Ten-year-old Terence Tao, or Adelaide, South Australia, is a prodigiously gifted young mathematician. Julian Stanley, Director of the Study of Mathematically Precocious Youth (SMPY) at Johns Hopkins University states that Terry has the greatest mathematical reasoning ability he has found in 14 years of intensive searching (Stanley, 1985).
In May, 1983, at the age of 8 years 10 months, Terry took the Scholastic Aptitude Test-Mathematics (SAT-M) at Stanley's invitation and made the phenomenal score of 760 out of a possible 800. Only 1% of college-bound 17- and 18-year-olds in the United States attain a score of 750 or more on SAT-M and, so far as Stanley knows, to this date only one other 8-year-old has ever scored higher than 700.
In some ways it is ironical that such a profoundly gifted student as Terry should have appeared in Australia, an obsessively egalitarian society where social antipathy towards gifted children and towards those who would set up special programs for the gifted is a powerful deterrent to the establishment of state-mandated gifted programs. Two Australian states, Western Australia and Victoria, do provide structured accelerated programs for highly gifted secondary school students within the government system, but these programs are under intense criticism from the teachers' unions, the media and many politicians. Terry's state, South Australia, has no such program; the few cases of acceleration which have arisen have proceeded from the interest and concern of individual teachers and have received little or no support from the state education system.
Paradoxically, Terry's father, Dr. Billy Tao, a pediatrician, feels that in Terry's case the absence of a formalized structure may have been an advantage rather than a hindrance:
Early ChildhoodBorn in Adelaide on 15 July, 1975, Terry is the eldest son of Billy and Grace Tao, the latter a first-class-honors graduate in mathematics and physics, who met at the University of Hong Kong where both were educated before emigrating to Australia in 1972. Terry has two younger brothers, Trevor, aged 7 and Nigel, 5.
Terry's intellectual precocity displayed itself at an early age. In common with a number of other intellectually gifted children (Salzer, 1984), he taught himself to read by watching Sesame Street; the difference, however, is that Terry acquired this skill before the age of 2. His reading came as a complete surprise to his parents; they found him playing with another child's alphabet blocks, arranging the letters in alphabetical order. Some of the blocks had numbers, and the Taos discovered that Terry could arrange these in numerical order and, shortly afterwards, do simple addition and subtraction.
A few months after Terry's second birthday, the Taos found him using a portable typewriter which stood in Dr. Tao's office; he had copied a whole page of a children's book laboriously with one finger! At this stage his parents decided that, although they did not want to 'push' their brilliant son, it would be foolish to hold him back. They began to borrow and buy books for him and, indeed, found it hard to keep pace with the boy. They encouraged Terry to read and explore but were careful not to introduce him to highly abstract subjects, believing, rather, that their task was to help him develop basic literacy and numerical skills so that he could learn from books by himself and thus develop at his own rate. "Looking back," says Dr. Tao, "we are sure that it was this capacity for individual learning which helped Terry to progress so fast without ever becoming bogged down by the inability to find a suitable tutor at a crucial time." By the age of 3, Terry was displaying the reading, writing and mathematical ability of a 6-year-old.
The Tao parents feel that the single most important event in Terry's education was, ironically, the 'failure' of his attempt at early entrance into formal schooling:
Terry entered a private (independent) primary school in February, 1979 (the Australian school year runs from February to December) at the age of 3 years 6 months. This particular form of acceleration did not, however, meet Terry's very specific needs. Intellectually, he was far in advance of the 5-year-olds in his class. Socially, however, he was not yet ready to spend extended periods of time with children 2 years older than himself. His teacher could not cope with the situation and complained that Terry distracted the other students. After several weeks his parents and educators came to a mutual decision that Terry be withdrawn from school. The Taos entered him in a neighborhood kindergarten with children of his own chronological age.
Numerous studies (e.g., Worcester, 1955: Hobson, 1979: Alexander and Skinner, 1980) have shown that where under-age children are admitted to formal schooling on the basis of intellectual and academic precocity and social readiness, they perform as well as, or rather better than, their older classmates. However, the majority of children studied have been within 12 months of the usual minimum date of admission to school, and emotional maturity is recognized as being an important prerequisite for the child's social and academic success (Reynolds, Birch, & Tuseth, 1962).
