Search

The radiative heating or cooling of a body placed in an environment, whose temperature is considered constant is described by Stefan's law. In this paper, an analysis is made of how a time-dependent environmental temperature influences the heating/cooling process. We compare experimental results for a resistor first heated by the Joule effect inside a glass vacuum tube and then cooled under two different conditions: in a bath at a constant temperature and in air. We also discuss a model that describes how the time-dependent tube temperature influences the radiative resistor cooling by identifying the properties of the environment that make the resistor cooling rate linear.

The concept of distribution is a fundamental component of statistical thinking. This paper describes a teaching approach for it that uses a specific activity related to the field of statistical mechanics. The concept of the velocity distribution of a particle system is dealt with using an inquiry-based approach involving an experimental examination of Maxwell’s distribution. Some outcomes of a teaching experiment held at the Faculty of Engineering of the University of Palermo, Italy are described.

In this contribution we describe a research aimed at pointing out the quality of mental models undergraduate engineering students deploy when asked to create explanations for phenomena/processes and/or use a given model in the same context. Student responses to a specially designed written questionnaire are initially analyzed using researcher-generated categories of reasoning, based on the Physics Education Research literature on student understanding of the relevant physics content. The inferred students’ mental models about the analyzed phenomena are categorized as practical, descriptive, or explanatory, based on an analysis of student responses to the questionnaire. A qualitative analysis of interviews conducted with students after the questionnaire administration is also used to deepen some aspects which emerged from the quantitative analysis and validate the results obtained.

A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having predictive validity are developed.

This paper describes an undergraduate experiment that yields the velocity distribution of thermionic electrons by analyzing the I-V characteristics of diodes and triodes. The experiment allows students to focus on the distribution function more than on difficulties arising from the complexity of thermionic emission. By using a simple model, the velocity distribution of thermionic electrons emitted by the vacuum tube cathode can be described by Maxwell’s distribution.

This paper reports the design process and the experimentation of a teaching-learning sequence about the concept of mechanical wave propagation and the role played by media where waves are propagating. The sequence focuses on the central issue of the relationships between observable phenomena, like macroscopic behaviours of waves, and their interpretation and/or explanation in terms of corpuscular characteristics of media. We describe the design process with respect to the general framework of the Educational Reconstruction Model and the pedagogical tools used. Results of a teaching/learning experiment, involving a sample of 75 high school students, are also reported. Data analysis is mainly based on qualitative research methods. The main focus is on students’ representations of phenomena and on the cognitive strategies put in action in order to modify or support their descriptive and interpretative mental models. Results are discussed by pointing out the efficacy of strategies focusing on the process of constructing predictive conceptual models and by identifying the concept of ‘level of analysis’ as different ways to look at the same phenomenon.

This paper presents some mechanical models for amplitude and frequency modulation. The equations governing both modulations are deduced alongside some necessary approximations. Computer simulations of the models are carried out by using available educational software. Amplitude modulation is achieved by using a system of two weakly coupled pendulums, whereas the frequency modulation is obtained by using a pendulum of variable length. Under suitable conditions (small oscillations, appropriate initial conditions, etc) both types of modulation result in significantly accurate and visualized simulations.

We report on a teaching approach oriented to the understanding of some relevant concepts of wave propagation in solids. It is based on simple experiments involving the propagation of shock mechanical waves in solid slabs of various materials. Methods similar to the generation and propagation of seismic waves are adopted. Educational seismometers, interfaced with computers, are used to detect and visualize the shock waves and to analyse their propagation properties. A qualitative discussion of the results concerning the propagation and the attenuation of the waves allows us to draw basic conclusions about the response of the matter to solicitation impacts and their propagation.

This paper reports an explorative study in which innovations in a piece of physics curriculum for high school level have been converted into innovations in methods and contents for physics teacher education. The case study concerns the teaching of physics modelling in a pre-service teacher training course. The structure and content of the course have been both organized in order to prepare teachers to carry out the teaching tasks required from the proposed teaching/learning approach. This approach involves substantial modifications in learning sequences as well as in the teacher's role and in teaching methods. The course intends to give to prospective teachers experience of the same learning environments as they are supposed to realize in their future classrooms and to make them reflect upon the dynamics of their experiences in order to generate metalearning development. The qualitative results that have been collected suggest that metareflection helps prospective teachers to generate significant changes ...

