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"Consider the following subtraction problem, which I will put up here:
three hundred forty two minus one hundred seventy-three. Now remember
how we used to do that: three from two is nine; carry the one, and if
you're under thirty-five or went to a private school you say seven from
three is six, but if you're over thirty-five and went to public school
you say eight from four is six; carry the on so we have one hundred
sixty-nine. But in the new approach, as you know, the important thing
is to understand what you're doing rather than to get the right answer."
- — "New Math" by Tom Lehrer
- on the album "That Was the Year That Was" (1965)
( ISBN-10: B000002KO7 )
The other day I saw a "sig" line on somebody's web post that said something like: "I became successful because someone was counting on me and I didn't want to disappoint them." I thought that sounded about right. I remember back in 1993 when I went to my first conference devoted to scientific visualization. I decided to take advantage of the collection of luminaries in one place, and I began asking people what had inspired them to enter this new and innovative field.
The most common answer I got was a mentor or teacher who had taken an interest in a student at a critical time.I've been thinking about this again lately because last fall one of my most important mentors passed away: Aubrey Dunne, who was my seventh and eighth grade math teacher at Parkway Junior High in La Mesa, California, near San Diego. I think the first time I laid eyes on him he was visiting my elementary school (grades K-6) with the junior high school glee club, and they performed "Stout Hearted Men."
When I arrived at junior high school, or middle school (grades 7 and 8 in my school district) it was our first year going to different classrooms all day instead of staying in one room with one teacher. On the first day they had us move from class to class and only spend about 15 minutes in each one, just for practice. Most of the teachers just told us their names and said hello. Mr. Dunne was different: he made everyone stop chattering and told us firmly that we were to report the next day with two W. S. pencils. "What's W. S. stand for?" he barked. Some hands went up. He asked these kids who their older siblings were, who'd been in his class before. He called on one who answered, "well-sharpened."
One the requirements for his class was that we keep a notebook of what we'd learned, and turn it in at the end of the year. I did a great job on my notebooks, and then didn't have to turn them in because I got high test scores, but I insisted on being graded on them anyway. I kept up the habit and the notebook evolved into a journal that I have kept my entire life.
I first heard an example of the comedy music of Tom Lehrer in Mr. Dunne's math class: he played the song "New Math" from "That Was the Year That Was" (quoted above), and provided a visual aid on the chalk board to follow the subtraction problem, first in base 10 and then in base 8.
Recognizing that I was a bright but rambunctious kid, a possible source of either joy or grief for a teacher, he distracted me with projects. The biggest was a bulletin board on the history of mathematics he asked me to make, to fill an odd triangular space above the chalk boards. I went at it with gusto, and so learned how the Egyptians invented geometry to re-survey farms along the Nile after flooding each August.
He encouraged me to read the mind-expanding math book by George Gamov, "One Two Three ... Infinity" (1947), and other writings by the same author.
- ( ISBN-10: 0486256642 )
When he volunteered to be adult supervision after school when students were departing on foot and bicycles, I used to hang out with him instead of going straight home, and we would talk about various blue-sky ideas. Once I asked him if light, which has mass, could orbit a body. We talked about that for a long time, and concluded the body would have to be extremely dense, but the orbiting light would not escape and so it would be dark. Later we realized from news articles that we had reinvented the black hole in astrophysics.
Once he gave me some excellent career advice, which I still quote; it's on my LinkedIn page.
One Halloween he wrote his address on the chalk board and invited us all to come by and "trick-or-treat" at his house. He and his family had an elaborate presentation ready (including an organ and a coffin) for those of us who were brave enougn to accept the invitation.
Now that I knew where he lived I started dropping by occasionally. It turned out he stayed up late, and encouraged me to come by any time. Sometimes I brought friends. His wife would serve us snacks. It was at one of these late night gatherings that he started playing us the unusual audio stylings of Ken Nordine, who invented a sort-of talking blues style he called "word jazz." One of the pieces was called "Roger," and Aubrey could recite it by heart. He loved to quote:
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"Oh, he had a game, by the way, that he played with me. He had me go to the
piano and strike a chord. And then with his back turned on the other side of
the room he'd name all the notes. I'd start with simple chords like a C chord
or an F chord, and then I'd get a distended eleventh chord or an augmented
seventh or a perverted twenty-seventh ... Still he'd name all the notes until
I wanted to lean on the piano. He had me on my bloody knees in front of his
superiority. And I hated him for having absolute pitch..."
