Burt Kaufman: An Appreciation

1949

Graduated from high school: Baltimore City College, Baltimore, MD.

1953

Graduated B.A. in Mathematics from Franklin and Marshall College, Lancaster, PA.

1953-54

Taught Mathematics at Southern Junior High School (now Digital Harbor High School), Baltimore, MD.

1954

Married Paulette “Pinky” Friedlander.

1954-55

Taught Mathematics at Garrison Junior High School (now Garrison Middle School), Baltimore, MD.

1955-1961

Taught Mathematics at Baltimore City College, Baltimore, MD.

1956

Graduated LL.B. from the University of Baltimore, having taken night classes since 1953.

Summer 1960

Attended a six-week National Science Foundation Institute studying under Dr. Arnold Ross [deceased, September 2002] at the University of Notre Dame, South Bend, IN, in a class comprising 75 practicing teachers together with 25 gifted high school mathematics students. In Burt’s words, the high school students “were quantum leaps ahead of us in knowledge, interest and ability to learn. They made us look bad and humbled us.” It was then that Burt decided, “If there’s an opportunity in my life for me to create a curriculum similar to what I’m studying now, I want to.”

1961-62

Spent a sabbatical year in a National Science Foundation Institute at the University of Notre Dame, South Bend, IN, studying again under Dr. Ross and earning an M.A. in Mathematics.

Summer 1962
Saw an ad in the South Bend newspaper seeking someone to develop the mathematics curriculum for the experimental Nova High School in the proposed South Florida Educational Park to be constructed on the land of Forman Field, the World War II air naval training base in Davie, Florida. The school would not be accepting any students until the fall of 1963. Burt applied and was hired for the job, even though it would mean a cut in salary and would necessitate his having to return his sabbatical pay.

1962-63

Studied in a National Science Foundation Institute at the University of Michigan, Ann Arbor, MI.

1963-66

Served as Mathematics Coordinator of the Nova Schools, Nova High School, Davie, FL.

1963

Charged with the task of designing a multi-track secondary school mathematics curriculum from scratch, Burt found himself learning the art of curriculum development on the job. Supported in part by funding from the Ford Foundation, he put together the Nova Mathematics Advisory Committee under the chairmanship of Professor Paul Rosenbloom (then of the University of Minnesota and subsequently of Columbia University [deceased, April 2005]). This committee rapidly decided on a tentative curriculum for the fast track students and chose what they thought were appropriate published texts (mostly written for a university or college audience).

In November, the Report of the Cambridge Conference, Goals for School Mathematics, was published and immediately had a powerful impact on the mathematics education community. Burt contacted all 28 conferees and offered the Nova Schools as a site for developing and trying out the curriculum advocated by the conference. This led to the involvement in Nova’s mathematics curriculum reform effort of the renowned Professor Robert Davis (then of Syracuse University and eventually of Rutgers University [deceased, December 1997]).

1964

The textbooks chosen by the Advisory Committee were proving to be too lacking in rigor to be used effectively with pre-college students. So Burt and a colleague, Joe Karmos, began the challenging task of rewriting the texts for a younger audience. Recognizing the impossibly demanding nature of this self-imposed task, the Advisory Committee recommended that Burt apply for funding to run a series of meetings aimed at establishing a large-scale curriculum development project.

1965

Funding was forthcoming from the U.S. Office of Education to run three planning meetings. The first of these was attended by Professor Robert Exner (of Syracuse University [deceased, August 1992]), who, following conversation with Burt, volunteered to write a logic course suitable for use with seventh graders. Their expectation was that early familiarity with logic and logical reasoning would so simplify the learning of the mathematics normally taught in secondary school that a significant amount of time would become available for learning more advanced material, thereby hastening the arrival at the forefront of mathematical, scientific, and technological research of those best equipped to make important contributions.

