10 Comments/Questions from "The Art of Problem Posing"

Reading response from the book "The Art of Problem Posing"

change the traditional method of teachers giving problems for students to solve(instead have a shift in the control of posing problems)
-What can we do to effectively encourage students to ask themselves "helpful" questions in order to solve problems? Sometimes I have troubles asking myself the "right questions" to solve a hard problem.

-What would this be like in an actual class of 30 students with all different skills and interest levels in Mathematics (including the time and curriculum constraints)? It might be interesting for students who like Math but it definitely would frustrate students with lower level of understandings

-Using x^2+y^2=z^2, the author demonstrates how we limit ourselves in learning by only interested in just finding the answer. I agree we definitely need to ask ourselves the significance behind the problem.

-The questions generated from the given x^2+y^2=z^2 are impressive. I can see that some questions are helpful in further extending the concepts and while some others provide space to play around with the concept. I also like the possible response of "it is the only thing I remember about geometry". I feel this questioning process can be an honest dialogue with yourself which in return can help organizing all the thoughts that have arise.

-But what can we do to stay on topic and to achieve the purpose of these questioning is to learn the concept desired?

-I think it's useful to have a list of guiding questions to ask students. This helps students to develop independent problem-solving ability. It is also a good assessment tool to use in checking student's understanding.

-In addition, all the related questions that we can ask about a given problem can help us make connections between concepts.

-From personal experience, it is essential to know how to rephrase a question or ask in another way. A lot of times I find that students need to be asked in another way to fully understand the question.