And to Josh, thank you ever so much for the information on the Four Essays by John Ruskin. I've never come across this philosopher and I am finding him fascinating. Thank you much. And the fact that he was an architect is a bonus as I enjoy that field of art and technology. I'm reading some of his other works in this field....and learning. Interesting guy.
Now a major heads up on an opinion piece written by one of my favorite writers and thinkers, Thomas Friedman of the New York Times. His latest article, entitled, "America's Real Dream Team" is a heart warmer (reading it made my heart feel better) about the 2010 Intel Science Talent Search. Every year there is a contest for high school students in the Mathematics and Science areas. Forty of the top applicants are chosen and there are several prizes with one top prize of $100,000 dollars.
I highly recommend the article as Friedman is an excellent thinker and writer. The part I liked the best is when he talked to one of the teachers who had two winners in this year's group. "My favorite chat, though, was with Amanda Alonzo, a 30-year-old biology teacher at Lynbrook High School in San Jose, Calif. She had taught two of the finalists. When I asked her the secret, she said it was the resources provided by her school, extremely “supportive parents” and a grant from Intel that let her spend part of each day inspiring and preparing students to enter this contest."
Being an emotional type of guy the article brought tears to my eyes. Here was a teacher allowed to work with students and given the resources. And the parents supported her. We teachers could do so much if allowed. Nice going, Ms. Alonzo.
And now I have to tell you about Tommy, a fourth grader in a school that I actually loved. It had great teachers, a principal who stayed out of the way (and told me to do likewise) and supported his teachers all the time. I had several student teachers at this elementary school and always looked forward to going there. I could spend pages telling you about this school but this is about Tommy.
I walked into the classroom one day expecting to watch my student teacher and Beth, the cooperating teacher grabbed me and asked if I would work with a student having problems with Improper Fractions. She handed me a textbook and called over to Tommy. Tommy helped me on some research I had done at the school involving computers so we were friends--sort of..... His dad was an important medical doctor in the community and his mom regularly volunteered at the school. Both parents were tall and Tommy was already on the way to being one of the tallest in the class. And he was deadly serious most of the time. I don't remember him smiling much. He attacked life at every level. And he questioned it all the time. A very bright student, he always wanted to know more about the subject. A great kid to have in your class.
So I was a bit surprised to find out he was having problems with improper fractions. We both sat at the table at the back of the room and I started in by making sure he had regular fractions under control No problem there. But when things got to 8/3rds, the concept wasn't flying through his brain. So I did the usual--drew two circles and made them into quarters, eight quarter in all. "Okay, Tommy, how many circles do I have?" "Two." "How many sections IN the circles are there?" "Eight" came the reply. "And each circle has how many sections?" "Four." We were on a roll. "Okay, so we're playing with quarters now, aren't we?" "Why," was his answer. So I explained that I had drawn the circles into quarters but I might have just as well cut the circles into eighths or thirds. I wasn't getting through.
So I pushed on. I shaded in six of the quarters and then asked Tommy, "How many sections are shaded in?" His correct answer was six. So I wrote six on a piece of paper and drew a line underneath and then a four under the line. 6/4ths. I explained how the top number could change but the bottom number had to be the same as we were using. You couldn't have one circle with quarters and the other circle with thirds and work out the problem. (yeah, I know mathematicians can do this but we were just starting on the concept).
Tommy still didn't get it. He could do the arithmetic of solving the problem of taking 6/4ths and changing it into 1 and a half. He could see the diagram and his numbers were correct but he just hadn't seen the concept of improper fractions. Tommy was trying very hard, he wanted to know. But I wasn't doing a good job of explaining. I remember we did it several times using both circles and squares cut up into pieces.
I can't remember what I was trying next in teaching this concept when all of a sudden, Tommy understood the concept of improper fractions. He turned to me and said, "Oh, this is easy! Why didn't you teach me this?" He really was somewhat peeved with me. And I don't know what went on in his head that suddenly clicked over. But he understood all of a sudden. It was fun to watch. We did several other problems--a couple of hard ones and he was cool with them. He knew all along that he had to know the concept behind improper fractions--he didn't want just to move numbers around. Once he understood, he was satisfied. I don't think he ever thought I had anything to do with his learning improper fractions. It was his "Aha" moment.
He went to his teacher and said he understood fractions with his usual serious face and that was that. "What's next on the learning path?" I know he has done well. I wonder if he ever smiled, however. But I'll always remember him saying, "Why didn't you teach me this?"
Thanks to all those elementary teachers teaching improper fractions. And there are a lot of adults that will say in their hearts, "thanks, teach!"