1966

The three planning meetings generated sufficient ideas for the detailed outline of a full-scale project to emerge. Writing a proposal to seek funding for such a project would clearly be a monumental task. So Burt was thankful for the assistance of Dr. Garrett Foster (of the College of Education, Florida State University, Tallahassee, FL), who happened to be residing in the Fort Lauderdale area in order to document the formation and growth of the Nova Schools. Just as their proposal-writing was nearing completion in April, they discovered to their dismay that the proposed mathematics curriculum project was being spoken about in public as a flagship project of Nova University, which was just about to open its doors. The public pronouncements made it sound as though Foster would leave FSU to take up a position at Nova University and that the mathematics project would be directed by the newly-appointed Dean of the College of Education, who was a science education specialist. All this without any prior consultation with either Foster (who certainly had no intention of leaving FSU) or Kaufman.

One of those helping Foster and Kaufman to complete the funding proposal was Dr. Jack Kelly, a former classmate of Foster’s who was on the education faculty at Southern Illinois University in Carbondale, IL. After consulting with the appropriate authorities at SIU, he encouraged Burt to leave Florida and take his ideas to Carbondale where he would be given the opportunity to finish the task of turning them into a funding proposal. Consequently, in the summer of 1966, Burt left Nova, accompanied by two colleagues, Joe Karmos and David Masters, and six Nova High School students who were eventually to complete their high school education at the SIU Laboratory School, living in university dormitories during the school year and visiting home in South Florida during vacations. One of the students, a girl, completed all four years of high school in this way. (About 30 Nova students wanted to make the move to Carbondale, but only six were able to persuade their parents.)

Immediately following the move to Carbondale, word came through that the U.S. Office of Education had awarded the sum of $10,000 to finance the proposal-writing effort. They were prepared to allow these funds to be paid through SIU in Carbondale. But this proved unnecessary because the university had previously decided to employ Burt and his colleagues as faculty members while the proposal was being written.

During this same summer, Burt participated in the planning conference and teacher training institute at Columbia University’s Teacher’s College which led to the formation of the Secondary School Mathematics Curriculum Improvement Study (SSMCIS) directed by Professor Howard Fehr [deceased, 1982]. At this conference, Burt met a number of eminent European mathematics education reformers and invited them the join the advisory group for the proposed development project. Among those who were later to be active in this advisory capacity were Hans-Georg Steiner (then of the University of Münster, Germany, and subsequently of the University of Bielefeld, Germany, and a member of the International Commission on Mathematics Education [deceased, December 2004]) and Lennart Råde (of the Chalmers Institute of Technology, Gothenburg, Sweden, and subsequently Chairman of the International Committee on the Teaching of Statistics [deceased, 1999]).

Once school started in the fall, Burt and his team continued planning the new project (which was to be known as the Comprehensive School Mathematics Program [CSMP]) and Robert Exner began writing what was to become Book 1 of the “Elements of Mathematics” series, entitled “Introductory Logic”. The writing proceeded interactively, with Exner writing a section, Burt teaching it and sending notes, comments, and suggestions back to Exner (and meeting with him face to face from time to time), and Exner revising the material in light of the classroom experience.

1967

Steiner paid a three-week visit to Carbondale, advising the project planners on curriculum design and administrative structure. In April, the Central Midwestern Regional Educational Laboratory (CEMREL) one of a nationwide network of twenty educational research and development centers set up under the Johnson Administration agreed to take CSMP as one of its federally-funded research projects, with SIU sharing some of the staff costs during the first year. CSMP would be based in Carbondale as a satellite of CEMREL’s St. Louis operation. The initial project staff was hired and development work began in the fall of 1967.

The need was soon felt for students to have intuitive mathematical experiences in addition to an education in formal logic. So the idea of “Elements of Mathematics” Book 0, “Intuitive Background”, was born, and CSMP staff members began writing appropriate material under the direction from abroad of Steiner. Meanwhile, Exner (at Syracuse) and Burt (in Carbondale) were interactively developing EM Books 2 and 3.

