IMACS celebrates influential career of co-founder Edward C. Martin
It is with bittersweet emotion that the co-founders of the Institute for Mathematics and Computer Science (IMACS) announce the retirement of partner, colleague, teacher and friend, Edward C. Martin. Ed has enjoyed a prolific career of nearly 50 years in mathematics education. What follows is a modest attempt by two of his students to share highlights of a life dedicated to inspiring young people through his exceptional writing and teaching to study mathematics.
For Ed, the most rewarding part of his career has been “witnessing students come to the realization that mathematics is a big, wonderful, logically-connected, all-encompassing, intellectually satisfying Garden of Earthly Delights.” If you were fortunate to have been a student or colleague of Ed’s, please take some time to leave a comment with your memories and wishes for retirement. He will enjoy reading every word!
From Cornwall to Cambridge
If there were ever a child destined to become a magical mathematician and teacher, it would be Edward C. Martin. The first auspicious sign of Ed’s future career came in 1948 when he was born in St. Ives, Cornwall, England, a town that is the subject of the famous arithmetical riddle As I Was Going to St. Ives:
As I was going to St. Ives,
I met a man with seven wives,
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits:
Kits, cats, sacks and wives,
How many were there going to St. Ives?
As a young student at St. Ives County Primary School, Ed found math to be “very routine.” Nonetheless, it was important to do well because in England at that time, a compulsory, nationwide exam determined whether a child would attend an academic secondary school with an emphasis on university preparation or a school akin to a trade school. Ed’s family actually moved to Brighton around this time, but he stayed in St. Ives with his grandparents to minimize any disruption in the year before the all-important exam.
After the exam, Ed joined his family in Brighton. His scores earned him a spot at the Varndean Grammar School for Boys where his father was a math teacher. Four years later, his father began teaching math at Worthing High School for Boys, and this is where Ed completed high school.
Ed credits his father, who was his math teacher during his last two years of high school, as the person from childhood who most influenced him to study mathematics. During this time is when the subject started becoming really interesting to him. “We were preparing for the nationwide final high school exams and the special entrance exams to Oxford and Cambridge,” Ed recalls. “It was the mental challenge I enjoyed rather than anything else.”
Interestingly, Ed’s father never addressed him by name in class, opting to call him “you” instead. But their bond was clearly a special one. “We would laugh ourselves silly over some incident that had occurred in math class that day, much to the bemusement of the rest of the family, who could understand neither what we were talking about nor why it was so funny,” remembers Ed.
After high school Ed attended Fitzwilliam College, one of the colleges that form Cambridge University. Unlike in the United States, a college student in Britain concentrates on one area of study and takes courses related only to that subject. Of course, Ed studied all courses in mathematics! At the time, the Department of Pure Mathematics and Mathematical Statistics was housed in an old multi-story building surrounding a quadrangle near the center of town in Cambridge. “It always amused me that, as you left the complex and went out onto the street outside, there was a notice on the archway that said Ã¢â‚¬ËœYou are now entering the real world’,” recalls Ed with a smile.
Throughout his years at Cambridge, Ed studied under several famous mathematicians, including John Horton Conway, Peter Swinnerton-Dyer and John Willis. Ed fondly recalls his weekly one-on-one tutoring sessions with Professor Conway. Ed was Conway’s student at the time Conway was working on one of his most famous discoveries, the classification of simple groups.
“On one occasion when I arrived, he was obviously very excited,” Ed recalls. “So I asked him what was going on.” Conway hadn’t gotten any sleep the previous night because his bath had been interrupted by a phone call from Fields Medal winner Professor John G. Thompson, then of the University of Chicago, who wanted help in analyzing a new discovery. So Conway jumped out of the bath, sat down soaking wet at his home office desk, and worked right through the night!
“I asked him what was involved in this work, and he explained that it could be thought of in terms of packing spheres in 24 dimensions,” Ed continues. “Of course, I was none the wiser! Incidentally, I subsequently learned that there is great significance in the fact that 24 dimensions are involved. It’s an amazing fact that the only natural number n such that 12 + 22 + 32 + … + n2 is itself the square of a natural number is 24.” (The sum is in fact equal to 702.)
The Making of a World Class Teacher
After graduating with his bachelor’s degree in May 1969, Ed did something completely unexpected but probably a lot of fun! He and two friends bought a Land Rover and spent three months driving through southern Europe. They traveled far enough to roam around northwest Africa and the northern limits of the Sahara Desert.
Upon returning home from this adventure, Ed learned that his father had enrolled him in a one-year postgraduate teaching course at Cambridge, so Ed headed back to school to pursue his teaching degree. There he met Alan Bishop who led the teaching course. Ed credits Bishop as someone who was “very influential in molding me into the kind of teacher that I am, emphasizing that there’s more to it than simply imparting knowledge.”
