The rest of the day I was really excited. I went over in my mind what I would do on Thursday and how I would do it. I felt that I was about to do something that would put me in the running for Teacher of the Year. Everyone would Oooh and Aaahh.
I thought back on my own school days and my exposure to math. I hadn’t learned my multiplication tables until I was in eighth grade. Somehow I had stayed under the radar long enough for this not to have been detected. That is, until one day in Mrs. Sage’s class when she began asking me what this times that was. I was discovered! From then on I had to stay after school until I knew my times tables. I hated it. With some maturity under my belt, however, I eventually came to bless Mrs. Sage.
I arrived in ninth grade right after my thirteenth birthday. Maturity-wise I was thirteen going on ten. The first day of Algebra class the teacher stood at the board and wrote X + 1 =. I looked at what she wrote: X + 1 =. I actually said out loud, “I don’t think so!” I was emphatic. One was a letter and the other was a number and no one in their right mind would suggest that a letter and a number could be added together!
My second experience taking Algebra came in summer school. The first day of class the teacher told us that Algebra was nothing more than a game. We would be looking for something we didn’t know. We would be like math detectives. For simplicity we would call what we didn’t know X. Everything we did that summer was to solve the puzzle of finding X. I was immediately enthralled. I loved games. From that day all the way through Geometry and Trig (now called Algebra 2), I loved math. I was playing games and finding the X.
I believe anyone is willing to learn if he or she sees the purpose, even if they don’t have a particular passion for it. The best way to present information is to tie it to something the person is already interested in. The next best way is to present it as something worthy of the person investing his or her time. The next best way is to make it enjoyable, a game. The worst way is to say “Don’t ask why. Just learn it. The Test is coming soon and failure is not an option.”
All that to say, I was stoked for tomorrow.
Thursday morning I arrived breathless and almost not early enough. On the way to school I had stopped at Walgreens to purchase several balls of string. Once at school I went next door to Mr. Cotton’s room and borrowed his yardstick. I took Mrs. Thornton’s yardstick and placed the two sticks on the floor in the front of the room end to end and taped them both to the floor, giving me a 6’ measuring stick. I set about cutting the string into 3 foot, 4 foot, and 5 foot lengths creating a big pile of different lengths of string on the table in the front of the room.
On the board, next to Mr. C.D. I drew a right triangle, adding an “a” next to the shortest length, a “b” next to the tallest length, and a “c” next to the diagonal length, or the hypotenuse of the triangle.
I watched happily as the students filed in with questioning looks on their faces. No one spoke.
“Please don’t step on the yardsticks,” I said.
While they were finding their desks, I asked, “By the way, how many feet are in a yard?”
Several moments passed.
“Well? How many feet are in a yard?”
One of the students finally spoke up. “Three feet are in a yard,” he said with no interest.
“Nope, that’s wrong,” I said.
“What do you mean? There is always three feet in a yard,” retorted several of the students. “How many feet do you think are in a yard?”
I was feeling frisky. “That depends on how many people are standing in the yard!” I laughed heartily. They rolled their eyes. Who was this guy who had invaded the controlled environment of Mrs. Thornton’s math class?
I began the day, “How many of you have heard of the Greek philosopher and mathematician, Pythagoras?” I didn’t expect anyone to know. They didn’t.
“Well, this guy, Pythagoras, was a really smart dude,” I declared. “He lived about 500 years before Jesus—in other words, about 2,500 years ago—and, while he was growing up, he decided to travel the world searching for smart people whom he could learn from. That’s a pretty good way to grow up and learn, don’t you think? Eventually he became a famous philosopher and a religious system grew up around his philosophy which had some pretty weird beliefs. One belief was that fire, water, and earth are all holy. Think about what that means: When a person dies, he can’t be buried because earth is holy and you don’t want to defile the earth with a dead body. But, water is also holy, so you can’t bury a person at sea. And, since fire is holy, you can’t cremate the dead body.
Some people even today practice the religion of Pythagoreanism. What do you think they do with the bodies of dead people?”
They didn’t know.
I told them. “People build buildings with lots of shelves built into the walls of the rooms. They don’t put a roof on the buildings so birds can fly into the buildings from the sky and pick apart the dead bodies until there’s nothing left but bones. Bones won’t defile anything, so what’s left can then be buried or burned. There was a famous English writer who was born in India where people followed the Pythagorean religion. His name was Rudyard Kipling. He wrote the Jungle Book (you may have seen the Disney movie). Anyway, one day Kipling’s mother was out working in her garden and an arm fell out of the sky and landed—plop!—right in front of her in the dirt.”
