Mathematical education and the role of mathematicians in mathematical education is a very important, loaded, and controversial subject. An old friend and fellow combinatorialist Ron Aharoni tried to teach mathematics at a junior high school. Here is Ron’s account of the experience as reported in Haaretz (English, Hebrew).
I admire Ron’s bold initiative and candid account of the experience.
Among Ron’s other endeavors: The recent startling proof (with Eli Berger) of the Menger theorem for infinite graphs, The study of topological methods in hypergraph matching theory, a book about mathematics and poetry (Hebrew), a forthcoming book about (or against) philosophy, and much activity in mathematics education including his book Arithmetic for Parents.
Comments and links about mathematical education in general and the role of mathematicians in mathematical education for children are most welcome.
Happy New Year, everybody!
From the Haaretz article:
“No one prepared me for what happened,” Aharoni explained. “My class quickly turned into a zoo – students would sing in class, get up freely, throw things at one another… Nothing I did helped, but on the other hand I wanted to use an ‘iron fist’ – even if I didn’t know how to. After two months I grew desperate and left.”
“I lost the feeling of omnipotence in education,” he said. “It was a dispiriting experience, it took the wind out of my sails. It is very frustrating trying to forge a connection, encouraging students to succeed and failing in that. So I returned to the ivory tower, which is far more comfortable and remunerative.”
“The truth is I left with my tail between my legs,” Aharoni said.
Combinatorics and more 
The article mentions another case of someone leaving his lucrative hi-tech job in order to become a Math teacher. Eventually he also had to resign for similar reasons.
Something very troubling is going on.
I wonder how long this has been going on… reflecting upon my years in high-school (also in Israel, about 2 decades ago) I seem to recall sparks of the same delinquent behavior.
Thanks for the post. I admire Dr. Aharoni’s boldness and honesty.
I have a Ph.D. in Mathematics (graph theory, no less) and teach at a public “elite” high school in the U.S. Our school is charged not only with teaching gifted students, but also with being a resource for math and science education across the state. Luckily, our school does not really have problems with discipline; our students are, on the whole, well-chosen and honestly appreciate the high-quality instruction they receive. I feel that the biggest hindrance to our work is the dichotomy between those trained in math and those trained in math education. Those trained in math want to make substantive changes to curriculum, and those trained in math education want to debate inane issues, mostly semantic in nature. Those in math eventually get upset and go the way of Aharoni.
Surprisingly, I have found through my work with other teachers at other non-elite high schools that most seem very open and welcome to learning new methods. Most seem to feel that their college educations were poor preparations for classroom teaching, and after a couple years teaching they are looking to fill in a lot of gaps.
This is where I think mathematicians can be of greatest service: in the professional development of current teachers. Perhaps those who want to serve the common educational good could speak at conferences and seminars meant for teachers. The teachers in attendance would really appreciate it, and it wouldn’t require mathematicians to leave the ivory tower.
I’ve been an Adjunct Professor of Mathematics for 5 semesters at one private university, and an Adjunct Professor of Astronopmy at a public college. I spent 2.5 years earning the California Full Time Teaching Certificate in Mathematics, from people who have neither my Math background nor my extensive teaching background. I am now able to teach fulltime where I’ve taught as a substutute, in public middle schools and high schools.
Th Federal Government has made this a lengthy, expensive, and frustrating transition. Yet there are some “overqualified” men and women who leap at the chance to take the big pay cut and make a difference in the lives of youngsters.
This article is revealing, in various ways, and an important topic in a system that, in the lower-middle class and poverty and rural areas of the country, de facto bankrupt.
Colleges of Education in the USA prepare well-intentiuoned but undertrained teachers to achieve standards in three orthogonal areas: (a) Instruction (Lectures, collaborative learning, peer learning, other techniques); (b) Management (including Time Management, Lesson Planning, and Classroom Management, where Aharoni seems to have flailed helplessly); (c) Assessment (including homework, quizzes, exams, self-assessment).
(1) With all due respect to the excellent professors and curriculum at
Charter College of Education, where I earned my teaching credential, it is not the techniques alone – not merely lesson plans and classroom management plans — that make a great teacher. Nor is it the pure art of a “natural born teacher” (the Buddha said that 1 person in 5 is a born teacher). It is a synthesis of the two: an innately motivated and talented teacher, with an armamentarium of technical cures to classroom ills.
(2) Beyond that necessary blend of the science of teaching and the art
of teaching, what matters is akin to color for a painter — a quality
of vision of the teacher. The teacher fails if he or she sees the
world through rose-colored glasses, filled with idealistic progressive
notions and great expectations, yet with no ability to handle the
challenges of the urban classroom. The teacher fails if he or she sees
the world through army camouflage, intending “tough love” and military
precision in shooting down inappropriate behavior, because the teacher
and the student are not enemies, and the classroom is not a
battlefield. What does the teacher envision, and how can that be
combined with the vision of the students?
(3) What is the revelation of the particular universe that the teacher
sees, and that other people don’t see? I have explained at length in
my 130-page draft Classroom Management Plan that revelation is one of 5 distinct forms of truth… The Axiomatic Truth of Mathematics is only one of them.
(4) Specifically, as I have written, my approach is the focus on 3 big
questions: what is the universe (and how does it work); what is a
human being; and what is the place of that human being in that
universe? …
(5) Caveat: style, like real life, cannot be too precious, controlled
or confining. There is a great deal of theory in this Classroom
Management Plan…. But theory alone ill-equips a teacher. (6) The
teacher, in his or her mind, narrates or paints an accurate portrait
of minute feelings. The human beings in the classroom are thinkers,
yes, but also human because of a full palette of emotions. Adolescent
students, going through a “phase transition” in their lives, their
brains rewiring themselves, their bodies flooded with hormones, have
their social network quivering like a spiderweb shaking in the morning
breeze, their sense of belonging to pairs and trios and subgroups in
and beyond the classroom under repeated reappraisal. The teacher must
respect the dignity of the student, giving attention to the minute
variations in feeling, encouraging the positive, enabling the negative
to be self- and group-regulated.
It’s always amusing when naive liberal fantasies of academics meet reality. I’d been a teacher for one year. That was enough. I could briefly do it again if I really had to, but I’ll definitely have none of the naive ideas I had going in.
A little off topic maybe, but a plea for people to consider the ethics of buying things like designer clothes. Do try and think about, for example, the materials the item is made with, the human rights of the employees where they’re manufactured and the green credentials of retailers. Oh, and try to share rather than throwing away. Thanks!!!!
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