# 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.

## Mathematical Problem Solving Process Skills

• 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

## Identify and Use Strategies

• 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%

## Meta cognitive

• 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.

## Disposition/attitude habits of mind

• 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