Didactical reconstructions for organizing knowledge in physics teacher education

Physics teachers are in a key position to form the attitudes and conceptions of future generations toward science and technology, as well as to educate future generations of scientists. Therefore, good teacher education is one of the key areas of physics departments education program. This dissertation is a contribution to the research-based development of high quality physics teacher education, designed to meet three central challenges of good teaching. The first challenge relates to the organization of physics content knowledge. The second challenge, connected to the first one, is to understand the role of experiments and models in (re)constructing the content knowledge of physics for purposes of teaching. The third challenge is to provide for pre-service physics teachers opportunities and resources for reflecting on or assessing their knowledge and experience about physics and physics education. This dissertation demonstrates how these challenges can be met when the content knowledge of physics, the relevant epistemological aspects of physics and the pedagogical knowledge of teaching and learning physics are combined. The theoretical part of this dissertation is concerned with designing two didactical reconstructions for purposes of physics teacher education: the didactical reconstruction of processes (DRoP) and the didactical reconstruction of structures (DRoS). This part starts with taking into account the required professional competencies of physics teachers, the pedagogical aspects of teaching and learning, and the benefits of the graphical ways of representing knowledge. Then it continues with the conceptual and philosophical analysis of physics, especially with the analysis of experiments and models role in constructing knowledge. This analysis is condensed in the form of the epistemological reconstruction of knowledge justification. Finally, these two parts are combined in the designing and production of the DRoP and DRoS. The DRoP captures the knowledge formation of physical concepts and laws in concise and simplified form while still retaining authenticity from the processes of how concepts have been formed. The DRoS is used for representing the structural knowledge of physics, the connections between physical concepts, quantities and laws, to varying extents. Both DRoP and DRoS are represented in graphical form by means of flow charts consisting of nodes and directed links connecting the nodes. The empirical part discusses two case studies that show how the three challenges are met through the use of DRoP and DRoS and how the outcomes of teaching solutions based on them are evaluated. The research approach is qualitative; it aims at the in-depth evaluation and understanding about the usefulness of the didactical reconstructions. The data, which were collected from the advanced course for prospective physics teachers during 20012006, consisted of DRoP and DRoS flow charts made by students and student interviews. The first case study discusses how student teachers used DRoP flow charts to understand the process of forming knowledge about the law of electromagnetic induction. The second case study discusses how student teachers learned to understand the development of physical quantities as related to the temperature concept by using DRoS flow charts. In both studies, the attention is focused on the use of DRoP and DRoS to organize knowledge and on the role of experiments and models in this organization process. The results show that students understanding about physics knowledge production improved and their knowledge became more organized and coherent. It is shown that the flow charts and the didactical reconstructions behind them had an important role in gaining these positive learning results. On the basis of the results reported here, the designed learning tools have been adopted as a standard part of the teaching solutions used in the physics teacher education courses in the Department of Physics, University of Helsinki.

Solutions of cubic equations in quadratic fields

Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equations, which represent elliptic curves defined over Q, in quadratic fields and prove some interesting results regarding the solutions by using elementary tools. As an application we consider the Diophantine equation r + s + t = rst = 1 in O-K. This Diophantine equation gives an elliptic curve defined over Q with finite Mordell-Weil group. Using our study of the solutions of cubic equations in quadratic fields we present a simple proof of the fact that except for the ring of integers of Q(i) and Q(root 2), this Diophantine equation is not solvable in the ring of integers of any other quadratic fields, which is already proved in [4].

Use of Fick's law and Maxwell–Stefan equations in computation of multicomponent diffusion

This article does not have an abstract.

The application of B-P constitutive equations in finite element analysis of high velocity impact

We present in this paper the application of B-P constitutive equations in finite element analysis of high velocity impact. The impact process carries out in so quick time that the heat-conducting can be neglected and meanwhile, the functions of temperature in equations need to be replaced by functions of plastic work. The material constants in the revised equations can be determined by comparison of the one-dimensional calculations with the experiments of Hopkinson bar. It can be seen from the comparison of the calculation with the experiment of a tungsten alloy projectile impacting a three-layer plate that the B-P constitutive equations in that the functions of temperature were replaced by the functions of plastic work can be used to analysis of high velocity impact.

Fluid Dynamics in Physics, Engineering and Environmental Applications

The book contains invited lectures and selected contributions presented at the Enzo Levi and XVII Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2011.