Mathematical Problem Solving Goals and Outcomes

Use a Heuristic

Recognize and use a general plan to solve all mathematical problems.
Identify steps of heuristic (a generalized pattern/strategy) to solve problems.
Identify steps to include: 1. Understand the problem, 2. Select and try a strategy, 3. Examine the solution, and 4. Verify the solution.
Describe ways to aid in understanding the problem as identify the words in a problem that describe mathematical relationships, operations and numerical values.
Accurately explain the problem in their own words.
Identify information needed to solve the problem.
Identify unneeded information in a problem.
Select a strategy to solve the problem.
Try a different strategy when one appears to be at an impasse.
Solve problems.
Solve problems in different ways to gain confidence in the solutions.
Reflect on what was learned and how it might be used in other contexts. the process and the accuracy of the solution.
Share the process, strategies used (successful and unsuccessful), attitudes, and solutions.

Analyze unfamiliar problems
Identify necessary and unnecessary information
Ignore nonessential information
Clearly state the problem or task
Identify what solution is needed
Select strategies
Develop a repertoire of problem solving strategies
Identify a variety of problem solving settings
Select and use a strategy or combination of strategies to solve problems
Justify solutions
Assess the reasonableness of a solution for a problem with respect to the information in the problem and the approaches used
Extend or generalize problems
Extent a solution or process from solving a problem with respect to the information in the problem and/or the approach used

Use of manipulatives to represent objects and actions in the problem.
Work a simpler problem.
Trial and error, guess and check.
Work backwards
Use smaller numbers
Use systematic steps.
Look for, recognize and describe patterns: quantity, AB/AB, ABBA/ABBA, size, area, volume, rotation, shading, shape, position, subtraction, addition, reflection, multiplication, analogy, and recursive
Break a problem into two related problems and solve the original problem in two steps: one for each problem.
Act out the problem. Physically or mentally.
Use a pictures, graphical representation - model, drawing picture or diagram
Problems can be solved with models and equations.
Categorize information to find relationships and patterns that will assist reasoning and proof.
Organize data to look for patterns sequence, chart, table, making a graph, Venn diagrams, and dichotomous key.
Process of elimination or process of identification
Write an open sentence
Use algebraic reasoning
Use logical reasoning: matrices, deductive, inductive, truth tables
Brainstorming
Use equivalent numbers 3/5, 6/10, 60/100, .6, 60%

Monitor and reflect on the process of mathematical problem solving and regulate their actions.
Have the habit and ability to monitor and regulate their thinking processes at each stage of the problem - solving process
Use self talk, group discussion, to talk through a problem and problem solving process to reflect on all the decisions that are possible to better insure an accurate solution.

Have self - efficacy in their ability to do mathematics and to confront unfamiliar tasks without being given a ready - made prescription for a solution
Have a willingness to attempt unfamiliar problem
Open-minded and skeptical
Not easily ready to declare a solution accurate without confidence in a solution
Have perseverance when solving problems and are not easily discouraged by initial setbacks
Enjoy and feel a sense of personal reward while doing mathematical thinking, searching for patterns, and solving problems

Dr. Robert Sweetland's notes