THE PRACTICE: Inquiry and Problem Solving in Middle School Mathematics
Content Presented By:
Eisenhower National Clearinghouse

What is it?

The Problem Solving Standard from Principles and Standards for School Mathematics (PSSM) stresses that problem solving is integral to mathematics learning (p. 52). Consequently, Grades 6-8 instructional programs should:

• 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; and
• monitor and reflect on the process of mathematical problem solving

Problem solving is a vehicle for deepening student understanding and appreciation of mathematics. As students work through good, thoughtful problems, they draw on skills and techniques from other contexts, building on the mathematical knowledge and understanding they have already acquired. As stated in PSSM, "The essence of problem solving is knowing what to do when confronted with unfamiliar problems" (p. 259).

Three guiding principles can be gleaned from PSSM's discussion of the role of problem solving in middle school mathematics:

• Problems should be carefully selected to be relevant to students' everyday experience and to important mathematical ideas in the curriculum.

• Teachers can encourage effective problem solving and inquiry through modeling, encouraging collaboration, and questioning.

• Students and teachers should reflect on their own experience with problem solving with an eye for how they might modify, expand, or clarify the process.

Questions to Think About:

• What does good problem solving look like?

• What tools are available to help teachers incorporate a problem-solving approach into their instruction?

• How can teachers support the growth of their students as problem solvers?

• How should instruction be structured to encourage the integration of truly open-ended problem solving?

• What are some sources of good problems for middle school mathematics instruction?

Another Consideration:

Establishing the use of open-ended problem solving in classroom settings requires flexibility on the part of the teacher and willingness to cope with potentially "messy" learning: heightened noise, increased bustle and movement in the room, and some level of student frustration as the problem defies easy solutions. The reward of using such a technique, however, includes greater student understanding and empowerment as they take ownership of their own mathematical learning and thinking. When solving real and engaging problems, students are challenged to apply their knowledge, make new connections, and explore creative solutions. In essence, problem solving is learning in action.

Answer This Question: How can teachers be best supported as they endeavor to effectively integrate a problem-solving approach into their instructional practices?

This resource is developed and maintained by The Education Alliance at Brown University. Seed funding was provided by the U.S. Department of Education. Send comments to: loom@alliance.brown.edu