The thermodynamic properties of a system consisting of a small number of non-interacting indistinguishable particles in the temperature range where the transition from quantum to classical behaviour occurs are discussed. The system is an extrapolation of a perfect monatomic boson gas contained in a box. We calculate the internal energy, specific heat and entropy and discuss their dependence on various factors such as the temperature, the number of particles and the box dimensionality. The results are compared with those obtained for a system consisting of distinguishable particles. The calculations are carried out without approximation starting from first principles, and the results have general validity since reduced units are used.

We provide a short response to Ganci's comment on our paper 'Measuring longitudinal wave speed in solids: two methods and a half'. The reply faces both the problems involved in the comment: the accuracy of experimental methods and pedagogical aspects.

This paper describes a model for the simulation of Boltzmann-like binary interactions useful for pedagogical purposes. The operating rules of the model are given in terms of arbitrary postulates and different microstates of the system are created on the basis of generalized particle interactions. The results show that there are no `most favoured' microstates and the system moves randomly or haphazardly between microstates following the ordinary laws of probability. A multiplicity of macrostates has been calculated in order to study the approach of the system toward equilibrium. Riassunto. Il lavoro descrive un modello di simulazione, a scopo didattico, di interazione tra particelle. Le regole di costruzione del modello sono formulate in termini di postulati arbitrari ed i diversi microstati del sistema sono costruiti come conseguenza di interazioni `generalizzate' tra le particelle. I risultati dell'implementazione del modello mostrano che non esistono microstati `piu favoriti' ma che, viceversa, il sistema evolve percorrendo a caso i vari microstati sulla base delle leggi ordinarie di propabilita. Sulla base del calcolo della molteplicita dei diversi microstati e possibile studiare l'evoluzione del sistema verso l'equilibrio e la conduzione di calore tra sistemi a diversa temperatura.

This paper describes a Computer‐based Learning Environment (CBLE) whose objective is to stimulate and support learning in the field of Newtonian mechanics through exploratory activities in various microworlds. The structure of the microworld TABLE is described in detail. A pilot study is presented: it concerns the modelling process of the learner knowledge in the topic involved and the evaluation of the impact of the exploratory activity on student learning. Some suggestions drawn from the results are discussed.

This article describes the process of building a computer-based diagnostic module concerning the understanding of the average velocity concept. The first step consists of the production of a student model that takes into account student errors and reasoning paths. The computer module formulates its diagnosis by leading users along different patterns foreseen according to the hypothesized student model. Results are reported concerning a correlation analysis between automatic and human diagnoses.

Mathematical modelling is gaining strength in undergraduate science courses and high school curricula, especially in physics, and many teaching strategies use the computer as a pedagogical tool. This paper deals with laboratory work and the inference of mathematical models based on measurements of physical quantities. Since errors are present in the measurements, one has to optimize the estimation of parameters. A simple estimation method has been used, suitable for students, based on a trial procedure. It can be regarded as a general-purpose curve-fitting program. Several case studies are briefly described. Use of the software allowed students to become comfortable with data interpretation and the use of mathematics in describing physical processes.

We present a method aimed at a stochastic derivation of the equilibrium distribution of a classical/quantum ideal gas in the framework of the canonical ensemble. The time evolution of these ideal systems is modelled as a series of transitions from one system microstate to another one and thermal equilibrium is reached via a random walk in the single-particle state space. We look at this dynamic process as a Markov chain satisfying the condition of detailed balance and propose a variant of the Monte Carlo Metropolis algorithm able to take into account indistinguishability of identical quantum particles. Simulations performed on different two-dimensional (2D) systems are revealed to be capable of reproducing the correct trends of the distribution functions and other thermodynamic properties. The simulations allow us to show that, away from the thermodynamic limit, a pseudo-Bose–Einstein condensation occurs for a 2D ideal gas of bosons.

This article presents a bi-dimensional model of flight and describes the implementation of a flight simulator able to describe the different phases of longitudinal flight of a real airplane. After identifying the relevant physical variables, the equations of motion are written and solved using a numerical integration method. Using computer simulations, flight paths and time evolution of the kinematics variables are analyzed for a complete flight of a light commercial airplane. The simulations take into account and reproduce the basic actions of a pilot to control the flight. The main maneuvers involved in pilotage are also predicted and explained in terms of model parameter variations inducing transitions in the phase space. Finally, the steady-state configurations are analyzed by means of the linearization of equations in order to gain meaningful information about the dynamical stability of the system. © 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 18: 144–156, 2010; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20177

The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment that, besides having a user-friendly interface, allows an easy interaction with the algorithm. The approach supplies pedagogical support for the introduction of the Boltzmann factor at the undergraduate level to students without a background in statistical mechanics.

