Math Module?
The June, 2005, issue of Scientific American describes evidence (from a few studies of brain damage) that adults may process mathematical operations in brain areas that survive when language areas are damaged. Evidence from some autistic people also suggests that some kinds of arithmetic or mathematical ability can develop to high levels of functioning independently of other cognitive abilities.
Of course, animals regularly achieve results that duplicate mathematical operations. For example, the dog that does calculus:
http://www.sciencenews.org/articles/20030607/mathtrek.asp
Humans probably do similar minimization problems. For example, in running errands, humans probably approximate some kind of least cost strategy. Researchers, with sufficient computer power, would probably find evidence that the humans do not use the “optimal” strategy. But these are researchers who don’t pay for computing time, programming, data entry, and the like.
Thinking about these modules makes me think of developments on computer science. Certainly one trend is the development of modules that can be called by a high level scripting language. The reasoning from people working in this area is that software can be efficiently customized for each user by selecting or adjusting the script.
I suppose we could view the development of human skills in a similar fashion. First people develop basic skills. Later they develop scripts to put the skills together in standard ways. Still later, they may develop the ability to write new scripts (plans).
In computer work, a person writing high level scripts would want to know about lower level modules. The person would want to know what the modules do and how they interface with each other. Such considerations might apply to educational plans as well as to concepts of self-growth.
Back to the mathematical and verbal modules: One educational problem is teaching children to translate word problems into mathematical operations. This looks like a problem of module interface. It also parallels the problem of instruction manuals, which seem to be planned as a demonstration that people can’t read. See:
http://thinkerer.org/Background/BakInsrtuct.htm
Both educators and some people who prepare instruction manuals have devised alternative presentations in the form of cartoons, maps, and animations. Presumably these are efforts to avoid problems with the language interface.
At another level, people could learn to do the same sort of thing for themselves. Children must learn to do this in word problems, since they eventually do learn to handle word problems. Adults will not have to learn to do this with assembly instructions if vendors pay for professionally prepared assembly instructions. But now that adult education is increasingly important, adults may have increasing need for “self-scripting.”
Do we know how to guide people in self-scripting? Does it just come naturally to people? Do people even realize that this is something they may want to learn?
Of course, animals regularly achieve results that duplicate mathematical operations. For example, the dog that does calculus:
http://www.sciencenews.org/articles/20030607/mathtrek.asp
Humans probably do similar minimization problems. For example, in running errands, humans probably approximate some kind of least cost strategy. Researchers, with sufficient computer power, would probably find evidence that the humans do not use the “optimal” strategy. But these are researchers who don’t pay for computing time, programming, data entry, and the like.
Thinking about these modules makes me think of developments on computer science. Certainly one trend is the development of modules that can be called by a high level scripting language. The reasoning from people working in this area is that software can be efficiently customized for each user by selecting or adjusting the script.
I suppose we could view the development of human skills in a similar fashion. First people develop basic skills. Later they develop scripts to put the skills together in standard ways. Still later, they may develop the ability to write new scripts (plans).
In computer work, a person writing high level scripts would want to know about lower level modules. The person would want to know what the modules do and how they interface with each other. Such considerations might apply to educational plans as well as to concepts of self-growth.
Back to the mathematical and verbal modules: One educational problem is teaching children to translate word problems into mathematical operations. This looks like a problem of module interface. It also parallels the problem of instruction manuals, which seem to be planned as a demonstration that people can’t read. See:
http://thinkerer.org/Background/BakInsrtuct.htm
Both educators and some people who prepare instruction manuals have devised alternative presentations in the form of cartoons, maps, and animations. Presumably these are efforts to avoid problems with the language interface.
At another level, people could learn to do the same sort of thing for themselves. Children must learn to do this in word problems, since they eventually do learn to handle word problems. Adults will not have to learn to do this with assembly instructions if vendors pay for professionally prepared assembly instructions. But now that adult education is increasingly important, adults may have increasing need for “self-scripting.”
Do we know how to guide people in self-scripting? Does it just come naturally to people? Do people even realize that this is something they may want to learn?
posted by Selby Evans at 10:54 AM
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