I have just moved from school teaching to working at Cambridge Mathematics. Despite sadness at leaving the classroom, one of the draws was the opportunity to explore why we teach mathematics the way we do and how could that evolve. I had looked at similar issues at an earlier workplace, the Nuffield Foundation, which is dedicated to education, research and innovation.
In the 1960s they initiated the ‘Nuffield Mathematics Project', a significant attempt at emancipating primary mathematics education from the shackles of ‘the tradition of Victorian arithmetic’. Here’s their beautiful illustration of the problem:
“The Victorian clerk, sitting on a stool in a counting house, kept his ledgers meticulously. He wrote in beautiful copper-plate, his immaculate figures were neatly underlined, and his calculations were always accurate. ... In the twentieth century the pace of life began to quicken ... Speed was also needed. Until comparatively recently [1960s] these three considerations predominated in the teaching of primary school arithmetic – meticulous presentation, accurate computation, speed.”
Current curricula being rooted in the needs of our ancestors is not a recent or local phenomenon. There is much we can delve into here but I’d like to use the words of Houman Harouni, an Adjunct Lecturer on Education at Harvard University. Harouni recently looked at why we teach mathematics the way we do, in particular “Why these topics? Why in this order? Why in this way?”
Early ‘word problem’ from clay tablets from Babylonia (Third Millennium BC):
If a man carried 420 bricks for 180 metres, I would give him 10 litres of barley. If he only carried 300 bricks, how much would I give him?
Harouni found that little has changed over a few thousand years, including the word problems we use! He tracks the inputs to three types of mathematics:
Money or mercantile mathematics (he refers to it as reckoning or commercial-administrative mathematics),
Artisanal mathematics (craft-based mathematics)
Philosophical mathematics
and puts forward a thesis as to why the ‘money mathematics’ has come to dominate our teaching. Another great source of information on this is the NPR ‘All Things Considered’ radio programme.
Our Victorian arithmetic-focused primary curriculum is a direct descendant of reckoning mathematics. Whereas some secondary school topics - such as trigonometry - relate to the artisanal needs of measurement and navigation, the secondary mathematics curriculum in England is still dominated by mercantile needs. And as for the philosophical aspects - they were reserved for the elite, by way of grammar schools and universities.
Harouni gives a nice set of questions to get a quick handle on what type of problems concern these types of mathematics.
- Reckoning mathematics: 12 + 15 = ?
- Artisanal mathematics: 12 of what? 15 of what? (more about measuring than counting)
- Philosophical mathematics: 27 = ?
We could reflect on how and why the mercantile/reckoning tradition became more dominant - Harouni explores this in his research paper, including implications for the present.
Given these ancient strangleholds on our curriculum, we could be asking the question, ‘why do we continue teaching the mathematics the way we do?’ Some would make a case that current school mathematics is divorced from any meaningful use and largely serves as a means of granting and gaining certification. We only study school mathematics to study more of the same until we get certificated. This could descend into a spiral of misery, so rather than looking back at the three roots of present-day mathematics teaching, for now, we will try wiping the slate clean and consider a different set of three questions that could inform future learning and teaching of the subject.
1. What is this beast called mathematics?
2. What are modern day uses of mathematics that could/should drive its learning?
3. How would the above translate to teaching and learning approaches for mathematics?
Interested? Then tune in for future episodes of this blog. In my next post we’ll make a start at defining the beast we call mathematics!