THINKING AND PROBLEM SOLVING

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.

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

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

Problem-Solving1. Trial and error: very basic, not recommended2. Means-end analysis: assess what outcome (end)

various actions (means) will have for us1. Ex. Problem: big college exam tomorrow

1. Means: get to sleep early tonight end: well-rested for test2. Means: All-nighter studying end: cram in that last bit of info

3. Break larger tasks down into smaller parts1. Ex.15-page term paper breaks down to research topic, develop

thesis, outline paper, write topic sentences, fill-out paragraphs, revise

Problem-Solving1. Work the problem backwards

1. You need to be at school by 7:38, in the car by 7:15, awake at 6:50.

2. Analogy: rethinking about a situation based on a similar situation you already understand

1. Ex. Problem: teaching freshman about how supply and demand impact price

2. Strategy: make an analogy to the price of Xbox 360 prices over time.

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.

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

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…

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?

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?

Problem Solving PracticeThe 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?”