Mathematical Talent Research Articles

Autism and Mathematical Talent

A utism is a developmental or personality disorder, not an illness, but autism can coexist with mental illnesses such as schizophrenia and manic-depression. It shows itself in early childhood and is present throughout life; sometimes it becomes milder in old age. Nowadays it is recognised as a wide spectrum of disorders, with classical autism, where the individual is wrapped up in his or her own private world, at one extreme. It is estimated that in the United Kingdom slightly under one percent of the population, about half a million people, have a disorder on the autism spectrum The corresponding figure for other countries is not available, although it is unlikely to be very different. Autism is present in all cultures and, as far as we know, has existed for untold generations. Hans Asperger, a Viennese psychiatrist, found that some of his patients had a mild form of autism, with distinctive symptoms that later became known as Asperger’s syndrome. He was not the first to describe the syndrome but he may have been the first to recognise a connection with mathematical talent. As he observed (see Frith [13]): ‘‘to our own amazement, we have seen that autistic individuals, as long as they are intellectually intact, can almost always achieve professional success, usually in highly specialized academic professions, often in very high positions, with a preference for abstract content. We found a large number of people whose mathematical ability determines their professions.’’ Later he wrote, ‘‘It seems that for success in science or art a dash of autism is essential. For success the necessary ingredient may be an ability to turn away from the everyday world, from the simple practical, an ability to rethink a subject with originality so as to create in new untrodden ways, with all abilities canalised into the one speciality.’’ He went on to describe autistic intelligence—a kind of intelligence untouched by tradition and culture— unconventional, unorthodox, strangely pure and original. The ability to immerse oneself wholeheartedly in work or thought is something that is seen time and time again in the Asperger genius. Asperger syndrome is not the only form of autism with this connection. The Irish psychiatrist Michael Fitzgerald, for example, tells me that virtually all the people he diagnoses as autistic have an interest in mathematics. Their greatest wish, he says, is to bring the world under the control of pure reason, to create order and meaning out of the chaos that they experience around them, particularly in the puzzling social domain. Such people are naturally attracted to science, especially to the mathematical sciences, since mathematicians tend to create order where previously chaos seemed to reign. He attributes this attraction to a feeling of security that they find in the rational world of mathematics, which compensates for their inability to make sense of the mysterious social world. Much has been written about this, and the general public are now more aware of the presence of mildly autistic people in everyday life. Since I first wrote about autism in mathematicians in the Intelligencer [20] some years ago, more has been learnt about the disorder and more has been published. In this follow-up article I begin by describing research that places the link between autism and mathematical talent on a firmer footing. Then I describe some of the more recent case studies of Asperger geniuses in mathematics and associated subjects. Simon Baron-Cohen, director of the Autism Research Centre in Cambridge, has tried to put the connection on a more quantitative basis. For this purpose he devised a selfadministered questionnaire for measuring the degree to which an adult with normal intelligence has the traits associated with the autistic spectrum. From the answers to the questions a number is obtained, which he calls the autistic-spectrum quotient, providing an estimate of where a given individual is situated on the continuum from normality to autism. (Anyone who wishes to take the AQ test will easily find it by googling Simon Baron-Cohen.) When

The Search for Mathematical Creativity: Identifying Creative Potential in Middle School Students

The identification of creative potential in mathematics poses many challenges. Much of the research into the identification of mathematical creativity has focused on the development of measurement instruments. Scoring of these instruments is time consuming and subject to scorer interpretation, limiting their use. This study sought a simpler means to obtain indicators of creative potential in mathematics. Existing instruments were used to explore the relationship between mathematical creativity and mathematical achievement, attitude towards mathematics, self-perception of creative ability, gender, and teacher perception of mathematical talent and creative ability. Data were gathered from 89 7th graders in a suburban Connecticut school. The regression model predicted 35% of the variance in mathematical creativity scores. Mathematical achievement was the strongest predictor accounting for 23% of the variance. Student attitudes towards mathematics, self-perception of their own creative abilities, and gender contributed the remaining 12% of variance. Interpretation of the relative importance of the independent variables was complicated by correlations among them.

