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Wednesday, January 5, 2011

Math and Reasoning

Math reasoning means thinking about a question and using a process to solve it. Presumably there are numbers involved somewhere in there too. The term might suggest a specifically mathematical process of  reasoning, deduction, and inference. Alternatively, it can imply a mix of quantitative analysis and subjective intuition. Or an intentional problem-solving process called trial-and-error.

Or maybe do we just skip the reasoning part and move directly to guessing?


QUESTIONS
Today I am going to list some questions about mathematical reasoning.

1. If mathematical reasoning does not involve numbers is it still considered "math"?

2. Is mathematical reasoning useful to anyone being compelled to learn it?

3. Is mathematical reasoning an measurable goal in school math classes?

4. Are classroom teachers capable of teaching mathematical reasoning?

5. Can mathematical reasoning be taught [or learned] by anyone?

6. Do calculation skills lead to understanding and reasoning?

 7. Can practicing math help develop mathematical reasoning?

8. Does "math anxiety" prevent or derail mathematical reasoning?

9. Do cooperative/group activities enhance or dilute individual understanding and reasoning?

10. Can calculators and computers increase or decrease mathematical reasoning?

11. Why do students feel that mathematics is a totally foreign experience for them?

12. Is knowledge of the context of a problem essential for mathematical reasoning?

13. Must students construct their own "math knowledge" in order to truly "get it"?

14. Is capacity for mathematics innate (you either have it or you don't)?

15. Is elementary school too early or too late to teach mathematics to children?

Whew! By just listing these questions it is clear to me that math is not only a science. Math and the way we pursue the process of math education rapidly becomes a worldview, a mindset, a philosophical position, a religion.

A critical question comes to my mind as I am contemplating mathematical thinking and assembling this blog:

Why do we always show a person holding their head or chin or chewing a pencil when we want to imply thinking? Is there a link between posture, gesture and rational thought?

 As in the The Thinker sculpture by Rodin


ANSWERS
Some day I may try to answer a few of these questions in light of our experience creating and selling elementary math curriculum. But not today.