A productive teaching and learning experience involves both the teacher and the student. Blake Peterson and Keith Leatham, both of the Department of Mathematics Education, recently published a peer-reviewed paper introducing new methods to improve student teaching. It is designed to benefit both professors and student-teachers as they collaborate on how to improve their respective efforts.
“We’ve restructured student teaching in our department,” Peterson said. “Our goal was to change the structure so people saw the purpose differently.”
Many times, student-teachers simply focus on surviving a class period. It is easy to become too focused on just getting through the day or keeping the students under control. However, it is imperative that teachers listen to their students’ comments and understand them. Instead of spouting off a monologue, teachers should structure the body of their lectures using their students’ ideas and questions.
To help their own students become more effective teachers, Leatham and Peterson have identified three stages that teachers need to progress through in order to effectively use students’ mathematical thinking.
First, teachers must listen to and understand class comments. To ensure that students are actually learning and grasping the concepts being taught, teachers must truly listen to their students and seek to understand their ideas.
Second, after teachers understand, they must exercise judgment in determining whether the comment would be worth discussing further. For example, if a student explains something wrong, a teacher should ask if this was just a mistake or if the student has some significant misconceptions. Or perhaps a student makes a comment that suggests a profound insight is emerging. The teacher needs to evaluate if the student was indeed on the verge of a breakthrough or just making a random comment. Quick, accurate judgment calls are key to recognizing opportunities to build on students’ ideas.
Third, once an important idea is recognized, a teacher must act upon it to “bring the thinking to the attention of the class,” Leatham said. “Effectively using students’ thinking in order to help the class develop mathematics concepts is a complex endeavor that takes a great deal of practice and reflection.”
It is also important to help students make connections between different methods of thinking. In every class, invisible groups exist. And the group members are separated according to their thought processes. In a math class, for example, each group may have their own way of solving problems.
Because so many methods of problem-solving may bring the same result, it is important that a teacher not limit a class to his own personal preferences. Leatham and Peterson suggest that choosing one student from each of the separate learning groups and explaining their different methods side-by-side would help all students in understanding the problem as well as the underlying mathematics.
Both Peterson and Leatham use the concepts presented in their paper in their own classrooms – and the quality of their students’ teaching is already improving.