Gender, culture, and mathematics performance

Using contemporary data from the U.S. and other nations, we address 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the mathematically talented? Do females exist who possess profound mathematical talent? In regard to the first question, contemporary data indicate that girls in the U.S. have reached parity with boys in mathematics performance, a pattern that is found in some other nations as well. Focusing on the second question, studies find more males than females scoring above the 95th or 99th percentile, but this gender gap has significantly narrowed over time in the U.S. and is not found among some ethnic groups and in some nations. Furthermore, data from several studies indicate that greater male variability with respect to mathematics is not ubiquitous. Rather, its presence correlates with several measures of gender inequality. Thus, it is largely an artifact of changeable sociocultural factors, not immutable, innate biological differences between the sexes. Responding to the third question, we document the existence of females who possess profound mathematical talent. Finally, we review mounting evidence that both the magnitude of mean math gender differences and the frequency of identification of gifted and profoundly gifted females significantly correlate with sociocultural factors, including measures of gender equality across nations.

The makings of a savant

Savants have phenomenal talents in music, art and mathematics, but are their gifts within everyone's reach?

Complexities. Women in Mathematics Bettye Ann Case and Anne M. Leggett, editors

Sophie Germain taught herself mathematics by candlelight, huddled in her bedclothes. Ada Byron Lovelace anticipated aspects of general-purpose digital computing by more than a century. Cora Ratto de Sadosky advanced messages of tolerance and equality while sharing her mathematical talents with generations of students. This captivating book gives voice to women mathematicians from the late eighteenth century through to the present day. It documents the complex nature of the conditions women around the world have faced--and continue to face--while pursuing their careers in mathematics. The stories of the three women above and those of many more appear here, each one enlightening and inspiring. The earlier parts of the book provide historical context and perspective, beginning with excursions into the lives of fifteen women born before 1920. Included are histories of collective efforts to improve women's opportunities in research mathematics. In addition, a photo essay puts a human face on the subject as it illustrates women's contributions in professional associations. More than eighty women from academe, government, and the private sector provide a rich melange of insights and strategies for creating workable career paths while maintaining rewarding personal lives. The book discusses related social and cultural issues, and includes a summary of recent comparative data relating to women and men in mathematics and women from other sciences. First-person accounts provide explicit how-tos; many narratives demonstrate great determination and perseverance. Talented women vividly portray their pleasure in discovering new mathematics. The senior among them speak out candidly, interweaving their mathematics with autobiographical detail. At the beginning of a new century, women at all stages of their careers share their outlooks and experiences. Clear, engaging, and meticulously researched, Complexities will inspire young women who are contemplating careers in mathematics and will speak to women in many fields of endeavor and walks of life.

Senate Majority Leader Hands NSF a Gift to Serve the Exceptionally Gifted

Buried in the $410 billion federal spending measure enacted last week is a congressional earmark that gives the National Science Foundation $3 million this year establish a mathematical institute devoted to the identification and development of mathematical talent.

Mathematically gifted and talented learners: theory and practice

There is growing recognition of the special needs of mathematically gifted learners. This article reviews policy developments and current research and theory on giftedness in mathematics. It includes a discussion of the nature of mathematical ability as well as the factors that make up giftedness in mathematics. The article is set in the context of current developments in Mathematics Education and Gifted Education in the UK and their implications for Science and Technology. It argues that early identification and appropriate provision for younger mathematically promising pupils capitalizes on an intellectual resource which could provide future mathematicans as well as specialists in Science or Technology. Drawing on a Vygotskian framework, it is suggested that the mathematically gifted require appropriate cognitive challenges as well as attitudinally and motivationally enhancing experiences. In the second half of this article we report on an initiative in which we worked with teachers to identify mathematically gifted pupils and to provide effective enrichment support for them, in a number of London Local Authorities. A number of significant issues are raised relating to the identification of mathematical talent, enrichment provision for students and teachers’ professional development.

