Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Redundant sensing for localisation in outdoor industrial environments

We describe our experiences with automating a large fork-lift type vehicle that operates outdoors and in all weather. In particular, we focus on the use of independent and robust localisation systems for reliable navigation around the worksite. Two localisation systems are briefly described. The first is based on laser range finders and retro-reflective beacons, and the second uses a two camera vision system to estimate the vehicle’s pose relative to a known model of the surrounding buildings. We show the results from an experiment where the 20 tonne experimental vehicle, an autonomous Hot Metal Carrier, was conducting autonomous operations and one of the localisation systems was deliberately made to fail.