(Salle F08)
Greiffenhagen, Christian
Sharrock, Wes
University of Manchester, Manchester
Gestures in the blackboard work
of mathematics instruction
Eric Livingston (1986, 1999) has argued that the heart of mathematics
is work at the blackboard. In this paper we will exhibit how
university lecturers work at communicating mathematical ideas to
graduate students. The topic thus is how mathematical arguments
are made visible through the use of gestures in relation to what is
written on a blackboard and what is said.
Lectures in mathematics consists almost entirely of the lecturer
writing defi nitions, theorems, and proofs on the blackboard (often
reproducing word-by-word what is distributed in advance in lecture
notes) while simultaneously commenting on what is being written.
The writing, talking, and gesturing conjointly formulate the cohesive
logic of the mathematical argument that the formulae instantiate.
In the fi rst part we examine the blackboard organization of the exposition :
what is written is not just written ‘anywhere’, but the physical
structure of the blackboard is organized into segregated fi elds
so as to re-order the formulae on the board in a way that displays
their mathematical role amongst the interrelated constituents of the
mathematical argument put forward.
The second part focuses on how gestures are used in conjunction
with and coordination of what is being written on the blackboard and
what is being said. Following McNeill’s (1979, 1992) early work on
gestures of mathematicians, we explore the way that gestural work
is embedded in the organisation of the spoken commentary - and
thus both articulated with, and used to capture, the progression
of the course of the mathematical reasoning under construction. In
particular, we show how gestures are used to exhibit the structure
and integration of the mathematical argument.
