## Adjunct Faculty Spotlight: Dr. Daniel Goroff, Mathematics Education

By mst • May 27th, 2013 • Category: Mathematics Education**Dr. Daniel Goroff**, a Distinguished Visiting Professor in the Mathematics Education program at Teachers College, is currently teaching Advanced Proofs this semester. This course helps students formulate, write, and critique rigorous mathematical arguments.

He was born in Boston, Massachusetts, grew up in Fair Haven, New Jersey, then spent most of his life in Boston but now resides in New York City.

He became interested in education because he always liked talking about mathematics, **“Once in a while when talking about mathematics you get a big kick out of understanding something that you didn’t understand before. Then when you see other people get a kick like that from talking about mathematics, it can be tremendously appealing and exciting. Sharing these kinds of experiences lead to my interest in mathematics education.”**

His curiosity about mathematics began before he started primary school. As a young child he engaged in discussion about abstract mathematical constructs by way of writing down the numbers he knew (1, 2, 3, 4,…), and then being prompted by his older cousin about extending his list of numbers to the right and the left. The extension to the right seemed plausible to him as a child, while the extension to the left was unsettling and intriguing.

Music was one of his passions; during high school he played in a rock band and he performed in different types of bands throughout college, too. Before his freshman year of college he was asked to rank his interests in potential college majors. His interests ranged across five subjects: physics, music, philosophy, economics, and mathematics. This posed a problem for him since he was equally interested in all five, however he placed mathematics at the top of the list since, to Dr. Goroff, mathematics seemed to have some connection with all of his interest, so he majored in mathematics. He continued to be involved in all of those interests; eventually he was able to teach physics, economics, engineering, and history of science at the college level as well as mathematics.

Dr. Goroff earned a B.A.-M.A. degree in mathematics *summa cum laude* at Harvard as a Borden Scholar, an M.Phil. in economics at Cambridge University as a Churchill Scholar, and a Ph.D. in mathematics at Princeton University as a Danforth Fellow. He also holds a Masters in mathematical finance from Boston University.

In 1983 Dr. Goroff accepted his first faculty appointment at Harvard University. He spent over two decades at Harvard, eventually becoming Professor of the Practice of Mathematics while also serving as Associate Director of the Derek Bok Center for Teaching and Learning and as a Resident Tutor at Leverett House. He is Professor Emeritus of Mathematics and Economics at Harvey Mudd College in Claremont, California, where he previously served as Vice President for Academic Affairs and Dean of the Faculty.

Professor Goroff describes a common thread that runs through most of his teaching and research as, **“Studying how systems evolve dynamically over time when they are optimizing some quantity. The Principle of Least Action in physics, for example, determines how mechanical systems evolve. Similar kinds of problems turn up in economics, too, when trying to maximize profits over time. It’s been fun to see – and to help my students see —how the same ideas and structures work in surprisingly different contexts.”**

In pursuing his research agenda on nonlinear systems, chaos, and decision theory, Professor Goroff has held visiting positions at the Institut des Hautes Études Scientifiques in Paris, the Mathematical Sciences Research Institute in Berkeley, Bell Laboratories in New Jersey, the Dibner Institute at MIT, and at TC.

Dr. Goroff was invited to lead a seminar at TC in 2009. Following his seminar presentation the Mathematics program coordinator asked Dr. Goroff to teach a course within the Mathematics Education program at TC. Dr. Goroff was delighted to accept his invitation and has been a visiting professor ever since.

He is currently teaching an advanced proofs course, where students are learning to write rigorous mathematical arguments. Dr. Goroff provides the resources from this course; his lecture notes and exercises are a part of a textbook project. The set of notes for this advanced proofs course will eventually be presented in textbook form to help students learn how to argue mathematically.

**“I’ve really been impressed by how all the students and faculty at Teachers College are so dedicated to helping everybody understand mathematics education. I just think that that kind of passion is great, especially when people are working very hard in both their jobs and in their courses.”**

He has written at length about Henri Poincaré, a great 20^{th} century mathematician. Poincaré invented a great deal of 20^{th} century mathematics. He wrote about mathematics education, the philosophy of mathematics, and the philosophy of science. Poincaré has been an immense inspiration for Dr. Goroff.

At the Alfred P. Sloan Foundation, Dr. Goroff serves as Vice President and Program Director. There he is particularly concerned with supporting research on economics, finance, mathematics, the scientific and technical work force, and higher education.

According to its web site, “The Alfred P. Sloan Foundation believes that a carefully reasoned and systematic understanding of the forces of nature and society, when applied inventively and wisely, can lead to a better world for all. The Foundation makes grants to support original research and broad-based education related to science, technology, and economic performance; and to improve the quality of American life.”

In 1994, Dr. Goroff was elected to a three-year term on the Board of Directors of the American Association for Higher Education. During 1996-97, he was a Division Director at the National Research Council in Washington and, during 1997-98, Dr. Goroff worked for the President’s Science Advisor at the White House Office of Science and Technology Policy. During the Obama administration, he also served part-time in that office as Assistant Director for Social, Behavioral, and Economic Sciences.

Dr. Goroff is a former Director of the Joint Policy Board for Mathematics, an umbrella group that serves the Mathematics Association of America, the American Mathematical Society, the Society of Industrial and Applied Mathematics, and the American Statistical Association. The Joint Policy Board for Mathematics helps these organizations promote mathematics and negotiate policy with the federal government in regards to mathematics.

As Director of the Joint Policy Board for Mathematics from 1998 to 2001, Dr. Goroff was called to testify by the House about educational and research priorities and again by the Senate during the 106th Congress. He also testified before the 109th Congress. Dr. Goroff was also Chair of the U.S. National Commission on Mathematics Instruction at the National Research Council. He was co-director with Richard Freeman of the Scientific and Engineering Workforce Project based at the National Bureau of Economic Research. The book they edited together is entitled *Scientific and Engineering Careers in the United State*s.

Dr. Goroff recounts experiences that have impacted his career and perspective on teaching and learning of mathematics, **“I’ve really been blessed by terrific mathematics teachers throughout my postsecondary career and I have spent many years associated with the mathematics department at Harvard. Almost every professor there has taught me valuable lessons of one kind or another.… But, if I had to pick out one experience or mathematician that had quite an influence on me, I would have to mention Dr. Henry Landau, who is now also a faculty member at Teachers College.”** When still a college student working on mathematics problems and conducting mathematics research at Bell Laboratories, Dr. Goroff became stuck on the particulars of a mathematics problem. Colleagues suggested he consult Dr. Landau, who spent most of his career at Bell Laboratories. Not only was Dr. Landau very patient, gracious, and insightful, he thought about the problem a little bit and actually came up with a wonderful idea. From this experience they became friends and remain so for many years now. **“That experience getting to know Henry Landau really inspired me. I thought that, if someone could take such joy and satisfaction in thinking hard, puzzling out, and working through mathematical questions, then I should see if I could do something like that, too!”**

Dr. Goroff still finds time to indulge in listening to music, although he does not have as much time to play his saxophone anymore. He also enjoys art and aesthetic experiences whenever he can, in addition to pursuing outdoor activities like hiking.

By Deiana Jackson, Graduate Student, Mathematics Education Ed.D.