Colloquium

Mathematics as a form of communication:what it means and how it adds to our understanding of teaching and learning

by Anna Sfard, Professor, The University of Haifa, Haifa, Israel

Abstract

In the domain of mathematics education, the term discourse seems to be these days on everybody's lips. Although traditionally regarded as only auxiliary to thinking, mathematical communication is believed to enhance mathematical learning. In my research, I am going farther than that: I conceptualize mathematics as a special form of communication. By doing this, I promote mathematical discourse from the role of a mere instructional means to that of the object of learning. In this talk I will explore the implications ofthe communicational perspective for our vision of mechanisms of learning andteaching. To make my points, I will present in parallel two classroomstudies, one devoted to the learning of signed numbers and the other dealingwith young children first introduced to school geometry. The analysis of theempirical data will be guided by three questions: What is it that issupposed to change in children's discourse in the course of learning? Whatis supposed to induce the change? What are the short- and long-term effectsof the discourse-molding attempts orchestrated by the teacher? The resultsof these analyses will compel me to take a critical look on a number ofpopular pedagogical beliefs.