The Taos believe they learned several important lessons from this early experience:
Secondly, we have become aware that it is not enough for a school to have a fine reputation and even a principal who is perceptive and supportive of gifted education. The teacher who actually works with the gifted student must be a very flexible type of person who can facilitate and guide the gifted child's development and who will herself model creative thinking and the love of intellectual activity.
Also, and possibly most importantly, we learned that education cannot be the responsibility of the school alone. Probably for most children, but certain for the highly gifted, the educational program should be designed by the teachers and parents working together, sharing their knowledge of the child's intellectual growth, his social and emotional development, his relationships with family and friends, his particular needs and interests... that is, all the aspects of his cognitive and affective development. This did not happen during Terry's first school experience but I am convinced that the subsequent success of his academic program from the age of 5 onwards has been largely due to the quality of the relationships my wife and I have had with his teachers and mentors (B. Tao, 1985).
During the 18 months Terry spent in kindergarten his mathematical ability progressed at a phenomenal pace. Guided by his mother, Grace, he completed almost all the elementary school math curriculum (normally 7 years' work) before the age of 5. One of Terry's early mentors, a professor in mathematics education at Monash University, has described Grace Tao's role as more one of guiding and stimulating Terry's development than one of teaching him. "She said that while she sometimes attempts to guide Terry's mathematical learning, she doesn't help him much because he 'doesn't like to be told what to do in mathematics' " (Clements, 1984). Most of Terry's learning was acquired through his voracious reading of mathematics and mathematics textbooks.
Involvement with SAAGTCDuring this kindergarten period the Taos began to read books concerning the education of gifted children and joined the South Australian Association for Gifted and Talented Children (SAAGTC), a group of teachers and parents of gifted students who run Saturday programs for gifted children and seminars and workshops for parents and teachers. Here, for the first time, Terry was able to work and socialize with other highly gifted children. Although he met no one sharing his own prodigious math ability (this is not surprising because in terms of IQ alone he is, statistically, one in a million and the entire population of Australia is less than sixteen million) he was able to mix with other children who shared his hunger for information, his ability to assimilate and integrate abstract concepts, and his delight in creative exploration. Even within the accelerated context of SAAGTC programs, however, it was found necessary to accelerate Terry still further beyond his gifted age-mates. I vividly recall one of my first meetings with Terry when, in my capacity as President of SAAGTC, I was informally assessing his mathematical ability for placement in SAAGTC programs. At just under 4, he was multiplying 2-digit numbers by 2-digit numbers in his head while I, the 'tester', required pen and paper to check his answers! Another image springs to mind of Terry, one month before his 5th birthday, working with a group of gifted 7- to 9-year-olds at an SAAGTC math workshop. The teacher challenged the students to find the next four numbers in the sequence 9182736. Terry thought briefly and responded, "4554." He was, of course, correct. The number sequence consists of consecutive multiples of 9.
Dr. Tao also benefited from his experiences with SAAGTC:
Primary/Secondary EducationDuring this period, through reading and talking with educators, Grace and Billy Tao developed the concept of a form of scholastic program which would meet Terry's intellectual and social needs. Although his performance in most subject areas was far above the level of his chronological age, he was not, nevertheless, uniformly advanced across the board. His prodigious mathematical ability was some years in advance of his language ability. They conceived a structure whereby Terry would 'ride' several class levels at one time, taking each school subject at the grade level appropriate to his ability. This structure would have the added advantage of permitting him to mix with children of all ages and ability levels as he progressed through school.
His parents investigated a number of local schools, seeking one with a principal who would have the necessary flexibility and open-mindedness to accept Terry within the program structure they had in mind. After meeting on a number of occasions with the principal, they enrolled Terry, 2 months after his fifth birthday, in Bellevue Heights Primary School, a government (public) school some 2 miles from their home. (Five is the usual age for school entry in South Australia, and children customarily enter on the first day of the term after their fifth birthday.) After a brief period of time during which Principal Keith Lomax and staff could assess his performance both academically and socially, he was promoted to a split grade ½ class where he did most of his work with the Grade 2 students except for mathematics which he undertook with Grade 5s.
This set the pattern for the 'integrated,' multi-grade acceleration program which his parents had envisaged and which was adopted, after much thought and discussion, by the school. By early 1982, when Terry was 6 years 6 months old, he was attending grades 3, 4, 6 and 7 for different subjects. On his way through school, he was able to work and socialize with children at each grade level and, because he was progressing at his own pace in each subject, without formal "grade-skipping," gaps in his subject knowledge were avoided.
