Sign In
Sign In
Register for Free
SecondaryMaths

“My Students Were so Engaged They Gave up their Saturday to Discuss Mathematical Proof” – #JustLetMeTeach

One secondary school's extracurricular masterclass sessions let high-attaining students explore topics not usually covered in school, and Leanne Shaw had the pleasure of leading some

Leanne Shaw
by Leanne Shaw
Year 7 maths worksheets
DOWNLOAD A FREE RESOURCE! Year 7 maths worksheets – 72 free, editable printables
SecondaryMaths

To support our new #JustLetMeTeach campaign, we have free primary and secondary teacher packs to download with practical advice to help you reduce your workload, refresh your teaching, and reignite a love of learning for you and your students.


I have recently been lucky enough to teach some masterclasses for the York Independent State School Partnership (ISSP).

The ISSP was set up in 2006 by Bootham School and the City of York Council and now works with nine state and three independent schools in York.

The masterclass sessions are designed for high-attaining KS3 and 4 students to spend nine hours learning about topics that are not usually covered in school.

The masterclasses that I was taking part in were three-hour sessions for Year 7 and 8 pupils, with a different subject each week for the pupils, all relating to the theme of “What is Truth?”.

So, as a mathematics teacher, mathematical proof seemed like an obvious way to link mathematics and truth.

All the pupils involved were able mathematicians who were excited about developing their understanding of mathematics on a Saturday afternoon.

They asked intelligent questions and enjoyed the challenge provided by the tasks. They worked very well with each other, valuing the contributions that they were all able to provide.

We started off by looking at some mathematical puzzles to allow them to become more confident working together, before exploring questions such as “what would life be like without numbers?”, and “what makes mathematics more truthful than other subjects?”.

We then explored what qualifies as a mathematical proof and “proofs without words”, more visual proofs which can convince us that something is true.

After a short break used to digest some of this information we began generalising, for example, how would we represent an even, or odd number, algebraically? What about the square of an even number? Or the square of an odd number?

We used these generalisations to prove facts about even and odd numbers.

When we first talked about proof at the start of the day, the idea of proving that a statement could be true for all numbers up to and including infinity seemed like an enormous task. However, they finished the masterclass being able to complete short, elegant proofs in a few lines.

The pupils left inspired and excited by the work that they had managed to achieve, and I really enjoyed the experience of being able to say #JustLetMeTeach.

Leanne Shaw is a maths teacher and blogger and an #MTPTProject Yorkshire Advocate. You can find her at mathsproblemsolving.wordpress.com and follow her on Twitter at @leanneshawahs.


We’re sharing this article as part of our #JustLetMeTeach campaign, in which we’re inviting teachers to share the moments when they’ve been able to pass on what excites them about their subject, and what has excited their pupils too – whether or not it helps children pass a test.
This is in response to our survey in which nearly 90% of teachers claimed to have taught ‘pointless’ lessons in order to help children pass national tests; 81% said they didn’t have time in the classroom to follow students’ interests; and 79% suggested that greater autonomy would improve the quality of their teaching.

Get involved by using the #JustLetMeTeach hashtag on social media, or get in touch with us on our Twitter and Facebook pages.

You might also be interested in...