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 Visuals to Problem Types

Math coaches and teachers can use this tool as a quick reference for examples of visual representations for different types of problems. See the sample material, Using Visual Representations for...

Tool
Document
03/03/2014
2699 views

Observation Note-Taking: Reflections on Multiple Approaches to Problem Solving

Teachers and mathematics coaches can use this tool to keep track of the approaches to problems used by different pairs and groups of students. The purpose of the tool is to provide a summary of the...

Tool
Document
03/03/2014
852 views

Walk-Throughs: Teaching Problem Solving

Instructional leaders can use this tool to frame observational walk-throughs of elementary and middle school math classes. Related Media and Files: Improving Mathematical Problem Solving...

Tool
Document
03/03/2014
1091 views

Learning Together About Using Visuals That Support Problem Solving

Math coaches can use this tool to help elementary and middle school teachers learn about the role of visual representations in problem solving through a series of professional development...

Tool
Document
03/03/2014
1070 views

Problems: Connecting Mathematical Ideas to Notation

In the media piece, Connecting Mathematical Ideas to Notation, Dr. Sybilla Beckmann presents two examples of problems showing how students can connect mathematical concepts and notation. This...

Sample Material
Document
03/03/2014
904 views

Pre-Algebra Fencing Task

At Papillion Junior High School, seventh-grade students work in groups on a non-routine geometry problem. This sample material has a fencing task worksheet and photos of students’ presentations of...

Sample Material
Document
03/03/2014
866 views

Fraction Problem: Part of a Part

Grade 6 students at Patriot Elementary use several strategies to solve a real-world, part of a part problem. This sample material has the scenario and statement of the problem along with pictures...

Sample Material
Document
03/03/2014
876 views

Using Visual Representations

Teachers can use these examples for ideas to help students create visual representations for different types of problems.

Sample Material
Document
03/03/2014
1038 views

Frank's Problem

Grade 6 students at Madison Elementary School use visual representations to present their solutions to Frank’s Fresh Farm Produce problem. The first page of the sample material has a statement of...

Sample Material
Document
03/03/2014
824 views

Roll Around the Clock

Students use a clock visual for fractions and problem solve with fraction concepts while playing Roll Around the Clock. This sample material presents instructions for the game along with a clock...

Sample Material
Document
03/03/2014
881 views

Who Finishes When?

At Worthington Hooker School, pre-algebra students work on the Who Finishes When? problem. They use visual representations to interpret the information in the problem. This sample material has the...

Sample Material
Document
03/03/2014
849 views
Multiplication of Fractions

Multiplication of Fractions

Listen to how a teacher considers the problem-solving strategies students use in a multiplication of fractions problem involving part of a part. She describes which strategies she chooses to...

School Example
Video
02/14/2014
693 views
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