At home, Terry continued his advanced study in mathematics. By the age of 6, having taught himself BASIC language (by reading a manual), he had written several computer programs on mathematics problems. He is a lively, creative child with a puckish sense of humour; something of his personality comes over in the introduction to his "Fibonacci" program, which is quoted in full by Clements (1984).
The program goes on to produce all the Fibonacci numbers up to the level requested by the player.
At the age of 8 years 3 months Terry achieved his first publication, a BASIC program to calculate perfect numbers (T. Tao, 1983).
By the time Terry reached the age of 7 he had far outpaced the Grade 7 students in mathematics and was working independently on Grade 10 math at home, in the evenings. It soon became clear to the principal that Terry needed the opportunity to work at his true mathematical level with other students. After discussing the situation with Grace and Billy, he successfully undertook the task of persuading the principal of the nearby high school (South Australian high schools cover Grades 8 through 12) to take him part time in a continuation of his integrated program. So, at the age of 7 years 6 months Terry commenced his study at high school for one or two classes per day, the balance of his time being spent at his primary school. By third term, 1983, when he was 8 years 2 months old, his progress at Blackwood High covered math 1 and 2 with Grade 12 students, physics with Grade 11, and English and social studies with Grade 8, while for the rest of the week he took the other subjects at primary level with Grade 5 and 6 students. The Taos insisted that Terry remain part time at primary school to provide socialization with children nearer his age.
Terry adapted to Blackwood High, and Blackwood High to Terry, with little difficulty. John Fidge, his Grade 11 math teacher, found that after the strangeness of the first 2 weeks he was accepted as just another member of the class and regarded as a friendly, well-adjusted, helpful and good-natured lad by his classmates (Clements, 1984). This, when one considers that Terry was, even at this early stage, finishing his work two lessons before his 16-year-old classmates, says much for his social skills. He is a delightful young boy who is aware that he is different but displays no conceit about his remarkable gifts and has an unusual ability to relate to a wide range of people, from children younger than himself to the university faculty members with whom he now works. Billy Tao believes that the two years of 'riding' several classes each term at primary school laid the groundwork for his being able to cope with much older students later.
An important factor in Terry's happy assimilation into high school was that, because of his extreme youth, he was not seen as a threat, either intellectually or socially, by the 16- and 17-year-olds with whom he worked. He was visibly not in competition with them for jobs, scholarships, or boy-girl friendships; paradoxically, this allowed him to be treated as just another member of the class, with the very occasional privilege of getting a piggy-back ride from teacher during bush-walking excursions! "I am now convinced," says Dr. Tao, "that it is in fact easier to integrate a highly gifted child into a higher grade in secondary school than a lower grade and Terry was lucky that he started math in Grade 11 instead of Grade 8."
Secondary/Tertiary EducationIn November of 1983, at the age of 8 years 3 months, Terry informally took the South Australian Matriculation (university entrance) examination in Mathematics 1 and 2 and passed with scores of 90% and 85%, respectively. In February the following year, on the advice of both his primary and secondary teachers, who felt he was emotionally, as well as academically ready, the Taos agreed that he should begin to attend high school full time. He was based in Grade 8 so that he could be with friends with whom he had undertaken some Grade 7 work the year before, and at this level he took English, French, general studies, art, and physical education. Continuing his integration pattern, however, he also studied Grade 12 physics, Grade 11 chemistry, and Grade 10 geography. He also began studying first-year university mathematics, initially by himself and then, after a few months, with help from a professor of mathematics at the nearby Flinders University of South Australia. In September that year he began to attend tutorials in first-year physics at the university, and 2 months later he passed university entrance physics with a score in the upper 90s. In the same month, finding that he had some time on his hands after the matriculation and internal exams, he started Latin at high school.
In early 1985, a few months before his 10th birthday, Terry was spending one-third of his time at Flinders University taking second year math and first year physics. The rest of his time was, and is, spent at high school working in Grade 12 chemistry. Grade 11 geography and Latin (after only 9 months' study of the language!), Grade 10 French, and Grade 9 English and social studies. In November, 1985, he took the university entrance chemistry examination to begin first-year chemistry at Flinders in February, 1986.
Full-Time University Entrance... When?The question now before the family is: What direction should Terry take? There is little doubt that, if he chose to enter university full-time, he would graduate in mathematics before his 12th birthday. (He would, incidentally, become the youngest person ever to do so; currently, the youngest graduate is Jay Luo who took a degree at Boise State University, Idaho, at the age of 12 years 42 days.) Terry's IQ has been assessed as between 220 and 230, and he has no areas of academic weakness. Even in English and social studies, which he considers his weaker subjects, he is working at a level 4 years above his chronological age.