During the decades to follow, Ed would go on to become a respected and beloved teacher of over 1,700 students, not counting the many more who benefited from the textbooks and online courses he wrote and edited. Whether in a classroom or online, Ed’s students know him to be the kind of teacher who brings clarity to complex ideas without watering down the rigor. He can instantly see the flaws in a student’s thinking and knows just what and how much to say to get a student back on track. In fact, one of those lucky students, Terry Kaufman, would one day co-found IMACS with Ed.
Terry remembers when Ed was his high school teacher for a college-level linear algebra course. “What I remember so vividly was that he would give us class time to work on our assignments, and he would sit at the front of the class with a loose-leaf notebook on his teacher’s desk. Whenever one of us would need help with a challenging problem, he would open his notebook, which contained copious notes he had taken in his college courses. The notes were so meticulously taken and in such small print that today it would appear to look like they had been printed at about an 8-point font. It was amazing how he always found the information needed to help us with our questions from within his notebook.”
Fate and the First Job
As Ed completed his postgraduate year at Cambridge, he applied to various American universities, seeking a graduate assistantship while simultaneously studying for his PhD in mathematics. The chairman of the math department at Southern Illinois University (SIU) received one of Ed’s applications and noted that he was qualified in both mathematics and education. As fate would have it, the SIU math department did not have the funds to hire Ed, so the chairman forwarded Ed’s application to Burt Kaufman.
At that time, Burt was director of the Comprehensive School Mathematics Program (CSMP), a federally-funded development project tasked with writing mathematically rigorous textbooks for talented middle and high school students. These books, which covered most of an undergraduate degree in mathematics, would eventually become known as the Elements of Mathematics (EM) series.
Burt was looking for an editor who could bring consistency to the EM books. Up to that point, each year a different visiting professor would spend a sabbatical year working with Burt’s team to write and then test out the material with actual students. “These professors all had different writing styles and didn’t have much, if any, experience working with secondary school students,” explains Terry, who was also Burt’s son.
As Terry recalls, his father decided to hire Ed sight unseen. In fact, the day that Ed received the reply from SIU explaining that there were no funds to hire him was the very same day that he received the offer letter from Burt. “The letter indicated that one of the CSMP advisors was on sabbatical in London, and I could go and interview him if I wanted to,” remembers Ed. “This I did, and we got on very well together.” Ed accepted Burt’s offer, which was unconditional, and began working as a Teacher/Writer in August 1970.
Comprehensive School Mathematics Program
The work of writing the original EM books had begun in 1966. So by the time Ed joined the effort in 1970, he had the daunting task of taking four years of material written by multiple authors and smoothing everything out from a stylistic point of view, introducing cross-references between the books, and ensuring that they all had complete answer keys.
“At one point, it was decided that the approach to set theory used in the advanced college-level books should be changed,” recalls Ed. “So we commissioned a new author to rewrite the book in question, and I then had the task of editing his work into what was by then EM style as well as chasing down every place in later books that referenced axiomatic set theory and editing them to match the revised approach.”
By the time Ed was promoted to Senior Editor of the EM series in 1974, math teachers across the US had heard about these uniquely engaging textbooks. CSMP offered summer workshops to train teachers on the EM materials, and among Ed’s responsibilities were helping to run the workshops. After attending these workshops, a number of teachers started using the EM books in their classrooms. Ed then provided ongoing professional development support during the school year.
Without a doubt, Ed’s profound influence on math education has rippled throughout the decades as the teachers he trained went on to bring the EM approach to students across the US, a number of whom became math educators themselves.
High School of Glasgow
Ed’s exceptional teacher-training abilities did not go unnoticed. In 1976 he was recruited by the High School of Glasgow to come in and disrupt the way mathematics was being taught at the school. “The headmaster, who also had a background in math, realized that his math department was not keeping up with current thinking in mathematics education,” explains Ed. “So I was charged with retraining the math teachers and improving the quality of math teaching at the school.”
Teachers who disagreed with the change either left or tried to preserve the status quo by complaining that Ed’s approach would not work with underperforming students. Undeterred, Ed volunteered to teach all the weaker students and showed that these concerns were unfounded. “Things turned around markedly during the six years I was there,” he is pleased to say.
In his spare time and on weekends, Ed continued to work remotely as Senior Editor for CSMP. During summers he would return to the US to focus on editing the EM books and training teachers on how to use them.
University of Bath
Ed’s next big challenge came in 1982 when he was asked to lead the development of a new mathematics curriculum for British secondary schools. This project with national implications was funded by textbook publisher Addison-Wesley and hosted at the University of Bath. As head writer, Ed’s job was to train a team of eight other writers in the art of textbook writing, to do some of the writing himself, and to do all the final editing and preparation for publication. “I’m proud of the math curriculum we produced,” says Ed, “because it represented a fresh and exciting deviation from the curriculums that were common at that time.”
