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Exam Maths versus School Maths

When Ofsted look for continuous progress in maths lessons, what subject is it that they are thinking of? When SLT make 10 minute snap observations in which they expect to see students making progress, are they talking about the subject we know as mathematics? In the introduction to the Horizon episode on the proof of Fermat’s last theorem, Wiles describes the process of doing mathematics very beautifully (YouTube Link). Martin Gardiner described that wonderful moment when you realise you have found a solution as an Aha Moment (Article). Cleary, Ofsted and SLT are not talking about this subject, because they would know that moving forward mathematically requires an indeterminate period of struggle, followed by a dramatic shift. Progress modeled not by a linear function, but by a step function. Continue reading Exam Maths versus School Maths

Why Learn Maths

Just before Easter I ran a session for the A Level mathematics groups in the Harris Academy group in South East London. I can tell you it was pretty daunting in the small hall, but with something like 120 sixth form students, who had chosen me over another talk, about options, I think. However, can I publicly thank (a) the teachers at Harris Crystal Palace who invited me and most especially (b) the students who attended for reminding me what fun it is to talk about maths to young people. I’ll be applying for a teaching job again, next … Continue reading Why Learn Maths

Maths Trails

The ATM/MA London branch meeting today was a wander round Parliament Square, up Whitehall and Round Trafalgar Square. Four groups of maths teachers made the trek and were intrigued to see this most famous bit of London in a different light. The trail is one of a number that I prepared during my time working for maths Year 2000 and it’s great to see it used again. To support the session, I set up a new web sight with the great URL of . You’ll find PDF and Word versions of all of my trails plus links and details of a load of other trails and trail related materials. Please visit and most especially, please contribute, you maths trail fans with your own ideas, materials and stories.

In the end, it’s just great to get out and about and look at things in a different way. So, take the opportunity and get your students out too!

Mathematics <> Calculating

There is much to agree with in Conrad Wolfram’s lecture in TED.

In Uncle Petros and Goldbach’s Conjecture Doxiadis’ main character refers to anything in a mathemaical problem that could be done by a machine as ‘shopping maths’. Wolfram has the same view and asserts that we should focus on those elements in the problem solving process that are NOT shopping maths. So far, so good.  The problem is that Wolfram is stuck in a world that sees practical problem solving as somehow mathematical. He even uses the tired example of keeping track of your mortgage. Clearly people actually do this by looking at their statement and seeing how much they are paying, they do not engage with the calculations required to analyse the payments. As he says, in the real world, solutions are messy. The trick is (a) to develop opportunties to solve such messy problems in a school setting while keeping them real and (b) to put learners into settings where they actually care about the outcomes to the problems. Serious past experience does not auger well for the possibilities.

It is also troubling that doing mathematics by hand is ridiculed quite so comprehensively. Those quirky souls in the Isaac Newton Institute for Mathematical Sciences at Cambridge had chalk boards fitted in the seminar rooms, specifically to ensure that they can do their mathematics by hand. The problem for Wolfram is that he sees mathematical activity as necessarily applied. He is right to critique a school curriculum which is essentially a curriculum in pure mathematics dressed up as somehow useful, with a cloth of applicationm draped over an algorithm exercise. However, that does not mean that we should only be solving problems coming from the ‘real-world’, implying the entirely mathematical, i.e. pure-maths world is not why we should be teaching maths.

It is a genuinely good thing to see these sentiments aired and tempts the next steps … (i) an inclusive view of mathematics as an end in itself and a language for application, and (ii) a critical, credible view of how such thinking can be formatted for an institutional, compulsory, age specific, school system such as we work with.

My Dear Watson

So, the producers of the new Sherlock Holmes movie went to real Oxford mathematicians to give a blackboard full of maths look authentic, but they go got more than they bargained for. They developed a code based on clues left for Moriaty’s interests and specialisms and even scripted a lecture he is shown giving. Now imagine the possibilities for the classroom. The desire to keep it real, consistent and authentic, even though no-one would ever check. That’s the real mathematical mind at work!

We have a neat double sided version of an old pub game called shut-the-box. You roll two dice and flip down numbered pieces totaling the dice score, your score is what’s left when you cannot go. There have been two types of response from secondary maths teachers to this:

1. That’s much too easy for our kids.

2. How could I analyse and describe the structure of this game.

I think we can call this the shut-the-box test to find out where people actually teach mathematics.


I had an interesting conversation with a former maths teacher who was telling me how much she disliked ‘investigations’. She said that you could never tell whether a student had done the work themselves or if their Dad had done it for them. It was clear to me that steering the conversation round to wondering about the difference between investigating mathematically and submitting GCSE coursework, wasn’t going to get me anywhere, so I had to nod and force a polite smile. On one level it was deeply depressing how pleased maths teachers were when GCSE coursework was abandoned for maths exams. On the other, the whole process had been so discredited … Continue reading Assessment

Check out my New HP39/40GS training page. It’s in the Courses Menu … Here you’ll find links to getting the emulators in the UK, my activities pack, the HP homeview site and I’ve created a couple of training videos to show different aspects of using the machines. Let me know what you think and what else you might like to help you get going with the calculators.

Hello from the Maths Zone

Welcome to my new site. I do a lot of work with ICT in maths education. Most recently I’ve been working with Hewlett Packard Graphing Calculators. Also, my students use TI-nspire and GeoGebra and I’ve been a long term user of Cabri, Sketchpad and Autograph. I’m interested in engaging with mathematical ideas and I think these are all great tools to support thinking to get deeper into the maths. I’m not really interested in practicing for public exams, but I know that’s really important to lots of you. I just think you’ll find the exams easy if you get to actually learn maths!