What have your students taught you?

I’ve been teaching/ studying maths for 7 years, so I always thought I was pretty good at factorising quadratic equations :sweat_smile:

But last year, one of my GCSE students showed me an amazingly simple method for factorising quadratic equations, that I had never seen before, and it completely stunned me!

The method was to split the middle term in two and cut the equation in half, factorising each side individually and then put it back together (I can give an example if anyone’s interested?). It completely changed the way I’ve been teaching the subject, and I’ve not looked back since!

Has anyone else had a similar experience? What have you learnt from your students?


That’s so cool!
I teach languages, mostly German, so my students teach me a lot about their various countries and origins, as well as their diverse backgrounds. I now know all about the housing situation in Sydney and what it’s like growing up in Luton! This cultural aspect is one of my favourite reasons for teaching language.
Also, they are very good at seeking out resources. Because of my students, I now know about a German bakery in London, several online German resources, and a book of simple German stories. This is really great because I can tell my other students about it, who can then benefit as well.


Yes! I absolutely love using this method especially when the coefficient in front of x^2 is not 1.

Similarly, one of my students showed me the Grid Method (also known as the Box Method) which is an alternative to FOIL for expanding brackets. It works so well for students who tend to forget about multiplying out certain terms or multiply out the same terms twice. You can also use it backwards for factorising quadratic equations. Here is a link to a YouTube video where you can find out more if you’re interested :blush:


I never really understood how FOIL method can help, so thanks for sharing the grid method, I’ll have to use that!

A student once pointed out to me that the ‘claw’ you draw over brackets when you expand them sort of looks like a Santa’s hat… and now I can’t not notice it!

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I have students living in Switzerland who I teach German to, and they teach me the Swiss variations. As a lover of dialects I find this fascinating.


My students teach me what it’s like where they live compared to where I live. I have a student who lives in Saudi Arabia and one day he showed me a sand storm outside of his window and I showed him the snow outside my window. They tell me about everyday things like having to travel an hour by bus to get to school. I love learning everyday things like this from them.


My maths students teach me all the time! Just one of the benefits of tutoring.

Here are some of my favourites:

For rounding numbers: five and above, give it a shove!

For mean, median, mode and range (sung like hey diddle diddle):
Hey diddle diddle
The medians the middle
You add and divide for the mean
The mode is the one you see the most
And the range is the difference between

The circle song!


That song is class! I think you’ll also like these.

It’s a whole playlist of Maths parodies of popular songs with “Quadrilaterals” (sung like Radioactive by Imagine Dragons) being probably the most cringe worthy :see_no_evil:

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Thanks Anna, I’m going to check that out!

I love these songs! :joy:

Just read your post and am intrigued. I have problems explaining where the coefficient of x^2 is not 1 giving issues with the x values. Methods I have seen are too complicated so I tend to get them to play with the possible integers and factors of the x^2 term. Help Please!

Hi David, I have factorised an example below. Basically multiply the first and the last coefficient, then look for factors. Then look for a pair of factors that add up to the middle coefficient. Hope it makes sense!


That’s exactly it! I think this method works so well because it simplifies something complicated to things that most students know how to do (look for factors with x^2 coefficient = 1, factorise a linear equation) :blush:

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Great: that is very neat. I will use it from today. Thanks!