## Sunday, March 1, 2009

### Problem Solving Tactics

 Tactic Action Outcome CLARIFYING Re-read the problem as if you were editing it: analyze givens, make unstated assumptions explicit, clarify 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 which should help you see relationships between givens and unknowns. ANALOGY Recall or use the text or notes to find a similar problem, method, result, useful theorem technique. A model to follow in solving your problem. SUBGOAL 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. BRAIN-STORMING 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 relationships involving units which can be multiplied or divided to get 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, 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, sleep on it, or leave it for a few hours. An opportunity for insights and ideas to develop. GO FOR HELP Ask for hints or explanations. Obtaining necessary insights and strategies.