While at the University of Bath, renovations caused Ed to have to share an office with computer scientist Iain Ferguson who was working on a different research project hosted at the university. This was surely a serendipitous allocation of space because the professional collaboration between these two scholars would come to last more than 30 years and continues today.
“In my first memory of collaborating with Ed, I was working on ways of displaying demographic and other geographic information on early desktop computers while he was editing a mathematics textbook,” recalls Iain. “I needed an algorithm for choosing which pixels to light up to draw a line across a screen.” Ed came to work the next day with such an algorithm, but Iain noticed immediately that something wasn’t quite right. After Ed gave it a few tweaks, it worked like a charm!
“Maybe that story typifies our collaboration over the years, with each of us feeding off of ideas from the other,” says Iain, “although I unequivocally attribute all the best ideas to Ed.”
Project MEGSSS of Broward County, Florida
In 1985 while at the University of Bath, Ed was again recruited by Burt Kaufman who was then heading up an effort in Broward County, Florida to teach the EM curriculum in a large, diverse school district.
Ed mentioned to Iain that he was thinking of accepting Burt’s offer to move to Fort Lauderdale and teach advanced mathematics to talented middle and high school students. “He gave me a couple of the old EM books to peruse,” recalls Iain. “I was astounded that anyone would try to teach mathematics of that type to students so young.” Iain was so intrigued that he convinced his then-fiancé-now-wife to emigrate to the US so that he could join Ed and Burt in this ambitious program known as Project MEGSSS (Mathematics Education for Gifted Secondary School Students).
Ed, as well as Iain, found the work to be very demanding but ultimately rewarding. While much of their time was spent planning lessons, teaching classes or grading papers, every spare minute was spent developing new material. “Burt insisted that what Iain and I produced should be good enough to teach him everything he needed to know to be able to teach these subjects to his students,” says Ed. “This was no small task because Burt’s lesson planning was meticulous and voluminous.”
The MEGSSS students certainly benefited from what was then a rare opportunity to study modern mathematics with some of the best teachers in the world. On one memorable occasion, some of the students came up with original solutions to puzzles from the book To Mock a Mockingbird by mathematician, philosopher and author Raymond Smullyan. They sent their solutions to Smullyan who later telephoned Burt to offer his congratulations!
For Ed, the best memories of MEGSSS are of the great kids that he got to work with, a good number of whom still keep in touch with him. Many went on to attend some of the most prestigious universities in the country followed by PhDs or accomplished careers in a wide variety of industries. Some are even parents of a new generation of EM students. In one of those “small world” moments, one of Ed’s star MEGSSS students ended up collaborating on research during his post-doctoral studies with a professor whose high school math teacher had attended Ed’s CSMP training workshops!
An official accolade was in the mix too. In 1993 Ed was one of 24 teachers nationwide to be honored with the Mathematical Association of America’s Edyth May Sliffe Award for Distinguished High School Mathematics Teaching.
Despite its successful track record for turning out some of the brightest math students in the country, MEGSSS was eliminated due to Florida’s statewide budget crisis in 1992. The project wound down at the end of the 1992-93 school year.
Institute for Mathematics and Computer Science
With such highly valued knowledge and skills, Burt, Ed and Iain could have easily pursued lucrative careers in the nascent technology industry that was just then witnessing the rise of America Online. Instead, they joined with Terry to establish IMACS in July 1993 with the goal of making the Project MEGSSS curriculum available as an after-school enrichment program.
Their complementary skill sets made them an effective team. “Ed is an amazing mathematician, Iain is a computer science wizard, and my father was an outstanding teacher with the vision for what was possible,” explains Terry. “I was the only one with any business experience, so I handled all operations and financial aspects of IMACS while learning from my father how to teach various aspects of our curriculum.”
What started with just 37 students in Plantation grew steadily to over 1,000 local students at four dedicated teaching centers and seven on-site school locations across South Florida. IMACS is also among the pioneers of distance-learning programs for precocious youth, having launched its first online course in 1998. Since then, over 30,000 students across the world have benefited from studying IMACS’ online curriculum.
Looking back at the company’s steady growth over the past 25 years, one might think that success was a foregone conclusion. Not so! “Founding IMACS was a fairly heart-stopping venture,” recalls Ed. The four partners took no salary for two years while recruiting a small part-time workforce and trying to attract local students. It was during those early days that they developed the IMACS Mathematics Enrichment curriculum based on books that Ed and Burt (along with two CSMP advisors) wrote back in the 1970s.
To create curriculum that is original, unique and engaging for bright and curious students requires tremendous labor and ingenuity. Luckily IMACS had Ed. “He was the key contributor to so many aspects of our curriculum development. We always knew we could count on him to solve any challenge,” recollects Terry. “As I learned working with Ed at IMACS, he could explain almost anything on any topic. In fact, I often refer to him as our Google before there was Google because if we needed to know anything, we would just ask Ed.”
