The Importance of Mathematical Thinking
“To solve math problems, you need to know the basic mathematics before you can start.” – Catherine Asaro
One thing that I have reiterated to all my students over the years is to consider Mathematics as a way of thinking. Kaye Stacey (2012, University of Melbourne) submitted that mathematical thinking is important in three ways.
- Mathematical thinking is an important goal of schooling.
- Mathematical thinking is important as a way of learning mathematics.
- Mathematical thinking is important for teaching mathematics.
As students are introduced to high school Mathematics, it would be wonderful if many students could have just a small taste of the spirit of discovery of Mathematics as described in the quote below from the Mathematician Andrew Wiles.
“One enters the first room of the mansion and it’s dark. One stumbles around bumping into furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are the culmination of, and couldn’t exist without, the many months of stumbling around in the dark that precede them.” (Andrew Wiles 1997)
Because Mathematical thinking is a process, l will discuss examples of what l do every time and again with my students in and out of the classroom.
- Logical Puzzles
A logical puzzle is a problem that can be solved through deductive reasoning.
In class we have used this website many times and my students find Mathematics easy if engaged in an interactive and fun way. They start to enjoy how mystifying, puzzling and challenging it is.
- 4 x 4 Magic Square Puzzles
Magic Square Puzzle
In conclusion, math skills are about much more than all the minutiae we teach in school because they are a strong indicator of broader cognitive abilities. And because cognitive aptitude is one of the most predictive factors of job success, testing my candidates’ math abilities is a great way to assess their ability to succeed in any given Maths test and after school activities.
Hebert Tapfuma
High School Mathematics
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