The new project generated quite a stir in the mathematics education community and many important contacts were made. Among those who were to become actively involved were the eminent topologist Peter Hilton (of the State University of New York at Binghamton) and the mathematics educators Max Beberman (of the University of Illinois at Urbana-Champaign and director of the University of Illinois Committee on School Mathematics [deceased, February 1971]) and Gerry Rising (of the State University of New York at Buffalo).

1968

In the fall, Lennart  Råde came to Carbondale as mathematician-in-residence for the 1968-69 academic year. During that time, he wrote a book entitled “Finite Probability Spaces” that would subsequently be incorporated into the EM series, and he planned and conducted an International Conference on the Teaching of Probability and Statistics. The conference was attended by many luminaries in the international mathematics and mathematics education world, including Arthur Engel (of the University of Frankfurt, Germany, who later would serve as coach of the West German Mathematical Olympiad team). In the following years, Engel would write two book-length chapters for EM Book 0, write the supplementary EM Problem Book, and make significant contributions to the development of the CSMP elementary school curriculum.

During the same year, the mathematics educator Peter Braunfeld (of the University of Illinois at Urbana-Champaign) and the algebraist W. Eugene Deskins (of the University of Pittsburgh) became involved with CSMP. Braunfeld was to contribute to a number of the EM Book 0 chapters as well as providing many ideas for the elementary curriculum, while Deskins was to write two EM Book 0 chapters, EM Book 10, “Groups and Rings”, and a preliminary version of the EM calculus course, Book 7.

1969

During the summer, Burt attended the first conference run by the International Commission on Mathematics Education, held in Lyon, France. There he met the Belgian mathematics educator Frédérique Papy [deceased, September 2005], who, with her mathematician and methodologist husband Georges Papy (of the Free University of Brussels, Belgium), was to have a seminal influence over the eventual form, style, and content of the CSMP elementary school curriculum.

1970

In the spring, CSMP and SIU hosted an International Conference on the Teaching of Geometry, under the leadership of Hans-Georg Steiner. Once again, an illustrious group of mathematicians and mathematics educators were gathered together.

In the summer, Edward Martin joined the CSMP staff fresh out of the University of Cambridge, England, beginning a professional collaboration that continues to this day. The efforts of the CSMP developers were divided between creating ideas and writing materials for the developmental work going on at the elementary school level, observing classes in local elementary schools where the newly-written materials were in use, and teaching EM classes at the secondary level. (Throughout the time that CSMP was in Carbondale, EM classes were taught at the CSMP offices to students who were bussed there from the city’s junior high and high schools just for their mathematics classes.) Some of the EM teaching was experimental in that it formed part of the ongoing, interactive process of writing new books for the EM series, while the rest of the teaching used EM texts that had already been through this process and existed in published form.

In the fall, an International Conference on the Teaching of Algebra was held under the leadership of Braunfeld and Deskins. Attendees included the eccentric, itinerant Hungarian mathematician and discoverer of mathematical child prodigies, Paul Erdős‚ ¶s [deceased, September 1996], and the flamboyant educator and inventor of the computer language LOGO, Seymour Papert (of the Massachusetts Institute of Technology).

Work continued on completing the EM series. The oversight of Book 0 had now fallen to the mathematician and educator Vincent Haag (of Franklin and Marshall College [deceased, December 2003]), who had been one of Burt’s college professors, had participated in the original three planning meetings in 1965, had been a member of the Nova Mathematics Advisory Committee, and had succeeded Råde as CSMP mathematician-in-residence. Exner was completing the production of Books 1 – 6; Lowell Carmony (then one of the CSMP Teacher/Writers and now Professor Emeritus of Mathematics and Computer Science at Lake Forest College, Lake Forest, IL) was producing Book 8 and collaborating with the geometer Robert Troyer (also of Lake Forest College) in the production of Book 9; and discussions were taking place with Deskins, Haag, and others about what form Book 7, the EM calculus book, should take.