This paper is concerned with the computer as a pedagogical tool for a physics teaching strategy focusing on model development and deployment. The importance and value of modelling in physics teaching is discussed from two different points of view: to teach physics as it is nowadays practised; to take into account research into cognitive science and learning. Two kinds of modelling software are briefly described: the first not requiring any competency in programming; the second needing only an elementary knowledge of the Basic code.

The concept of average velocity is often misunderstood, even by students at university level. To analyse student reasoning about average velocity, students who were being instructed in kinematics in an introductory physics course were shown a series of computer animations of two cars moving independently. Their answers to subsequent questions tended to use partial knowledge elements present in the problem. On this basis, a list of eight procedures used by students was drawn up and used as the basis of a computer-based diagnostic tutor, Velo. The performance of Velo is being compared with human tutors.

We present a pedagogic approach aimed at modelling electric conduction in semiconductors in order to describe and explain some macroscopic properties, such as the characteristic behaviour of resistance as a function of temperature. A simple model of the band structure is adopted for the generation of electron–hole pairs as well as for the carrier transport in moderate electric fields. The semiconductor behaviour is described by substituting the traditional statistical approach (requiring a deep mathematical background) with microscopic models, based on the Monte Carlo method, in which simple rules applied to microscopic particles and quasi-particles determine the macroscopic properties. We compare measurements of electric properties of matter with 'virtual experiments' built by using some models where the physical concepts can be presented at different formalization levels.

This article discusses the microcomputer simulation of dynamical systems that have a few degrees of freedom but which illustrate the properties associated with ergodicity and mixing shared by more realistic many‐particle systems. The models discussed are a stadium‐shaped billiard table model, and a particle moving in a regular array of hard disks or two‐dimensional Lennard–Jones particles. The examples show the need for a statistical description and are very useful for pedagogical purposes.

A Monte Carlo simulation of a simple two-dimensional model of a water-like system is presented. A dilute solution of an apolar molecule in the same fluid is also described. The results of the two simulations will be compared in order to evidence the characteristics features of hydration around the solute particle. The objective of the described software is principally pedagogical in order to give students some insights concerning the structure of water and its role as a solvent.

A set of teaching materials dealing with harmonic oscillations was developed as part of a research project investigating the influence of different pedagogical tools on physics learning. The materials incorporate simulation software and laboratory activities associated with Teacher and Student Units. The project involved research groups at seven Italian universities and the materials have been trialled in high schools nation‐wide. This paper describes the experimental protocol for the use of these materials in pilot classes and the evaluation of student learning and teacher training results. The intervention was found to improve physics education at school praxis level and to promote understanding of the content area as well as appreciation of the role of experiments and simulations in the construction of scientific knowledge

Three methods to analyse longitudinal wave propagation in metallic rods are discussed. Two of these methods also prove to be useful for measuring the sound propagation speed. The experimental results, as well as some interpretative models built in the context of a workshop on mechanical waves at the Graduate School for Pre-Service Physics Teacher Education, Palermo University, are described. Some considerations about observed modifications in trainee teachers' attitudes to utilizing physics experiments to build pedagogical activities are discussed.

This paper addresses the question of how to develop prospective teachers’ pedagogical content knowledge (PCK) in science teacher education. The main focus is on the knowledge transformation process and on the cognitive strategies used to shift prospective teachers’ explanations within the domain of modelling thermal physical phenomena. This study investigates the development of PCK within a group of 28 pre-service physics teachers during the first semester of their two-year post-graduate teacher education program. It focuses on the central issue of the relationships between observable phenomena, like macroscopic thermal properties of matter and their interpretation and /or explanation in terms of corpuscular characteristics and/or thermodynamics theory. The strategy is based on the consideration that knowledge transformation is not a one-way process from subject matter knowledge to pedagogical content knowledge, as literature suggests, but a bidirectional process involving deepening of subject matter knowledge and increasing awareness of pedagogical issues.

