The fight against innumeracy and the teaching of mathematics – The story of Herbert Gross

The epidemic of innumeracy

There are many statistics for each country on the illiteracy rate. A country is said to be more developed if its citizens can read and write. An equally important measure is that of innumeracy. This is the inability to understand math. For most of the 7.9 billion now on earth that have gone through or are in school, math is their most challenging subject. This may be a reason why getting data on a countries innumeracy is extremely difficult. Not only are millions of ordinary people innumerate, but so are those in governments, hence the inability to understand how important this issue is and why it continues to remain a plague in societies.

Numeracy is not just the ability to count a few integers and thus keep track of the amount of money in one’s pocket, important though that is for basic survival. Numeracy is a prerequisite to being an informed, free citizen in a democracy. It is the ability, as mathematician John Allen Paulos writes, to be able to address issues such as, “How many? How long ago? How far away? How fast? What links this to that? Which is more likely? How do you integrate your projects with local, national, and international events? With historical, biological, geological, and astronomical time scales?” This ability to “look at a situation quantitatively, to note logical, probabilistic, and spatial relationships” is a matter of life and death. Innumeracy is one of the causes why millions refuse to take their vaccination shots, despite clear data showing its effectiveness.

Teaching math to the everyday person

Herbert Gross (1929 – 2020) spent most of his life fighting against innumeracy. He was more than just a great math teacher; he was an exemplar of a human being—kind, friendly, and, most importantly, aware of the plight of the less fortunate. After a Bachelor’s degree in math from Brandeis University in 1953, Gross joined MIT to get a Ph.D. He however, left in 1958 without completing his Doctorate and then spent all but five years of his life teaching at community colleges and prisons (where he believed in the redeeming power of education) and advancing the cause of better math teaching.

Peter Chipman, an Educator Assistant at MIT, said that Gross taught “often to those students most in need of patient encouragement and support.” Even the five years he spent back at MIT’s Center for Advanced Engineering Study (1968-73) as a Senior Lecturer resulted in the wonderful video course “Calculus Revisited”.

Chipman wrote that Gross was “always been dedicated to the idea that the best teaching materials should be made freely available to as wide an audience as possible.” Thus he put in a tremendous amount of work behind each of his math videos. Gross said that “It took several days to prepare each lecture. While this seems to be a very long time, the beauty lies in the fact that the lecture is there forever and is available to any viewer, in any place and at any time.” These videos are now available on MIT’s OpenCourseWare and have been viewed well over a million times. Together with his many other video lectures for students and teachers are valuable resources for all of us.

Gross started teaching math when he was at school, and he helped tutor his fellow students to pass their exams. He said that “I guess it was at that time that I realized that it was ‘fun’ trying to teach others (which is probably the time when I decided that my professional goal would be to teach math at the high school level).” The following are two of Gross’s key pieces of advice for teaching math:

Math teachers

Gross said that “Professors who are excellent mathematicians tend to believe that because of that, they are also the greatest math coaches.” However, Professors at top universities such as MIT have the most interested and capable math students. The results are self-selecting, in that these students naturally do well in math, only partly because of the teaching. Using the same teaching methods in community colleges fails. Gross uses an analogy with sports. The greatest of coaches are usually not the best players. Similarly, the best math teachers need a deep understanding of math but are generally not the greatest of mathematicians.

Understand your students and their perspectives

Gross mentions that it is not the Golden Rule (Do unto others as you would have had others do unto you) that needs to be followed but what he called the Platinum Rule (“Do unto others as others would have done unto themselves.” Gross said that “Too often we teach students in the way we would have liked to have been taught, and too often we fail to look at things from the students’ point of view. We might not know what the students’ point of view is, but we should at least be trying to think about it from the students’ point of view.”

“I invoke a theory along the lines of ‘rigor is a function of the rigoree.’ So in formulating my approach, I teach [math] in a way that will make it easier for my students to internalize the content.”

The Joy of Math

There is a third aspect to teaching math that Gross did not talk about but personified. From the first “Hi,” he says when starting his lectures to the last “till next time,” he demonstrated sincerity and contagious joy in his subject matter, whether differential equations or simple arithmetic. He was also always accessible. Even after becoming an internet star, he wrote, “I want my viewers to know how much I appreciate their comments and their email messages. Feel free to write to me, especially if there are times when you feel that my input might be helpful to you.”

Ernie Danforth, a math teacher who Gross inspired, wrote, “He helped me understand that my job was not to teach math, but it was to teach people.”

In response to the thousands of students who wrote to him, Gross said, “It gives me great pleasure, especially at my advanced age, to know that my videos have helped so many viewers globally, and I hope they will continue to do so in the years ahead. Your comments have made me realize that I have been truly blessed.”

Gross’s advice to students “who understand what it means to be a mathematician and still aspire to become a mathematician” is to get an “undergraduate degree from a college that values teaching. Then, once you have a good foundation, pick a graduate school that is staffed with professors who are good mathematicians.”

The importance of teaching

A good teacher helps students gain a real education, and Gross defined education as “the part that is left after we have forgotten everything else that we’ve been taught.”

When Gross passed away, his son Steven posted the following quote from Gross “Nobody chooses to be born. Few choose to die. But all of us can choose to make someone else’s journey from birth to death a little better because we were there to help along the way.”

© Kaikhushru Taraporevala

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