1. The problem solving approach teaches students to figure out a way to find an answer a problem as opposed to regurgitating a equation when they see a certain type of problem when you only teach certain math skills. A down fall with teaching math skills is that you are limiting yourself only that certain type of problem.
2. I think I will try to push the concepts students form about math. I would want the students to think about what we are doing and try to find out why the concept works rather than just give them the concept. For example, I would want the students to figure out squares are rectangles by working with the definition of what a rectangle is rather than just say a square meets the definition of a rectangle.
3. When only teaching basic facts and ideas you are really limiting the student to only those facts and concepts. You are not allowing the student to explore and gain a better understanding of what math is about. Another concern is that math in real life is not simple basic facts and concepts so not teaching the student how to explore math would not allow the student tools to solve real life problems.
4. I would say it is easy because it might be difficult for the student. Instead of helping, I would rather see what the student is thinking. I would ask something like, "how are you going about this problem" and "does that method make sense." I would try to work with what the student is thinking and not try to go about how I would solve the problem because everyone thinks differently.
5. It allowed the student to work and be flexible in how they went about solving a problem. It was individualized to each student since they were all able to approach it in their own way. The students were able to bring their prior knowledge and use it to connect with the task.
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