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An Overview of the Problem Solving Standard for School Mathematics? 2

3 Instructional programs from prekindergarten through grade 12 should enable all students to— Problem Solving Standard Build new mathematical knowledge through problem solving; Solve problems that arise in mathematics and in other contexts; Apply and adapt a variety of appropriate strategies to solve problems; Monitor and reflect on the process of mathematical problem solving.

4 Problem Solving Standard for Grades 6 – 8.

5 What should problem solving look like in grades 6 through 8? Through problem solving, students can experience the power and utility of mathematics. Problem solving is central to inquiry and application and should be interwoven throughout the mathematics curriculum to provide a context for learning and applying mathematical ideas. continued

6 Students will benefit from frequent opportunities for both independent and collaborative problem-solving experiences. Students will engage profitably in complex investigations, perhaps occasionally working for several days on a single problem and its extensions. What should problem solving look like in grades 6 through 8?

7 What should be the teacher’s role in developing problem solving in grades 6 through 8? Make problem solving an integral part of class activities. Allow students to develop and create their own problems. continued Choose interesting problems that incorporate important mathematical ideas.

8 What should be the teacher’s role in developing problem solving in grades 6 through 8? Help students to become reflective problem solvers by providing open ended problems. Use technology to allow for the solution of real world problems that may not have “nice” numbers in them. Provide problems that have extensions that expand the mathematics learned.

9 Problem Solving Standard for Grades 9 – 12.

10 What should problem solving look like in grades 9 through 12? Students will have to adapt and extend whatever mathematics they know. Successful problem solvers are resourceful, seeking out information to help solve problems and making effective use of what they know. In high school, students' repertoires of problem-solving strategies expand significantly

11 What should be the teacher’s role in developing problem solving in grades 9 through 12? Present problems that will allow the students to learn important mathematics through their exploration. Present problems that have a wide range of strategies involved in their solutions. Develop in students a disposition to pose and solve problems.

12 Work in two groups (6-8 and 9-12) to develop a lesson for students in that band width that will illustrate at least one of the bullets in the problem solving standard. We will leave time at the end of the period to present your ideas. Only develop the mathematics of the lesson. Do not worry about the mechanics of the lesson plan. Pick a topic and develop the way in which you will present it so that at least one of the bullets is used.

13 Assignment Read: NCTM Principles and Standards p 56-59, , and