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Reposted by @teacherbowtie.bsky.social

Maths Inspiration @mathsinspiration.bsky.social · 08/07/2026

On 18 Sept 2:15-3:30pm we're putting on a Year 12 show in Dulwich called 'The Civil Engineering Show'. It'll be FREE. It's not part of the formal MI programme, we won't put it on the website, but if you think your school might want to come email sarahATstandupmathsDOTcom to register your interest.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 13/05/2026

My place might be persuaded. How should I contact you?

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 15/03/2026

I don't disagree with any of the facts here, but the instantaneous dismissal of teacher workload as a consideration could only come from someone who hasn't been at the front of a classroom for a decade. Perhaps he should have tried talking to some teachers as part of his MA?

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 04/02/2026

I translated it all so that they were distances from the origin, thought about the equation they satisfied, and did an expansion to find the product of its roots. I think you can avoid the point case as there is a factor of z everywhere.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 04/02/2026

That sounds like we did it in very different ways!

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 04/02/2026

I can't remember where I adapted it from - it certainly isn't wholly original.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 15/01/2026

In #MathsToday, my Y13 class really enjoyed the first five of these questions (and then the sixth shortly thereafter).

A series of six differential equations for which the left hand side first five is the total derivative of a product.

The sixth, not so.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 11/01/2026

We teach OCR, and never have to do the correction*, I think for more or less this exact reason. *Except in Further Maths.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 11/01/2026

It is worth adding that this does not happen for the mean. Averaging lots of sample means tends to the true mean (which we know from Normal Distribution Hypothesis tests).

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 11/01/2026

That is mean! 'These data' in particular, even though we are told it is a sample.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 11/01/2026

I agree! The real answer is along the lines of: If we repeatedly do this, and average our answers, the average tends to a predictable amount below the real answer, relative to sample size. In order to 'unbias' this, we need to multiply by a factor of n/(n-1), and the n terms cancel out.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 11/01/2026

Hence, by analogy, sample statistics will almost always underestimate population ones. Dividing by n-1 makes th result slightly bigger than dividing by n does, which is good enough.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 11/01/2026

Someone once explained it to me by thinking about the range. If you calculate the range of a sample, you are very unlikely to randomly pick the largest and smallest values, so the range of a sample is almost always going to be too small.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 11/01/2026

n-1 when you are using sample data to estimate the population parameter. n when you have all the data. (But whether you have to do this varies by exam board and Single/Further Maths.)

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 09/12/2025

Could it be along the lines of the numerator having to be always larger than the denominator when added, so there must be an intersection, hence they can't be mutually exclusive?

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 28/10/2025

One of the most interesting and exciting Maths books I have read for some time. Very balanced on its view of Babbage and his contemporaries, and stuffed full of fascinating detail. An excellent way to do some Maths (sort of) over half term.

The Cogwheel Brain by Doron Swade with an empty pint glass.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 23/10/2025

After looking at trig derivatives and the chain rule, I differentiate sin^2 x for my class, ask them to do cos^2 x, and then we look at cos^2 x + sin^2 x, which should obviously be more complicated...

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 08/10/2025

en.m.wikipedia.org/wiki/Anamorp... Is it this? I remember reading something recently about how in some sports they are now added digitally to look 'wrong' from a particular camera angle, and therefore more realistic.

en.m.wikipedia.org

Anamorphosis - Wikipedia

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 13/08/2025

This is also the shape that an orange makes if you peel it in one piece starting at the top. (Presumably for similar reasons?)

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 16/07/2025

The red feels like the odd one out to me.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 16/07/2025

Which gives me back your original graph. Maybe it was right all along?

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 16/07/2025

Here is my suggestion then: Convert it to something parametric (not sure what). Stretch the two x and y equations separately. Make it cartesian again.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 16/07/2025

I think one needs to be 0.5, and the other 2, not both the same.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 14/07/2025

I can reason that out, but it could definitely confuse a pupil.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 14/07/2025

It is neater, but this version doesn't feel complete to me without, for example, a justification that k(sqrt(2)-1) must be an integer. It is tacitly assumed above.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 07/05/2025

A class did one for me an unspecified number of years ago. Such a good gift.

What I like about the Quadratic Formula is not the Quadratic Formula.

You don't need all these big numbers, like ten.

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Reposted by @teacherbowtie.bsky.social

Dr Lucy Rycroft-Smith @ljrycroftsmith.bsky.social · 21/04/2025

Do you like maths? Do you like entertainment? Want to be entertained in a variety show about maths? Come along to the latest Clopen Mic Night and see these cool people (also me and my excellent bandmates): clopenmicnight.com/events/2025-...

clopenmicnight.com

Clopen Mic Night

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 20/03/2025

And there was another page of them somewhere else in the magazine as well.

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Reposted by @teacherbowtie.bsky.social

Karen Campe @karencampe.bsky.social · 08/03/2025

Great post about teaching in the age of LLMs /AI Not #iTeachMath but pertinent to the question of what do we want our students to get out of the learning process. thewalrus.ca/i-used-to-te...

thewalrus.ca

I Used to Teach Students. Now I Catch ChatGPT Cheats | The Walrus

I once believed university was a shared intellectual pursuit. That faith has been obliterated

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 04/02/2025

Did AI discover Prosthaphaeresis? en.m.wikipedia.org/wiki/Prostha... (No, but it is very interesting nevertheless.)

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 03/01/2025

It is Venus! If you look North West of it, you may be able to faintly see Saturn as well. www.timeanddate.com/astronomy/ni... I use this website to find out what things are. There is also a meteor shower tonight that you might be able to see some of!

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 28/12/2024

A modern paradox of the heap! What proportion of watching a film counts as watching a film?

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 24/12/2024

In addition to this, with music it is easy to see/hear the application. Why should I practise scales? Listen to this Mozart concerto. With maths, it is sometimes harder to directly point at the end goal.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 24/12/2024

I picked up Hardy's A Mathematician's Apology for the first time ever this week, and it is full of this. The result is that I am finding it very difficult to read. (Also the relentless classism and sexism, but that is a separate issue.)

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 24/12/2024

When I was at school, we used to look up the assembly hymn in the metrical index, and then pick a different set of words from everyone else. Minutes of fun to be had. (I have enjoyed sight-reading yours a lot - the joy is in when you suddenly recognise the tune.)

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 17/12/2024

It is either lots or not very many is my instinct. Some moderate number like 15 doesn't feel right.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 16/12/2024

Should that third instruction be 'add one more to the third number'? It gives something a little more noteworthy then.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 15/12/2024

There was a session on 3D vectors and Geogebra at the recent AMSP conference. @tombutton.bsky.social may be able to point towards the excellent Geogebra files that were shared.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 15/12/2024

They could both be going in the opposite direction. The dot product always finds the angle between the vectors when they are going 'away' from each other.

Vectors in different directions produce different angles through the dot product.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 15/12/2024

No problem! The angle between a line and a plane is similar. Questions usually specify that they want the acute angle, but sometime you end up with the other one after a calculation.

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teacherbowtie.bsky.social @teacherbowtie.bsky.social · 15/12/2024

I once showed this to a class (having just worked through the quadratic one), and promised them 10 extra points on a future test if they learned it and wrote it down. One of them nearly did it correctly!

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