Perhaps some background information is in order here.
Peter Fraser is the legendary (at least to a group of people) mathematics teacher of TED Ankara Koleji. He was the head of the mathematics department, author of the middle school books, and above all, an excellent teacher who has won the hearts of many students over a career of thirty-six years, if I am counting correctly. I was lucky enough to end up in his two of his classes; mathematics and computer programming (for which he also wrote the book).
Just yesterday, I noticed he now has an account on Facebook, and many former students have contacted him there. So, I decided to write … about my memories. Since the Facebook interface is kind of awkward (pressing enter sends the whole thing) and I already have a blog, I decided to write it here first. So here it goes…
I am really not a regular user of Facebook. Last night, I got so excited when I saw that you (finally?) had an account. I sent a friend request, and in the meantime read through everything that all your former students had written on your timeline, and your responses. I was a bit sad to reach the end; I think this represents only a small fraction of the students you have had over the years.
You have had so many students over the years – at least 3,000 students – and that is a really conservative estimate. Yet, each one of them – us – wants, or at least hopes to be remembered. Having been on the other end of such a one-to-many relationship myself, I fully understand how that is not possible. Yet, the fifteen-year-old youngster inside me still wants to be remembered.
But, before trying to shamelessly force you into remembering some not-too-distinct student from 28 years ago, I want to share my own impressions that I still can recall – they were that strong.
I never really liked secondary school. It was almost fully a boring experience for me. I remember counting the minutes to the end of the lesson. Four hours before lunch. First hour, I count the last five minutes. Second hour, the last fifteen minutes. Third hour, the last thirty minutes. Fourth hour – the whole time…
It must have been one of our first few mathematics lessons with you; you were telling us about the rules of divisibility. You really got my attention. You were going through the rules, 2, 3, 4, 5… I remember for the first time looking at my watch and thinking, “Oh boy, the bell is going to ring – I really want to hear the rest of this!”. I really wanted to hear seven, and eight, and eleven!
I remember SOHCAHTOA – most other people do. But, getting “too much” of an education afterwards, I did not need that so much. Trigonometry became second nature. Yet, there are two things taught by you, which I repeatedly used when necessary, and never forgot.
First one is the following, which I can hear in my head with your sentences and with your voice, still:
“Write the whole number. Subtract those which are not under the bar. Draw the line. Write a nine for each digit under the bar. Write a zero for each digit not under the bar. Stop at the decimal point.”
(Note for the benefit of others reading this: This is the rule for converting a repeating (or not!) decimal fraction to a rational number.)
It works like a charm – whether your understand how it works, or not.
The second one is the traversability rule for graphs. I still remember you explaining how Euler figured it out – by scribbling. (That is when I learned the word “scribble” too.) Whether the Euler story is true or not, I still remember you can have either zero odd-nodes, or two odd-nodes, and you must begin at one, and finish at the other. All other cases are untraversable.
Now, time to desperately try to get remembered.
I was your student in 3-B, in the 1987-1988 academic year. Mathematics, and computer class. That was the year with the infamous 8-0 score.
My best chance to get remembered is not in the mathematics class, but in the computer class.
I was the student who already knew too much about Commodore 64 Basic to be in that class. We sat with Emre Burma (two students per computer) and finished the exercises way too fast. Once you told me that since I knew how to program already, I should have been in the “English Conversation” class. I do not recall how I responded, but I was hoping that it was impossible to switch at that point – English class was boooo-ring!
Another time, we were trying to write a program to calculate the Fibonacci series – iteratively. (Not that recursion was possible.) I figured out how to update the variables at each loop, and I remember you saying “You can figure these things out. I always thought you should be on the TÜBİTAK course.” The funny thing is, I only had a vague idea of what that was, and in my mind it sounded like “more schoolwork than absolutely necessary”. That did not happen, either.
Exhibit C: At some point, we entered a program into the computer that asked simple arithmetic questions (addition, subtraction, multiplication, division) repeatedly until a timer (two minutes?) ran out. At the end, it displayed the score on the screen. You also had a “top score” on the corner of the board in the lab. I broke the record the first time I gave it a try. You looked at my screen, and updated the top score. In about fifteen minutes, a couple of other guys broke my record, by a few extra points. Then, I gave it a really hard try, and broke the record with quite a large margin – and I am pretty sure that record stood for that year.
I think you were a little suspicious – I believe the record was at least from the previous year. The smart guy who knows too much programming breaks the record by a margin of 50%? I would be suspicious too. I kept playing with it during one break – and scored close to my own record. I realized you were standing behind me, watching the whole time when you said something along the lines of “You are really fast with that!” I think that is when your suspicion cleared.
Exhibit D: You were telling the class about the INT() function in Commodore 64 Basic. You (quite correctly) stated that it always rounds down, and any and all fractions would be removed. When exercise time started, being the smart alec that I am, I called you over, and typed:
on the screen, which the Commodore 64 happily evaluated to:
Now, this happens because of the finite word size – make the literal number too close to 3, and it actually becomes 3 for the computer. You looked at the screen, and went, “Hmm, yes, but I don’t think I am going to go back and change the lecture.”
Exhibit E: If I am not mistaken, at the time you were trying to update the computer programming book to a new edition. You asked us (me and Emre Burma) to type in some programs, and get things printed on the printer, so they can be inserted into the book. I think we spent quite a few lunch hours (or so I remember) doing that. We really liked to be of assistance.
I rest my case. Now I think I wrote so much that you will feel guilty to say you still do not remember. No matter – please don’t – the fun part was sharing the memories.
You are, as all your former students think and say, a truly excellent teacher. But only part of it is being able to explain mathematics in a way people can understand. I believe there is more to being a memorable, even unforgettable teacher that just explaining things. Let me try to put how I felt at the time, and how I still feel about it in words – not an easy task, but I will try.
You were on our side. One would think there should not be any sides – people are there to learn, others, to teach. But what happened with most teachers is that there was sort of a cold war – like we were there to refuse to learn, and they were there to force us to learn. Neither of which is true. In your class, it felt like there was a common enemy – not knowing mathematics – which you were leading us into battle with. You wanted us to be successful. You never made any one of us feel bad about ourselves, or any bad grades we got (which some of us did). There was never any blame to go around – just things to learn.
You had respect for your students. To be fair, a lot of teachers love their work, and love their students. Unfortunately, few have respect for their students. You respected our rights. Exams were graded oh so rapidly, and fairly. You never entered the classroom before the bell. Never stretched the lesson beyond its time.
The atmosphere you created for us, and your other students, made us want to learn. And you were there to help us with it. For thirty-six years. Thank you for that.
I think this is the point where I need to tell about myself. This has slowly worked itself to be something of a problem for me – I do not a clear-cut answer like some people; I even envy the ones who can say “I am a lawyer” or “I am a heart surgeon”.
I think I am sort of a jack-of-all-trades in the software/IT world. With a Ph.D. in Physics from MIT. With a double major in Physics and Electrical and Electronics Engineering. Who is essentially self-taught in software and IT. (Sound familiar?)
Oh, and I promise to support England for this European Cup, as per your request!
Your former student