Mathematical Intelligence

Mathematical Giftedness

The construct of intelligence in general and mathematical intelligence in particular have been topics of great controversy since the advent of psychometric testing. For example, most modern-day intelligence tests, which have evolved out of the original Binet-Simon test and the Stanford-Binet test developed by Lewis Terman, consist of subtests that measure numerical reasoning, digit memory, letter–number sequencing, digit symbol-coding, picture completion, block design, matrix reasoning, symbols, and object assembly. In other words, logical, quantitative, and visual-spatial reasoning play a significant role in IQ tests. This view of intelligence has been criticized as being problematic, however, because the items do not take into consideration sociocultural and environmental variables that can influence performance, particularly among minorities and non-native English speakers. High scores on the Stanford-Binet have been traditionally used as an indicator of giftedness and a predictor of academic success in school and beyond. Similarly, psychometric batteries such as the SAT, ACT, and GRE (Graduate Record Examination) consist of a mathematics portion that claims to predict academic success in college.

In the studies conducted in the domain of cognition, mathematical intelligence in an individual can be defined in terms of the following: (a) the ability to abstract, generalize, and discern mathematical structures; (b) the ability to employ data management techniques; (c) the ability to master principles of logical thinking and inference; (d) analogical, heuristic thinking and posing related problems; (e) flexibility and reversibility of mathematical operations; (f) an intuitive awareness of mathematical proof; (g) the ability to independently discover mathematical principles; (h) the ability to apply decision-making abilities in problem-solving situations; (i) the ability to visualize problems and/or relations; and (j) the ability to distinguish between empirical and theoretical principles.

Mathematical intelligence in the general population has been classified by numerous theorists using a hierarchical model. For instance, Zalman Usiskin, a mathematics educator at the University of Chicago, proposed an eight-tiered hierarchy to classify mathematical talent, which he ranges from Level 0 to Level 7. In this hierarchy Level 0 (No Talent) represents adults who know very little mathematics; Level 1 (Culture level) represents adults who have rudimentary number sense as a function of cultural usage, and their mathematical knowledge is comparable to those of students in Grades 6–9. It is obvious that a very large proportion of the general population would fall into the first two levels. The remaining population is thinly spread out into Levels 2 through 7 on the basis of mathematical talent. Level 2 represents honors high school students who are capable of majoring in mathematics as well as those who eventually become secondary math teachers. Level 3 (the “terrific” student) represents students who score in the 750–800 range on the SATs or 4 or 5 in the Calculus AP exams. These students have the potential to do beginning graduate-level work in mathematics. Level 4 (the “exceptional” student) represents students who excel in math competitions and receive admission into math/science summer camps and/or academies because of their talent. These students are capable of constructing mathematical proofs and able to “converse” with mathematicians about mathematics. Level 5 represents the productive mathematician. This level represents students who have successfully completed a Ph.D. in mathematics or a related mathematical science and are capable of publishing in the field. Level 6 is the rarified territory of the exceptional mathematician; it represents mathematicians who have made significant contributions to their particular domains and been conferred recognition for their work. Finally, at Level 7 are the all-time greats, including the Fields Medal winners in mathematics. The Fields Medal was established by John Charles Fields (1863–1932) and is the equivalent of the Nobel Prize for the field of mathematics. This level [Page 546]is the exclusive territory of giants or exemplary geniuses like Leonard Euler, Karl Friedrich Gauss, Bernhard Riemmann, Srinivasa Ramanujan, David Hilbert, and Henri Poincaré, among others. The hierarchical model of Usiskin has been extended by Bharath Sriraman by taking into consideration the need to differentiate between the constructs of mathematical giftedness and mathematical creativity implicitly assumed in the model.

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