Murray Britt & Kay Irwin: Returning to rote learning 'condemns future to failure'

Children learn to use strategies to build a wide repertoire of mathematical knowledge. Photo / Thinkstock

Over recent days much has been written and said about the Numeracy Development Project. The project began in the mid-90s in recognition that children's understanding and use of numbers in New Zealand schools was very limited and quite unsatisfactory.

Such limitations were not confined to New Zealand - Australia had similar experiences. Indeed a New Zealand group travelled to Australia to discuss the directions already under way there, which had been gleaned from research work carried out in the US and Britain by outstanding academics.

The New Zealand group refined these international ideas before testing different approaches to teaching numeracy with one school in Auckland and then more widely across several schools in NZ.

Throughout this and subsequent phases, the New Zealand and Australian groups maintained a strong professional relationship. NZ Ministry of Education officials worked closely with the New Zealand project leaders throughout the development. Independent researchers followed progress in schools.

Decisions to widen the scope were taken by ministry officials in consultation with teachers, researchers, principals and project staff. Research results were published and reported widely here and internationally.

One aspect that has received much comment is the role of basic fact knowledge. The project staff recognised the importance of such knowledge and ensured basic knowledge would occupy an up-front position by dividing project material into knowledge and strategies.

Essentially students were assisted to think mathematically by employing a growing number of mathematical strategies. One simple strategy can be likened to the "both ways" rule where, for example, 7 + 9 = 9 + 7. Another simple strategy can take this further by splitting numbers such as the problem being modified to become 9 + 7 = 10 + 6 = 16. Column addition is only a strategy for adding. Children learn to use strategies to build a wide repertoire of mathematical knowledge.

And as soon as they see how to think in this way, children are required to practise these newly learned facts. Such practice must be ongoing until each fact can be retrieved in an instant from the memory bank of each child.

Teachers omitting such a curriculum requirement are really not carrying out a prime function of mathematics teaching. It is a function of principals and the Education Review Office to check this is done.

Other aspects of mathematics that some critics argue are not being taught are the standard algorithms for addition, subtraction, multiplication and division. Not so. What we can say is that they seldom have a role as first steps. They can surely have a role once the necessary foundations are formed.

Try teaching long multiplication or long division without first knowing all the multiplication facts and the meaning of multiplication and division. These algorithms or procedures are really strategies for resolving more challenging arithmetical problems.

We have briefly detailed here how the project was established and its role. Crucially the project was driven by research in NZ and in other countries.

We demonstrated in a separate research project that students who successfully reached the higher levels in the project were more likely to be successful with school algebra.

We argue that an awareness of the relationships from exploring ideas of numeracy is basic to learning mathematics. We also argue that those who want a return to rote learning, i.e. mathematics without meaning, are merely condemning our future to failure.

• Murray Britt is former principal lecturer, University of Auckland (retired).

• Dr Kay Irwin is former senior lecturer, University of Auckland (retired).