From the editor
What do your students believe that mathematics is? What do they think that doing mathematics is all about?
Mathematicians create, invent, conjecture, and experiment. And it is only by doing in school those kinds of things, by thinking mathematically, that students can use mathematics effectively outside and beyond school.
Students who believe that mathematics is a given body of knowledge and standard procedures, a set of truths and rules that they need to be shown, struggle with mathematics in school and in the outside world. They often fear and dislike mathematics, avoiding it if they can. Inspectors reported – in Mathematics: understanding the score (Ofsted, 2008) – that many pupils say ‘I don’t like maths because I’m no good at it. It’s boring. I prefer active or creative subjects.’
For generations, teaching mathematics was concerned with communicating established results and methods. Teachers tried to prepare students for dealing with mathematics in life by giving them ‘a bag of facts’. Consequently avoiding mathematics has become respectable. Many otherwise successful people are happy to announce that they ‘cannot do maths’, whereas few people would say publicly that they cannot read or write.
In their paper, The Mathematics Education Landscape in 2009, the Advisory Committee on Mathematics Education (ACME) expressed their belief that many students are not doing mathematics as well as they could, or not really doing it at all. We were reminded that mathematics teaching too often depends on telling students methods, rules and facts, and too rarely on helping them to make sense of what they can find out so that they can use mathematics independently.
In the 21st century we want to empower students; we want to help them develop genuinely mathematical ways of thinking. And these can be developed from the natural abilities that all people are born with.
Caleb Gattegno explained in his book What we owe children that we all used natural thinking powers when, as babies, we taught ourselves how to speak a language.
So, what are these powers? Well, as human beings we naturally:
- imagine and picture things in our minds, and talk about what we imagine
- notice differences and similarities between things
- find what is the same about things we come across that in other ways are different
- conjecture – make an ‘educated guess’ about what is true
- use various forms of reasoning, or argument, to try to convince others that what we believe is true.
One of the best ways to help students to think mathematically is to look out for opportunities for them to make use of their natural abilities naturally. Then you can point out to them what they did by themselves. While being interviewed in 1985 Caleb Gattegno said: “Everybody wants to work on weakness, but I work on strengths.”
I hope that this issue helps us think about how we can implement these ideas.