This paper describes a method aimed at pointing out the quality of the mental models undergraduate engineering students deploy when asked to create explanations for phenomena or processes and/or use a given model in the same context. Student responses to a specially designed written questionnaire are quantitatively analyzed using researcher-generated categories of reasoning, based on the physics education research literature on student understanding of the relevant physics content. The use of statistical implicative analysis tools allows us to successfully identify clusters of students with respect to the\ud
similarity to the reasoning categories, defined as ‘‘practical or everyday,’’ ‘‘descriptive,’’ or ‘‘explicative.’’\ud
Through the use of similarity and implication indexes our method also enables us to study the consistency\ud
in students’ deployment of mental models. A qualitative analysis of interviews conducted with students\ud
after they had completed the questionnaire is used to clarify some aspects which emerged from the\ud
quantitative analysis and validate the results obtained. Some implications of this joint use of quantitative\ud
and qualitative analysis for the design of a learning environment focused on the understanding of some aspects of the world at the level of causation and mechanisms of functioning are discussed
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.
The problem of taking a set of data and separating it into subgroups where the elements of each subgroup are more similar to each other than they are to elements not in the subgroup has been extensively studied through the statistical method of cluster analysis. In this paper we want to discuss the application of this method to the field of education: particularly, we want to present the use of cluster analysis to separate students into groups that can be recognized and characterized by common traits in their answers to a questionnaire, without any prior knowledge of what form those groups would take (unsupervised classification). We start from a detailed study of the data processing needed by cluster analysis. Then two methods commonly used in cluster analysis are before described only from a theoretical point a view and after in the Section 4 through an example of application to data coming from an open-ended questionnaire administered to a sample of university students. In particular we describe and criticize the variables and parameters used to show the results of the cluster analysis methods.
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.
Student understanding of the laws that describe the flow of a fluid is often hampered by a defective knowledge of basic classical mechanics (kinematics, statics, dynamics, and conservation laws) and by wrong common-sense ideas about quantities related to fluids, such as velocity and pressure. A pedagogical discussion about the Venturi effect, based on experiments inspired by historical instruments, may be an effective way to introduce students to these laws. In this paper, we discuss an approach to the understanding of the Venturi effect based on the study of historical instruments and on simple experiments. In particular, after a presentation of the Venturi effect, also from a historical point of view, we illustrate some interesting applications, the Venturi meter, the Bunsen burner, the Venturi vacuum pump, and propose some simple experiments.
1 People's reasoning is often described as the "running" of the procedures present in their mental models [1-4]. Gilbert and Boulter [5] define expressed models as the external representations expressed by an individual through actions, speech, or writing. We understand "path, or line of reasoning" as the external representation of the mental models used by an individual when they try to describe, predict, or explain the physical world.
Many research papers have studied the problem of taking a set of data and separating it into subgroups through the methods of Cluster Analysis. However, the variables and parameters involved in Cluster Analysis have not always been outlined and criticized, especially in the field of Science Education. Moreover, in the field of Science Education, a comparison between two different Clustering methods is not discussed in the literature. In this paper two different Cluster Analysis methods are described and the variables and parameters involved are discussed in order to clarify the information that they can supply. The clustering results obtained by using the two methods are compared and showed a good coherence between them. The results are interpreted and compared with the literature. More detail about the relationship between different student conceptions of modeling in physics was obtained.
Abstract:We study the phenomenon of the "walking droplet", by means of numerical fluid dynamics simulations using the Smoothed Particle Hydrodynamics numerical method. This phenomenon occurs when a millimetric drop is released on the surface of an oil of the same composition, contained in a tank and subjected to vertical oscillations of frequency and amplitude very close to the Faraday instability threshold. At appropriate values of the parameters of the system under study, the oil droplet jumps permanently on the surface of the vibrating liquid forming a localized wave-particle system, reminding the behaviour of a wave particle quantum system as suggested by de Broglie. In our study, we made relevant simplifying assumptions, however we observe that the wave-drop coupling is surely obtained. Moreover, the droplet and the wave travel at nearly constant velocity, as observed in experiments. These facts suggest that the phenomenon may occur in many contexts and opens the possibility to study it in an extremely wide range of physical configurations.
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