When I got into high school I invited him to social gatherings at my house. I'll never forget the time he showed up for a pool party in a Victorian era swimsuit, knee and elbow length, with red and yellow stripes, and a felt hat and wire glasses that had no lenses. He leapt into the pool off the diving board in this getup. Later he claimed that he'd worn the same outfit to a tour of a new school opening in the district, and wandered about asking, "Where does the learning take place? Show me where the learning takes place."
We continued to be friends for the rest of his life. I would come back to visit, even when I didn't live in the San Diego area, and keep in touch. He also frequently came to birthday parties and other gatherings we invited him to. I made it a point to drop by his place on Halloween to see how his household decorated. The last time I saw him was Halloween 2013. He was in poor health, and the next time I called to check on him, regrettably almost a year later, he had passed away the day before.
His daughter Desiree Dunne Hall asked me to speak for about 10 minutes at his memorial service. Here is approximately what I said:
- Hello. My name is Alan Scrivener, and I had Aubrey Dunne as my math
teacher in seventh and eighth grades at Parkway Junior High in La Mesa,
California. I graduated Parkway in 1967.
After he passed away I posted to Facebook about him, on a page about growing up in La Mesa. I was quite surprised at how many comments it got and how quickly. In just one day there were over 200 follow-up posts.
One of the common threads I saw was that Aubrey was goofy, or zany: he was fond of pranks, and he sang in a barbershop quartet called "the Sweatermen."
So when Aubrey's daughter Desiree invited me to speak today, I realized I had to come here to defend his reputation. [laughter]
Aubrey was Up To Something. He was a great teacher. He believed in the idea of "no child left behind" before it was a political slogan. I want you to know that what he taught me has stayed with me. I looked up here today and saw that we are reading Psalm 90 and singing Hymn 671. I immediately thought to myself: "Ninety is ten times nine, and ten is two times five while nine is three times three. So ninety is two times three squared times five, and those are its prime factors. Six hundred seventy one has two factors, eleven and sixty-one, and they are both prime, so those are its prime factors."
There must be thousands of students who took math from Aubrey at La Mesa Junior High, and later at Parkway Junior High, and of them probably hundreds who are like me, who see a number and immediately find its prime factors.
Sure, he could be zany and goofy, but those were just tools in his chest. He also be harsh, scary, even mean. He would use whatever technique was needed to connect with an individual student. Let me give you two quick examples.
This first one I didn't experience, I read about it on Facebook from another one of his students. One year there was a fad at school of students making rubber band guns. Most of the teachers banned them in class, which meant as soon as they turned around to write on the chalk board they got a barrage of rubber bands in the back, and then spent class time trying to figure out who the guilty parties were. Aubrey instead announced that the first five minutes of class were for rubber band wars, and then the guns were to be put away. But if any rubber bands were fired after the five minutes was over, rubber band wars would be cancelled. You didn't want to be the student who spoiled it for everyone else.
The second example was something he told me about. He used to volunteer for difficult projects. That's how he became a math teacher, even though he didn't take any math in college. Nobody else wanted the job. But one year they had a class of emotionally challenged students that nobody wanted to take, and he volunteered to work with them. After a few days of chaos he concluded that it wasn't just that they didn't want to sit down and be quiet — he thought they literally couldn't do it, because they didn't have the skills. So he gave them concentration lessons. One by one he would bring them up to the front of the room and have them stand still and silent while he would try to distract them with goofy faces, noises, pantomimes, stupid jokes, lurching to startle them, etc. He would time how long they could last until they lost control. Over time they got better.
This was what he was up to: finding a way to connect with every student. Thank you.
Afterwards the minister lead us in prayer, and we turned our hymnals to 671 and sang "Amazing Grace."
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