Advanced Mathematical Thinking in a Technological Workplace

This paper examines the use ofmathematics in a computer aided design andmanufacture setting. It reports on a casestudy which focuses on technicians'calculations of the internal volume ofmoulds they produce for glass factories. Itexamines the mathematics the techniciansuse, whether this mathematics is related toschool mathematics, how the techniciansunderstand this mathematics and the role oftechnology in the technicians'mathematics-related problem solvingactivities. Saxe's four-parameter modelforms a background for discussingobservations. Although the technicians didnot consider their activity was related to(school) mathematics there is evidence thatin making sense of their practice theyresorted to (a form of) school mathematics.The role of technology in technicians'mathematical activity was crucial: not onlywere the mathematical procedures they usedshaped by the technology they used but themathematics was a means to achievetechnological results. Further to this themathematics employed by the techniciansmust be interpreted within thegoal-oriented behaviour of workers who`live' the imperatives and constraints ofthe factory's production activity cycle. This revised version was published online in August 2006 with corrections to the Cover Date.