A number of factors have influenced the Tao family's thinking about Terry's future study. In September, 1984, at the age of 9, he was invited, with a small group of senior high school students, to compete in an Australia-wide math competition to choose candidates to participate in the Australian Mathematical Olympiad. Despite being the youngest candidate by a margin of 5 years, he top-scored in South Australia and ranked sixth nationally. However, in the Australian Mathematical Olympiad, which was held 6 months later, he lost his sixth place and consequently was not selected for the Australian team which competed in the International Mathematical Olympiad in Finland, in July, 1985.
The Taos feel there is an important message in this result. "Terry's development in Maths has been so fast," says Dr. Tao, "that like rapidly growing grass in fine weather, he has not had time to put down deep roots. When he was faced with really challenging work at a level he had not encountered before, that was when the weakness showed up. However, it is much kinder to Terry," he adds, "for him to 'fail' within his own state rather than at the International Olympiad where he would have attracted a lot of attention, even among the other competitors, because of his extreme youth."
In May, 1985, at the invitation of Julian Stanley, Terry and his parents spent 3 weeks in the United States, visiting a number of university campuses, including Johns Hopkins, Purdue, Columbia, Princeton, Berkeley, and Stanford, and talking with experts in mathematics and gifted education. This experience, the Taos say, has helped to clarify their thinking on Terry's future education.
Terry's parents now feel that he should probably wait at least 3 more years before he enters university full-time. "In 3 years he will be 13," says Billy Tao:
It is important for Terry to have a broad initial education. I can see two different models of how his education could progress. The first is what I might call a "columnar" model, where his acceleration would be directed vertically upwards in maths and physics with little expansion into other areas of knowledge. The problem here is that, although progress may be fast and easy at the beginning, as the column gets taller it becomes more difficult to build on further knowledge, and, to continue the metaphor, the taller the structure grows, the shakier it may become. The other model, which we have selected, is pyramidical in shape, where Terry's work in mathematics and the sciences is integrated with many other areas of knowledge. Initial progress may be slowed down while he explores the relationships between all these areas of study, but as the pyramid gains height it becomes easier and faster and the whole structure rests on a sound base of interrelated knowledge.
This broad base of knowledge is essential. At the highest level of any subject the boundary between science and arts, between mathematics and philosophy, becomes less and less distinct. You cannot enter this highest level of sophistication if you are too specialized. Even in pure mathematics there will be many problems which you cannot answer simply by applying mathematical techniques. Take Einstein and the theory of relativity, for example; it is not so much mathematics as concepts beyond computation.
If Terry entered university now he would certainly be able to handle the work but he would have little time to indulge in original exploration. Attending part-time, as he is now, he can progress at a more leisurely rate and more emphasis can be placed on creativity, original thinking, and broader knowledge. Later, when he does enter full time, he will have much more time for research or anything else he finds interesting. He may be a few years older when he graduates but he will be much better prepared for the more rigorous graduate and post-doctoral work.
It is easy to label a child a prodigy, but not all prodigies achieve genius. Genius is not related to speed of development. It requires qualities of creative thought and exploration…the ability to break through and make a unique or original contribution (B. Tao, 1985).
Another factor in the Taos' decision is their on-going concern for Terry's social development:
Home Environment Research on Highly Gifted ChildrenTerry Tao has been extremely fortunate in his home environment. Both Terry's upbringing and the relationships within the Tao family reflect many positive characteristics of the families of the highly gifted children studied by Hollingworth (1942), Witty (1940), Goertzel and Goertzel (1962) and Bloom (1985). These include a deep love of learning for its own sake within the family, a valuing of intellectual achievement, a modeling by both parents of a persistent drive towards goals and a warm acceptance of the gifted child for his own sake, not merely for his accomplishments. Interestingly, Terry's home, where parents and children enjoy each other's company and share a very visible and deep affection, where the children are given considerable intellectual freedom and where there is a definite but not oppressive code of family ethics, is highly characteristic of the 'trouble-free' homes which produced the scientists and physicians of the Goertzels' study.
