Teach students to use visual representations, employ multiple problem-solving strategies, and relate mathematical concepts and notation to problem solving.

To help students develop proficiency in mathematical problem solving, teachers need to guide them in translating quantitative information into symbolic equations—the arithmetic/algebraic statements that will provide a solution—and encourage the comparison and use of various problem-solving strategies. Students who have practice using multiple problem-solving strategies, sharing and comparing strategies with other students, have greater flexibility in solving math problems and understand that problems can be solved in more than one way depending on the method that makes the most sense to them. By explaining notation in the context of problem solving, prompting students to provide mathematically valid explanations, and introducing algebraic notation, teachers can help students develop new ways of reasoning. In addition, using appropriate visual representations (e.g., table, graph, and/or diagram) helps students solve problems by linking the quantitative relationships in the problem with mathematical operations.

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Connecting Mathematical Ideas to Notation

Connecting Mathematical Ideas to Notation

Dr. Sybilla Beckmann uses two different problems to demonstrate how to develop mathematical concepts and present mathematical notation in problem-solving situations. Related...

Expert Interview
Video
02/14/2014
506 views
Non-Routine Problem in Geometry

Non-Routine Problem in Geometry

See how a class approaches "Pre-Algebra Fencing Task," a non-routine geometry problem that challenges their mathematical reasoning. Related Files: Pre-Algebra Fencing Task (Sample...

School Example
Video
02/14/2014
593 views
Representing a Problem Visually

Representing a Problem Visually

See how different groups of students use double number lines and other visuals to tackle "Frank's Problem," which involves figuring out the most efficient travel routes in terms of...

School Example
Video
02/14/2014
623 views
Problem Solving in Pre-Algebra

Problem Solving in Pre-Algebra

Watch as a teacher challenges her students with the real-world problem of a race in Who Finishes When? Visual representations help students think about how the problem can be solved. Solution...

School Example
Video
02/14/2014
600 views
Algebraic Notation in Problem Solving

Algebraic Notation in Problem Solving

Dr. Ken Koedinger provides examples that demonstrate the importance of bringing mathematical notation into the problem-solving process.

Expert Interview
Video
02/14/2014
467 views
Multiple Problem-Solving Strategies in Instruction

Multiple Problem-Solving Strategies in Instruction

Dr. Driscoll explains how use of multiple strategies contributes to student learning by letting students see problems in new ways. He stresses the importance of worked examples and comparing and...

Expert Interview
Video
02/14/2014
527 views
Matching Visuals to Purpose in Problem Solving

Matching Visuals to Purpose in Problem Solving

Dr. Asha Jitendra shows and discusses the role of different types of visualizations in problem solving, especially their usefulness for students struggling with math.

Expert Interview
Video
02/14/2014
756 views
Effective Problem-Solving Instruction

Effective Problem-Solving Instruction

This summary describes a wide range of research-based recommendations for guiding instruction in problem solving. Three important strategies that apply at all grade levels and in all areas of math...

Overview
Video
02/14/2014
998 views
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