Modelling Environments to Scaffold the Construction of Phenomenological Mental Models: An Experimental Survey

Aspetti teorici e simulazioni delle statistiche quantistiche: un approccio stocastico

In questo articolo viene analizzata una procedura per la modellizzazione e simulazione di sistemi quantistici di particelle identiche non interagenti. In particolare, viene illustrato un algoritmo numerico che si dimostra in grado di prendere in considerazione gli effetti quantistici di indistinguibilità delle particelle identiche, in generale, e del Principio di Pauli per i fermioni. I risultati delle simulazioni condotte, per semplicità, su sistemi bidimensionali, permettono di rendere conto delle principali proprietà termodinamiche di diverse tipologie di sistemi (classici e quantistici) evidenziandone, al tempo stesso, analogie e differenze.

A PROJECT-POSED APPROACH TO REAL BODY DYNAMICS: THE ROLE OF CONSTRAINTS IN ELASTIC WAVE PROPAGATION

In this paper we present some results of a project-posed approach to the teaching of mechanical wave propagation focused on observations and measurements of wave properties in solids and on modelling of these properties by using different simulation tools. In particular, the propagation speed of sound waves in metallic rods is studied by using simple experimental arrangements based on the measurements of contact times between a small body and long metallic rods with which the body can collide. An interesting effect of this approach is the revision of students’ ideas about the rigid body model, studied at high school or college level and usually hardly followed by deepening on the fundamenta…

Modelling Mechanical Wave Propagation: Guidelines and experimentation of a teaching–learning sequence

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…

Two experiments to approach the Boltzmann factor: chemical reaction and viscous flow

In this paper we discuss a pedagogical approach aimed at pointing out the role played by the Boltzmann factor in describing phenomena usually perceived as regulated by different mechanisms of functioning. Experimental results regarding some aspects of a chemical reaction and of the viscous flow of some liquids are analysed and described in terms of macroscopic variables whose temperature dependence is proportional to the Boltzmann factor. A description of a workshop implementing the approach in the framework of an undergraduate course for engineering education and some preliminary results about its pedagogical relevance are then reported.

Mathematical Modelling of Dynamic Systems: A Case Study of Teaching/Learning Strategies Involving Icon Oriented Computer Programs

Portraying Pedagogical Content Knowledge: a Case Study of Pre-Service Physics Teacher Education

Reply to comment on ‘Measuring longitudinal wave speed in solids: two methods and a half’

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.

Modelling Ideal Classical/Quantum Gas by Connecting Microscopic Properties and Emergent Behaviours

The main goal of statistical mechanics is to relate macroscopic properties of matter to microscopic characteristics of its constituent particles. Because of the large number of particles usually involved in real macroscopic systems, statistical mechanics has to face several mathematical difficulties that very often lead to the impossibility of performing exact calculation of thermodynamic properties, especially at high school or at undergraduate level. Nowadays, some simulation tools designed to look at and visualise the behaviour of interacting micro-agents and patterns emerging from their interactions are available. Their use makes possible to obtain good estimations of thermodynamic prop…

Measuring longitudinal wave speed in solids: two methods and a half

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.

Mechanical models of amplitude and frequency modulation

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.

L’algoritmo come strumento didattico in fisica: modellizzazione dei gas ideali classici e quantistici

Viene discussa una procedura per la modellizzazione dei gas ideali quantistici. Inoltre, viene evidenziata l’importanza di supportare le incomplete rappresentazioni mentali degli studenti, in relazione ad argomenti complessi di meccanica statistica e termodinamica, con accurati modelli fisici aventi validità predittiva e fondati sull’ipotesi di possibili meccanismi di funzionamento. L’idea alla base dell’approccio proposto è quella che, in alcuni casi, anche la sola discussione dei risultati di un algoritmo o di un modello può essere sufficiente a migliorare la comprensione di un sistema fisico particolarmente complesso.

Visualising Statistical Mechanics. The Case of Energy Distribution

Prospective elementary teachers’ perceptions of the processes of modeling: A case study

In this paper we discuss a study on the approaches to modeling of students of the 4-year elementary school teacher program at the University of Palermo, Italy. The answers to a specially designed questionnaire are analyzed on the basis of an a priori analysis made using a general scheme of reference on the epistemology of mathematics and physics. The study is performed by using quantitative data analysis methods, i.e. factorial analysis of the correspondences and implicative analysis. A qualitative analysis of key words and terms used by students during interviews is also used to examine some aspects that emerged from the quantitative analysis. The students have been classified on the basis…

AN INTRODUCTION TO THE BOLTZMANN FACTOR BY USING INFORMATION TECHNOLOGY TOOLS

We present an experiment and simulations aimed at introducing the Boltzmann factor mathematical expression and at illustrating the fundamental concepts on which it is grounded. The experiment uses an easily available Microcomputer Based Laboratory apparatus. Simulations are developed in the Net-Logo environment that, besides having a friendly user-interface, allows an easy interaction with the algorithm. The approach supplies a pedagogical support for the introduction of the Boltzmann factor at undergraduate level to students without a background in statistical mechanics.