International Teachers’ Judgment of Gifted Mathematics Student Characteristics

Teachers play a key role in the identification and training of talented mathematicians, and their attitudes are important in improving math instruction for gifted students. We surveyed secondary mathematics teachers from South Korea, Turkey, and the United States. These teachers completed a survey instrument called the Teachers’ Judgments of Gifted Mathematics Student Characteristics (TJGMSC) that measured how important they believed 40 behaviors were with regards to students’ mathematics giftedness. They also evaluated different strategies for teaching mathematics. The more years teachers taught mathematics, the more likely they were to report that students’ computational skills, students’ ability to relate mathematics to everyday life, and students’ ability to generate multiple and unique solutions to problems were indicators of mathematical talent. The opposite was true for the highest level of mathematics taught. The higher the grade level of mathematics teachers taught, the less they valued each of these. Teachers with advanced degrees were less impressed with computation skills. Teachers from South Korea, whose students score near the top on international mathematics exams, were less likely to view mathematical talent as innate. They saw mathematics as an abstract subject in which students who were having difficulty should be given time in class to practice by themselves. They were less likely to regard mathematics as a practical topic or a formal way of representing the world. They were also less likely to use a variety of representations (pictures, concrete objects, and symbols) when teaching mathematics.

Parental perceptions of mathematical talent

Parents often become frustrated when their perception of their child’s talent in mathematics differs from that held by the school. Yet for the young child, research suggests parents have a much deeper insight into the interests and talents of their child. Failure to recognize talent can result in lost opportunities for the child as well as a loss to society. This article evaluates the development of an instrument designed to assess parent perceptions of mathematical talent. Parental perceptions and family demographics were collected for third grade students participating in Project M3: Mentoring Mathematical Minds, a research program conducted collaboratively by the University of Connecticut, Northern Kentucky University and Boston University, and for second grade students under consideration for the program. The data were correlated with other identification tools used for the identification of talented second graders for Project M3 to explore a research-based means of parent identification of mathematical talent.

Mathematical Talent is Linked to Autism.

A total of 378 mathematics undergraduates (selected for being strong at "systemizing") and 414 students in other (control) disciplines at Cambridge University were surveyed with two questions: (1) Do you have a diagnosed autism spectrum condition? (2) How many relatives in your immediate family have a diagnosed autism spectrum condition? Results showed seven cases of autism in the math group (or 1.85%) vs one case of autism in the control group (or 0.24%), a ninefold difference that is significant. Controlling for sex and general population sampling, this represents a three- to sevenfold increase for autism spectrum conditions among the mathematicians. There were 7 of 1,405 (or 0.5%) cases of autism in the immediate families of the math group vs 2 of 1,669 (or 0.1%) cases in the immediate families of the control group, which again is a significant difference. These results confirm a link between autism and systemizing, and they suggest this link is genetic given the association between autism and first-degree relatives of mathematicians.

Joannes della Faille, S.J.: Mathematics, Modesty and Missed Opportunities (review)

