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Tuesday, February 24, 2015
TRAITS OF MATHEMATICALLY ABLE CHILDREN
TRAITS OF MATHEMATICALLY ABLE CHILDREN
• Ability to make and use
generalisations—often quite quickly. One of the basic abilities, easily
detectable even at the level of primary school: after solving a single example
from a series, a child immediately knows how to solve all examples of the same
kind.
• Rapid and sound memorisation of
mathematical material.
• Ability to concentrate on mathematics
for long periods without apparent signs of tiredness.
• Ability to offer and use multiple
representations of the same mathematical object. (For example, a child switches
easily between representations of the same function by tables, charts, graphs,
and analytic expressions.)
•
An instinctive tendency to approach a problem in different ways: even if a
problem has been already solved, a child is keen to find an alternative
solution.
• Ability to utilise analogies and make
connections.
• Preparedness to link two (or more)
elementary procedures to construct a solution to a multi-step problem.4 A. V.
BOROVIK AND A. D. GARDINER
• Ability to recognise what it means to
“know for certain”.
•
Ability to detect unstated assumptions in a problem, and either to explicate
and utilise them, or to reject the problem as ill-defined.
• A distinctive tendency for “economy of
thought,” striving to find the most economical ways to solve problems, for
clarity and simplicity in a solution.
• Instinctive awareness of the presence
and importance of an underlying structure.
• Lack of fear of “being lost” and having
to struggle to find one’s way through the problem.
• A tendency to rapid abbreviation,
compression or a curtailment of reasoning in problem solving.
• An easy grasp of encapsulation and
de-encapsulation of mathematical objects and procedures. These terms are less
frequently
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