Strength in Numbers Dividing a class into two teams and having them play game of soccer is giving the one with the ball practice with soccer and the rest practice with running. Often in an elementary math class the teacher gives one question for the entire class to answer. The question is usually somewhere in the middle of the students' abilities, too hard for some and too easy for others. Even though most of the hands go up, the teacher only picks one student to answer. It is difficult sometimes to have focus on more than one student. Imagine watching a substitute teacher doing soccer with a class of grade 5 students. Mr. Blackstone divides a class into two teams and has them play a game of soccer. He is not a physical education specialist and this is the best way he knows to teach soccer. As you watch, you notice that any given time one player is practicing soccer with a ball and the rest are practicing running.One way to look at the idea of 'one at a time' is from my experience as a swimming instructor. While teaching swimming lessons, I've had the chance to try many different types of teaching methods. Each week I had a new group of swimmers that I could work with, so in a very short time I learned many ways to make the most of our time in the water. I found discipline was very important as it is impossible to teach a class when the students don't listen. However discipline alone does not mean anyone is learning or that the class is effective. I watched a senior high gym teacher teach a class of thirty boys how to dive. A fellow lifeguard told me to watch as he really knew how to teach. His approach was simple: every one of the boys waited patiently without disrupting the class while one boy would try his dive. Though it was very impressive to have trained these boys to wait their turn, I wasn't convinced this was the most effective for learning skills. By the end of twenty minutes of a very disciplined class each boy had 'tried' a total of three dives. Here is a different approach to the same activity. Have the students make five lines with enough space beside them that it is safe. The first person dives straight out then returns to the wall. When he touches the second person in line can go while the first is climbing out of the water and going to the back of the line. With all the safety addressed the students can continue practicing their dives with feedback on how to improve. The approach is similar except instead of doing only three dives the boys are able to do over thirty dives or more. Feedback could be given continuously without disrupting the practice and each swimmer would immediately have a chance to use this to improve. With five times more practice the swimmers were not just able to 'try' a skill, but develop or improve it. You can't become proficient with just a couple of tries. A basketball player doesn't become good at free throws by trying a couple of them. An artist doesn't become good at drawing after a few sketches. A chef doesn't become good at cooking after just a few dishes. The lecture or explanation of the skills doesn't give them the practice so it doesn't need to be long. People need to build up a number of experiences in order to start having success. Sure, some people can accomplish something the first time they try it, but to develop, improve or master a skill, hours of repetition are needed and there is no getting around this. Now, with math there are several ways to give students more practice in class. Instead of asking one 'middle range' question and only letting one student answer, the teacher puts a few questions on the boards and has all the students answer with colored blocks that correspond to numbers. Here is an example of this might work with algebra questions: The teacher, Ms. Greywood explains what algebra is. This isn't the first time they have done it, so the students have an understanding of how to use letters instead of numbers. Before they start she gives each student a set of 10 colored blocks and assigns a color to each one (1-yellow, 2-blue, 3-red, 4-purple, 5-orange, 6-green, 7-brown, 8-black, 9-grey, 0-white). They students will use these to answer the questions allowing the whole class to answer instead of just one. The teacher puts 4 questions on the board and gives the students a few minutes to solve. The students are reminded that the goal is not to finish all of the questions, but to work as far as they can. Question 1: A + 4 = 9 Teacher: Did anyone figure out question one? What plus four equals nine? Instead of raising hands, the students hold up an orange block to show that the answer is '5'. Each student holds the block in front of their chest so Ms. Greywood can see it but no one else. She gives smiles, thumbs up's and whispers of 'good job' to those who got it right then picks Sarah, one of the students who struggles, to say the right answer as this might be the only question she gets. Question 2: A + 5 = 7 + 6 Teacher: Did anyone get the second question? It's a little more difficult. The students hold a black block to show the answer is eight. The teacher takes the time to explain that both sides have to balance, like a scale. She explains that the right side is thirteen and asks what you add to five to make the left side thirteen too. Question 3: A + B = 7 A - B = 3 Teacher: Did anyone get the third question? You need to find two numbers that will work in both equations. Ms. Greywood asks how many different ways to make seven by adding. Some students hold up green and yellow for six and one. Others hold up orange and blue for five and two. A few hold up brown and white for seven and zero. After recognizing all the right answers Ms. Greywood asks which one would work for the bottom equation. Question 4: A X B = 24 A - B = 5 Teacher: If you tried the last one, hold up what you think the answer is. Ms. Greywood shows how eight and three would work in both equations. It can be intimidating for some students if too much time is spent on high level questions. She smiles as she checks the few students who tried it but quickly moves on to the next set of questions. Considering how many students were able to answer the questions, Ms. Greywood adds one more question for the next round: A X B = 48 A - B = 13 The class is now excited about algebra. Each student can work at his or her own level and challenge the next level. The class is able to do four or five sets of questions in a thirty minute class. This gives the students enough practice to start having success with algebra. Both the students have a good idea of what level they are at and this can be shared with the parents. The next day Ms. Greywood gives the students more opportunities to answer questions. The students are put into group of three or four. Similar questions are put on the board, but instead of the teacher explaining the answers, each student is responsible for giving or explaining the answer to the group. Each student can choose which question they want to answer, empowering them with choice and confidence knowing they can answer the question. They will try to answer different questions, but if they happen to choose the same question, they simply take turns going first each round. This will give may give them a chance to see and explain the question with different methods or simply validate that their method works. At the end of the week the students will answer a set of algebra questions as well as sets from units they have already covered such as ones based on addition, fractions and perimeter. Since they are now familiar with the levels, they will also have the option of creating a set of questions for the class to try. Now the students being challenged and are improving as they now have opportunities to truly develop their skills. In this type of environment, you can feel the energy and excitement from students who are engaged. Here is where you find strength in numbers.
By Darren Michalczuk