This file give more details about the problem solving strategy for conceptual problems that I introduced in my talk “Problem Solving without the Problems” at the SCAAPT Spring 2010 meeting. These slides are used in a lecture early in the semester for a general studies Earth Science class at a 4-year university. The purpose of this lecture is to introduce students to the problem solving strategy and give some examples of how the steps of the strategy might be applied to problems in the class.

Problem solving in this class 5 Step Problem Solving Method 1.Focus the Problem Visualize and/or diagram Find keywords 2. Describe the Problem Brainstorm concepts related to keywords Choose main concept 3. Plan the Solution Find cause-effect statement related to main concept 4. Execute the plan Link cause-effect pairs 5. Evaluate the answer Check with your intuition or experience

Test stats Step #1 72% Drawing a diagram or visualizing can help The following statistics come from analysis of multiple-choice questions on last year’s tests. 23% Relevant diagram is provided for you Step #2 21% Nontechnical description of a phenomenon is given 68% Technical terms used without definition Step #3 92% Require matching of a term or concept to a cause or effect Step #4 13% Require linking more than one cause-effect step Step #5 18% Can be answered or easily checked from your experience 89% Require using keywords to identify the concept

Example problem Earth’s orbit is not exactly circular, but slightly eccentric. Eccentric means that the orbit is an ellipse. Earth is about 1% closer to the Sun during January than in July. Which of the following is a result of Earth’s eccentric orbit? (a)Days are slightly longer in January. (b)Earth moves around the Sun with greater speed in January. (c)Earth is closer to Mars in January. (d)Earth is on average colder in January.

Suggestions for carrying out steps Step #1 Study textbook and lecture diagrams Draw key objects Play “mental movies” Don’t be afraid to move, “hand waving” Use “initial” and “final” diagrams when something changes

Suggestions for carrying out steps Step #2 Underline keywords Brainstorm all concepts that relate to each keyword Choose concept that relates to most of the keywords Narrow down search (unit, chapter, section, concept) Example Underline keywords – Ellipse, closer, speed, days, colder Brainstorm all concepts that relate to each keyword Ellipse – Gravity, force, period, speed Closer – Temperature, planet size, period, speed Speed – force, radius Days – rotation Choose concept that relates to all of the keywords The main concept is Kepler’s 2 nd law

Suggestions for carrying out steps Step #3 To study, write a definitions, descriptions, or cause-effect statements Some concepts will have several statements Watch for things that stay the same or things that change Check each answer to see if it matches a cause-effect statement Example Cause-effect statements for Kepler’s 2 nd law concept Closer to Sun causes faster motion Watch for changes Distance to the Sun is changing Match answers to cause-effect statement Answer B is just a rephrasing of the cause-effect statement

Suggestions for carrying out steps Step #4 Use when no concepts relates all keywords Look for links between cause-effect statement Work forwards and backwards

Example problem Comets are sometimes described as “dusty snowballs” because they are made mostly of ice with a little bit of rock embedded in the ice. Comets have highly elliptical orbits. They can only be visible from Earth when the ice in the comet starts to melt. A comet will be visible (a)Throughout its orbit around the Sun. (b)Only when it is near its closest point to the Sun. (c)Only when it is near its furthest point from the Sun. (d)Never.

Example Keywords: comet, melts, elliptical, closest, furthest Brainstorm connections: Melts – Temperature Distance – Temperature Look for common link: Melting and distance are both related to temperature Build cause-effect chain Getting closer to the Sun causes the comet to get warmer, which causes the ice to melt. Suggestions for carrying out steps Step #4 Use when no concepts relates all keywords Look for links between cause-effect statement Work forwards and backwards

Suggestions for carrying out steps Step #5 Make sure your answer makes sense Refer to similar situations you have experienced

Example problem A researcher looks through a telescope observes two stars. Both stars are blue. Star A appears to be less bright than star B. What can the researcher infer about these two stars? (a)Star A is hotter than star B. (b)Star A is bigger than star B. (c)Star A is closer to Earth than star B. (d)All of these (e)None of these

Example of test problem with problem solving steps (5 points) The Sun emits light by atomic transitions, producing four colors of light with wavelengths of 656 nanometers (red), 486 nanometers (light blue), 434 nanometers (blue), 410 nanometers (purple). Observations of a distant star show light from atomic transmissions with wavelengths of 654, 484, 432, and 408 nanometers. What can you conclude about the star? (a)The star is hotter than the Sun. (b)The star is moving towards us. (c)The star is smaller than the Sun. (d)The star contains more mass than the Sun. (1 point) Identify at least two keywords in this question. (2 points) Identify the main concept or concepts of this question. (1 point) Write a cause-effect, definition, or descriptive statement for the main concept