Phillip Kent

Characterizing the Use of Mathematical Knowledge in Boundary-Crossing Situations at Work

The first aim of this article is to present a characterization of the techno-mathematical literacies needed for effective practice in modern, technology-rich workplaces that are both highly automated and increasingly focused on flexible response to customer needs. The second aim is to introduce an epistemological dimension to activity theory, specifically to the notions of boundary object and boundary crossing. We draw on ethnographic research in a pensions company and focus on data derived from detailed analysis of the diverse perspectives that exist with respect to one symbolic artifact, the annual pension statement. This statement is designed to facilitate boundary crossing between company and customers. Our study shows that the statement routinely failed in this communicative role, largely due to the invisible factors of the mathematical-financial models underlying the statement that are not made visible to customers or to the customer Enquiry Team whose task is to communicate with customers. By focusing on this artifact in boundary-crossing situations, we identify and elaborate the nature of the techno-mathematical knowledge required for effective communication between different communities in the pensions company, and suggest the implications of our findings for workplaces more generally.

Improving Work Processes by Making the Invisible Visible.

There is a growing movement for industrial companies to modify their production practices according to methodologies collectively known as process improvement. After World War II, Japanese companies such as Toyota developed new manufacturing paradigms (e.g., lean manufacturing) under the guidance of American experts, particularly W.E. Deming. Since the 1980s, the Japanese methodologies have been spreading to the West in a major way, in the form of programmes such as Total Quality Management (TQM) and Total Productive Maintenance (TPM) (Deming, 1986; Nakajima, 1988).

Role of Context in Risk-Based Reasoning

In this article we report the influence of contextual factors on mathematics and science teachers reasoning in risk-based decision-making. We examine previous research that presents judgments of risk as being subjectively influenced by contextual factors and other research that explores the role of context in mathematical problem-solving. Our own approach has been to develop carefully designed software tools that support the user to empathize with a hypothetical person, Deborah, who suffers from a medical condition. The tools were used by a group of teachers who were asked to help Deborah decide whether to have an operation that could cure the condition but which carries particular risks. In order to make this decision, the teachers were required to model the risks of the operation and also the lifestyle decisions that Deborah might make. We trace the teachers efforts to coordinate judgments of likelihood and impact. The data emphasize the sensitivity of reasoning to matters of context; we set out in detail the various ways in which the process was affected by context.