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
- 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.
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