PSYCH 240 1ST Edition Lecture 18 Outline of Last Lecture: Motor SkillsI. Skill AcquisitionII. Motor Program RepresentationsOutline of Current Lecture: Episodic MemoryIII. Skill AcquisitionIV. Motor Program RepresentationsCurrent Lecture: Lecture 18: Problem Solving (April 6, 2015)I. Problems and problem representationi. Problem: consists of some initial state in which a person begins and a goal sate that is to be attained, plus, a non-obvious way of getting from the 1st to the 2nd b. Types of Problemsi. Well-structured (well-defined)1. Completely specified starting conditions, goal state, and methods for achieving the goala. Geometry proofsii. ill-structured problems (ill-defined)1. some aspects are not completely specifieda. finding the perfect mateb. choosing a careerc. writing the best novelc. Stages of Problem Solving (Polya, 1957)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. Goal StateInitial StateMethodsi.ii. Problem Solving Concepts1. Initial goal states2. Intermediate goal states3. Representation of problem4. Operators: actions that move btwn states5. Problem space: whole range of possible states and operators, only someof which will lead to goal stateiii. Example1. The price of a notebook is four times that of a pencil. The pencil costs $.30 less than the notebook. What is the price of each?a.2. The Nine Dot Problema. There are 9 dots arranged in a square. Using no more than 4 lines, connect all the dots w/o lifting your pencili. Initial and goal states definedii. Operators: four connected linesiii. Representation: graphical layoutiv. Problem space: all possible lines you can drawd. The importance of problem representationi. For many problems, the representation may make it easier or harder to solve1. Algebra problems easier as equations2. Geometry problems easier graphically3. Decision problems easier when relevant info is laid out in a gridii. Examples1. Monka.b. Problem representation: Is there a spot along the path that the monk will occupy on both trips at precisely the same time of day?i. Text-based representation difficultii. Imagining a single monk walking up and down the mountain misleadingiii. Modify representation to an isomorphic problem: two monks1. Both leave at the same time2. One from the top of the mountain3. One from the bottom of the mountain4. At some point, they must meet2. Paper Foldinga.b. How Thick? Visualization doesn’t helpi. .01*2^50 inches = 177.7 million miles3. Number Scrabblea.b. Two players, each draws one card at a time. First player to hold 3cards that sum to 15 wins.i. Isomorphs: equivalent problems, different representationsII. Common flaws in problem solvinga. Analogiesi. Retrieve a representation of a problem from memory that is similar to the problem you currently faceii. People tend to miss deep similarities btwn problems, b/c they tend to focus on surface similarities1. Duncker’s Ray Problem2.3. Real world solution: use sub-lethal doses coming in from different directions4. 10-2-% of subject came up w/ this spontaneously5. Would analogy help?a. Gick and Holyoak (1980) presented subjects w/ story about a general6. Military Problema.b. Analogous to Ray problemc. Participants were either asked to solve ray problem alone, or after reading military problem (analogy)d. Some in analogy condition were given hint: “Can you use the military problem to help you solve the ray problem?”e. Results: few subjects spontaneously used analogyi.f. Keane (1987) asked ppl to “Recall Analogous Stories”g. Subjects heard military problem, ray problem, and a modified military problem (general destroying fortress w/ rays)i. Same deep problem structureii. New problem had more similarity of surface featuresh. Problems w/ greater surface similarity recalled more oftenb. Hindrances to forming appropriate representationsi. Top-down preconceptions1. When we look at a new problem, we need to encode it in a way consistent w/ LTM2. Functional fixedness: see an object as having only a fixed, familiar function3. Duncker’s Candle problem demonstrates this effect: how can you use the following items to support a candle on a wall?a. Candle Problem: i. Initial problem state affects the types of solutions people will entertainii. Improvements when tacks are not initially inside the boxiii. Improvements when the box is referred to explicitly4. Maier’s two-rope problema. Demonstrates functional fixednessb. People think of the pliers as a grabbing device, not a pendulum5. Trains Meeting Problema.i. Trapped by a familiar perspective1. Most people take perspective of bird2. Some might use adv. Math of infinite series and limits3. BUT, just notice how long the trains will travel (1hour)4. Bird, flying at 100 miles/hour, travels 100 miles6. Luchin’s Water Jar Problema.b.c. Interim Summaryi. Problem solving components: 1. Problem space, operators, statesii. Importance of representationiii. Ability to notice analogy1. Improved when surface features are similariv. Functional fixednessv. Stuck in set: improper application of analogous solutionsIII. Problem solving methodsa. Algorithms: completely specified sequence of steps that is guaranteed to produce an answeri. Usually guaranteed to produce the correct answerii. But may be slow and laboriousb. Heuristics: short cut/”rule of thumb”i. Never guaranteed to produce correct answerii. But usually quick and easy1. Difference Reduction a. Hill climbingi. At any point, select the operator that moves you closer to the goal state: is new state more similar to goal?1. (never choose an operator that moves you away)b. Lord of the Ringsi.2. Means-ends analysisi. Identify the largest difference btwn current state and goal stateii. Set as a subgoal reducing the differenceiii. Find and apply an operator to reduce the difference iv. (if operator can’t be applied, new subgoal = remove obstacle that prevents applying the