Adamson Wing, Baker Hall
T/Th 9:00-10:20
| Fall 2000
Adamson Wing, Baker Hall T/Th 9:00-10:20 |
|
85-411/85-711/15-886A
Cognitive Processes and Problem Solving
Past Topics for Term Project
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version of this list.
A. Memory
1. Capacity of visual memory. A widely accepted hypothesis about short-term acoustic memory is that subjects retain the information by rehearsing it (silently or aloud). Capacity is explained by the length of the internal loop as well as the time required to rehearse. It is not known whether visual STM can be explained in the same way. This might be tested by using as stimuli diagrams (line drawings) of varying degrees of complexity and composed of chunks of various sizes and various degrees of familiarity to different subjects, to see how much and what kinds of information can be retained, after what length of exposure to the stimuli.
2. Organization of a memory to hold information about specific events and information about general concepts. People are able to retain information about specific events in their lives (episodic memory), and also about general concepts and information relevant to them (semantic memory). Design a program that will accommodate both kinds of memory in a way that is consistent with experimental and observational evidence. In particular, are there ways of accommodating both kinds of memory in an EPAM-like structure?
3. Differences among professions in ways of representing and solving problems. It has been hypothesized that people trained in different professions use different problem-solving styles in tackling the same problem. Ask sets of subjects from different professions (e.g., law, engineering, medicine, economics, physics) to construct a set of public policy recommendations on a topic like disposal of nuclear wastes, unemployment or public education. There seem to be quite striking differences in the ways these professions reason about risk taking and assignment of liabilities for social costs of various kinds. Take thinking-aloud protocols while they are planning and writing their answers to problems. Analyze the protocols for differences in the aspects of the situation they take into consideration and in their styles of reasoning. The latter — styles of reasoning, is an especially promising area. (See also other topics on problem representations, below.)
4. Memory storage of information about "how things work."
Instruct subjects to plan a set of annotated diagrams and drawings that
will explain to a layman how a telephone (an automobile, a can-opener,
a radio, canal locks) operates. From protocols infer the extent of
subject's information about the device, and how that information is organized
in memory
B. Methodology of Thinking Aloud Procedures
1. Effects of thinking aloud on problem solving.
Some studies have shown that think-aloud instructions may improve, rather
than hurt, problem-solving performance, and, in particular facilitate transfer
of skill from the 4-disk Tower of Hanoi problem to 5-disk and 6-disk problems
(Gagné & Smith, 1962; Wilder & Harvey, 1971). These
studies have generally measured only amount of talking, and have not done
thorough analyses of the protocols. One hypothesis is that transfer
will be assisted only for subjects who try to reflect on their moves to
discover why they do or don't work (Anzai & Simon, 1979). Test
this hypothesis, using protocol analysis.
C. Effective and efficient learning
1. Teaching and learning problem-solving strategies. Subjects who learn to solve the Chinese ring puzzle, or any of its many isomorphs, are seldom able, even afterwards, to give a coherent account of just how they go about solving it — what their strategies are. The effects of teaching them specific strategies explicitly have not been studied. Devise three or four different strategies that will solve the puzzle reliably and test how long it takes to train subjects to use the strategies effectively. Explain the differences in trainability that are revealed. [A similar project could be undertaken for many tasks besides the Chinese ring puzzle. What other tasks — perhaps a little more complicated than tying shoelaces — can you think of that people perform without being able to describe what they do and why?]
2. Structure of text and ease of memorization. On the basis of the memory theories we have studied, we would predict that the speed with which people can memorize poetry would depend upon the presence or absence of rhyming and regular rhythms, the complexity of grammatical structures, and perhaps other factors that would determine chunk size and redundancy. Formulate a set of more specific (and quantitative) predictions, and test them experimentally. [This need not be done with poetry; how about memorizing cooking recipes; or directions for getting to a restaurant on Mt. Washington?]
3. Textbook presentation for effective learning.
In a textbook for one of the courses you are taking, select a section of
a chapter that deals with a specific learning goal. After analysing
the structure of the task, and what learning it requires, write an alternative
version of that section which you think will be more effective in helping
students reach the learning goal, and test your product by taking and analysing
think-aloud protocols of students using each of the versions of the text.
D. Problem representation
1. Effectiveness of alternative problem representations. Pick a problem in a subject familiar to you (e.g., electric circuits, Gothic Revival architecture, football strategy, . . .) and design two quite different computer displays for presenting the problem to subjects who are asked to solve it. The different presentations might use different kinds of diagrams, or one with and one without diagrams, or diagrams versus equations, or moving versus static computer displays. Use protocols to determine and explain the effects of these differences in presentation upon behavior in understanding and solving the problems.