1971-72

A major crisis blew up which threatened CSMP’s very existence. The Nixon Administration set up the National Institute of Education (NIE) and announced the transfer from the U.S. Office of Education to NIE of the funding of all educational research projects. Every such project in the country had to submit at two months’ notice and following guidelines that changed three times during the writing period a comprehensive report to NIE essentially justifying its continued existence. The Office of Education set up a number of specialist panels of outside advisors, each panel to evaluate a specific type of program.

CSMP was evaluated by Panel D, which was concerned with curriculum projects in general. It turned out that CSMP was the only mathematics project under review and that the 10-member panel included only one person proficient in mathematics (the other nine members comprised a musician and a collection of psychologists and program evaluation generalists). They based their findings on the hurriedly-produced report and an account provided by a panel officer of a 4-hour briefing session with one member of the CSMP staff. There was no direct contact with CSMP at all.

Not surprisingly, Panel D arrived at some monumental misconceptions and recommended the phase-out of CSMP by June 1973. This generated a storm of protest from around the world, including the marshaling by Peter Hilton of written support for CSMP and its work by more than 3,000 practicing mathematicians and mathematics educators from the nation’s colleges and universities. Perhaps in response to this groundswell, and most certainly as a result of the involvement of the renowned mathematician Andrew Gleason (of Harvard University) in the review of the panel’s findings, Panel D’s final report ended up commuting CSMP’s death sentence to a 50% budget cut, on condition that a significant portion of the remaining money should be spent on a large-scale evaluation of the project’s work.

1973

In the summer, Frédérique Papy joined the staff as Director of Research. She was to continue in that position, guiding the direction of the development work at the elementary level, writing profusely, and teaching in the experimental classes for the next five years. Her presence on site prompted periodic visits to Carbondale (and later, St. Louis) of her husband, Georges Papy, whose idiosyncratic but exceedingly insightful writings and seminars were to become a major source of inspiration to the CSMP staff.

1974

Edward Martin became Senior Editor of the EM series, charged with producing a second edition that implemented a uniform editorial style and took into account the experience derived from several years of classroom use of the first edition. In addition to his continuing responsibilities as a Teacher/Writer, he was also to upgrade the quality of the Teacher’s Manuals and Answer Keys for the series, writing those that did not already exist.

By this time, word of the materials being produced by CSMP had spread widely, and a number of teachers from schools across the country were using the EM books in their classrooms after having undergone training at CSMP during summer workshops. Martin’s responsibilities included helping to run the training workshops, providing teachers with any necessary support during the school year, troubleshooting delivery problems, answering questions that arose during the course of teaching, alerting people to errata, and so on.

1975

CEMREL had moved into more extensive premises in St. Louis during 1972. Since the ensemble of CEMREL’s projects were being touted as meeting the needs of “the school of tomorrow”, increasing pressure had been exerted on CSMP to move from Carbondale to St. Louis so as to facilitate collaboration between CSMP and the other CEMREL projects. Since the lifeblood of CSMP’s work was daily classroom contact with children, this pressure was resisted until there was an assurance that no break in its classroom-based research and development would occur. In 1975 a suitable agreement was reached with the schools of University City on the western edge of St. Louis, so the project moved out of Carbondale during the summer.

1976

In the summer, Edward Martin left CSMP to take up a post as Mathematics Department Chairman in a high school in Glasgow, Scotland. He continued, however, as Senior Editor of the EM series, working in his spare time and returning to St. Louis for 4 – 6 weeks each summer to help with training workshops and do some concentrated writing. The amount of new writing required in producing the second edition had substantially increased as a result of a decision in 1975 no longer to use the naïve set theory that had formed the foundation of the first edition from Book 2 onward. This decision was in response to a number of criticisms that had been made by specialists in the foundations of mathematics who complained that the wrong impression of such basic issues was being given to students. The logician and set theorist Wilson Zaring (of the University of Illinois at Urbana-Champaign) offered to rewrite Books 1 – 3 and the beginning of Book 6, which encompassed the principal locations where foundational matters made an appearance. During 1976 – 84 Martin carried out the necessary editing of Zaring’s work as well as completely rewriting Books 4 and 5 so that they matched well with the other revised books, reorganizing their contents in a way that classroom experience had shown to be more manageable. He also re-edited or radically revised all fourteen Book 0 chapters.

