Has teaching students how to solve math problems hindered their own ability to think for themselves and problem solve. What are the benefits of allowing students to solve problems their own way without giving them a specific method, and does this help them to become stronger thinkers and problem solvers?

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I believe that math must be taught from a problem-solving approach. I see too many assignments that are 2 - 32 even and no real "problems" are given. Sure, the fundamentals must be taught. But if you don't have any opportunities to use the fundamentals on "real" problems, what's the point. If you approach math from a problem-solving perspective, then students don't mind the fundamentals as much since they see the need for them. As far as a specific method, students should be given many tools to analyze a problem. Common problem solving strategies include guess & check, estimation, tables, patterns, models, simplify & work backward. Using these strategies in math transfers to all disciplines and prepares students to be critical thinkers.
Thank you for your reply, I agree that math should be taught from a problem-solving approach as well because it engages students as thinkers rather than just going through the motions. I believe that when students are given the opportunity to solve a problem without a specific formula to follow it allows them to make sense of the problem and gain a better understanding of mathematical concepts.

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