Sunday, December 30, 2007

A New Year's Resolution: Paying Tribute to our Favorite Math Teacher(s)


First of all, I wish to thank Denise over at Let's play math! for recognizing me as one of her favorite math bloggers. The feeling is mutual Denise and, if I were to have my own list of all-stars you'd be one of them.

However, there's something I've been wanting to do for a long time and that's to provide a forum for bloggers and others to acknowledge and pay tribute to one or more math teachers who made a difference in their lives. I know each of us can think of someone and I'd like to provide a place for this recognition. Truthfully, there should be an entire web site devoted exclusively to this -- you never know! In addition to naming the math educator(s) who had this kind of effect, I would ask you to include a short anecdote.

I'll start...

The 3 teachers who most affected me in my life were my dad, Mrs. Hill from Lincoln High School and Dr. Silvio Aurora from Rutgers University. All have passed on but their impact on me is everlasting. As my students will attest, I mentioned one or more of them in virtually every lesson I ever taught. There were many other outstanding educators I could mention here and I certainly don't mean to slight anyone I've omitted. But these individuals changed my life...

My dad: Although not a teacher in name or by profession, he was nonetheless the greatest teacher I ever knew. To this day, I quote his oft-repeated phrase: "If you understand part-whole relationships you can solve virtually any math problem." I'm paraphrasing this somewhat and clearly it's an overstatement of the central ideas of mathematics, but, for K-12 mathematics, it's not far off. My dad always used the Socratic method of questioning and I know that I have always done the same in the classroom. He seemed to know just the right question to ask, just how much to lead me in the right direction, but never giving it away. He wanted me to discover the ideas for myself and feel the satisfaction of doing it on my own. Moreover, he understood that no matter how simply he explained some concept, I was the one who had to internalize it and make it my own. Oh and he believed in 'practice makes perfect!' He cared deeply about me both on a personal level and in my intellectual development. Whatever I was as a teacher was because of you, Dad. Thank you.

Mrs. Hill: My students will immediately recognize this name! I must have mentioned her thousands of times over the years because every time I use her chart/table methods in solving algebra word problems, I'm paying tribute to her! In her algebra 2 class, back in the fifties, a chart had to be used for rate-time-distance problems, age problems, mixture problems (dry vs. liquid!), etc. This was not optional! In the back of my mind I was thinking I could do these without that rigid structure but I complied until it became an ingrained habit. Fifty years later, I'm still teaching those tried-and-true methods that Mrs. Hill was the only math teacher who ever gave out composition notebooks at the beginning of a math course and by the end we had filled it up with every known algebraic formula known at that time or so it seemed! In particular, factoring forms for x^3-y^3, x^5-y^5, x^7-y^7, etc. This would be considered a complete waste of time today by curriculum specialists and experts but the grounding I received was invaluable. It's hard to recognize patterns in mathematics when one has no base of knowledge and she provided that base. Thank you, Mrs. Hill.

Dr. Aurora: My general topology teacher... You taught me how little I knew about mathematics! I came into the class believing I was fairly competent with math and within one or two sessions I realized that I had only the most superficial understanding of mathematical proof. You gave us these innocent looking problem sets of proofs, which, if worked through painstakingly, developed the entire foundation and theory of the course. I feel as though I learned more about set theory after one or two these than from all other math courses combined! Some of the questions appeared impossible even with your cryptic clues. You knew we would work together on these late into the night and you knew the elation we would feel if we could actually get a few done, never mind the entire set. We had a week or so to complete each paper and your critique of our work was always incisive and thorough. Later on, we learned that, when you were at Columbia, you had the responsibility to assess the validity of each new proof of the Pythagorean Theorem that was submitted. I'll never forget your florid face or the oversized handkerchief you took out of your back pocket to wipe the sweat off your brow when lecturing. I know that you were directly responsible for my decision to pursue mathematical research. Thank you, Dr. Aurora.

Your turn...


Lynx said...

My favorite math teacher was probably Dr. Gwen Fisher at Cal Poly. SHe was my professor for 2 out of 3 of my elementary math prerequisites to enter the Multiple Subject Credential program. As I was an architectural engineering major, my math abilities were beyond most of my classmates. Despite this, Gwen did a fantastic job of meeting their needs as well as mine. The topics of the class were rather basic, but I was still challenged and learned a lot. I know this is mainly due to how Gwen taught, as my other course is this series (taught by someone else) was a giant waste of time. Gwen knew how to challenge those of us that needed a challenge and how to help those that were struggling with the material. I remember working with other base arithmetic - something I hadn't done before. I caught on relatively quickly and it was amazing how much insight this gave me about how children struggle with arithmetic. Had we stayed in base 10, I wouldn't have learned that because it's all second nature to me.

