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Problem Solving Tactics

TACTIC

ACTION

OUTCOME

Clarifying

Re- read the problem as if you were editing it: analyze givens, make unstated assumptions explicit, clarifying goals.

A restatement of problem- its givens, assumptions, and goals- in your own words.

Visualizing

Draw a figure and label givens, close your eyes to form a mental picture and then imagine what the experiment would look like if you set up the equipment.

A figure, diagram, model that should help you see relationships between givens and unknowns.

Analogy

Recall or use the text or notes to find a similar problem, method, result, and useful theorem technique.

A model to follow in solving your problem.

 

Sub-goal

Break problem into simpler problems; do only part of the problem.

Partial solutions leading towards goal.

 

Algebraic

Introduce variables for unknown; write equations, relations.

Symbolic representation of the problem.

Brainstorming

Think of every formula or definition related to the concept or terms.

A list of formulas, conversion factors, or definitions to be used.

Questioning

Assume you are going to ask the instructor for help: what would you ask? Identify what you need to know to solve the problem.

A list of questions whose answers lead to a solution.

 

Unit Analysis

Compare units in answer you want to compute with units in given information; look for conversion factors involving these units.

A series of units that can be multiplies or divided to get a desired goal.

Identifying

Identify concept behind problem, type of problem, section of book from which taken.

Once you know the concept behind the problem you can use brainstorming, analogy, or other tactics.

Team

Work with a classmate or friend.

Discussion of ideas which can lead to broader understanding.

Trial-Error

Hit- miss attempts; try special cases.

Corrective feedback, better understanding of problem; may lead to induction.

Induction

Try cases, searching for a pattern.

Generalizations and insights about problems.

Work-Backwards

Begin with answer if given, or approximate an answer, and try to figure out how it was obtained.

The process for solving the problem.

Look Back

Check and verify your work; is solution reasonable?

Verification of solution.

Incubate

If making no progress after 30 minutes, stop working on problem

An opportunity for insights and ideas to develop.

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