Up to the present time there has been little research into the part played by parents in the education of profoundly gifted children. Much of what has been written has centred on the exploitative tendencies displayed by what Montour (1977) terms "creator parents." These parents of young prodigies such as economist John Stuart Mill (Mill, 1924; Packe, 1954), mathematician William James Sidis, Norbert Wiener (1953), Edith Stern (1971), and the remarkable family of Welsh children described by Deakin (1972) reject the idea that superior ability may be innate and believe that their child's genius is uniquely a function of the educational program they have designed and supervised. As Montour notes, this egocentric belief is often accompanied by an eccentric social or educational ideology that the parent attempts to express through exhibiting the child.
There is little doubt that creator parents comprise an extremely small minority among parents of profoundly gifted children; they are, however, highly visible because of their compulsive publicizing of their child's genius. More research needs to be undertaken on what I would call "nurturant parents" such as the Taos who become keenly involved in the design and development of their profoundly gifted child's scholastic program but who see their role as guides and facilitators, rather than originators, of their child's exceptional abilities.
Terry's Affective DevelopmentProfessor Miriam Goldberg, in her visits to Australia on behalf of the Australian Commonweath Schools Commission, noted that "the spectre of elitism which haunts Australian educators" is accompanied by the peculiarly Australian belief that the ability to "get along" with everybody is of major importance in childhood and the resultant concern that "any school procedures which single children out as being more able than the generality may jeopardize their sense of identity with and acceptance by the 'common man'" (Goldberg, 1981).
In this educational and social climate, programs such as Terry's evoke distrust, even hostility, not least from within the educational community. Most of the criticism, of course, stems from teachers who have never met or worked with Terry and who, indeed, have never spoken with any of the teachers involved in his education. Those teachers who have worked with him quickly realise the absurdity of any suggestion that he should spend all or even most of his time with children of his own chronological age; the general view, however, is that he should be "left alone to be just a normal kid." Terry's parents and teachers would endorse Feldhusen's view (Feldhusen, 1983) that forcing a highly gifted student to be like an average child is forcing him or her to be abnormal -- or, indeed, subnormal!
Despite such an unfavourable social climate, Terry as an individual is almost universally liked and admired by the teachers and students with whom he works. Having had the opportunity to study the development of his personality over the last 6 years, I am sure that this warmth and acceptance are largely due to the gentleness and modesty of Terry's nature. He is able to talk frankly and confidently to strangers as well as friends, but displays no arrogance or conceit. His parents have taught him not to posture but, at the same time, not to conceal his ability. Unlike most profoundly gifted children, he seems to have no difficulty in relating to people of lesser ability (Hollingworth, 1942). He has no conception of himself as "better" than others, merely different. To Terry everyone is of value, everyone has something to contribute.
Terry's motivation to excel, to discover and to create is a burning force in his life. The results of his endeavours--the award, the prize, or whatever--are of much less importance to him than the delight of intellectual speculation. Billy Tao tells of Terry's reaction to the news that he had achieved the highest score Stanley had ever found for a child of his age, on the SAT-M:
Terry's capacity to analyse and comment on his own intellectual growth and development is surprizing in one so young. During his visit to Purdue University he spoke to the faculty and graduate staff of the Gifted Education Resource Institute about his early experiences:
I discovered I could learn better and remember more if I taught my brothers what I had learned. So I taught one brother chess and the other music. My music has never been very good--in fact I hated it until I gave myself the motivation to teach Trevor. Now I actually quite enjoy playing duets with him. I spent a lot of my spare time working out interesting ways to teach them, and I probably learned more from teaching them than they did from me (T. Tao, 1985)!
Terry's educational program contains five elements which Van Tassel-Baska identifies as essential elements of a successful gifted program (Van Tassel-Baska, 1985): content acceleration to the level of the child's abilities; thoughtfully planned, relevant enrichment; guidance in selecting courses and directions; special instruction with the opportunity to work closely with other gifted youth; and the opportunity to work with mentors who have high-level expertise in the child's area of giftedness. It will be interesting to have Terry's reaction to his unique "integrated acceleration" program in a few years' time. A SMPY survey of 21 mathematically precocious boys who had been radically accelerated found that, in comparison with equally talented youths who had not been accelerated, the accelerants had higher educational aspirations, believed that they had used their educational opportunities more effectively and felt that their educational program had had markedly positive effects on their social and emotional development (Polling, 1983). In Australia as well as in the United States, teachers and parents argue against acceleration of gifted children on the grounds that the child's social and emotional development may be jeopardized. In fact, reviewers who have examined this issue (Daurio, 1979; Gallagher, 1975; Robinson, 1983) find no evidence to support the notion that socio-emotional problems arise through well-run acceleration programs and suggest that we should concern ourselves rather with the maladjusting effects that can arise from inadequate intellectual challenge. To quote one gifted teenager writing in the American Association for Gifted Children's book On Being Gifted: "You can always catch up socially, but if a talent is dormant too long it may deteriorate." Terry Tao has at all times been closely involved in the planning of his educational program. He recognizes the need to broaden the range of his knowledge by exploring further into the humanities and languages, while at the same time putting down deeper roots in mathematics and physical sciences, areas in which his achievements are already quite breath-taking. Recently he handed his father the following quotation, which he had discovered in Tolkein's Lord of the Rings.
