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# Problem-Focused Teaching (page 3)

By J.E. Schwartz
Pearson Allyn Bacon Prentice Hall
Updated on Dec 22, 2010

Following the initial solution, students are asked to share with the class the methods that they found for solving the problem. Several different students are asked to share. This gives the whole class an opportunity to hear and see a variety of methods of solving a given problem. We work hard to create a safe and comfortable classroom environment in which students can explain their thinking to one another. The goal is for each child to fully understand the methods presented by each of his or her classmates. In the case of users of this text, we recommend that math coaches or faculty development leaders establish a community of inquiry among teachers in order to facilitate a dynamic exchange of ideas. The goal of this dynamic exchange of ideas is to deepen understanding of the powerful ideas.

After classmates have presented a variety of different methods, the teacher finally offers a standard algorithm, or the more formal mathematical way of solving the problem. By this point in the lesson the students are equipped to see this more formal mathematical solution as simply one more way to approach the problem. Since they have already seen the problem solved in a number of different ways, and since these various ways of solving have been sensible and meaningful to them, they can expect to see the formal mathematical method in the same light. They expect it to make sense, and they work to understand how it works. This method of beginning with problems, asking students to find their own ways of solving, having students share their methods with one another, and following this with instruction from the teacher is what we mean when we say that we are teaching mathematics in the context of real-world problems. This is what we refer to as problem-focused teaching.

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