There are many ideas from these two chapters that I would use with my students during problem solving. the authors raised a very interesting thought when they mentioned that, against what some people might think, using concrete materials when solving a mathematics problem do not make a student less of a mathematician. I do agree with this point and I would strongly agree with using manipulative materials whenever it is possible in a classroom. I support the belief that a student choosing the appropriate materials to help solve a problem is part of the process of finding the solution.
Another approach that I would like to share with my students is to make them feel at ease when being stuck and help them to be aware that being stuck is part of the challenge. I want them to understand that it is only when they are solving an easy problem, they don’t get stuck. That reminds me of Vygotsky’s ‘zone of proximal development’ which the space between what we know and what we are about to learn and how learning happens within that space. When the students realize that being stuck is part of the process solving a problem, then they will not get frustrated or discouraged and they will put more effort to solve the problem.
I also liked the idea of extension which is something we are already doing in our EDCP 342. I think working on extending the problem gives the chance for students to pose their own question and challenge themselves.
Another procedure I would like to apply in my classroom is having students reviewing the process they used to solve a problem by using a different method, if possible. I would like to add here that after reviewing their solution, I would like them to look at the final answer and ask themselves “Does this make sense?”
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