Overt and Covert Classroom Communication (Speaking Mathematically)

David Pimm (1987)

Chpt3: Overt and covert classroom communication



The author mainly explores two topics in mathematical dialogues in classrooms. Firstly, he introduces teacher’s speaking gambit in asking and answering questions. One of the gambits is a clozed question which leads to narrow the students’ scopes and ideas and to confine their perspectives although it enables the teacher to maintain the class. Additionally, as a gambit in answering questions, mathematics teachers often deliberately ignore to respond to students’ questions in order to make the students inquiry or shift to a student-centered class from teacher-centered.


The second theme is who “we” is in mathematical discourses in classes. Mathematics teachers often use the word “we” in their explanations/introductions/questions/answers when the students are not aware of what the teacher explains. In addition, the teachers utilize “we” to tell their students the message that the students need to do the same way in mathematics as other community members. (For example, a teacher explains the student “We put it in the … units column, don’t we?”) The author argues that the public image of mathematics is “objective, absolute, impersonal, and permanent” while the individual mathematics in mind is “subjective, partial, and relative.” It is, therefore, rational for mathematics teachers to avoid exposing unique and personal insights in mathematics from students in classrooms.



Both benefits and drawbacks of teachers’ gambits in asking and answering in mathematics classrooms are mentioned in this chapter, and I agree with the author’s idea. Regardless teacher-centered or not, mathematics teachers work with those strategies. What I am very curious in this chapter is the meaning of “we” in English in mathematics discourses because the Japanese language often allows the speakers to abbreviate the subject in the sentence. However, in like the situation the author explains that mathematics teachers utilize to persuade or justify their students when students are not aware of what they have to do, Japanese mathematics teachers also describe appropriate ways as a suggestion or advice. This implies that “we”, teachers and students, have to do the same way as other community members.
 
Additionally, I agree with the author’s argument about the difference of the public image of mathematics and image in learner’ mind: one is abstract and the other one is concrete, I think. But I am wondering how that public images, mathematics is objective, are formed from individual minds that mathematics is subjective.