What is the impact of teaching mathematics through problem solving on students’ ability to become mathematical thinkers?
I want to incorporate a problematic based method of teaching that allows students to become mathematical thinkers. Mathematical thinkers have developed habits of mind that are their tools when attacking problems. To make mathematics problematic to students, I would base my instruction around problems that may cause a slight struggle to the student but could be used to teach concepts and habits of mine. By introducing concepts this way, students will be able to take ownership of their learning and develop confidence in their skills. My purpose is to measure how influential this style of teaching is on improving student’s habits of mind and their confidence when faced with problems.
This is an interesting topic, and I may not fully understand it. Are you attempting to teach your students how to think analytically? Do you want to teach them how to approach math problems systematically? Do you want them to be able to determine what information from problems is useful? It sounds like you might use scaffolding methods or inquiry based learning when you present a topic to the class to get them to think about and generate the right steps in the process. It seems like you could do a survey or interview students before and after treatment to understand the effect of this on their confidence. How will you measure how influential this thinking is on students’ habits of mind? I think you could present problems to them that they have not been taught how to solve and interview them to understand their thought process.
ReplyDeleteThis is a good idea. But I don't think you mean "problematic" based method. That is a bit different from "problem" based learning. I am not sure you mean either of those. It sounds like you are talking about ZPD (Vygotsky), but I am not sure that is it either. As I recall our conversation, you are really talking about problem solving skills, which involve "habits of mind." I think that yields the benefits you mention particularly confidence. You will have to do some more reading to define clearly what you mean by "habits of mind" and how you might go about teaching them.
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