2. Processes for understanding problems prior to solving them. Describe and program an improved version of the UNDERSTAND program, a theory constructed by Hayes & Simon to show how a human problem solver can construct an internal representation of a problem that is presented verbally, and how the internal representation varies with changes in the precise language of presentation.
3. How are effective problem representations discovered? Some tasks are easy if formulated and represented in the right way, difficult if they are not represented appropriately. (The mutilated checkerboard is a classical example.) Select such a task and (1) take protocols of subjects who arrive at a good representation (with or without hints), then (2) write a program that is capable of detecting the need for a change in representation, gathering information for designing it, and constructing it. (See Kaplan & Simon for the mutilated checkerboard example.) Chemistry, with its different notations for representing molecules and reactions might be a suitable domain. Examples of good problems might be found in textbooks on object-oriented programming, which generally emphasize selection of appropriate problem representations, even if they don't yet have much of a theory about how to do it.
4. How students find mathematical representations for problems that are presented verbally. Replicate the findings of Paige and Simon (Simon I:4.4) using "impossible" problems (problems that violate real-world conditions) in physics or chemistry instead of algebra.
5. Selecting the objects and representations in object-oriented
programming. Research by Kim, Leech and Simon has shown
that success in creating an effective program for solving a class of problems
may depend critically upon the choice of objects and representation.
This was demonstrated on materials as simple as isomorphs of the Tower
of Hanoi problem. How could programmers be trained to discover and
choose problem representations and objects that would facilitate OOP. (HAS
has a set of problems that could be used in this project.)
E. Problem solving
1. Relative power of different problem-solving methods. You are probably familiar with water-jug problems: there are N jugs, each with a different (given) capacity. You may fill or empty these jugs, or pour from one to another. The problem is to construct a sequence of operations that will produce a specific quantity of water in one of the jugs. (E.g., given jugs of 2, 6 and 11 gallons; measure out exactly 7 gallons). Write three programs (production systems) embodying different methods for solving such problems. Evaluate these alternatives for the psychological demands they make (e.g., demands on STM) and their advantages and disadvantages for transfer to more or less similar problems; and predict the circumstances under which humans will learn to use one or another of the methods.
2. Individual differences in problem-solving strategies. Construct a computer program that solves cryptarithmetic problems and matches closely the behavior of the subjects whose protocols are reported in Newell & Simon. The program will need to have several variants to match the behavior of different subjects. Construct these variants in a psychologically plausible manner that reveals the underlying similarities in strategy as well as the differences.
3. Effect of instructions upon problem solving strategies. How easy or hard is it to alter the strategies people use in solving a problem by varying the problem instructions? (We can provide relevant materials to elaborate on this theme, deriving from the work of Medin and Smith on pattern classification and recognition).
4. Describing student skills as systems of productions.
Describe (and construct, if possible) a production system that will solve
the problems at the end of one of the chapters in one of your textbooks.
Analyze the text of the chapter to determine whether the information in
it is appropriate in order that a student may acquire the requisite productions
by studying it. If it is deficient in any respects, show how the
deficiencies can be remedied.
F. Scientific discovery
1. Processes for discovering new scientific instruments. Construct a computer model to simulate the process of using observed phenomena to invent new measuring instruments. (E.g., a model that, on observing the expansion of certain materials on heating, would invent a thermometer.) The main thing here is to specify what the system would have to know in order to do this; what observational capabilities you would have to postulate, and what goals.
2. Processes for finding lawful patterns in pictorial data. The data from some experiments in biology consist of microscope slides with certain kinds of objects (cells, chromosomes, bacteria) distributed over them. Detection of patterns in these distributions can sometimes lead to the discovery of important laws. Write a computer program capable of detecting interesting patterns in these kinds of data. The program should use only processes that, on the basis of our psychological knowledge, we believe people would be capable of using.
3. Representations of magnetic induction of electrical current. Several researchers have sought to model the successive representations that Michael Faraday used to hypothesize about electromagnetic induction. Considerable additional work needs to be done to program the representations so that their effectiveness can be tested. (HAS can supply relevant reprints.)
4. Extension of the BACON system by addition of exponential, logarithmic, and trigonometric functions. The BACON scientific law discovery system finds laws by looking for patterns in data sets it is given, without knowledge of any theory relating to the data. At present it only uses rational functions in its search. What additional examples of discovery could it handle if its stock of functions were increased, with appropriate measures taken to prevent the amount of search from exploding? Construct such an extension of BACON and demonstrate its ability to solve some historically important scientific problems.
5. Sources of representations used in quantum theory and quantum mechanics. Quantum theory has gone through a whole series of changes in representation from the early formulation of Planck, in 1900, through Bohr's planetary model of the hydrogen atom, in 1912, to the wave mechanics of Shrödinger and the matrix mechanics of Heisenberg, in 1926. How could any or all of these representations be generated from experimental evidence and/or analogies?