Reviewed by: Joannes della Faille, S.J.: Mathematics, Modesty and Missed Opportunities David Lindsay Roberts Joannes della Faille, S.J.: Mathematics, Modesty and Missed Opportunities. By Ad Meskens. [Institut Historique de Belge de Rome, Bibliothèque, LIII.] (Brussels: Institut Historique Belge de Rome. 2005. Pp. 177. €36.00 paperback.) This book describes the life of Joannes della Faille (1597-1652) and provides commentary on his mathematical work. Ad Meskens makes meticulous use of earlier scholarship and archival sources, including previously unstudied material held privately by the della Faille family. Meskens seeks to raise awareness of della Faille's mathematical accomplishments, published and unpublished, judging that a proper assessment would lead to recognition in the same company as more celebrated contemporaries such as Blaise Pascal (1623-1662) and Girard Desargues (1591-1661). Meskens situates the life of della Faille within the civil and religious strife in the Low Countries during the late sixteenth and early seventeenth centuries. Joannes, son of a wealthy Flemish merchant, was born and raised in Antwerp, at that time under Spanish rule and a center of the Counter-Reformation. The young della Faille attended the Antwerp Jesuit College, early exhibiting both an attraction to a religious vocation and a talent for mathematics. His initiation into the Jesuit tradition of mathematical scholarship was accomplished especially through the instruction of Gregorius a Sancto Vincentio (1584-1667), himself a student of Christopher Clavius (1537-1612), a pioneer investigator in infinitesimal calculus. Della Faille, ordained in 1621, was dispatched to Madrid in 1629, where King Philip IV had encouraged the Jesuits to found the Estudios Reales of the Colegio Imperial in an effort to build up Spanish technical expertise. While in Madrid della Faille published his only book, a short treatise deriving the center [End Page 409] of mass of a sector of a circle. This was a tour de force of geometric reasoning, explicated by Meskens in one of his chapters. Della Faille's skills were recognized at the highest level of the Spanish court. In 1646 he became mathematics tutor to Philip IV's son, Don Juan of Austria, and later accompanied the latter's military expeditions in the Mediterranean. Della Faille died in Barcelona in 1652, shortly after Don Juan had suppressed a rebellion in that city. Gregorius a Sancto Vincentio asserted that della Faille may have written as many as thirty unpublished mathematical manuscripts. Meskens is unable to confirm such a large number, but has found several such manuscripts, of which he gives special attention to those on conic sections, composed of carefully crafted sequences of theorems without proofs. Meskens has succeeded, with considerable ingenuity, in providing anachronistic proofs by means of analytic geometry, and he expresses his confidence that della Faille was in possession of synthetic geometrical proofs. While acknowledging that della Faille was not so audacious an innovator as Desargues, Meskens is eager to credit della Faille with anticipating later developments in projective geometry, and urges that his name be attached to theorems usually associated with Pascal and William Braikenridge (ca. 1700-1762). These claims on behalf of della Faille's prowess cannot be incontrovertibly supported by the available evidence, but Meskens makes a plausible case. Meskens concludes by musing provocatively, albeit superficially, on the conditions contributing to della Faille's obscurity in the history of mathematics. Factors mentioned include the relative weakness and isolation of Spanish mathematical activity during della Faille's time, the failure of Don Juan to memorialize properly his tutor, and (as alluded to in the subtitle of the book) della Faille's Jesuit spirituality that urged modesty. The book is produced in a handsome paperback volume with numerous illustrations, including a cover reproducing the notable portrait of della Faille by Anthony Van Dyck. There are a few typographical errors, awkward phrasings, and missing words, but the most distracting blemish is provided by the exceedingly mechanical right justification of the text, resulting in numerous unconventional hyphenations. David Lindsay Roberts Prince George's Community College Copyright © 2007 The Catholic University of America Press

On the 75th Birthday of V. M. Zolotarev

February 27, 2007, was the 75th birthday of the eminent mathematician, Professor Vladimir Mikhailovich Zolotarev. In 1949, Vladimir entered the faculty of mechanics and mathematics of Moscow State University. As his specialization field he chose probability theory and began his studies under the supervision of Eugene Borisovich Dynkin. After graduating from the university he was recommended to graduate studies, where his advisor was Andrei Nikolaevich Kolmogorov. Other distinguished mathematicians also have had a potent effect on Zolotarev's mathematical talent. Later, he mentions more than once not only his teachers E. B. Dynkin and A. N. Kolmogorov, but also B. V. Gnedenko and Yu. V. Linnik. In his graduate studies, Vladimir begins to study the properties of stable distributions. He continues to be interested in this theme even today. At first he was dealing with the stable distributions in the scheme of summation of independent identically distributed random variables. Later, he extended the concept of...

Investigating the Influence of Attribution Styles on the Development of Mathematical Talent

In this article, the authors examine the influence of attribution styles on the development of mathematical talent. The study employs a Self-Confidence Attitude Attribute Scale questionnaire, which measures ability and effort attributions. Participants are three groups of highly, moderately, or mildly mathematically gifted Finnish adolescents and adults ( N = 203). The results of Bayesian classification modeling show that items attributing success to effort and failure to lack of effort are the best predictors for the level of mild mathematical giftedness and gender (females). The results of multivariate analysis of variance show that highly and moderately mathematically gifted students reported that ability was more important for success than effort, but mildly mathematically gifted tended to see effort as leading to success. Moderately and mildly mathematically gifted students attribute failure to lack of effort, whereas highly mathematically gifted students attribute failure to lack of ability.

