Tuesday, December 14, 2010

Real Mathemetics


Is this work by Escher art or maths? Increasingly once fixed lines between subject areas are becoming blurred.

Over the years there have many attempts to develop a more active math programme but for all this far too many students leave school with anything but a positive feeling for the subject. The introduction of the mystery of algebra finishes most of us off.

With this in mind one wonders why maths takes up so much time in the primary school day. One reason is tradition - left over from the era of the three Rs. Another is that politicians seem fixated on literacy and numeracy as the key to success. No doubt they are important but they need to be seen as foundation skills to be used in learning contexts. And of course schools simply do what they have aways done without questioning the real purpose of mathematics and the time they give to it.

Recently I read a Intermediate School Maths scheme. The introduction was brilliant -all about linking math to real life contexts ( ideas lifted from the revised NZ Curriculum) but when I turned the page the programme was just a series of traditional maths topics.

For many students maths is a 'no mans land that has never quite yielded its secrets' according to Australian educationalist Garth Boomer. He continues saying like most teachers he, 'dwelt largely on the edges of this domain, secretly envious of the very few people...who are truly mathematicians.' I know the feeling; as do too many students.

Where many teachers now make use of their language times to develop ideas and skills to be used in their inquiry programme maths remains watertight. Maths is taught as cut and dried abstracted from real life; a matter of learning the predetermined processes and steps. Many teachers and students actually like this 'right/wrong' approach.

But maths can be so much more than this and many attempts have been made over the years to introduce a more active exploratory approach but these are lost as children grow older and teachers teach mathematics as this is how you do it. Boomer calls this way of teaching catechism - 'the act of asking questions to which one usually knows the answers and where answers are unchanging'. This kind of maths is 'school, learning' and not related to real life problems. No time for exploring, discovering hidden patterns and challenging ones understandings - more like following a pre-planned tourist guide book. This sort of teaching, Boomer writes, 'does not encourage teachers to leave the beaten track' and to use maths to explore and express ideas. Mathematics teachers, he writes, are among the most conservative of teachers.

Mathematics teaching seems decades behind the the teaching of the language arts and science ( although there is not much science to be seen). No matter what suggestion are made, teachers stick to traditional expectations, no doubt reinforced by expectations of parents, politicians and even the students.

Teachers will only change if their learning theory about teaching maths changes. They will need to change from teaching maths as catechism to one where where they see knowledge as being personally constructed and applied by each learners. This is reinforced in the New Zealand Curriculum which states that learners should be their own 'seekers, users and creators of their own knowledge'.

If teachers change their minds about maths students, in turn, will develop a more positive 'feeling for' mathematics. This needn't mean changing all mathematics. There will still be basic things that will need to be learnt until recall is automatic but for the rest a couple of ideas come to mind. The first is to introduce realistic maths experiences for students to explore (and where possible linked to the current inquiry study) and to do fewer things well. And, as well , if teachers do introduce an active maths programme them less time could be given to maths as it would be demanding to use all current time in such an active way. And maths will be a integral part of other curriculum areas.

One idea would be to make it clear to students the difference between 'practice maths' and 'real maths'. Mathematics is a great field to introduce inquiry learning processes. There are some excellent maths resources in schools to help teachers to begin such an active programme. Most physical science studies require mathematics to solve problems. The field of art provides wonderful areas to introduce aesthetic maths. Mathematics itself has plenty of interesting ideas to explore. Such things as number patterns, symmetry, history of zero, maths in other cultures, and so on. Every subject , once the right maths mindset has been established, involves realistic mathematics.

Such an active approach will need to involve collaborative group work. Students need to explore student questions, recording their findings, and then to share their knowledge. Some teachers might like to start with one group of 'real ' maths' while others are busy with 'practice' maths. Or maybe, now and then, a 'real ' maths study could replace the more formal programme.As such ideas are introduced the teachers role will also change. Teacher are already used to interacting with students, valuing students prior ideas and theories, in other areas.

Seymour Papert the computer educationalist has written that there should only be applied maths ( and science).Too much current maths is anything but applied and is only comprehended by students who appreciate the demands of 'pure' or abstract maths.

Another mathematician Dr Z P Dienes ( of dienes block fame) described the classroom situation when he said, 'It is suggested that we shift the emphasis from teaching to learning, from our experience to the children's, in fact, from our world to their world'.


We can't afford students who do not see maths as vital form of communication -a special but accessible language to help them make sense of their world. Currently some students gain a 'feeling for' maths the rest simply give up.

We need an education that sparks children's mathematical imaginations but first we must rekindle our own.

2 comments:

Anonymous said...

You are right - maths needs to be sorted out to make more room for inquiry learning. Maths would improve as well if seen as a means to an end.

Bruce said...

Teachers need to 're-frame' both literacy ( first call this time the language arts) and mathematics so as to place the emphasis on developing both inquiry skills and in depth content understanding.

Until this is done schools will remain locked in their past orientated programmes.