I teach high school mathematics in a small town in Connecticut. Though I am only in my first year as a full-time teacher, I have already had many great experiences. One incident that stands out in my mind was a day when a student's help was key in getting a difficult concept across.
It had been a long day, and it was almost time for my somewhat dreaded, hyperactive, seventh-period algebra class. I had spent the three previous periods trying to get my other algebra classes to understand the concept of adding polynomial equations. Now it was time to try to get these noisy, anxious-to-get-home students to grasp it.
This class of sophomores is my biggest and rowdiest class. Because of the group's size, it's hard to give individual attention, and I often have another teacher to assist me. This day, however, I was alone. I felt ready nevertheless to conquer this task.
The class took awhile to quiet down. After I checked the homework and went over it, answering all questions, it was time to introduce the new material.
The concept was a rather basic one, the rule of thumb being when you have like labels, you can add the two terms together: 2a + 3a = 5a.
When you have a polynomial (an expression with more than one term) you can only add similar things. In the case of 3a + 5= 11, for example, you cannot add the 3a and the 5, but you can bring the 5 over to join the 11 by subtracting it from both sides.
Well, the explanations went on and I tried more examples. I could see that some students were indeed understanding the concept, but others kept asking me to do more. The looks on their faces said it all. They were just not getting it.
I was feeling pretty disappointed, as I immediately realized that I had not planned on this need to modify my lesson so drastically. I began to try more and more sample problems, hoping it would just eventually sink in.
As I walked around, checking the students' work from the examples on the board, I could hear one of my students, Mike, explaining the procedure to a fellow classmate.
"It's simple," he said. "You just remove the number by bringing it to the other side and ... ." And then he paused and said, "Miss Sarmuk, can I stand up for a minute and go to the chalkboard?" And I, knowing he really did understand this lesson, said, "Sure, Mike."
What happened next was one of the neatest things I have ever witnessed in a classroom. It's also a technique that I've used many times since when students have hit a roadblock in class.
Mike began writing out a problem, going through it step by step, explaining each step and stopping to ask if anyone had any questions.
Another student raised his hand and asked a question. Mike answered, and the student responded, "Oh, I get it now!" I could see, very clearly, what was happening.
It may have simply been that the words I had chosen in my explanation were not on the same level as these students; or that I was going over it too fast; or even that my previous knowledge of the material inhibited me from taking a more open perspective on how students would learn it. Whatever it was, the students could relate to what Mike said and he really helped them to understand.
I was thankful for his eagerness to help. He felt good about it, and I learned an even more important lesson that day: that sometimes the greatest teachers of all are the peers right there in the classroom.
* Patricia Sarmuk teaches mathematics to ninth- through 12th-graders at Vinal Technical High School in Middletown, Conn. She hopes to coach basketball or softball as well in the future.