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Tuesday, February 24, 2015


• 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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