1978-83

While teaching the EM materials in the University City schools, Burt began to feel that an audience of much broader geographical scope could be reached if only the organization existed to make it possible for the many small school districts and private schools in the metropolitan St. Louis are to work together. So in 1978, with CEMREL’s help, he set up the first Project MEGSSS (Mathematics Education for Gifted Secondary School Students). After school each day and at no cost to the school system, students from most of the western suburbs of the city were transported by parents to the CSMP offices, where they studied the EM materials. As their part of the arrangement, the schools and school districts participating in this project allowed the MEGSSS students to take a study hall instead of their regular mathematics class. The project proved so popular with both students and parents that the decision was made to expand its scope, starting the 1979 – 80 school year in separate premises at Kirkwood North Middle School in a southwestern suburb of St. Louis.

By this time, CSMP’s developmental work at the elementary school level had essentially been completed, and all that remained was the time-consuming and laborious task of producing the resulting teacher and student materials in revised, publishable form. Burt felt that the time had come for him to relinquish the reins of leadership and move on to the next challenge, namely that of developing possible models of use of the EM materials, starting with the large-metropolitan-area-many-small-school-districts model.

CEMREL had helped Project MEGSSS obtain sufficient federal funding to enable it to function through November 1981, but no longer. With the prospect of the eventual closing down of the project as a stimulus, the parents of MEGSSS students incorporated the project during 1980 and set up a tuition fee structure which meant that, when the federal money dried up, the project was able to support itself. Indeed, its operations continue to this day.

Having achieved his immediate goal of establishing a functioning model of EM usage, Burt left St. Louis in 1981 and returned to South Florida. There, he re-established contact with Larry Wantuck, the Curriculum Supervisor for Mathematics in the Broward County Public Schools, who had worked under him in the sixties during his Nova days. He interested Wantuck in the possibility of setting up a Project MEGSSS in Broward County, one more suited to the needs of a large countywide school system. In the course of time, Grace McDonald, the Curriculum Supervisor for the Gifted Program, became involved, with the result that School Board approval to start Project MEGSSS in Broward County was granted in August 1982. The process of identifying suitable students began, and the first Broward County MEGSSS students embarked on their studies at Plantation Middle School in January 1983.

1983-89

The next school year, classes also began at Driftwood Middle School, where Burt began training Mathematics Department Chairman, Dennis Caruso, to teach the EM curriculum. Dennis, in turn, began training Marcia Friedman. In 1984, all the students and the teaching team converged on Plantation Middle School, where they were joined by Peg Carson. The pioneer group of middle-schoolers (among them Ms. Carson’s son) studied the EM materials as their mathematics course throughout their middle school and high school careers.

In the summer of 1985, Burt was rejoined full-time by Edward Martin, who had just completed a two-year stint as curriculum-writing team leader for a publishing-house-sponsored mathematics curriculum development project based at the University of Bath in England. Martin brought with him a colleague with whom he had shared an office at Bath, the computer science specialist Iain Ferguson, who soon set about developing what was to become the MEGSSS computer science curriculum. To begin with, the programming language used was Seymour Papert’s LOGO. But, following contact with and an on-site visit from Dan Friedman (professor of Computer Science at Indiana University, Bloomington, IN), the switch was made to Scheme. Burt collaborated with Ferguson and Martin in producing a published version of the resulting curriculum: The Schemer’s Guide.