Book Review: Developing mathematical talent: A guide for challenging and educating gifted students

Book Review: Developing mathematical talent: A guide for challenging and educating gifted students

Problems to discover and to boost mathematical talent in early grades: A Challenging Situations Approach

Several studies of mathematical giftedness conducted in the past two decades reveal the importance of creation of learning and teaching environment favourable to the identification and nurturing mathematically talented students. Based on psychological, methodological and didactical models created by Krutetskii (1976), Shchedrovtiskii (1968), Brousseau (1997) and Sierpinska (1994), we have developed our challenging situation approach. During 7 years of field study in the elementary K-6 classroom, we collected sufficient amount of data that demonstrate how these challenging situations help to discover and to boost mathematical talent in very young children keeping and increasing their interest towards more advanced mathematics curriculum. In this article, we are going to present our model and illustrate how it works in the mixed-ability classroom. We will also discuss different roles that teachers and students might play in this kind of environment and how each side could benefit from it.

Actualizing Mathematical Promise: Possible contributing factors

The study reported in this paper is intended to highlight some factors which may contribute to the fulfillment of mathematical talent with special reference to pupils aged 10–11 within inner-city schools. The findings are based on the authors' experience of setting up and evaluating a Mathematics Enrichment Programme (MEP) over a period of 2 years. The context of this study, funded by the Department of Education and Skills within the Excellence in Cities initiative, is the on-going efforts of the British government to identify gifted pupils and make effective provision for them. The findings reported in this study draw on the data collected over the 2-year period through the involvement of 11 Local Education Authorities within inner-city areas. A number of components, which may enhance provision for mathematically talented pupils, are identified and should have significance for a wider audience. The terms ‘mathematically promising’, ‘gifted’ and ‘able’ are used interchangeably to refer to children who demonstrate a special aptitude for mathematics.

Creative Thinking in Mathematics in Israeli High School Students

The authors distinguished both theoretically and empirically between academic and creative abilities in mathematics. The former was postulated as intelligence applied to mathematics and the latter as creative thinking, operationally defined as ideational fluency, applied to mathematics. The findings of a large-scale study of 10th and 11th grade students (N = 1,090) conducted in Israel indicated that creative thinking constitutes a necessary but not sufficient component in creative thinking in mathematics. The practical implications of these findings are that it would be worthwhile to add reliable measures of both general creative thinking and domain-specific creative ability in mathematics, such as the ones developed in the current study, to IQ scores and school grades in order to identify pupils with such abilities and to help them realize their mathematical talent.

Sex Differences in Intrinsic Aptitude for Mathematics and Science?: A Critical Review.

This article considers 3 claims that cognitive sex differences account for the differential representation of men and women in high-level careers in mathematics and science: (a) males are more focused on objects from the beginning of life and therefore are predisposed to better learning about mechanical systems; (b) males have a profile of spatial and numerical abilities producing greater aptitude for mathematics; and (c) males are more variable in their cognitive abilities and therefore predominate at the upper reaches of mathematical talent. Research on cognitive development in human infants, preschool children, and students at all levels fails to support these claims. Instead, it provides evidence that mathematical and scientific reasoning develop from a set of biologically based cognitive capacities that males and females share. These capacities lead men and women to develop equal talent for mathematics and science.

Congruent Number Problem

The following article reproduces the notes of a lecture I gave on October 5, 2002, in the Enrichment Programme for the Young Mathematics Talent of the Department of Mathematics and the Institute of Mathematical Sciences of the Chinese University of Hong Kong. I am very grateful to the anonymous students who wrote these very detailed notes of my lecture.

Cross‐cultural predictors of mathematical talent and academic productivity

The main goal of this paper is to investigate cross‐cultural factors that predict academic ability among mathematically gifted Olympians in Finland and the United States. The following two research problems are formulated: (1) What factors contribute to or impede the development of the Olympians’ mathematic talent? and (2) Do the Olympians fulfill their potential by making contributions to their fields? The results regarding the first research question indicate that the amount of cross‐cultural distinctive factors (computer literacy) is less than the amount of connective factors (school hindrances, effort attributions, negative home influences) contributing to the development of the Mathematic Olympians’ talent. The results regarding the latter research problem show that some factors are culture invariant (socioeconomic status, effort attributions) and some are culture dependent (school hindrances, computer literacy) in relation to both US and Finnish Olympians’ later academic productivity. Results show that high school grade point averages do not necessarily predict academic productivity in Olympians’ careers.