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Problem Solving
Lecture 19 Novick & Discussion 4/16
| Question | Answer |
|---|---|
| given that a problem has been identified, the nature of peoples background knowledge pertaining to that problem has important implications for the solution-related thinking they do & to understand this thinking it is important to distinguish | the solvers representation of the problem & the sequence of steps the solver takes to get from the given situation to the goal |
| a problem representation is a | model of the problem constructed by the solver to summarize his or her understanding of the problems essential nature |
| ideally a problem representation includes info about | the goal, the objects and their interrelations, the operations that can be applied to solve the problem, and any constraints on the solution process |
| for some problems the primary work of the solution is to | find the best representation; for other problems there is little uncertainty about the representation and the primary work is to discover a solution path form the initial state to the goal state |
| initial state in problems is | the situation as initially presented to the solver |
| the goal state of a problem is | what a person wishes to know or attain |
| the Tower of Hanoi problem the participant must | move a stack of disks arranged from largest to smallest on the leftmost peg to the rightmost peg but one at a time |
| researchers who study problem solving present people with various types of problems for which they don't have a pressured solution in memory and attempt to | find regularities in the resulting problem solving behavior |
| regardless of the specific problem type problem-solving behavior involves | an inherent interaction between constructing a representation and generating a solution |
| Newell and Simon constructed the General Problem Solver (GPS) | a computer program that modeled human problem solving and solved even very different problems using a single general-purpose strategy |
| what is the fundamental weakness of the GPS? | it lacks domain knowledge |
| the step-by-step solution process is the | sequence of actions solvers take to find and execute a procedure for generating a solution to the problem as they understand it |
| an algorithm is a | procedure that is guaranteed to yield to solution |
| exhaustive search a type of algorithm involves | checking every possible move |
| heuristics are | problem-solving strategies that accomplish the goal of pruning the number of possible moves to a solution but does not guarantee a solution but is highly likely to lead to success |
| the term problem space refers to | the solver's representation of the task as presented |
| a problem space consists of | a set of knowledge states (initial state, goal state, and various possible intermediate states), a set of operators that allow movement from one knowledge state to another, and local information about the path one is taking through the space |
| the current knowledge state is | the state at which the solver is located at any given point in the solution process |
| what is search? | a serial method for making incremental progress toward the goal by applying operators to move from one knowledge state to another adjacent knowledge state |
| think-aloud protocols involve | having the participants say out loud everything that they are thinking through verbal working memory as they solve a problem |
| the heuristic hill climbing is where | at each step the solver applies the operator that yields a new state that appears to be the most similar to the goal state |
| hill climbing can be used whenever | solvers can define an evaluation function that yields information about the similarity of the problem state generated by a candidate operator to the goal state |
| the heuristic means-end analysis doesn't depend on simple similarity to the goal and follows the 4 steps | identify a difference between current & goal state find operator to remove the difference apply operator directly if you can of set a subgoal to remove the obstacle that is preventing execution of desired operator repeat steps until problem is solved |
| what is the key difference between hill climbing and means-end analysis? | the online generation of subgoals in means-end analysis |
| what does adding new subgoals during problem solving do? | greatly increases the power of heuristic search because subgoals provide direction & prune the space of possible states and allows solvers to plan several moves ahead |
| by assessing progress toward a required subgoal rather than the final goal | solvers may be able to make moves that otherwise seem unwise |
| what heuristic does GPS use to successfully model human problem solving across a wide variety of tasks | means-end analysis |
| what is peoples preferred solution method for novel problems that are relatively free of specialized content and for which a definite goal is given? | means-end analysis |
| what doest the view of problem solving a search through a problem space not do? | doesn't provide a complete understanding of how people solve problems |
| in general whenever solvers have some relevant background knowledge they tend to | use stronger, albeit more narrowly applicable, domain-specific methods |
| in ill-defined problems | the goal is not well defined, nor is it clear how to determine that the goal has been accomplished |
| various aspects of the problem situation aw well as people's background knowledge affects | how people represent problems and, in turn how they generate problem solutions |
| a representation has 4 components | represented world, a representing world (set of elements to be used to depict the objects & relations), set of rules that map elements of the represented world to elements of the representing world, a process that uses the info in the representing world |
| without a process that uses the information in the representation fro some purpose.. | the so-called representation has no symbolic meaning |
| the representation a solver uses support and guide problem solving can be either | internal or external |
| problems that are presented as visual displays or diagrams may provide | information about the configuration that solvers deem relevant to the solution an include in their problem representation |
| Maier's 9 dot problem arranged in a 3 x 3 grid & the task is to connect all the dots by drawing 4 straight lines without lifting the pencil from the paper | initially people have difficulty because their initial representations include a constraint that the lines cannot go outside of the boundary however the solution involves going outside the imaginary box |