Because many eminent educators have been involved with Terry Tao and his talents, G/C/T thought it appropriate to invite several of them to share their opinions and reactions with our readers.
Comments, John F. FeldhusenI had dinner with Terry Tao and his parents recently and was struck by the intellectual intensity of Terry and his parents. Throughout the dinner Dr. Tao's conversation centered on Terry's precocity and conditions which would facilitate his intellectual growth. Meanwhile Terry interacted constantly with his mother about puzzles and about little curiosity experiments he was doing at the table, such as holding a spoon in a candle flame. I was told by another family whose home he visited that he had been extremely active in exploring things around the house. He seems to have an ever active need to be investigating and learning.
Terry's father seemed to have the same intensity--an absorbing need to understand Terry's development and how best to facilitate his growth. The family tour of the United States to visit major centers for research and development on education of the gifted exemplifies this profound concern. I believe that few families would exhibit such intense concern for the development of a precocious child. The result is clearly that Terry emulates his father's intensity.
Miraca Gross has captured the essences of Terry Tao very well. She notes that Terry is deeply involved in the planning of his own educational activities. So it should be with all gifted children.
Impressions, A. Harry PassowI was fortunate to have an opportunity to meet Terence Tao and to hear his father describe the discovery and nurturing of this mathematical prodigy. As I listened to Terence's father, I focused on Terence. Here was a very attractive, alert, intelligent, articulate child who had obviously heard his parents discuss him and his development many times before and who, while bored with the discussion, seemed very patient to me. Several times I tried to provide him with advanced mathematics texts on which he might work but they were not of the right kind and he soon closed them and let his eyes wander about my library and artifacts.
The Taos left two documents with me which I have read and reread. One is titled, "My Recollections" which is Terence's recollections of his early childhood experiences and consists of as he puts it, "some memories which are very dear to me, some are actually a bit embarrassing, some funny, but most rewarding." The second is a document titled, "Reflections on Terry's Education," which is a talk which Billy Tao gave. Both are fascinating documents: Terry's because it conveys to the readers an impression of a very intelligent, very insightful, and very sensitive young person. Terry concludes his little presentation as follows: "I may be labelled as an intelligent child by some of my teachers, but I still have a long way to go yet before I can become as wise as anyone of you here today." I read this after Terence had left my office--but I could hear him saying it, seriously and sincerely.
Billy Tao's discussion of his son's development and education concludes with what he calls "the danger areas ahead," possible scenarios of what could happen to Terry. These range from Terry's possibly becoming "too big-headed," to his losing "interest in one subject, such as maths, and want to study another, such as rock music," to the possibility that "he may burn out completely and lose all his brilliance, creativity and productivity." A fourth possibility suggested is that Terry "may suddenly think that he had been conned, that all his hard work, his good marks, had all been carefully orchestrated so as to fulfill my (his father's) own personal ego."
In my office, I have a card which talks about "your ordinary, everyday, run-of-the-mill genius." Terence Tao may or may not become a mathematical genius. He is certainly a mathematically precocious child with unusual potential and achievement. Moreover, he is, if you will, a "nice kid." I worried about whether he was being exploited by his parents. Having met Terence Tao and his parents, I no longer am worried. Those of us interested in gifted education and, in particular, the education of what one of my friends calls the "severely and profoundly gifted," will find the Taos a fascinating family with three children — one mathematically precocious and another with learning disabilities but all being raised and educated intelligently, sensitively, and reflectively. I look forward to hearing more about Terence Tao as he matures, and we are fortunate that Dr. and Mrs. Bill Tao are on hand to serve as participant observers of that development.