Ed’s mathematical brilliance and all-around problem-solving skills would prove to be invaluable once again as IMACS pursued its most recent curriculum development project — the ambitious Elements of Mathematics: Foundations (EMF) online program for talented middle school students.
Elements of Mathematics: Foundations
Ed’s focus these past four years has been on developing the EMF online curriculum in modern mathematics for highly advanced middle school students. Launched in 2012, EMF leverages advanced web technology to make EM’s Book 0: Intuitive Background material available anywhere in the world as an online, self-study program. This development is particularly important in locations where mathematically talented students have little or no access to appropriately challenging material or instruction that makes them have to think harder instead of merely work faster as with acceleration.
Change can be uncomfortable, as Ed knows from his time at the High School of Glasgow. “The primary difficulty was and continues to be the inertia that characterizes mathematics teaching in the US,” laments Ed. Because EMF treats the subject as a unified whole built upon solid logical foundations, teachers would need to know how everything fits together and to be equipped for laying groundwork that allows for later developments to connect back. “It was partly because of the difficulty of finding suitably qualified teachers that we created EMF in the form of dynamic web-based courses supported by an online help forum,” he explains.
EMF is currently licensed by a growing number of partner schools, school districts and after-school organizations that are looking for a cost-effective way to keep their most advanced math students engaged beyond what acceleration can offer. Having seen math education trends come and go over his career, Ed is all too familiar with how they squander the potential of bright students by failing to challenge them at their ability level. So it should come as no surprise that he would like to see the EMF program adopted by school systems all over the United States and around the world.
How can EMF students learn modern mathematics, much of it college-level, with no teacher? The secret is in the painstakingly drafted text, all of which was written or edited by Ed. Whether through timeless passages from the original textbooks or in newly written material, Ed’s unparalleled ability to anticipate students’ thought processes and to write for a young audience without watering down content are why talented and motivated students can learn from EMF as if a master were there teaching it.
It’s amazing to think that the EMF curriculum, which started with mathematicians from around the world traveling to the US to work with Burt, is now online and traveling out through the internet to students in over 20 countries! Needless to say, Ed is very proud of the role he played in bringing to fruition the vision that Burt had back in the 1960s of a math curriculum that is worthy of the nation’s and now the world’s brightest young minds and that will prepare them for the needs of tomorrow.
Back Across the Pond
Following the completion of EMF’s main development work this past summer, Ed and his wife returned to England where most of their families live. While he will continue to make occasional contributions to IMACS’ curriculum development efforts and teach the most advanced online IMACS students, Ed is looking forward to devoting more time to musical composition, which gives him almost as much pleasure as his math education activities.
Of course, Ed is already missed at IMACS for many reasons, not the least of which is his British sense of humor. He’s got some wickedly clever jokes! “Like the one about the three types of mathematicians — those who can count and those who can’t,” says Iain with an impish grin.
When someone accomplishes so much for so long, it’s hard to imagine them retiring. But that time has come for Ed and deservedly so. “My hope is that he continues to be healthy and lives for many years to come,” says Terry, “and that he continues contributing to IMACS for as long as he is able.”
What has mathematics taught Ed about life? “A mathematical approach can often help to make sense of many of life’s mysteries,” he explains. “Thinking mathematically gives you an expectation that there will be linkages and underlying structure that will make it easier to see your way through whatever you might be facing.”
Dearest Ed, thank you for this wonderful parting wisdom and for so much more than words can fully express. May your rest be anything but routine!
About the Co-authors
Skylar Gamberg is a 7th grade student from Weston, Florida where she lives with her parents and younger sister. Skylar attends Falcon Cove Middle School and is part of Broward County Public School’s EMF program. She loves learning math and foreign languages. Skylar is grateful for the opportunity to work with Mr. Martin who has taught her much about mathematics, its history, and the lives of mathematicians, especially John Conway. Skylar credits Mr. Martin with influencing her future career choice and goals. She hopes to become a math teacher and a mathematician.
Natasha Chen was Ed’s student during her 10th, 11th and 12th grade years in Broward’s Project MEGSSS program. She went on to earn her BS in Mathematics as a Trustee Scholar at the University of Southern California followed by an MBA from New York University and career in finance. Natasha now balances her duties as Communications Director for IMACS with being the homeschool parent of an EMF and online IMACS student. She has fond memories of Ed’s spellbinding lessons, especially on group theory, and his infinite patience.
The co-authors are immensely grateful to Ed, Iain and Terry for taking the time to answer their interview questions in detail. Special thanks go to Ed for organizing, editing and writing the foreword to Burt Kaufman: An Appreciation, which provided essential background material for this article.
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