10 Questions / Comments for the Authors

1) It's a hard exercise to come up with all those ideas after seeing one line of math. I certainly wasn't able to think up of all those questions and ideas on x^2 + y^2 = z^2

2)What are the different things students think about while playing with the geometric board?

3) How has the study / resources of this topic changed from the first edition of this book to the third?

4) How clear must the question be when we pose it?

5) Should we enlighten the students what questions to ask when we give them a question?

6) How much exploring should we allow for a student?

7) If the student has problems with the basic operations (addition/subtraction/multiplication/division), how much should the student explore on the particular math topic?

8) How long should we leave a child with a geometric board? How much exploration (guided by questions) should a student do?

9) I like how when approaching the topic one:

1. makes the observations
2. asks the questions
3. comes up with the conjecture

10) I like how the authors pointed out internal versus external exploration. Often we focus on internal exploration but don't ask the external questions that uses the skills from a certain topic. A lot of external questions were presented when exploring the Pythagorean triple.
.