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Thinking Mathematically

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Thinker Magazine Issue 01: Thinking Mathematically

Written by: Willy Gollan (Lecturer) & Robyn Dunbar (Literacy & Numeracy Coordinator)

When Primary Pre-Service Teachers begin learning about what it means to teach Mathematics, the following questions often come up:

“Isn’t Mathematics just about getting the right answer?”

“About following the rules or formula?”

“Don’t I just tell the students how to do it?”

These questions might be answered with a ‘yes’ if Mathematics is seen as a body of facts and procedures that need to be memorised However, Mathematics is so much more.

To think mathematically is a complex activity: a process requiring a wide range of skills and abilities.

Mathematical thinking is encouraged by beginning with an interesting problem.
A problem may be defined as any task or activity that has no prescribed rules or methods, no clear path or direction to a solution nor is there a perception that there is a ‘correct’ solution method.

The problem gives a context for using the skills and knowledge of Mathematics. The problem invites engagement. Anyone can begin.

When tackling a problem data may need to be collected and organised. Patterns may emerge. Discussions will ensue and thinking will be recorded. Mathematical skills and tools will need to be used. Strategies applied. Hypotheses are made and tested. A solution or solutions are found which can be justified to others. Then a new problem may be posed. Collaboration is encouraged so several perspectives are brought to bear on the problem.

Mathematical thinking occurs when there is an exploring of possibilities, answers are searched out, connections made and patterns found. The learning experience is memorable.

To think mathematically is a complex activity: a process requiring a wide range of skills and abilities.

How much more engaging would Mathematics be if there was a purpose and a context for using the mathematical skills learnt? Mathematics can then actually be enjoyed.

What needs to be developed is an appreciation of what mathematicians do. Mathematicians are people who enjoy the challenge of a problem, who see the beauty in a pattern, a shape, a proof, a concept. They think mathematically.