What is Maths?

When you ask children, who have been taught traditionally, what is maths? their typical answer is that maths is all about numbers, calculations and rules. They also say it is about formulas and procedures that need to be memorised. However, when you ask this question of any mathematician they usually say maths is the creative study of patterns and relationships in life. Mathematicians usually describe maths as a powerful way of expressing relationships and ideas in numerical, graphical, symbolic, verbal and pictorial forms. Why is it then that students develop such a distorted view of the subject? This is largely because teaching maths by the traditional approach rarely  incorporates the true features of the work of mathematicians. When you think about these features, then compare this to the class room experience of most students, you will understand why the discrepancy exists. These features are as follows;

Problem solving - problem solving is at the core of a mathematician's work. It requires creativity, original thinking and ingenuity. Mathematicians work on long and complicated problems that involve combining many different areas of mathematics. Such problems not only strengthen mathematical knowledge but also encourage the important life skill of persistence. Working mathematically on a problem often starts, believe it or not, with the making of a guess. This may surprise many of us who have experienced traditional maths classrooms that guessing is an important mathematical skill. This is because we have never experienced any encouragement to guess and estimate in their maths class. Because they have learned, wrongly, that maths is all about precision students do not develop a good feel for numbers. Often students are set to work on narrow and closed questions. Boaler (2009) quotes Robin Wilson, a British mathematician, as saying that  mathematics and music are both creative acts - when you are sitting with a bit of paper creating mathematics, it is very like sitting with a sheet of music paper creating music.

Collaboration - in the traditional mathematics classroom, students often sit working in isolation. They are not encouraged to share ideas and hence develop a solitary stereoytpe of mathematical work. On the other hand, the majority of mathematicians prefer to collaborate when working on problems. Such collaboration with colleagues allows mathematicians the advantage of learning from one another's work, increasing the quality of ideas and sharing the challenge of problem solving. When students are given the opportunity to work together to extend problems into new directions this means not only do they enjoy mathematics more, they also feel ownership of their work and ultimately learn more.

The opportunity to work in different ways - mathematicians work in many different ways to solve problems. They have the opportunity to take a problem and represent it in symbols, words, pictures, tables and diagrams or any other method they feel fit. This allows them to freely explore ideas. With such flexibility of choice it means there are so many more ways to successfully solve a problem. If such an approach is successfully used in the classroom students have the flexibility to choose how to work on given problems. They can then experience so many more ways to success that are tailored to their particular way of learning.

Unfortunately, it seems it's only those students who stumble upon the ideas of mathematicians that develop a true sense of the topic. Students need the opportunity to work in the ways mathematicians do - posing problems, making guesses and conjectures, exploring with and refining ideas and discussing ideas with others. I'm not saying all students should want to become professional mathematicians in their careers. What I am saying is that if students are given a sense of true mathematical work and have the opportunity to enjoy mathematics and learn it in the most productive way, they are more likely to have a wider variety of mathematical skills to use in life. Click on the 'How we learn Maths' tab at the top of the page to see how working mathematically can be used in the classroom.