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.

Searching for chronic hepatitis B patients in a low prevalence area – role of racial origin

Abstract Background Clinical studies for testing new drugs against hepatitis B ought to be carried out in low prevalence areas despite difficulties on patient recruitment. In such areas, relatives of chronic hepatitis B patients are considered to be at risk of acquiring the hepatitis B virus (HBV). The aim of this study was to evaluate the prevalence of HBV markers (anti-HBc, HBsAg and anti-HBs) in familial members of chronic hepatitis B (CHB) patients according to their origin (Asian or Western) in a low prevalence area, the city of São Paulo, Brazil. Methods Twenty three Asian CHB probands and their 313 relatives plus 31 CHB probands of Western origin and their 211 relatives were screened for HBV serological markers; the study was carried out in the outpatient clinic of the University of São Paulo School of Medicine. Results Mother to child transmission was greater in the Asian group whereas sexual transmission was more frequent in the Western group (p < 0.0001). Anti-HBc was positive in 90% and 57% of the Asian and Western parents (p = 0.0432) and in 97% and 33% of the Asian and Western brothers (p = 0.0001), respectively. HBsAg was more frequent among the Asian (66%) than the Western (15%) mothers (p = 0.0260) as well as among the Asian (81%) than the Western (19%) brothers (p = 0.0001). We could detect 110 new HBsAg-positive subjects related to the 54 index patients, being the majority (81%) of Asian origin. Conclusion In low prevalence area of hepatitis B, family members and household contacts of chronic HBV carriers are at high risk for acquiring hepatitis B.

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.