id: 02345645
dt: j
an: 2002c.02031
au: DeFranco, Thomas C.; Hilton, Peter
ti: Distinguishing features of mechanical and human problem-solving.
so: J. Math. Behav. 18, No. 1, 79-84 (1999).
py: 1999
pu: Elsevier, New York, NY
la: EN
cc: D50
ut:
ci:
li: doi:10.1016/S0732-3123(99)00019-X
ab: Over the years, research in mathematical problem-solving has examined
expert/novice problem-solving performance on various types of problems
and subjects. In particular, DeFranco examined two groups of Ph.D.
mathematicians as they solved four mathematics problems and found that
although all were content experts, only one group were problem-solving
experts. Based on this study, this article posits the notion that one
distinguishing feature between experts and novices is that experts tend
to look for special features of a problem and use algorithms only as a
’fail-safe’ system while novices act like ’machines’ relying on
algorithms to solve the problems. Why? The article explores the idea
that novice problem solvers learned to solve problems the way they
learned proof, that is, in a formal, abstract and mechanizable way.
Beliefs about proof and the culture in which it is practiced help frame
a mathematician’s view of the discipline and ultimately impacts
classroom practice. The authors believe that current classroom
instruction tends to create a culture that fosters algorithmic
proficiency and a ’machine-like’ approach to the learning of
mathematics and problem-solving. Further, they argue that
mathematicians need to be aware of the distinction between knowing a
proof is true and explaining why it is true. When these distinctions
are appreciated and practiced during classroom instruction, then and
only then will students begin to acquire the mathematical knowledge to
become better problem solvers.
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