updated for Fall 2005
Examples of items allowed and not allowed in a library. http://www.ils.unc.edu/dataMining/examples/davis.htmlWork by Jerome Bruner led to the "classical view" of concepts. According to the classical view, concepts are mentally represented by abstract rules that are learned. For example, the concept of "dog" might be represented by:
* has four legs
* has tail
* does not say "meow"
However, the classical view can not account for fuzzy concepts, dogs with three legs, etc.
Another approach is the prototype view of concepts. According to the prototype view, humans store a single prototype (typical example) for each concept. New instances are judged according to how similar they are to the prototype.
The exemplar view is a third theory of concepts, according to which the person remembers a number of examples for each concept.
All Scots are mortal.
Robert is a Scot.
Therefore Robert is mortal.
Robert is mortal.
Robert is a Scot.
Therefore all Scots are mortal.
Robert has red hair.
Robert is a Scot.
Therefore all Scots have red hair.
Pure discovery learning, in which children are provided materials but no learning goals or scaffolding, rarely works.
"There is sufficient research evidence to make any reasonable person skeptical about the benefits of discovery learning....Overall, the constructivist view of learning may be best supported by methods of instruction that involve cognitive activity rather than behavioral activity, instructional guidance rather than pure discovery, and curricular focus rather than unstructured exploration."
-- Richard Mayer (2004, p. 14)
Algorithms = Rigid procedures that always produce the solution.
Heuristics = Guidelines that are not guaranteed to produce the solution.
Problems that can be solved by algorithms are well-defined, well-structured problems. Problems that can only be solved by heuristics are ill-defined, poorly structured problems.
Experts are able to:
* Perceive large, meaningful patterns in given information.
* Perform tasks quickly.
* Deal with problems at a deeper level.
* Recall larger chunks of information.
* Spend greater portion of time in problem analysis phase.
* Monitor and correct their own performance more effectively.
By repeated practice, experts have automatized response patterns and chunked information into more complex patterns. This frees cognitive resources for the deeper aspects of the problem.
Example: Musicians practice to automatize the mechanical aspects of performance so they can concentrate on interpretating the music with deep emotional expression.
Herbert Simon
1916-2001
Herbert Simon won the Nobel prize in economics in 1979 for research in human decision making. Among his many contributions were general problem solving strategies used in Artificial Intelligence (AI).
A problem can be defined as a start state, a goal state, and a set of possible operations. The operations implicitly define a "state-space" including the start and goal states. To solve the problem is to find a sequence of operations that will allow one to move from the start state to the goal state. For example, see this web page about how computers can solve the eight puzzle.
The diagram below shows a state space containing a start state and a goal state. The black lines represent possible transitions (operations) between states.
Means-ends analysis is a method described by Simon where the problem solver tries to divide the problem into smaller problems (sub-problems). To define a sub-problem, one of the intermediate states is treated as a temporary goal state and another is treated as a temporary start state. Then the problem solver tries to find the path between the start and goal states of the sub-problem.
Often, solving a few sub-problems will make it easy to solve the whole problem.
One heuristic for selecting an operation (transition) is to choose one that makes the greatest reduction in distance between the current state and the goal state.
Another heuristic is to work backwards from the goal state (the "working backwards" strategy).
One finding of research in problem solving (AI and cognitive science) is that general strategies are weak compared to strategies that use context-specific information.
In other words, problem solving expertise tends to be specific to a domain. Studying means-ends analysis won't improve your ability to solve algebra word problems very much. Studying (and doing) more word problems is a better path to word problem expertise. Expertise is developed by practice with real problems in the domain.
Transfer of learning is fundamentally important to education. Unless school learning transfers to situations outside the classroom we are wasting our time!
Psychologists talk about near transfer (transfer to similar situations) and far transfer (transfer to dissimilar situations).
Very little research has looked at far transfer of school learning. We have a poor understanding of the direct usefulness of school learning outside the classroom. What are the implications of this ignorance?
Low road transfer results from practice and automatization of knowledge.
Positive transfer. Example: From tennis to raquetball.
Negative transfer. Example: When pilots switch to a different aircraft, differences in the cockpit design have been known to result in unsafe actions.
High road transfer results from mindful abstraction.
For example: When you learn about a specific case, you generate a general principle that is consistent with the case and is useful in understanding other cases.