What's the point of doing maths?
[Article by Lynne McLure - http://nrich.maths.org/10367 ]
I wonder what answers your class would give to this question. In a research project a few years ago I asked children of all ages what they thought maths was all about, and why they learned it at school. The answers were, in my view, depressing, and I would be prepared to hazard a guess that they would be much the same ten years on.
If you ask mathematicians what maths is, they will usually answer something along the lines of ‘the study of patterns’. Ask most children what they think maths is and they will say it’s all about rules which they need to learn, or facts they have to remember. Ask them why they learn maths and the most frequent answers include something about passing tests, or perhaps being better at handling money when shopping. Those answers arise because many children don't experience real mathematics in their classrooms – they get a proxy for it.
What children should be doing is solving problems, their own as well as those posed by others. Because the whole point of learning maths is to be able solve problems. Learning those rules and facts is of course important, but they are the tools with which we learn to do maths fluently, they aren’t maths itself. It’s similar to the way that learning scales is an important part of learning to playing music fluently – but there’s far more to making music than playing scales.
What could problem solving look like in a primary maths classroom?
In his chapter on thinking mathematically (1992), Alan Schoenfeld suggests that whilst the idea of problems have been a part of the maths curriculum for ever, problem solving has not. And furthermore there are different definitions of what a problem is, and hence what problem solving means.
At one extreme we have sets of 'problems' which are all about practising a technique. In the classroom this typically involves the teacher introducing a task and illustrating the technique, and then the children do lots more 'problems' on the same theme so that they master the technique which becomes part of their mathematical toolkit. Problem solving is interpreted as working through a series of related and predictable questions in order to acquire a particular skill.
However an alternative interpretation is that of Polya (1945). Problem solving in Polya's view is about engaging with real problems; guessing, discovering, and making sense of mathematics. (Real problems don't have to be 'real world' applications, they can be within mathematics itself. The main criterion is that they should be non-routine and new to the student.) Compared to the interpretation as a set of questions on a theme, Polya's is a much more challenging interpretation of problem solving for a teacher to come to terms with, - but has the potential to be much more effective in developing young mathematicians who have an 'understanding of the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics and a sense of enjoyment and curiosity about the subject'.
For Polya, problem solving is:
- Seeking solutions, not just memorising procedures.
- Exploring patterns, not just memorising formulas.
- Formulating conjectures, not just doing exercises.
International Mathematics Competitions
The International Maths Competition (IMC) is an event held every year, in a different country each year, while the The Po Leung Kuk Mathematics competition is held annually in Hong Kong. About 200 pupils from many schools in the greater Cape Town area took part in the first round of the selection competitions to select 8 pupils to represent these two teams. This was narrowed down to 40 pupils (of which 7 were from Sweet Valley) who wrote the second round. Justin O'Connor and Gary Allen were selected to go to Hong Kong.
Previous Hong Kong and IMC representatives
- 2008 Nicole Dunn, James Nevin
- 2009 Jason Bright
- 2010 David Kube
- 2011 Martin Killick
- 2012 Nicholas Lambrecht
- 2013 James Falconer, Tristan Collis, Bradley Farrell
- 2014 Gary Allen, Justin O'Connor
- 2015 Thomas Falconer, Steffan Brundyn
- 2016 Thomas Hobden, Justin Heathcote-Marks
Sweet Valley Resources
There are a number of resources on the link below for Maths at Sweet Valley, including old Grade 7 tests and exams, the Problem of the Week, and Olympiad information.