Thinking and Problem Solving

1. Thinking and Problem Solving

2. The Basics of Thinking • Thinking: changing reorganizing, and using info stored in your memory to create new information • Convergent Thinking: systematic attempt to reach a specific goal/answer. • Used to solve math problems and accomplish personal goals. • Ex. What is 2 X 5? • Divergent Thinking: free flow of thoughts with no particular plan. Relies more on images • Day-dreaming or “goofing around” can still lead to solutions to problems • Ex. Leaving the tape recorder on between “takes” may capture the perfect guitar hook for a future song.

3. Problem Solving • One of the main functions of convergent thinking; the gap between the present situation and a desired goal • Ex. Hunger  Food. Failing Senior English  Actually graduating. debt  able to pay bills

4. Algorithms & Heuristics • Algorithm: step-by-step procedure for solving a problem • Math & science love these, think formulas like • Also applies to set rules we follow, like rules in chess • Heuristic: a short-cut problem-solving strategy • Heuristics often lead to bad decision-making • More often to believe a coin will continue to come up tails if it has 5 times in a row • More likely to believe murder’s on the rise because of the local news

5. Problem-Solving • Trial and error: very basic, not recommended • Means-end analysis: assess what outcome (end) various actions (means) will have for us • Ex. Problem: big college exam tomorrow • Means: get to sleep early tonight  end: well-rested for test • Means: All-nighter studying  end: cram in that last bit of info • Break larger tasks down into smaller parts • Ex.15-page term paper breaks down to research topic, develop thesis, outline paper, write topic sentences, fill-out paragraphs, revise

6. Problem-Solving • Work the problem backwards • You need to be at school by 7:38, in the car by 7:15, awake at 6:50. • Analogy: rethinking about a situation based on a similar situation you already understand • Ex. Problem: teaching freshman about how supply and demand impact price • Strategy: make an analogy to the price of Xbox 360 prices over time.

7. Problem Solving • Insight: sudden realization of the solution, the “ah-ha!” moment. • most likely a swarm of unconsciously processing that occurs before we are consciously made aware of it.

8. Obstacles to Problem Solving • Everyone has a “mental set”: the typical strategies/ patterns of problem solving • Ex. Luke’s mental set held the belief that heavy objects cannot be moved with the Force

9. Obstacles to Problem Solving • Functional-fixedness: inability to imagine new uses for familiar objects. • Ex. Not using a dress-shirt as a bandage for a stranger’s bleeding wound. • Ex. Not using a dining hall tray as a sled (trust me, you will) • Can also assume certain restrictions on a problem. Define going “through” the maze…

10. Problem Solving Practice • A man and his son are in a car accident. The father dies on the scene, but the child is rushed to the hospital. When he arrives the surgeon says, “I can’t operate on this boy, he is my son! ” How can this be?

11. Problem Solving Practice • A woman had two sons who were born on the same hour of the same day of the same year. But they were not twins. How could this be so?

12. Problem Solving Practice The Cabin in the Woods Riddle. Don’t ruin it for those who have not heard it. “A man walking through the woods comes upon a cabin. Inside he finds a group of people (6 total), all of whom are dead. There is no evidence of a weapon or suicides (or of all dying of old age simultaneously). How did the people die?”