thing to make them aware of. Today I was trying to get them to make up their own possible integrals so not too far off, really.
November 13, 2025 at 3:42 PM
I like this. This is a very nice thing to make them aware of. Today I was trying to get them to make up their own possible integrals so not too far off, really.
That's reassuring, thank you. Thank you for your perspective.
November 13, 2025 at 2:00 PM
That's reassuring, thank you. Thank you for your perspective.
It sounds like, for you, time is the biggest factor in proposing that inspection is the better method for these questions. Are there any other factors?
How about ones like this?
How about ones like this?
November 13, 2025 at 1:40 PM
It sounds like, for you, time is the biggest factor in proposing that inspection is the better method for these questions. Are there any other factors?
How about ones like this?
How about ones like this?
I see, like these common forms.
November 13, 2025 at 1:40 PM
I see, like these common forms.
I'm very interested in the arguments for and against offering them substitution as a replacement to inspection at this stage of learning, appreciating that substitution is not explicitly required.
November 13, 2025 at 1:37 PM
I'm very interested in the arguments for and against offering them substitution as a replacement to inspection at this stage of learning, appreciating that substitution is not explicitly required.
I can see the argument that I should ask them to persist with inspection. However, I think I realistically would use substitution to reduce some of the mental load with constants where mistakes with fractions and negatives are easy to make.
November 13, 2025 at 1:37 PM
I can see the argument that I should ask them to persist with inspection. However, I think I realistically would use substitution to reduce some of the mental load with constants where mistakes with fractions and negatives are easy to make.
Yes, we did lots of that. The task I chose was the attached, from mathshelper.co.uk. I allowed them to choose between inspection and using subsitution and they generally selected substitution for 19, 22, 25, etc., with fractional exponents.
November 13, 2025 at 1:37 PM
Yes, we did lots of that. The task I chose was the attached, from mathshelper.co.uk. I allowed them to choose between inspection and using subsitution and they generally selected substitution for 19, 22, 25, etc., with fractional exponents.
Interesting. What makes an inspection question explicitly inspection, and not substitution? Do you have any reasons for this?
November 13, 2025 at 1:19 PM
Interesting. What makes an inspection question explicitly inspection, and not substitution? Do you have any reasons for this?
I did the standards unit matching of mixed derivatives and integrals. And we did it on coloured paper because it was an "important lesson". It took an hour. I think it was worth it.
November 13, 2025 at 1:18 PM
I did the standards unit matching of mixed derivatives and integrals. And we did it on coloured paper because it was an "important lesson". It took an hour. I think it was worth it.
I have taught them both, and I am allowing them to follow their instinct on when to choose each. But the curriculum has really divided these up as separate skills and I worry I am overlooking something.
November 13, 2025 at 9:19 AM
I have taught them both, and I am allowing them to follow their instinct on when to choose each. But the curriculum has really divided these up as separate skills and I worry I am overlooking something.
Should we specifically delineate "integration by inspection"/"integration by substitution" questions and teach them separately?
November 13, 2025 at 9:19 AM
Should we specifically delineate "integration by inspection"/"integration by substitution" questions and teach them separately?
What would you do? I could go and work on number sense, but I'm mindful of the Alf Coles argument that you can't keep going back. Maybe I need a task something like: which of these derivatives/integrals have been done correctly (spot the error)?
November 13, 2025 at 6:02 AM
What would you do? I could go and work on number sense, but I'm mindful of the Alf Coles argument that you can't keep going back. Maybe I need a task something like: which of these derivatives/integrals have been done correctly (spot the error)?
As much as normal. But number sense is weak. Consistency in subtracting one from the exponent was already challenging when a fraction or negative. Now we're lost on when to add one, when to subtract one, and knowing what they actually did when they go from -4 to -5, for example. We're in a pickle.
November 13, 2025 at 5:59 AM
As much as normal. But number sense is weak. Consistency in subtracting one from the exponent was already challenging when a fraction or negative. Now we're lost on when to add one, when to subtract one, and knowing what they actually did when they go from -4 to -5, for example. We're in a pickle.
What might I have done wrong? #Mathschat #Alevelmaths
November 12, 2025 at 4:30 PM
What might I have done wrong? #Mathschat #Alevelmaths
I'm not good at, and do not enjoy, teaching geometric constructions. I find it is such a gear shift from the rest of the curriculum -- and lots of behavioural issues to worry about!
November 9, 2025 at 8:09 AM
I'm not good at, and do not enjoy, teaching geometric constructions. I find it is such a gear shift from the rest of the curriculum -- and lots of behavioural issues to worry about!