I had the privilege today of being asked in my role as the current President of Engineers Ireland to chair a national symposium on mathematics teaching, organised by Professor Clive Williams and the TCD Faculty of Engineering, Mathematics and Science and hosted at the RIA. The full programme of speakers is here, and about 90 people nationwide attended – third level academics, second and primary level teachers and associations, professional bodies, business associations and public servants – and, for part of the afternoon, the Minister for Education and Science, Batt O’Keefe.

I’ve written a summary of the event here. But I wanted to write a few personal thoughts in this posting.

PJ Rudden, a current Vice President of Engineers Ireland, has led an extensive study on the education of mathematics and science a second level, and we will be launching the study and its recommendations next week during Engineers Week. PJ has heard many anecdotes during his research, but one in particular resonated with me: a secondary school mathematics teacher being astonished that her first year students, straight out of primary school, could not do a simple mental multiplication such as “6 by 8” and needed to resort to a calculator.

I started the symposium this morning by recounting that story, and all that it implied for the use of calculators in primary school and the junior cycle. But then I went live on the internet, and showed the audience the wonderful Wolfram Alpha computational engine – typing in prompts from the audience for complex mathematical manipulation; chemistry; music; a genome sequence; and finishing with the weather forecast for Dublin. If such wonderful and powerful tools extend the use of the simple desktop calculator, what then is the role of the teacher of mathematics, and the lecturer in engineering (or chemistry or music or genomes or weather..) ?

I then proceeded to play one of the various versions of “Shift Happens”, and specifically the version produced for the UK education sector with the conference microphone on full volume and full bass… (:-))

I’ve previously blogged about what I perceive as the revised role of teachers in the internet age: Google (and Bing and Yahoo and perhaps especially Wolfram Alpha) know more than any teacher. Students use the internet and know this, and therefore what today is the value of a teacher ?.. I also noted in that particular posting “It’s not that today’s students have attention deficit, and are incapable of absorption or focus: on the contrary, they immerse themselves deeply – for hours sometimes – in what they find interesting, such as specific games and challenges. The difference today is that students have found a way – the internet – to so much more easily quickly find out what is really interesting, and to rapidly filter out and discard what is mundane.”

So: what is the role of the mathematics teacher in the internet age, how can we in Ireland raise the general level of mathematics competence in our secondary school system, and how can we truly inspire our most talented students ?

For me personally, the true value of mathematics is the training it gave me in spotting patterns. Observing commonality in different situations, abstracting and learning from these to produce a generalisation, and then finally applying a specific generalisation to solve a new situation which I have never met before. As an engineer, and even more so as a software developer, these are absolutely critical core skills. In the world of rapid technology change – “we are currently preparing students for jobs that don’t yet exist, using technologies that haven’t been invented, to solve problems that we don’t even know are problems yet” as “Shift Happens” notes – we need analytical skills for life.

After the lunch break, I reinforced these ideas by explicitly showing visual patterns. There are the absolutely exquisite 3D hypercomplex fractals by Paul Nylander – “Take a good look at God’s wonders: they will take your breath away”. I showed the wonderful polynomial portaits by Sam Derbyshire and Dan Christensen, reported by John Baez. I finished on the more prosaic beautiful fourier transforms of whale songs, generated by Mark Fischer and published this week by New Scientist .

I strongly believe that we need to reset our nation’s view of mathematics. It is not confined to nerds and geeks (like myself, I admit!). It has a timeless beauty, a wonderful inspiration to our soul and what it means to be a human, and a timeless and technology-neutral foundation for wisdom and understanding.

Mathematical appreciation underpins science and the humanities, business and the arts, engineering and innovation. In building the Celtic Phoenix, all of us must rediscover the intense value of mathematics.

Chris

Enjoyed your comments. And I think the close out is what it’s all about. This was touched on again at the EI on Monday. I have been involved in discussion on same in linked in (Irish executives). This ‘beauty’ of mathematics is at the heart of it. Difficult to market the beauty if you have not seen (or recognised) the promised land. People can see it at different ages. Unfortunately, though, unless the mind is opened at primary school, very early secondary level, I see very little hope. A major challenge in primary education. I think we shoudl start there.

Dear Chris,

I was an attendee and although familiar with mathematica, I found your usage of Wolfram Alpha very impressive. I have since shown it to my large science classes in a university here (I lecture mathematics) and it provoked one student to say that “Those last 5 minutes were more useful than all the other lectures”. It’s as close to praise as is likely to come my way for lecturing.

While trying to focus on insight and interpretation of mathematics, rather than procedures which are best relegated to a computer I am faced with a dilemma: that intimacy with functions which I developed by performing countless (menial) derivatives and integrals by hand (which is perhaps common to all successful mathematical graduates of our generation) I am trying to bypass in my own teaching by having students interpret derivatives from contour graphs or data tables rather than compute them from rules. (In general my students dislike this approach but that can be remedied later.)

Introducing the power of this technology to school curriculum maths will displace other “pencil-and-paper-knowledge”. It is a great challenge for us educators to think clearly about which mathematical skills should be technology-independent and which should be developed early as a foundation for evaluating the rather deep knowledge that are only the click of a mouse away. We need to evaluate what consists of a classical education in the information age. I’ll be following your blog for ideas.

Regards,

Kevin

Hi Kevin,

for some reason, your comment ended up being automatically classified as spam – I’ve just found it, very sorry!

I think the best way to introduce mathematical concepts is always visually – anything that can be drawn or shown to illustrate an idea I think always gets best impact.

And with the internet and laptops, visual maths should be increasingly possible..

best wishes

Chris

Hi Chris,

I do a bit of maths teaching part-time and am struck by the lack of calculation skills some students have as a result of over reliance on calculators. I’m getting third year students who can’t figure 2 minus 7.

One other observation. Why are no teachers uploading video tutorials to youtube?

Why doesn’t the government just pick out a few top maths teachers (using ratemyteacher to source) and get them to record a series of videos over the summer. Put the results on a blog and let every teacher use them as a resource. Any student who falls behind on a topic, can then access a video on said topic.

This can be done very cheaply with a normal digital camera, a tripod, a marker and a piece of paper.

see a good example here from an american tutor

Absolutely.

But why rely on the Government at all – why not just go ahead and do it ? [Did the American Tutor in the video need the US Government to help him ?..]

See my further thoughts at http://bit.ly/4ahj9 — specifically suggesting that wikis could be used to foster best practice across our teachers ?

As you say, it just needs a few good maths teachers to work together and put their own initiative together..

best wishes

Chris