Beginning

Learning is beginning. It's important to realize that technology is by definition a means to an end, not the end in itself; however, that means or craft or art or way of doing things will ultimately shape the end. Below is a longer version of an article that appeared in Independent School Magazine in the Fall of 2008 issue. It has nothing to do with publishing business models, Twitter, Kindles, Iphones, podcasts or Youtube schools. It's just about learning. That's where we have to begin.
 

Beginner’s Mind, Geometry Mind[i]

 

To begin; to start all over again. It creates a unique feeling: a mixture of excitement and fatigue. In mid-career, it is difficult to go from being the expert to being the novice again.

 

Last year, at the age of 46, I taught Geometry for the first time. I began teaching when I was 23 – but not Geometry. I am a Classicist. I’ve taught Latin and Greek for over 20 years, grades 7 through 12 and beyond. I have two octogenarian Greek students who have been with me for 15 years and are now reading the Odyssey in Greek. Together we have rambled through some Plato, a lot of Herodotus, Sophocles’ Antigone, and many of the great passages of the Iliad. My master’s degree is in Classics and I majored in Classics as an undergraduate. I began learning Latin in 7th grade and Greek in 9th grade.

 

I studied Geometry a long time ago, in 10th grade, just like my own students, and I remember liking it a lot. But there are no particular moments, no unfulfilled longings that I remember from Geometry class that could account for my strange attraction to the subject so many years later. That happened in Greek class.

 

My 9th grade Greek textbook was an old-fashioned, pocket-sized, cloth-bound affair we called “Crosby and Schaeffer” for the two long-deceased authors. On the first page of the first lesson was the quote, “ἐν ἀρχῇ ἦ ὁ λόγος,” John I.1: “in the beginning was the word.” That caught my attention right away. The Bible was written in Greek? And I could go ahead and read that most enigmatic of sentences in the original in the very first lesson? I was sold.

 

A few chapters later, though, we came across something even more surprising, “τὰ τοῦ αὐτοῦ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα"  “things equal to the same thing are also equal to each other.”  In that chapter and a later one, the masters Crosby and Schaeffer did me the favor of including several other sentences straight from Euclid’s “Elements”, the foundational work of what we know as geometry.

 

I didn’t read Euclid again for many years. I studied Geometry in 10th grade in the kind of traditional curriculum that is still used here at The Episcopal Academy, including the notorious two-column proof, reviled by the more numberish math types and welcomed with relief by logophiles. We learned the well-worn ways of proving triangles to be similar: angle-side-angle (ASA), side-angle-side (SAS), side-side-side (SSS), but definitely not angle-side-side which makes an “ASS” of you and me. Little did I understand how closely my textbook reproduced many of the steps that had been laid out more than 2000 years earlier in the tiny city-states of Greece and redacted by the great scholars of Alexandria.

 

Many years into my career as a Classics teacher, I spent the summer in the library studying Euclid and the strange story of the circuitous route of ancient Greek mathematics and science from Greece to Egypt to Damascus to Morocco to Spain and finally into the early European universities. It was my own research. I was in no program, had no teacher, and got no degree credit. Just quiet afternoons in the library gazing at illustrated manuscripts. I wrote up a one-week unit on Euclid to use in our Geometry classes and collected some materials that would be good for some fun in my Greek and Latin classes.

 

I forgot about Geometry for a long time. And I even moved away from Classics, joining the technology department and taking on a whole new challenge. One of the administrative duties I assumed was academic scheduling. And in the process of scheduling the 2006-2007 academic year, I realized that we were half a teacher short in a math department that was already stretched. With a little more stretching, they could probably cover one more section, but then what? Thinking that nothing would come of it, I wrote a brief note to the math chair, offering to cover one geometry section. He bit. He came over with a textbook and said, “take a look at it and see if it’s really what you want to do.” It was what I wanted to do.

 

That summer I sat with my textbook in free moments and dutifully solved one problem after another, checking my work against the answer key in the back. There were times when I found it tedious. I felt I was wasting my time, starting at such a basic level. I am a well-trained Classicist, a self-taught database programmer, a competent network manager, a savvy administrator, but just a beginning geometry teacher. I found the problems difficult sometimes. I made mistakes.

 

Around the second week of school I became elated: I was actually pulling it off. The kids were doing the work and learning the material. I was using all my old teaching techniques but I sometimes got ahead of myself. For example, I knew I wanted to do about 7 minutes of demonstration, give about 2 minutes for questions, then assign 5 problems for everyone to work on in groups, and then finish with a contest to see who could find the problems in other groups’ solutions and who could get the solutions right. I had done the problems; I was prepared for class; the only problem was that I simply didn’t know geometry as well as I knew Latin and Greek. There were never problems involving our network or database systems that I hadn’t seen several times before. But this was my first time standing up in front of 16 itchy 10th graders and explaining why perpendicular was neither acute nor obtuse.

 

My answers bubbled up too slowly; I was rearing to go but I didn’t have the horsepower. I stepped on the accelerator and got nothing but hesitation. I was a beginner: enthusiasm, adventure, discovery, but no experience.

 

About the time that interim grades were reported, the complaints started coming in. “I know he’s been teaching his whole life, but this is the first time he’s taught math.” “Shouldn’t he stick to administration? Why is he in the classroom?” And I had made the mistake of saying at Parents’ Night, “just as your children are beginners, so I too am a beginner at geometry.”

 

For better or worse, we are in an age of professionalism in independent schools. Try hiring a girls’ varsity soccer coach who last played in high school and has never coached before and you immediately understand this. Parents want more than just amateur coaches, they want pros. The teacher-counselor-coach model continues to become more and more difficult to sustain.

 

So now I was up against more than just my own struggle to master the subject as it was presented in the text book; I was also being challenged by parents and students on my qualifications. But I’m no shrinking violet. With an Ivy League degree, a master’s degree in Classics, twenty some years of work experience, and a successful career shift to database and network management, I was not intimidated. Nor was the school. Criticisms were forwarded to me directly. I felt complimented by the administration’s openness. At the suggestion of a colleague, I gave my class an evaluation form, reported the results back to them, and explained several changes I intended to make to respond to their criticisms. I was happy with how I had met these new, unexpected challenges.

 

But what struck me was this: how is a novice teacher expected to navigate these waters? There is no substitute for classroom experience as far as promoting growth. Although some teachers stagnate at certain points in their careers, most continue to improve. But with little or no experience, the classroom is daunting. My foray into the world of the beginner renewed my respect for the courage of novice teachers as well as my respect for the authority, knowledge and competence of master teachers.

 

My career as a mathematician is on hold for now. This year I am filling a gap in my home department of Classics, teaching a beginning Greek class. I have not taught beginning Greek in a long time, and I chose to teach it using a new text book that is very different from what I am used to, but the class challenges me at a completely different level than geometry had the year before. It is more like the experience of a trained pianist responding to a favorite piece, changing dynamics to adapt to his mood and audience, than the experience of a nervous amateur sweating it out in an audition.

 

My students missed something because they didn’t have a “geometry pro” giving them their lessons, but, if they were paying attention, they gained an understanding of how to begin something. I was their “beginner pro:” learning, adapting, correcting, and growing as an adult. If we want our students to be life-long learners, we should give them examples. Pasting it into our mission statements will not do the job; we should show them.



[i]     My title, and the inspiration for my interest in the benefits of beginning come from “Zen Mind, Beginner’s Mind” by Shunryu Suzuki, Shambhala Publications, Inc., Boston: 2006

 
 
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