“Grooooss!” said several of the girls.
I continued, “But that’s not all. This guy Pythagoras invented a magic math trick that has been used for 2,500 years by every builder in the world. In fact, without this magic math trick, you can’t even build a wall or door or put up a fence in your yard that is straight.”
In our community, a lot of construction is going on and several of the students spoke up to say that their father or uncle or brother worked in construction.
“Well then,” I said. “You’ll have to ask them if they’ve ever heard of Pythagoras. Even if they haven’t, they can’t build anything without knowing his magic math trick. The ‘trick’ is called the Pythagorean Theorem. The word ‘theorem’ means something most people accept as being true.
I asked them to repeat the name: Pythagorean Theorem.
“So since Pythagoras came up with this Theorem, it was named after him.
“OK, now look at the board. What kind of triangle is this on the board?”
“Right Triangle,” they answered correctly. I thought, “Bless you, Mrs. Thornton. You have made my job easy.”
“Yes, that’s right” I said, emphasizing the word Right. “A Right Triangle has one angle that’s always right.” Again eyes rolled.
“And what size angle is always right?”
“Ninety degrees,” they said. They were growing weary and I knew I had to do something soon other than talk about some dead guy.
I asked someone to go to the board and point out which of the three angles was ninety degrees. A boy from the front row obeyed.
I said, “So, if these two lines that come together and make the ninety degree angle were actually two walls (I pointed out two of the room’s walls where they joined)—“or if these two lines were the frame on a door like this” (I went to the door and pointed to where the upright and top of the door frame met)—“then the angle that is made where the walls join, or where the door frame meets, they are ninety degree angles. Would that be right?”
They nodded, and I knew they were wondering what was going on.
“Ninety degrees is also called square. If you are building something, in order for walls to be square with each other, and door frames to be square so the doors will open and close, and in order for your desk top to be square, you have to know Pythagoras’ magic math trick—called the Pythagorean Theorem. You have to know how to make a ninety degree angle.
I then put on a serious face. “I have walked all over this school. It is really old. Sometimes old buildings fall apart if they weren’t made well in the first place. How could we tell if our school was built right in the first place? You probably never though about it. You just come to school and expect that it won’t fall down while you are in class. But, schools are falling down all over the country because they are getting too old. Some of them are actually dangerous. Some of them have been closed because the walls can’t be trusted to stand up.” With each statement I had raised the level of concern in my voice.
“Did you know this school could fall down if it wasn’t built right when it was first built?”
“Here’s the deal,” I said, coming to the point. “Let’s say that the School Board has just hired me to inspect the school to find out if it is still a safe place for students to come to. How many of you would like the school to be condemned and closed so you couldn’t come here to school any more?”
Most of them raised their hands. Right away I wished I hadn’t asked the question.
“What we have to do is see if the walls, the door frames, the window frames and the brick walls are all square. It’s a big project and you are going to help me do the inspection.
Now I had their attention.
One of the boys pointed to the board. “What does Py—what’s his name—have to do with all this?” he inquired.
“Pythagoras. And I thought you’d never ask,” I said.
I went to the board. “The trick that he came up with—his Theorem—says that if you measure the length of one side of a triangle and square it—fortunately they knew what square meant—(I pointed to the “a” on my triangle on the board); and if you measure the length of the other side of a triangle and square it (I pointed to the “b” on my triangle on the board); then if you add those two squared numbers together, the hypotenuse of the triangle (I pointed to the diagonal line of the triangle) will be the square root of those two numbers if this angle is 90 degrees.”
I knew they needed an example, so I offered them one. “Let’s say this shorter, bottom part is 3 feel long. If we square 3 feet, what do we get?
“Nine feet,” they all said.
“Good. Now if this tall part, the one going up, is 4 feet and we square it, what do we get?”
“Sixteen feet,” they answered.
“Now add together the square of three (which is nine) and the square of four (which is sixteen) and what do you get?”
“Twenty five,” they all said.
“Here is Pythagoras’s Theorem written out.” I wrote on the board a2 + b2 = c2. “Therefore,” I said, “if a = 3 and b = 4, then c equals what?”