MEGSSS moved the project offices and base of operations to Plantation High School when the lead group of students transitioned from middle school to high school, leaving the middle school teaching in the more than capable hands of Caruso, Friedman and Carson. Upon the graduation from high school of that first class in 1989, the School Board decided, as a cost-cutting measure, to move Project MEGSSS to Nova Middle and Nova High School, since at the time the Nova schools were open-boundary and had an established countywide transportation network. In this way, the mathematics curriculum that was conceived at Nova returned to Nova after an interval of 26 years.

1989-93

For the first year at Nova, Edward Martin commuted back and forth to Plantation High School so that the MEGSSS students who were high school seniors that year would not have to switch schools in order to continue their MEGSSS course work. Also moving to Nova Middle School was the teaching team of Caruso, Friedman and Carson.

Among the highlights of these years was the achievement of Daniel Dugger (now Assistant Professor of Mathematics at the University of Oregon, Eugene, OR), who, as a high school senior in 1990, submitted an original research paper entitled “On the Homomorphisms between Finite Abelian Groups” to the 41st International Science and Engineering Fair, winning – among several other honors – the first place award from the American Mathematical Society.

Throughout this period, the presence of Project MEGSSS (and the students it attracted) at Nova High School significantly boosted the number of seniors graduating from that school who were accepted to the most prestigious universities in the land. Notwithstanding, when a statewide budget crisis in 1992 forced a $42 million cut in education spending, the School Board tapped Project MEGSSS as one of the programs whose closure would help the county to meet its obligations under the cost-cutting requirements that had been imposed upon it. The MEGSSS parents’ group mounted a fierce campaign demanding the continued provision of the program. As a result, a compromise was reached whereby the School Board would continue to employ the MEGSSS middle school teachers, Caruso, Carson, and Friedman, while a not-for-profit organization, the Project MEGSSS Foundation, formed by the parents, provided the funds for the high school portion of the operation. This arrangement lasted only through the 1992-93 school year, whereupon the School Board definitively wound up the project.

1993-2007

At the insistence of the parents’ group, Burt together with his son, Terry, and his colleagues, Martin and Ferguson established the Institute for Mathematics and Computer Science (IMACS) in July 1993 for the purpose of making the Project MEGSSS curricula in mathematics and computer science available within the private sector. When classes opened in the fall, IMACS began operations with a grand total of 37 students.

From those humble beginnings, IMACS has extended its reach across all pre-college grade levels, developing a multi-level mathematics enrichment curriculum (inspired by the CSMP elementary curriculum) for the elementary grades, an elementary computer enrichment curriculum that leads into an advanced, university-level computer science curriculum, and an online, distance-learning version of the early EM curriculum. In addition, IMACS offers an introductory course in electronic engineering that was developed by a senior Motorola engineer.

Particularly gratifying to Burt has been the hiring of two former students as full-time staff: Ted Sweet, who was a member of the first Plantation High School graduating MEGSSS class and who has since earned his Ph.D. in Probability from the University of California at Los Angeles, and Brandi Parsell, who followed the MEGSSS program through her sophomore year at Plantation High School and who came to IMACS’ attention again when she was teaching at a tough school in Fort Lauderdale after having earned her BA in Mathematics at the University of North Carolina at Chapel Hill.

Within its South Florida operation, IMACS has (so far) peaked at a little over 1,200 students, and affiliate enterprises offering the IMACS curriculum are currently in operation in the neighboring counties of Miami-Dade and Palm Beach as well as in Connecticut, Philadelphia, North Carolina, and St. Louis. Including its online courses, IMACS now serves over 4,000 students across the U.S. and in more than 10 countries.

The day-to-day operation of IMACS in Broward County is now under the direction of Dr. Sweet, who in addition is contributing to the ongoing development work by creating an exciting new elementary school curriculum in Virtual Robotics.

The philosophy of mathematics education and the vision that Burt developed back in the 1960s have given rise to a gold mine of wonderful educational opportunities that is very far from being mined out. On the contrary, it seems set to continue to bless generations of talented youngsters for many years to come.