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| | Characteristics of "Good/Successful"
Problem Solvers
There are no exact set of characteristic that guarantee that you will
be a "good problem solver". But there are some characteristics
that many "good problem solvers" seem to posses.
In the studies on how "good" and "poor" problem solvers
differ (mostly developed by Alan Shoenfeld, 1985, 1987)
it was pointed out that the distinguishing characteristics between the two
groups include five important respects:
- Good problem solvers know more, and what they know, they know differently
-- their knowledge is well connected and composed of rich
schemata.
- Good problem solvers tend to focus on structural features of
problems, poor problem solvers focus on surface features.
- Good problem solvers are more aware of their strengths and
weaknesses.
- Good problem solvers are better at monitoring and regulating their
efforts.
- Good problem solvers tend to be more concerned about obtaining elegant
solutions.
Of the research that has been done, the following key results were
observed (Lester, 1994):
- Students must solve many problems to improve problem solving
abilities.
- Problem solving abilities develop slowly over a prolonged period.
- In order for students to benefit from instruction, they must believe
that their teacher thinks problem solving is important.
- Most students benefit greatly from systematically planned problem solving
instruction.
- Teaching students about problem solving strategies and heuristics
and phases of problem solving does little to improve students’ ability to
solve mathematics problems in general.
Research indicates that problem solving can be improved through
teachings in the classroom, but to teach directly the steps of a system of
strategies alone does not benefit the student. The ability to learn and
use strategies and heuristics develop slowly over time in much the same way that
other mathematical ideas are known to develop (Lester, 1994).
Suggestions for increasing problem solving effectiveness in the classroom
include:
- Encourage a spirit of play
- Avoid teaching algorithms as a primary method for solving.
- Make "looking at the problem" a meaningful first step - for
example, to exploit any special features of the problem that might lead to
an insightful solution
- Engage in creative exercises - get students to feel comfortable thinking
"outside of the box"
- Value multiple approaches to a problem
- Look back and evaluate which solutions are more elegant than others
- Value error as an opportunity for insight
- Encourage students to verbalize, explain and/or prove that their solution
is a valid one.
- Reflect, Reflect, Reflect - on solutions, even if correct - take the
opportunity to build mental schemata
- Create a culture of "sense-making" in the classroom
This facts in this document are based on studies found at this
web site
Source: http://www.tvdsb.on.ca/banting/ICS3U/unit2/Good.htm
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