BELIEFS AND NORMS IN THE MATHEMATICS CLASSROOM

Beliefs And Norms In The Mathematics Classroom By Erna Yackel And Chris Rasmussen

The primary purpose of this study is to examine the possibility of changing student’s expectations of the mathematics classroom. The “beliefs about one’s role, others’ roles, and the general nature of mathematical activity in school and specifically mathematical beliefs and values.” Students usually believe that mathematics classroom means listening to a teacher who teaches a mathematical subject, taking the notes and solving the questions via formulas. In such a class, students can ask the questions and teacher must explicitly answer these questions. Besides, student’s answer to mathematical questions must be clarified by the teacher. So, it means that there is not any mathematical discussion or debate in these classrooms. The authors put emphasis on the social norm of the classroom and state that it is different in the context of math. In fact “social norms are regularities in interaction patterns that regulate the social interactions in the classroom. By contrast, socio-mathematical norms refer to regularities in the interaction patterns that relate specifically to the fact that the class is a mathematics class.”

This study attempts to investigate to what extend changing teaching methods might change students’ beliefs of the regular mathematical classroom. In this study, a university level mathematics class with the subject of differential equations was tested. In this classroom, instead of focusing on solving several equations, the instructor presents real examples and asks students to solve them using differential equation. However, students must explain and discuss their solutions to prove the answer. The point of view of these students, regarding this method, was registered via a journal writing. The instructor could not directly respond to the student’s questions rather leads them by asking more questions.

At first most of the students did not understand the new method, and even some of them feel the class is not useful and practical. They could not understand how discussing a mathematical equation can help learning the abstract mathematics or how it is possible to use words to describe a mathematical equation. However, after several sessions and observing and contributing to the discussion, students get the main point of the method and classroom. They finally learned how to communicate to come up with the right solution. It is interesting that students realize there might be several solutions to get the same answer. They understand the role of the instructor as a facilitator to lead them toward the right solution instead of offering the right answer.

Honestly, I had the same beliefs of these students that mathematics is numbers, signs, and symbols and it is not rational to prove it by words. From my point of view, the best and shorter way of solving a mathematical question is using numbers to find the answer. However, reading this article open a new view for me that discussing a mathematical question in the classroom and involving all student in solving this question is a new method of education. In fact, it helps students to remember the answer because they have found it via an extended discussion or even debates. Some students might not be good at numbers and formula, but they might be good at making the rational explanation, so it is an excellent opportunity for these students to learn math. I do not have many experiences of teaching math by interaction method, however, whenever I have started teaching new topics by making a conversation and asking questions, students gradually understand the lesson. And I realized that students learned and memorized these lessons better than the regular teaching methods. In this process, students feel that they are in charge and they are discovering something new. They did not understand that I am pushing them towards the answer or new idea. They accompany me to find the right answer or learn the new topic. From my point of view, this feeling makes a pleasure that students hardly forget it.

What do you think of involving students in teaching process? Do you have any experience doing this? What is your student's belief of mathematics classroom?