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Gifted Education

Nurturing Mathematically Gifted Children

This article was originally published by Deccan Herald.

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A  crucial part of a nation’s human potential lies in individuals gifted in STEM: Science, Technology, Engineering, and Mathematics. Identifying and nurturing children gifted in STEM deserves special attention and presents special challenges.

First, research suggests that the mathematically gifted stand out less than the verbally gifted, making identification from casual observation less likely. Second, the ability profiles of the mathematically gifted may be less balanced (Benbow C P & Minor L L 1990, Gifted Child Quaterly): their probably average performance in other areas may mask their mathematical ability. This applies to both classroom performance and IQ tests. Teachers as well as psychometrics pay more attention to the overall performance rather than the standout performances in specific areas. Finally, while early identification is important for all gifted children, it may be particularly so for the mathematically gifted.

In Mathematics, achievement tends to occur in a relatively short timespan, early in life. Early identification and appropriate support increase the chances of mathematically gifted children developing their potential. So, how do we identify mathematically gifted children? Among standardised ability tests, there are two options:

Culture-free tests: These are especially appropriate for identifying mathematically gifted children from disadvantaged backgrounds, who may be missed out by verbal IQ tests.

Performance-based IQ tests: Pay attention to subscores for quantitative reasoning, spatial ability, memory, and speed — key areas in which the mathematically gifted stand out.

Mathematical ability often emerges early. It is sometimes confused with computational power or mental arithmetic skills. While research is mixed on whether mathematicians were skilled at computation as children, it is clear that computational power is distinct from the much broader construct of mathematically ability. Some mathematically gifted children excel at computation, but not all children good at mental arithmetic are mathematically gifted.

Who are the gifted?

Mathematically gifted children tend to show:

Interest in numbers and mathematical concepts.
Skills for abstract thinking and logical reasoning. Understanding the concept of mathematical proof. Age-atypical use of logical connectives: “if-then, because-so, either-or.”

Ability to identify patterns and rules.
Interest in construction toys and pleasure in balance and symmetry.  
Interest in simple, elegant solutions, and in conciseness. 

Ability to transfer mathematical concepts to novel problems or contexts. For instance, ‘deep transfer’ occurs when a child grasps the underlying similarity between two problems that look superficially different. Normal children identify misleading superficial similarities between problems.

Ability to use inductive reasoning to identify the principle underlying a type of problem and to formulate new mathematical problems using synthetic thinking.

Flexibility : being able to switch between problem representations and strategies (graphical, algebraic, or numerical).

Their persistence when facing novel and challenging mathematical problems contrasts with the fear and frustration of most children in the same context.

In fact, a good context to assess ability is by presenting potentially gifted children with novel and challenging problems.  When children are asked to think aloud while solving hard Maths problems, the mathematically gifted show a systematic approach. They take the time to understand the problem, spend more time in the planning stages, develop an appropriate problem representation, plan their approach instead of using trial-and-error, self-monitor their progress, are able to track back when they encounter difficulties, can flexibly switch strategies, and spontaneously check their own work. 

It is seen that parents themselves are unlikely to be able to stimulate mathematically gifted children. Some options to explore are:

Subject-specific acceleration is the simplest way to meet the educational needs if your child excels in Mathematics, but is average in other subjects. 

Advanced and college-level Math courses online.
Identify a (preferably still active) mathematician or Maths educator.
Participate in Mathematics competitions. For instance, the Maths Olympiad. Well-organised competitions encourage self-directed learning skills, and provide rare and valuable opportunities to interact with other gifted children.

Teachers can play a great role in this context. It is observed that in many classrooms, one barrier to the identification of such kids is the insistence on the final answer by following one specific method. Many mathematically gifted children skip steps; their tendency not to “show work” may lose them marks or even attract accusations of cheating. Try to orally elicit the method followed, and focus more on the child’s process of exploring and evaluating different strategies for the same problem.

Children who regularly engage in high-level thinking and problem-solving out-perform those without such opportunities. Mathematically gifted children themselves tend to prefer hard problems; they find it difficult to tolerate the slow pace, scaffolding, and revision characterising most mixed-ability classrooms (Carmel M Diezmann & James J Watters 2002, Proceedings 25th Annual Conference of the Mathematics Education Research Group of Australasia).

It is true that average and weak students benefit from scaffolding — the teacher breaking the problem into sub-steps and providing levels of support appropriate to each child’s ability. But for the mathematically gifted, scaffolding renders Maths class even duller. An alternative is “problematisation” — a type of curriculum differentiation where existing problems, presented to the whole class, are elaborated to make them more challenging for the gifted.

For instance, a problem given to the class reads as follows: Raj, Priya, Sanjay, and Sushma are having a party. Raj spends Rs 120 on balloons; Priya buys a cake for Rs 300; Sanjay engages a DJ for Rs 500; and Sushma buys snacks and drinks for Rs. 400. To share expenses equally, how much should each of them give or get from the others?
The add-ons that you could give to the mathematically gifted are:

Represent this paper graphically.

Raj and Priya have no money now, so apart from their own expenses, they pay nothing now. They will repay the others six weeks later, paying interest at nine per cent per annum. How much will Raj and Priya now be repaying?

Sanjay and Sushma each bring three guests, and must also pay their guests’ share. How much do Raj, Priya, Sanjay, and Sushma now owe each other?

For a class four child whose maths ability is at a sixth standard level,  problematisation allows creative teachers to generate appropriately challenging problems. Having said that, problems should be challenging but still within the child’s limits. Otherwise, you will just end up irritating the child.

Allowing children to bring games, puzzles, or workbooks after finishing classwork is a simple way to engage them productively. But this doesn’t relieve teachers of their obligations. Some gifted children value achievement over learning, and may always prefer easy tasks rather than risk undertaking a challenging problem, at which they may fail. Teachers must regularly monitor mathematically gifted children to ensure that their classroom pursuits provide a balance of achievement and challenge.

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By Amita Basu

I'm a writer based in Bangalore, India.

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