Insights, Julian C. StanleyThere's no doubt that Terry Tao reasons almost incredibly well, mathematically, and learns mathematics and related subjects astonishingly fast. His performance in mathematics competitions in Australia and on the mathematical portion of the College Board Scholastic Aptitude Test (SAT-M) at age 8 is phenomenal. He was taking the 60-item 60-minute multiple-choice SAT-M for the first time. On it, only 1 percent of college-bound male 12th-graders in the United States score 750 or more (College Board, 1985). He scored 760. Only one other 8-year-old of whom I am aware has done as well. That boy, who lives in a suburb of Chicago, was taking the test for the fifth time! He managed to score 800 before becoming 10 years old. Terry was not retested on SAT-M at age 9, because that seemed unnecessary.
Yet at age 8 years 10 months, when he took both the SAT-M and the SAT-Verbal, Terry scored only 290 on the latter. Just 9% of college-bound male 12th-graders score 290 or less on SAT-V; a chance score is about 230. The discrepancy between being 10 points above the minimum 99th percentile on M and at the 9th percentile on V represents a gap of about 3.7 standard deviations. Clearly, Terry did far better with the mathematical reasoning items (please see the Appendix for examples) than he did reading paragraphs and answering comprehension questions about them or figuring out antonyms, verbal analogies, or sentences with missing words.
Was the "lowness" of the verbal score (excellent for one his age, of course) due to his lack of motivation on that part of the test and/or surprise at its content? A year later, while this altogether charming boy was spending four days at my home during early May of 1985, I administered another form of the SAT-V to him under the best possible conditions. His score rose to 380, which is the 31st percentile. That's a fine gain, but the M vs. V discrepancy was probably as great as before. Quite likely, on the SAT score scale his ability had risen appreciably above the 800 ceiling of SAT-M.
If his SAT-V score continues to increase 90 points per year (it may not go up quite that fast), he will reach the average of beginning undergraduates at Harvard and Yale by age 12, and the top of the scale (800) by 14. He was not nearly there at age 9, however! That is one of the main reasons why I counseled the Taos to hold off the more verbally abstract school subjects, including "pure" mathematics, for a while, pending the natural growth of Terry's reading and verbal reasoning abilities.
These SAT-V scores may help to explain why Terry did not qualify for the Australian team for the International Mathematical Olympiad at age 9 after the intensive training session. Part of the reason may have been his extreme youth, but part may have been the verbal reasoning edge the older competitors probably had (higher mental age, though not as high IQ).
How could Terry possibly learn mathematics and physical and computer sciences so well with only 290-380V development? We of the Study of Mathematically Precocious Youth (SMPY) at Johns Hopkins have discovered, chiefly by testing able 12-year-olds, that when the examinee's SAT-M score vastly exceeds his or her SAT-V score the youth is almost certain to score high on a difficult test of nonverbal reasoning ability such as the Advanced Form of the Raven Progressive Matrices, often higher than a high-M high-V examinee does. To test this out, on 6 May 1985 I administered to Terry the RPM-Advanced, an untimed test. He completed its 36 8-option items in about 45 minutes. Whereas the average British university student scores 21, Terry scored 32. He did not miss any of the last, most difficult, 4 items. Also, when told which 4 items he had not answered correctly, he was quickly able to find the correct response to each. Few of SMPY's ablest protégés, members of its "700-800 on SAT-M Before Age 13" group, could do as well.
Excellent nonverbal reasoning ability seems a necessary, though almost surely not the sufficient, condition for excelling in mathematics of the algebra-geometry-trigonometry-calculus variety at an early age. The test-triad of SAT-M, SAT-V, and RPM-Advanced can give considerable insight into a mathematically apt youth's intellectual powers. To those three I would add appropriate spatial and mechanical reasoning tests. For youngsters whose total score on a general achievement test battery of the kind usually administered in schools is high (e.g., 90th percentile or greater on seventh-grade norms), the 8-part Differential Aptitude Test battery of The Psychological Corporation in New York City may be a good place to start.
Sometimes I think we of SMPY are learning even more from Terry than he and his parents are learning from us.
AppendixHere are some sample items from "Taking the SAT," published by the College Board, New York City, in 1985. These sample test questions are reprinted by permission of the Educational Testing Service, Princeton, New Jersey, the copyright owner.
For detailed explanation of how to solve these problems, see the booklet, a copy of which is obtainable at most senior high schools in the U.S. The booklet also contains a complete practice SAT.
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