Ian deGroot
Ian deGroot has revamped his teaching style to create an atmosphere in which students learn by cooperating with their peers. By rearranging the traditional classroom into a collection of round tables, he has helped students learn not only mathematics but also how to work and learn together. The failure rate of students in the math department at Sutherland Secondary School in Vancouver has dropped from 25 percent to about 10 percent in the last five years.
Ian has shared his experience with his colleagues in British Columbia through in-service training presentations. He has also encouraged female students to excel in mathematics and science, and supplied them with role models by inviting successful women to speak at the school. Since he became head of the math department at his school eight years ago, female enrollment in advanced math classes has grown from 30 percent to 50 percent.
Approach to teaching
"I am convinced that more effective learning occurs when students are encouraged to work in groups."
My decision to refine my teaching style was based on three factors: my sense that while rapid changes were occurring in society, very little change was taking place in the way we teach and expect students to learn mathematics; several research articles dealing with the positive aspects of group learning; and my positive experience conducting a workshop for mathematics educators during the summer of 1989.
The principal at Sutherland was very enthusiastic about providing funds to replace conventional desks with tables so that four students could work together as a team. I originally asked for rectangular tables but, by accident, I was sent large round tables. These proved to be a better idea, as they made it easier for students to get physically close to each other and to work cooperatively.
Once the desks were replaced by tables, there was no turning back. I was compelled to teach all my classes in a small-group format, and I do not think I could revert to my former style in a teacher-centered classroom. Although I had to devise new strategies and learn different class-management techniques, I was excited by the change and the positive manner in which students at all grade levels accepted the new structure. The biggest surprise to me was how naturally the students cooperated with each other from the beginning, and how quickly they adapted to this new method of instruction.
Transferable experience
A teacher could create a good environment for group learning simply by rearranging desks. Although round tables are ideal, there is no reason you cannot begin with groups of desks arranged into rectangles.
Initially, I formed groups of four students by randomly selecting names from a bag. As I have learned more about the abilities of individual students, I have been able to pick groups more formally. For example, I ensure that there is always at least one strong math student in each group who can act as captain and facilitate discussion. I also try to have an equitable male-female ratio and racial mix whenever possible.
I change the composition of groups frequently, at least every three weeks. This allows each student to get to know all the others, and to learn the necessary social skills for successful group interaction. I have learned never to let students select their own group-mates: the inevitable result is social cliques.
In mathematics, it is not possible to use this approach exclusively. There are times when you will want to explain general concepts to the entire class. I work this way about 50 percent of the time. It is quite easy to integrate traditional teaching with group learning, although the different seating arrangement is not always ideal for conventional approaches.
The new seating and working arrangements should be complemented by a method of awarding marks based on group assessment rather than solely on the results of written quizzes and unit tests. I assess students and award marks based on my observations of group work and for group presentations to the class.
- I award marks for contribution to group discussions, understanding of concepts, and ability to clarify and explain concepts to other members of the group. This also allows me to identify students who need individual assistance outside regular class time.
- I don't consider a problem solved until every member of the group is able to explain the solution and answer questions about it. This makes the students who quickly see the answer responsible for explaining it to the other members of the group. Students are chosen randomly to present their group's findings, and a group mark is awarded for quality and clarity of presentation, creative solutions and correct results.
Another technique that has worked successfully has students working quietly and independently on a quiz for an allotted time. Then they find a partner by matching numbers from a deck of cards and each pair submits one solution. Students enjoy this method, learn from each other and feel responsible for each other's results.
In a cooperative-group classroom, students are always talking; for the traditional teacher, this is the most difficult adjustment. Before long, I recognized that, for the most part, the increased noise level was due to students meaningfully and productively discussing math.