It has been said, although I would hardly claim this as an absolute fact, that a person only will need to read a year’s worth of my blog posts to learn, as much, or more than any traditional four year program at Harvard University or Trinity College in Cambridge.
It has been said, although, I have never had the theory tested, that readers of this blog will see their IQs grow by no fewer than 25 points over the course of a calendar year.
Mind you, these are just claims with no definitive proofs. Because we’d need proof. Or so they told Srinivasa Ramanujan. But, alas! I am getting ahead of myself.
I recently read a book titled Finding Zero. This book is about a mathematician’s quest to find the origin of our number system. The tale includes his travels to uncover the civilization that first invented the concept of zero. It is a fascinating book.
I LOVE learning new things. It’s a passion. I think it is a result of my profession. There is just so much knowledge and information out there. When I read, when I study, I am always amazed of the wealth of information that is available to learn – if only we have the time.
I am in awe of what I don’t know…
And, I will admit this – As 2015 closed, I had never heard of Ramanujan. The name meant nothing to me.
Of course as one reads about numbers and great thinkers, he’s bound to come across Ramanujan. He makes a brief, but impressive appearance in Finding Zero. In the few paragraphs that he is mentioned, one is immediately taken in by him. Ramanujan leaves an impact.
But, as he only appears on two pages in the text, after reading about him, since I read about so many other things, and I don’t often read about math, I figured we wouldn’t meet again any time soon.
A few months ago, I received an offer for two tickets to a free screening of a new movie that was planned to come to movie theaters. I immediately said “YES” and that night my wife and I were at the AMC Theater in Paramus watching a movie about none other than Srinivasa Ramanujan.
The title of this movie is “The Man Who Knew Infinity.” (It was just released!)
This is a movie that I recommend that you MUST go see it. As a big fan the Rocky movies, I was disappointed that there are no boxing scenes or scenes of mathematicians running up steps, but the movie is great. You must see it. It is that good. On the form we had to complete after the screening, I called it “Brilliant.” That was also what I told the film’s producer – “That movie was brilliant.”
This was the first time that I had ever been to a Hollywood screening before. It was a nice experience. The movie starts on time, there are not endless commercials before the film – and there are no previews either. They just show the movie. Neat!
Oh, when these things occur, as I found out, the producer of the movie sometimes sits just in front of you.
(I only know this because the seats were “saved” using the old masking tape across the aisle method. A man sat down in one of the seats, and later, another member of the production team who had been all around the theater went over to introduce himself. I couldn’t help but hear him say, “We worked together on (and he mentioned a film)…” In that short conversation, the man’s name, Ed Pressman, came up. Google can be very informative. I looked him up on my phone and learned he was the producer of the film.
Ed Pressman, I later researched, has been involved with producing no fewer than 88 Hollywood films. At least two of the films he produced starred a certain Sylvester Stallone. Neither, though, was titled Rocky or had anything to do with a fighter from Philadelphia. Too bad. If they had, Ed Pressman would have immediately become my best friend.
After quietly tapping my wife on the shoulder and whispering “That is the producer,” I focused on the film that was just about to start. (I think producers only enter the theater moments before the film starts.) )
The movie was mesmerizing from the beginning. I loved it. My wife loved it as well.
And I kept thinking, “A week ago I never heard of this mathematician and now I’m watching a movie about him – and loving it.”
There is a lesson in this. A huge lesson. A lesson that we must especially share with children – always:
We can never stop learning.
Just when we think we know about anything, just beyond that there is a world of information that we haven’t even begun to tap. There is knowledge yet to be found. We can never stop trying to learn more and trying to be better. As we strive to be our best selves, we must share that passion with the students. As educators, that might be the most important thing we can do.
Teaching children to continually learn is more important than mini-lessons or conferring notes or Problems of the Day. Children must know that they have the ability to learn, that learning is a lifelong process, and that learning is what makes us great – and fuels our potential as individuals and as a society.
This is why we never want to cut corners. By striving, by being better than ourselves, by doing the extras, we teach children so much more than just what is on the surface. It’s a deep and profound thought – and it gets lost sometimes amidst other things. It is why, as educators, even in challenging times, we need to continue to set the highest bar.
When we stop doing our best and rely of our past reputations, we begin to erode our future reputations.
People don’t want to hear how great a program was two years ago. Or what we did five years ago. Or yesterday. They want to know what we did for their kids today. That’s how we continue to forge a great reputation.
After the 2007 baseball season, the Yankees management didn’t want to hear that Joe Torre had won four World Series. They wanted to know why no World Series had been won in the previous eight seasons. Torre was let go.
A similar lesson just out last January with the two-time Super Bowl championship New York Giants and their head coach Tom Coughlin. It’s a common question we ask, “What have you done for me lately?”
But, back to Ramanujan…
Ramanujan’s biggest challenge, at least according to the movie, was not that he wasn’t a gifted mathematician…it was that his line of thinking and reasoning, possibly because of his background in India, was not congruent with the great minds of western culture at Trinity College in Cambridge.
While it seems that much of his mathematical reasoning was solid – and that the theorems he developed were correct – he did not have the “proofs” that western thought asked of him – and needed from him. It’s a powerful story on many levels.
Ramanujan struggled with trying to think as a westerner and provide proofs for mathematical concepts that he seemed to figure out in a different way.
It wasn’t that he was wrong.
I have told this story before, but it is a powerful one. Before he went to school, my youngest son could do all sorts of mathematical computations in his head. As a pre-schooler. He understood (in his way) carrying numbers, double digit addition and subtraction, and even some multiplication and division. In his head. He didn’t write this stuff down, but he’d be able to answer tricky math questions we’d pose to him.
Then, he went to school, and somehow, somewhere, that ability was turned off. He learned methods or formulas and his ability to solve things in his head with his own methods disappeared.
Now, maybe my son’s original math had limitations. Maybe his math wouldn’t have allowed him to advance beyond what he already knew. Maybe the math he was taught, and is being taught, has opened his mind in new and better ways. We’ll never know. All I do know is that “our math” (the math of school) turned off my son’s own way of correctly solving equations.
Ramanujan faced this problem with the most detailed of mathematical reasoning. He didn’t have the proofs. And some western proofs, calculated from others, seemed to prove some of his findings incorrect.
I’ll admit, I’m not enough of a mathematician to understand all of this to explain it beyond the most simplistic.
But it does bring me, finally (some may say) to the main point.
I do think that allowing children to try to make sense of numbers in their own ways can be effective. This is happening in many schools today. But, that being said, we also need to get to the solid and true and effective formulas that we all know But we still must look at instruction creatively…
The movie made me think that, at least with some gifted students, that maybe we need to accept the idea that they just do know the answers. Maybe there are times we don’t need to make them “show the work.”
Ramanujan stumbled when they made him “show the work” in the way they wanted the work to be shown.
Today, there may be times when students say, “I know the answer” and they do, but they can’t necessary explain how or why they know it. I’m not ready, quite yet, to say that that is ok, but I am saying that it might be ok.
I can ride a bike. I cannot explain, in the least bit, how to do it. I just know how to do it. It might be that way with some kids and math. They might just know.
If there is a child in your classroom, and they may come along only once in a career, if ever, but if there is a child that is truly understanding something, not just in math but in any area, there may be times when we just need to let that child fly.
Maybe sometimes, by continually asking for reasoning and proof we’re pulling against a soaring thought and a creative mind. We need, we must, continue to find ways that allow children to think and reason in profound ways. We need to continually give children the tools that allow them to soar.
When we do this, we might be doing our very best teaching…