Later, I worked with Gwen and helped her develop an art/math course. We also coauthored a paper on snowflakes (real, paper, both cut and folded) and dihedral symmetry.

I'm definitely glad to have meet her and experienced her teaching. Thinking about it now, I guess she's sort of an inspiration to me.

Dave Marain said...

Thank you, Lynx. That is precisely the kind of tribute I enjoy seeing. Perhaps the greatest teachers never need to be told how much of a difference they have made in our lives, but, then again, maybe they occasionally do need to hear it!

You have also described some of the qualities that set some teachers apart from others. They seem to have an intuitive sense of what each of their students need. You were lucky indeed to have had Prof. Fisher and to think you got to collaborate on a project!

Sol Lederman said...

Three great Math teachers come to mind.

1. Mark Saul. He was one of my teachers in high school: the Bronx High School of Science. He saw my potential and encouraged me on. He supported me in submitting a paper to the Westinghouse talent search that won an award. He encouraged me to go to the Ohio State University summer Math program for gifted kids. He is well known in the Math contest world, especially in New York City.

2. Sheila Krilov. She was a teacher of mine at Hunter Junior High School in New York City. She also nurtured my love of Mathematics. She is also known in the Math contest community.

3. Professor Arnold Ross. He has passed on. When he was alive he ran the Ross Program for gifted kids. It was a very hard program for me but it, among other experiences, has helped to feed the fire of the love of Math that keeps burning strongly more than 25 years later. Professor Ross taught us Number Theory. He built up to a big theorem, quadratic reciprocity, over many weeks, with daily explorations. He gave us PODASIP problems: prove or disprove and salvage if possible. These were really hard problems. He was a brilliant man and a gifted teacher.

Thanks, Dave, for getting me to reminisce about something much more important than how my blog has done in 2007.

Totally_Clueless said...

I tried thinking back, and could not recall any math teachers in the early years who inspired me in any way. However, my math teacher in the 11th and 12th grades was quite good, and you could see that he loved teaching the subject. His inspiration, and the extremely interesting subject matter led me to solve all problems in the book for fun!

My undergraduate math professors were eminently forgettable. However, I had some wonderful professors in grad school who did teach like they cared. My matrix theory professor was enthusiastic and made the subject matter extremely interesting. My professor for advanced analysis and optimization methods also was great.

I also picked up lots of mathematics in non-math courses, where the professors had to review the necessary background in order to ensure that the class could follow the material. In particular, the professor from whom I learned finite fields was great - he made things seem so simple in class, it was after you went home and looked at your notes that you realized that you did not understand stuff as well as you thought you had, nothing that a couple of hours of work could not cure.


Dave Marain said...

Thank you Sol & TC --
I really believe those special teachers in our lives are underappreciated. It isn't as if the great teachers receive more compensation, at least not the tangible kind!

Then there's that one teacher who was the most demanding teacher you ever had, whom you could not manipulate. If you received a grade of B you were happy and if you got an A you really had to earn it. Can each of us out there think of someone like that? Was it a math teacher?

GS said...

Peter Brown at UNSW (Australia) is a wonderful teacher of university mathematics. I believe his teaching skill is greater than his mathematics research skill, and the world is better for it. Too many university lecturers focus on research only and see teaching as a necessary evil. He had a sense of fun with the material and his presentation of it. I take the same approach in my (high school) maths teaching. It's important to recognise that students are different, though, and such an obvious positive as a teacher having a sense of fun is not universal. Some students of mine prefer that I just get on with it and only teach them as much as they need to know; others clearly appreciate anecdotes and humour. I'm sure Peter Brown would agree.

Anyway, two excellent high school teachers were Mr. Ottery (the deputy headmaster) whose dry wit and straightforward old-school style appealed, and Mr. Barrett, who taught the hardest course, which meant spending a lot of time with that class. He didn't pretend to know everything and made a great effort to work through difficult problems with us.

I'll also credit Mr. Weiss for giving me a good kick up the butt when needed :) His approach to classroom management is something I emulate, with some good results and some not-so-good results. Sigh... why can't teaching be easier...

GS said...

Just a quick question, Dave. I want to know about the chart/table approach to solving algebra word problems. I've never heard of it, and by the sounds of it, it's something I oughta know.

If you could email me some info at (without the x, to avoid spam), I'd really appreciate it.