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Secondary Magazine - Issue 16

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 08 August 2008 by ncetm_administrator
Updated on 14 August 2008 by ncetm_administrator

Secondary Magazine

Welcome to issue 16 of the NCETM Secondary Magazine. Read on to discover our regular fortnightly features. Why not let us know what you want to see in forthcoming issues? If you have thoughts to share you can also add your comments on the portal.
Never Underestimate Alex
Let me describe Alex.  Alex is the student in top set Year 11 who doesn’t appear to do much. In fact he’s reluctant to put any of his thoughts onto paper for fear of getting it right in front of his peers. He contributes to discussions by asking awkward yet poignant questions. His appearance is becoming increasingly ‘alternative’, pushing the uniform rules to their limits.  So, do you recognise Alex or at least someone similar? Is your Alex the brightest student you are ever likely to teach?

Pierre Fermat (1601 – 1665) might have been an Alex. His peers certainly didn’t perceive him as conventional in his approach, yet his ability to comprehend complex mathematics was remarkable.

“His reputation as one of the leading mathematicians in the world came quickly but attempts to get his work published failed mainly because Fermat never really wanted to put his work into polished form.”  (JJ O’Connor and E F Robertson, MacTutor History of Mathematics)

Fermat was a lawyer by profession and unlike many of the great mathematicians and scientists of his day, pursued his interest in numbers on a part-time basis.  Consequently, he published very little of his work, most of which had only been documented through the many exchanges of correspondence with other mathematicians of his day.

Fermat’s contributions influenced many branches of mathematics, including analytical geometry, calculus, number theory and probability.  Today however, he is best known for ‘Fermat’s Last Theorem’, a conjecture which had infuriated many mathematicians until proved correct by British mathematician Andrew Wiles in 1994.  Ironically, the problem posed did not originate from Fermat but a Greek mathematician called Diophantus of Alexandria, the ‘father of algebra’. The problem posed by Diophantus states that:

xn + yn = zn
has no non-zero integer solutions for x, y and z when n > 2

In response to reading this within Claude Bachet’s published text of Diophantus’ Arithmetica, Fermat wrote in its margin:

“To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain.”

Is this the kind of response which might be anticipated from Alex while answering a GCSE question in his mock exam?

Fermat’s work has withstood careful scrutiny and he was held in high regard by his peers. It is debated as to whether or not Fermat had found a proof to Diophantus’ conjecture. However, unsuccessful attempts to prove the theorem over the following 300 years led to a wealth of other mathematical discoveries.

So does the spirit of Fermat have a place within modern day curriculums as a source of inspiration?  Are his ideas, conjectures and proofs transferable to a Key Stage 3/4 lesson?  Is there a Pierre Fermat in your school?

There are a number of key concepts that underpin the study of mathematics. Pupils need to understand these concepts in order to deepen and broaden their knowledge, skills and understanding.

Applications and implications of mathematics
1.3c Recognising the rich historical and cultural roots of mathematics
(Extracted from The National Curriculum 2007 – Mathematics).

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Secondary Focus - Take a tour of the portal and see what tehre is to bring a sense of enjoyment to your maths lessons  
Visit the Secondary Magazine Archive

Browse... Issue 16
The Interview, Around the regions, An idea for the classroom, 5 things to do, The Diary, Focus on

Browse... PD Activities
Self-evaluation, Why do we teach mathematics?, Learning mathematics in my school, Pathways and options at KS3 to KS5, Mathematical Vocabulary, Revision, Group Work, C/D Borderline, Planning teaching and learning, Technology for learning
Departmental Workshops - Structured professional development activities

Focus on


The Diary - real issues in the life of a fictional Subject Leader


An idea for the classroom


5 things to do


The Interview


Around the regions - news, views and updates from the NCETM Regional Coordinators


Explore the Secondary Forum

Contact us - share your ideas and comments 


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