| in an insight problem the solution | appears suddenly, accompanied by an "aha!" sensation, immediately following the sudden restructuring of ones understanding of the problem |
| the phenomenon of functional fixedness is that | if an object has been used for one purpose, or is habitually used for certain purpose, it is difficult to see that object as having properties that would enable it to be used for a dissimilar purpose |
| and example of functional fixedness is the candles problem where | there are 3 candles to be mounted on a door and subjects are given 3 boxes filled with candles, tacks, and matches the solution is to mount the boxes to the wall with the tacks but most subjects don't realize the box is more than a container |
| in general the story content and phrasing of the problem text may affect | how the solver represents the problem |
| differences in the descriptions of the operators in two isomorphic problems yielded | quite different representations with important consequences for the problems relative difficulty |
| isomorphic means | structurally equivalent but different representations |
| in general solvers' background knowledge affects | whether and to what extent. they focus their attention on problem aspects that are or are not relevant to determining the solution |
| an example problem can be helpful for solving a novel problem only if | the two problems have a similar underlying structure because a problems structure is what determines appropriate solution methods |
| solvers' understanding or representation of a novel problem can be facilitated by | prior experience with an analogous problem |
| people may fail to retrieve an analogous problem of fail to apply an analogous solution if | they focus their attention on the solution-irrelevant differences between the example and the novel problem |
| Duncker's ray problem involves finding a way to use rays to destroy a stomach tumor which at high intensity will destroy the tumor but will also destroy healthy tissue & at lower intensity won't harm healthy tissue but also won't destroy the tumor | the solution is to project multiple low intensity rays from several points around the patient that will converge on the tumor and their intensities will sum to a level sufficient to destroy the tumor |
| solvers may fail to spontaneously notice the relevance of problems stored in memory for understanding and solving a current problem although | they are able to use the prior problem appropriately when its relevance is highlighted |
| an important factor that mediates the spontaneous retrieval and use of analogous solutions is | peoples understanding of the learned example |
| peoples ability to exploit analogous solutions also depends on | their domain expertise |
| solvers have in memory abstract schemas for | types of problems, types of solution procedures, and types of representations |
| schemas for solution procedures can be induced by | comparing 2 or more analogous problems (with their solutions) or by successfully solving one problem by analogy to another (solved) problem, and such schema induction facilitates understanding and solution of subsequent analogous problems |
| college students possess abstract schemas for 3 spatial diagrams that are important tools for understanding and solving problems from a variety of domains | matrices, networks, and hierarchies |
| a matrix is appropriate whenever: | all possible combinations of items across 2 sets must be considered, the relation between items is associative, it is imp. to be able to distinguish between items that are related and those that are not |
| abstract schemas provide a more reliable source of knowledge for understanding new problems that do specific example problems because | the schemas do not contain specific story content while example problems contain specific content that must be ignored when it mismatches the novel problems |
| experts and novices in a domain focus their attention on | different aspects of that domain, leading them to construct problem representations that are quite different |
| experts attention is quickly captured by meaningful configurations with an a presented stimulus so in a domain experts tend to | highlight solution-relevant structural features (in particular meaningful causal relations among the objects in the problem |
| novices attention is focused on isolated components of the stimulus so in a domain novices representations tend to | highlight solution-irrelvant superficial features (e.g. the particular objects themselves of how the question is phrased) |
| the domain of chess study involves participants viewing 20 or more chess pieces either from a real game or random for 5 seconds and have to reconstruct what they saw on a new chess board | when from areal game recall improves dramatically as a function of expertise from 5 pieces for novices & 20 for experts recall for random improves with expertise although the effect tis much stronger |
| there is better real of structured or meaningful stimuli by | experts than by novices |
| with increasing expertise/knowledge there is gradual change in | the focus of attention and in the problems that are seen as related, and the extremes are not quite as extreme as summaries of the differences often suggest |
| a problem consists of some | initial state in which a person begins and a goal state that is to be attained, plus a non-obvious way of getting from the first the second |
| a well structured or well-defined problem has | completely specified starting conditions, goal state, and methods for achieving the goal |
| what are the stages of problem-solving? | form a representation, construct a plan, execute plan, checking/evaluation and reformulate |
| in analogies people tend to miss deep similarities between problems because | they tend to focus on surface similarities |
| in top-down preconceptions when we look at a new problem | we tend to encode it in a way consistent with long-term memory |
| what is an operator in problem solving? | mental actions that will transform states |
| what is an intermediate state in problem solving? | what you visit on your way to the goal state |
| in problem solving you can be trapped by | your perspective that may not be helpful for the problem at hand or by a formula that was useful in the beginning so you stick to it even after it stops working or a quicker method is introduced |
| what is the isomorphic if the Duncker's ray problem? | the military problem of the general sending small groups of troops down several paths to meet at the castle and overthrow the dictator |
| in problem solving difference reduction is when | at any point you select the operator that moves you closer to the goal state |
Created by:
kzegelien2005
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