My Frequently Asked Questions

1. (p.14) It has appeared to me so many times as to try to understand some explainations from the text or of the teachers that the saying "it is obvious to see..." or "because you can tell..." always precedes the understanding of some students. I was not a very smart student to begin with, to be honest, and I am sure that the "because you can tell..." or the "it is obvious to see..." often confuse and frustrate some students, including myself, even more when, at times, they really do not understand why they can or why it is obvious to carry onto the next step.

2. (p.15)Pythagoras Theorem: What is it, really, other than "accepting" it as a given whether related or insightful activities are arised for students to participate? Other than the explaination that it is an essential element that makes up a right angle triangle, what other purpose does it serve? What other ways can I explain to my students other than its generic purpose? What

3. (p.20)Very so often that it is through questioning, especially with seemingly meaningless questions, that a situition is cleared, even though at times some meaningless questions really are meaningless.

4. (P.25) If the starting point is about propositions, how are teachers able to make it intersting and engaging for students in the first place?

5. (p. 25) It is sometimes fun to ask the questions the other way around and some insightful concepts may surface.

6. (P. 26) Due to the construction of how problems are asked, students can be more engaged and interested in exploring the problems. Traps! Teachers set traps in a way for students to step in and then learn the mathematical concepts inside usually before they realize the fact.

7. (p. 26) Relations from one subject matter to another and patterns to create concepts of a subject matter remind me of this question: Is Mathematics an invention or a discovery?

8. (p.27) Do we have to have answers to all problems? So far, we cannot prove that there are no answers for some problems. Can, on the inverse, we prove there are answers to all problems?

9. (P. 27) It is the curiosity that encourages and drives people to pursue the investigation of certain subject matters. In English, the pattern of past tense is set but there are some verbs make exception to that pattern, but why? The solution may usually be obvious once the history of those verbs are given. Is it the case for some of the Mathematical investigations? Is it enough just to know the history?

10. (P. 31) Is this relevant? Are these questions for deeper investigation in Mathematical studyings or Are they for developing problem sovling skills?Though generalizing problems with HOT list of questions makes it easy for students and teachers to attack problems, will they limit our mind?