About the Founding Director
James Tanton is a research mathematician with a passion for sharing the joys and beauty of real mathematics. He received a Ph.D. in mathematics from Princeton University in 1994 and won the Princeton University Engineering Council Teaching Award for his work in teaching multi-variable calculus. Tanton pursued his interests in education, as well as an active research program, while working at New College of the University of South Florida, St. Mary's College of Maryland, and Merrimack College. He won the Homer L. Dodge Award for college-wide teaching excellence in 1999 as a faculty member of St. Mary's College of Maryland. He also taught graduate mathematics courses for teacher-training purposes at the Harvard Extension School and at Northeastern University.
Tanton served for three years as co-director of The Math Circle, a Boston-based program of mathematics courses for students of ages 5 through 18 who enjoy mathematics and want more than the typical school curriculum offers. His attention then turned to the delight of being a high-school teacher himself at St. Mark's School and directing the St. Mark's Institute of Mathematics. In 2006 he won the Kidder Faculty Prize at St. Mark's School.
As a frequent contributor to Math Horizons, an upper-high school and college mathematics periodical distributed by the Mathematical Association of America, Tanton works to make sophisticated mathematics accessible, relevant, and fun. He won the national Trevor Evans Award in 2001 for his article "A Dozen ‘Areal' Maneuvers" and again in 2002 for his article "A Dozen Questions about the Powers of Two." His book Solve This: Mathematical Activities for Students and Clubs, published in 2001, was noted by CHOICE as an exemplary mathematics text. He won the 2005 Beckenback Book Prize for this work.
Tanton continues to pursue research interests in pure mathematics and to publish new results. He has a particular interest in bringing a younger audience to the forefront of mathematical thinking and has succeeded in conducting original research projects with high school students. Many of these projects have led to results worthy of national publication. (See Student Discoveries.)
Tanton also wrote The Encyclopedia of Mathematics, a comprehensive resource designed to be of use to high school and first-year college students, to educators, and to the interested general reader. This text encompasses the entire mathematics and statistics curriculum covered at the secondary and beginning college levels, providing context, meaning, and historical perspective to the concepts encountered. It is available at www.factsonfile.com.
Many other book projects and projects with young students are in the works
Tanton’s Teaching Philosophy
Adapted from the Introduction of the Facts on File Encyclopedia of Mathematics.
Mathematics is often presented as a large collection of disparate facts to be absorbed (memorized!) and used only with very specific applications in mind. Yet the development of mathematics has been a journey that has engaged the human mind and spirit for thousands of years, offering joy, play, and creative invention. The Pythagorean theorem, for instance, although likely first developed for practical needs provided great intellectual interest to Babylonian scholars of 2000 B.C.E. who hunted for extraordinarily large multi-digit numbers satisfying the famous relation a² + b² = c². Ancient Chinese scholars took joy in arranging numbers in square grids to create the first "magic squares," and Renaissance scholars in Europe sought to find a formula for the prime numbers, even though no practical application was in mind. Each of these ideas spurred further questions and further developments in mathematics — the general study of Diophantine equations, semi-magic squares and Latin squares, and public-key cryptography, for instance — again, both with and without practical application in mind. Most every concept presented to students today has a historical place and conceptual context that is rich and meaningful.
Sadly, however, mathematics suffers from the ingrained perception that primary and secondary education in the subject should consist almost exclusively of an acquisition of a set of skills that will prove to be useful to students in their later careers. With the push for standardized testing in the public school system, this mind-set is only reinforced, and I personally fear that the joy of deep understanding of the subject and the sense of play with the ideas it contains is diminishing. For example, it may seem exciting that we can produce students who can compute 376 × 859 in a flash, but I am saddened with the idea that such a student is not encouraged to consider why we are sure that 859 × 376 will produce the same answer. For those students who may be naturally inclined to consider this, I also worry about the response an educator would give upon receiving such a query. Is every teacher able to provide for a student an example of a system of arithmetic for which it is no longer possible to assume that a×b and b×a are the same and then lead a student through a path of creative discovery in the study of such a system? (As physicists and mathematicians have discovered, such systems do exist.) By exploring fundamental questions that challenge basic assumptions, one discovers deeper understanding of concepts and finds a level of creative play that is far more satisfying than the performance of rote computation. Students encouraged to think this way have learnt to be adaptable, to not only understand and apply the principles of a concept to the topic at hand, but to also apply those foundations and habits of mind to new situations that may arise. After all, with the current advances of technology in our society today, we cannot be sure that the rote skill-sets we deem of value today will be relevant to the situations and environments students will face in their future careers. We need to teach our students to be reflective, to be flexible, and to have the confidence to adapt to new contexts and new situations.
There is a creative aspect to mathematical thinking. Even fundamental, "elementary" questions provide the fodder for deep inquiry and insight: Why is the product of two negative numbers positive? What is pi and why is the value of this number the same for all circles? What is value of pi for a shape different than a circle? Is every number a fraction? Why does the long division algorithm work? Why is dividing by a fraction the same as multiplying by its reciprocal? What is the value of i^i? Why should a number to the zeroth power equal one? Why is "zero factorial" equal to one? (Is there such a thing as "one half factorial"?) What is the fourth dimension? Is there anything wrong with leaving a radical in the denominator of a rational expression? Questions like these often trouble student and teacher alike (if they are ever asked). Yet these are wonderfully rich questions, worthy of exploration, consideration, and deep thinking — and there is no need to accept the rote answers to them typically provided!
As a researcher, author, and educator in mathematics I have always striven to share with my students the sense of joy and enthusiasm I experience in thinking about and doing mathematics. Intellectual playfulness, adaptability, flexibility, creative enquiry, and the "throwing away of boundaries" are the tools that allow mathematicians working at the research level to succeed. They are also the tools that allow mankind to make new discoveries, develop innovations, and to thrive, and are the skills I hope educators ultimately teach our students.
St. Mark’s Institute of Mathematics25 Marlborough Road
Southborough MA 01772
Phone: (508) 786-6126
Fax: (508) 786-6123