Claudia Stanny wrote:
> You might be interested in John Anderson's work on teaching
> mathematics. He is particularly interested in the way that children, when
> confronted with a problem that requires knowledge of a mathematical
> operation they don't know, will misapply an operation that they do know or
invent an
> operation of their own. (He calls these computational bugs.)
Alternatively, the phrase "cognitively guided instruction" should provide a
nice search term for what you're interested in (sorry - I don't have the
time right now to provide summaries of the actual works). Elizabeth Fennema
or Penelope Peterson would be the authors you'd want to look into. I did
some of the grunt work on their research in the 80s, aimed directly at
improving elementary/secondary mathematics education through attention to
cognitive principles.
Paul Smith
Alverno College
Milwaukee