They looked at the board for awhile. Finally one student said, “It equals the square root of 25, which is 5.”
I then went to the pile of strings on the front table. “In this pile of strings you will find some 3 foot, 4 foot and 5 foot pieces of string.” From the pile I pulled out one of each length.
“I need three helpers,” I told the class. Up went everyone’s hands and I picked three. “Come up here,” I said. They left their desks and came to the front. I gave each a piece of string. “Now, go to the door and stretch the 3 foot string across the top of the door frame with one end at the corner. Put one end of the 4 foot string against one end of the 3 foot string.” They had to get chairs to stand on. “Now, you with the 5 foot piece of string should put each end of your strings at the ends of the others’ strings and they should meet exactly if the door frame is square.”
We did this several times with window frames, walls, and desk tops until I was convinced that they understood. So far, everything had been square.
I had them form themselves into groups of four. Three would be string holders and the fourth would take notes. Once they were formed into groups, I told them, “OK, now each group come to the front and find the three strings of 3 foot, 4 foot, and 5 foot. The measuring stick on the floor is there if you need it to help you find all three lengths.”
Before letting them go, I said, emphatically, “Please understand that this is a serious matter. You are determining if your school is a safe place for students to be. Each group should go to a different part of the school because you only have about 45 minutes to do this. Return five minutes before the end of the class period. Tomorrow, each group will give their report. Now go check out your school.”
Off they went, in groups of four, pencil and paper in hand, trailing string behind them.
I did this with the students in each of the three math classes. After going all over the school, each class returned just before the bell rang. They wanted to give their reports right away but I told them there wasn’t time and we would have plenty of time on Friday.
One of the girls could not hold in her excitement. “We even asked the principal if we could measure his office,” she said.
“Oh, really,” I was surprised at their courage. “What did he say?”
“He thought it was cool. He said it was OK with him.”
Next morning was Friday, my last day substituting for Mrs. Thornton. As I entered the school, I saw Nicholas coming out of the school office. Nicholas was one of Mrs. Thornton’s math students.
“Hi, Nicholas. How are you this morning?” I asked.
Nicholas had a somber look as he walked toward me. “Hey, Mr. C.D. You know we are all in trouble, don’t you?” he asked. I didn’t know. As he got close to me he whispered, “You are especially in trouble!”
“Trouble?” I was surprised. “Why ‘trouble’?”
I quickly found out. The night before, Mrs. Thornton had received several calls on her cell phone while she was in her husband’s hospital room. Other teachers wanted to know why she had allowed her classes to run around the school and make noise in the hallways. Noise in the hallways during class period is not routine, and it was distracting all the other classes in the school.
Most of the students were unaware of the trouble I had caused. They bounced into class ready to give their reports.
I apologized to each class in turn. They promised that they had not been running around or making too much noise.
“We had a lot of fun, Mr. C.D.” They all agreed. Several had asked their fathers or uncles or brothers if they had heard of Pythagoras or his Theorem. None had heard of Pythagoras, but each one had said, “Of course, I know about 3 feet, 4 feet and 5 feet. I use it all the time.”
All the kids had pretty much the same report about the structural integrity of the school. “The only place we found that might not be square was in the upstairs stairwell. Other than that, we think the school was pretty well built.”
I asked them, “So you feel pretty good about coming to school?”
One of the boys said, “Not about coming to school, but we don’t think it will fall down. Too bad, huh?” he added with a wry smile.
By the end of the day I had made the rounds of all the classrooms and personally apologized to every teacher. Fortunately, there were only three grades in the school and the school was relatively small. Most of the teachers were philosophical about what I had done, telling me they understood that I wasn’t a regular teacher and that I probably didn’t understand that 12 and 13 year olds cannot be allowed to go about unsupervised. What if one of the students had simply left school and gone home? I smiled at this because it reminded me of the time I was in seventh grade and one of my teachers had yelled at me in class. I simply walked out of his class and went home. I don’t remember the details, but I must have decided I’d had enough schooling that day.
The storm I had caused blew over quickly. Although no one Ooooed or Aaaaahed (and I was not even considered for Teacher of the Year), still I was called in to sub the very next Monday. I immediately found Mrs. Thornton and apologized to her. She said the calls had caught her off guard and she didn’t appreciate what I had done, even thought she understood I was only trying to be creative. The rest of the year I continued to be asked to substitute teach at this school. But, never again for Mrs. Thornton.