Gestures in the blackboard work of mathematics instruction

Lectures in mathematics consists almost entirely of the lecturer writing definitions, 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 first 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 fields 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.