The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions. - Ronald L. Graham
Over the many years of what our teachers have taught us, and the experiences that we have had
to get us out of the rain, find where the berries are, and keep us from getting killed, we forgot or we never learnt that mathematics is fundamentally about problem solving and thinking. But the best of tonight's lesson was to rediscover the wonders of developing problem solving and thinking skills through
- Generalization (looking for patterns, relationships and connections)
- Visualization
- Communication (reasoning, justification, representation )
- Number sense
- Metacognition
More important than arriving at the right answer, a student should be taught the ways to engage in thought-processes to understand the problem and justify the rationale behind a solution they have found. Just like at a debate! I found the interconnection of the 5 elements even more clearly when I read through the [
Primary Mathematics Syllabus]. There is so much more than just computation to Mathematics and getting the right answers the way your teacher have taught you. As an educator in Singapore, more than often, we forgot the essence of education is to
educate children to educate themselves throughout their lives - because results are more important to some many parents.
Indeed, if our brains hadn't evolve, it would be better to look at things in a hundred thousand dimensions.
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