Elastic Waves: Common Representations and Related Teaching/Learning Sequences

Modelling Dynamic Systems: Examples Involving an Iconic Oriented Environment

We present a modelling environment based on the use of iconic representations consisting of elements, as containers and connected flows, able to describe the relationships between relevant variables of dynamic systems. The procedures involved are aimed to make students aware of the reasoning processes to describe, formalise and explain complex system behaviours. Moreover, we show how these strategies may allow the overcoming of some well-known difficulties involved in pupil understanding of mathematical formalisms, such as derivatives and differential equations and their real meaning. Our reported modelling examples were experimented on during some laboratory sessions of the Pre-Service Sch…

Designing and Validating a Teaching/Learning Sequence about Elastic Wave Propagation: The Role of Pedagogical Tools

A Stochastic Approach to Quantum Statistics Distributions: Theoretical Derivation and Monte Carlo Modelling

Abstract. 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…

Collisions and Mechanical Wave Propagation in Elastic Rods

Some results from experiments intended to measure the propagation speed of sound waves produced by collisions between small bodies and metallic rods are analysed. Elementary models of elastic collision and of the reflection and transmission of waves at media boundaries are discussed and tested with experimental data, in the framework of a workshop on mechanical wave propagation that featured at the University of Palermo in a two-year graduate programme for prospective physics teachers and in courses for undergraduate engineering and physics students.

An experiment on the velocity distribution of thermionic electrons

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.

A Problem Based Approach to Sound Propagation in Different Materials

In this paper we present a problem-based approach to the study of sound propagation devoted to pre-service physics teacher education at University of Palermo, Italy. Small groups of trainee teachers are proposed with real life situations and must organize themselves, define objectives, conduct researches, analyze results, and present conclusions. In particular, the problem of wave propagation in different materials is discussed, by starting from the real life situation of soundproofing a house. Examples of experiments performed by the trainee teachers with Real Time Laboratory (RTL) equipment and of interpretative models built and tested by using computer simulation environments are reporte…

A Problem Based Approach to Elastic Wave Propagation: The Role of Constraints

A problem-based approach to the teaching of mechanical wave propagation, focused on observation and measurement of wave properties in solids and on modelling of these properties, is presented. In particular, some experimental results, originally aimed at measuring the propagation speed of sound waves in metallic rods, are used in order to deepen the role of constraints in mechanical wave propagation. Interpretative models of the results obtained in the laboratory are built and implemented by using a well-known simulation environment. The simulation results are, then, compared with experimental data. The approach has been developed and experimented in the context of a workshop on mechanical …

The Boltzmann Probability as a Unifying Approach to Different Phenomena

We discuss a pedagogical approach to the role of the Boltzmann probability in describing the temperature dependence of three simple experimental situations. The approach has been experimented in an introductory course on statistical mechanics for undergraduate engineering students at University of Palermo.

Onde Elastiche: Rappresentazioni Comuni e Sequenze di Insegnamento/Apprendimento

The elastic body model: a pedagogical approach integrating real time measurements and modelling activities

In this paper, we describe a pedagogical approach to elastic body movement based on measurements of the contact times between a metallic rod and small bodies colliding with it and on modelling of the experimental results by using a microcomputer-based laboratory and simulation tools. The experiments and modelling activities have been built in the context of the laboratory of mechanical wave propagation of the two-year graduate teacher education programme of Palermo’s University. Some considerations about observed modifications in trainee teachers’ attitudes in utilizing experiments and modelling are discussed.

MICROSCOPIC AND MACROSCOPIC ASPECTS OF STUDENT KNOWLEDGE IN ELECTRIC CONDUCTION IN METALS

This paper presents some preliminary results of a research aimed at portraying individual models of description/explanation of electrical conduction in metals shown by physics prospective teachers and at studying how a specifically designed pedagogical environment can support an adequate evolution of their knowledge and disciplinary competencies. A teaching/learning sequence (TLS) on the subject matter, making use of custom Information Technology tools, aimed at facilitating and scaffolding learning, is shortly described. Some relevant points of the research pilot phases, like the analysis of prospective teachers’ spontaneous models of electrical conduction, the identification of significan…

Modelling dynamic systems: an example involving graphic oriented computer programs

EDUCATIONAL ICT TOOLS TO IMPROVE WAVE PHYSICS UNDERSTANDING

MODELLING THE DISPERSION PROPERTIES OF MASS LINEAR CHAINS: EXPERIMENTS AND SIMULATIONS

We analyze and discuss the results of an experiment with the goal of revealing the phonon-like acoustic dispersion curve. The experimental apparatus consists of a sonometer and an electromagnetic driver connected to a signal generator in order to establish standing waves along a stretched metal string (a guitar string) upon which a set of beads (used normally for fishing) has been fixed. The oscillation amplitude is measured by means of a detector connected to an MBL interface. We detect the resonance frequencies as function of the wave-number and obtain the corresponding dispersion curve. The results show that deviations from linearity occur when the wavelength is comparable with the dista…

Modelling systems of classical/quantum identical particles by focusing on algorithms

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.

Un Approccio Innovativo allo Studio delle Proprietà delle Onde Elastiche in Mezzi Diversi

Searching for the Maxwell Distribution and the Boltzmann Factor: an Inquiry-Based Approach

We report the development of a Workshop involving experimental and modelling activities aimed at facing two relevant problems currently addressed by the Physics Education Research community. These involve the organization of curricula aimed at showing the unity of physics as a subject and the ways to design affective learning environments.