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.

Modelling shared attention through relational reinforcement learning

Shared attention is a type of communication very important among human beings. It is sometimes reserved for the more complex form of communication being constituted by a sequence of four steps: mutual gaze, gaze following, imperative pointing and declarative pointing. Some approaches have been proposed in Human-Robot Interaction area to solve part of shared attention process, that is, the most of works proposed try to solve the first two steps. Models based on temporal difference, neural networks, probabilistic and reinforcement learning are methods used in several works. In this article, we are presenting a robotic architecture that provides a robot or agent, the capacity of learning mutual gaze, gaze following and declarative pointing using a robotic head interacting with a caregiver. Three learning methods have been incorporated to this architecture and a comparison of their performance has been done to find the most adequate to be used in real experiment. The learning capabilities of this architecture have been analyzed by observing the robot interacting with the human in a controlled environment. The experimental results show that the robotic head is able to produce appropriate behavior and to learn from sociable interaction.

MR-Radix: a multi-relational data mining algorithm

Abstract Background Once multi-relational approach has emerged as an alternative for analyzing structured data such as relational databases, since they allow applying data mining in multiple tables directly, thus avoiding expensive joining operations and semantic losses, this work proposes an algorithm with multi-relational approach. Methods Aiming to compare traditional approach performance and multi-relational for mining association rules, this paper discusses an empirical study between PatriciaMine - an traditional algorithm - and its corresponding multi-relational proposed, MR-Radix. Results This work showed advantages of the multi-relational approach in performance over several tables, which avoids the high cost for joining operations from multiple tables and semantic losses. The performance provided by the algorithm MR-Radix shows faster than PatriciaMine, despite handling complex multi-relational patterns. The utilized memory indicates a more conservative growth curve for MR-Radix than PatriciaMine, which shows the increase in demand of frequent items in MR-Radix does not result in a significant growth of utilized memory like in PatriciaMine. Conclusion The comparative study between PatriciaMine and MR-Radix confirmed efficacy of the multi-relational approach in data mining process both in terms of execution time and in relation to memory usage. Besides that, the multi-relational proposed algorithm, unlike other algorithms of this approach, is efficient for use in large relational databases.

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.