An application of the Monte Carlo method to the diffusion of neutrons passing through a slab of a moderating material is presented. This method can be used as a tool to improve the student's comprehension of the statistical properties of many particle systems, showing the necessity of simulation procedures to obtain information on the expected results of real experiments. We have chosen a very simple example to illustrate it: the evaluation of the transmission, reflection and absorption probabilities of a monochromatic beam of neutrons diffusing through a slab of a moderator material. After a collision with a nucleus of the moderator the neutron may be either elastically scattered or captured. The transmission, reflection and absorption properties of the neutrons diffused by different moderating materials are visualized with the help of an appropriate animation program.

Learning physics is usually considered a difficult task. Various rationalizations are put forward to justify this belief. The most frequent argues that students come to the classroom with their own pre-existing ideas about the world upon which they base their explanations. These ideas are often not mistaken but of a very general nature and cannot qualify as theoretical statements.

This chapter deals with a tutoring system concerning diagnostic and remedial actions on the average velocity knowledge. The diagnosis of the reasoning procedure used by each student is carried out on the basis of a task sequence tailored on a detailed student model. The remedial section provides diagnosis-dependent learning activities.

This article discusses the computer simulation of a classical model of electric conductivity in metals. Its objective is mainly didactic. It allows a microscopic interpretation of the phenomenological laws studied in introductory physics courses. The model is implemented in the one‐ and two‐dimensional copper lattice. In the latter case, the results are in partial agreement with the experimental data concerning the conduction in copper. The model considers the collisions between a free electron gas and the nuclei oscillating around the equilibrium lattice positions with average energy proportional to the room temperature and velocity distribution according to Maxwell–Boltzmann statistics. The collisions are supposed to be elastic, and a suitable lattice relaxation mechanism is considered. The results of the simulation concern the calculation of various quantities such as the electron root mean square velocity, the mean free time, the drift velocity, etc., either in the absence of an external electric field or in the presence of electric fields of various intensities. The dependence of the results on electric field intensity is reported and commented on and the validity of the model is verified. © 1996 American Institute of Physics.

The authors describe some simple programs for the simulation of the molecular dynamics of two-dimensional systems with a Lennard-Jones interaction potential. The software has been prepared for introductory physics courses at high school and college level, but different kinds of accompanying guides are required for these two levels. They take as their starting point the study of a two-particle system, in order to analyse the trajectories and to show the effect of the interaction.

A simple two-dimensional model of an ideal gas is described in order to study the time evolution of speed distribution in the framework of Newtonian mechanics. The results of a computer simulation of a system of 16 particles are shown. The approach to equilibrium is followed by observing changes in the experimentally obtained values of Boltzmann's H. An example of a possible way to use this simulation program in an introductory physics course is also given.

Summaries English A study has been carried out to compare students’ cognitive development and their learning of physics concepts at different taxonomic levels. We refer to the Piaget's theory for the intellectual development and to Bloom's taxonomic levels of understanding and application for the evaluation of physics achievement. Correlations among Piagetian tasks and physics concepts achievement are reported and discussed. Misconceptions are found to exist among students showing formal reasoning patterns. Relationships between misconceptions and students’ performance on a test designed to measure their ability to apply knowledge are presented and discussed.

Reports a simulation experiment for educational purposes. The experiment aims to clarify the effects of repulsive and attractive forces on a two-dimensional Lennard-Jones fluid. The simulation uses a molecular dynamics method. Relationships between spatial structure and thermodynamic properties of the system are discussed. The spatial correlation function and the virial equation of state are calculated and the behaviour of the model in different density ranges and at different temperatures is discussed. Computer experiment results are also related to the van der Waals' state equation.

Summaries English This is the first report of our research into the correlation between intellectual development and students’ understanding of scientific concepts and operational science processes. The main aim of the research is the reorganization of the physics contents of high‐school courses. We refer to Piaget's cognitive theory because of its relevance to the learning of the formal structure of science. Problems connected with measures of formal level are discussed. Results are reported concerning the reliability and validity of a Piagetian or Piagetian‐like task as a measure of students’ level of formal reasoning. Correlations between performance on tasks and chronological age, socio‐economic status, students’ sex and type of school, are reported and compared with similar known results, obtained in different social and cultural environments. Implications for curricular planning and evaluation are discussed. Conclusions are drawn concerning the necessity of planning science courses in terms of conce...