Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Reasoning about shadows in a mobile robot environment

This paper describes a logic-based formalism for qualitative spatial reasoning with cast shadows (Perceptual Qualitative Relations on Shadows, or PQRS) and presents results of a mobile robot qualitative self-localisation experiment using this formalism. Shadow detection was accomplished by mapping the images from the robot’s monocular colour camera into a HSV colour space and then thresholding on the V dimension. We present results of selflocalisation using two methods for obtaining the threshold automatically: in one method the images are segmented according to their grey-scale histograms, in the other, the threshold is set according to a prediction about the robot’s location, based upon a qualitative spatial reasoning theory about shadows. This theory-driven threshold search and the qualitative self-localisation procedure are the main contributions of the present research. To the best of our knowledge this is the first work that uses qualitative spatial representations both to perform robot self-localisation and to calibrate a robot’s interpretation of its perceptual input.