The problem of positivity in 1+1 dimensions and Krein spaces

The possibility of introducing a positive metric on the states of the massless scalar field in 1+1 dimensions by mean of Krein spaces is examined. Two different realisations in Krein spaces for the massless scalar field are compared. It is proved that one is a particular case of the other. The peculiarities and advantages of both realisations are discussed.Comment: 8 pages, presented to Accadem. dei Fisioc. Sien

On Understanding Statistical Data Analysis in Higher Education

Data analysis is a powerful tool in all experimental sciences. Statistical methods, such as sampling theory, computer technologies necessary for handling large amounts of data, skill in analysing information contained in different types of graphs are all competences necessary for achieving an in-depth data analysis. In higher education, these topics are usually fragmentized in different courses, the interdisciplinary integration can lack, some caution in the use of these topics can missing or be misunderstood. Students are often obliged to acquire these skills by themselves during the preparation of the final experimental thesis. A proposal for a learning path on nuclear phenomena is presented in order to develop these scientific competences in physics courses. An introduction to radioactivity and nuclear phenomenology is followed by measurements of natural radioactivity. Background and weak sources can be monitored for long time in a physics laboratory. The data are collected and analyzed in a computer lab in order to understand the importance of statistical analysis in a not trivial case.Comment: 4 pages, 6 figures, presented at International Symposium on Interdisciplinary Research, Education, and Communication: IDREC 2012 in the Context of The 3rd International Multi-Conference on Complexity, Informatics and Cybernetics: IMCIC 2012; March 25th - 28th, 2012 ~ Orlando, Florida, US

An inquiry-based laboratory on friction

Sliding friction is usually introduced in high school, but rarely through activities in laboratory. A qualitative introduction to friction is presented by proposing exploration of different kind of materials in order to suggest which aspects can be relevant and which interaction is involved. Different quantitative experiments are proposed for studying Leonardo's laws for friction. The learning path was tested with two high school classes during an instruction trip at department. Students were engaged in the inquiry-based introductory activity and seemed to realize with care the measurements. However, the analysis of their reports shows some learning difficulties.Comment: 7 pages, 9 figures, presented to ICPE-EPEC 2013 The International Conference on Physics Education PRAHA, CZECH REPUBLIC August 5-9, 2013, to appear in the ICPE-EPEC 2013 Conference Proceeding

Fostering Student Enrollment in Basic Sciences: the Case of Southern Tuscany

In recent decades it has been detected in Italy a decrease in enrollment in basic sciences, i.e. Mathematics, Physics and Chemistry. The increase in specific orientation is strategically crucial to achieve the goal of maintaining and increasing the number of motivated and capable students who enroll in these courses. With the purpose of increasing scientific vocations, workshops were organized in high schools and teachers involved in planning and implementation of laboratories, conferences for scientific outreach, thematic exhibitions, guided tours of research laboratories, summer's schools for students and courses for teachers were realized for developing a cultural enhancement in teaching basic sciences. Particularly significant is the case of activities organized by the Department of Physics of the University of Siena for students and teachers in Southern Tuscany. The methods used in cultural enhancement of teachers and activities designed to support schools with limited laboratory facilities, together with stimulating activities for motivated students are allowed to take root for some good practices in physics teaching and orientation to scientific degrees. Beyond describing the main activities for orientation to Physics, activities done in partnership with chemists, biologists and geologists are reported, as well as an activity in which the Departments of Mathematical Sciences and Physics are both involved in looking for introducing new interdisciplinary methodologies to increase students' understanding in high school of some selected topics in which both disciplines give a contribution in the construction of important and mutually reinforcing basic concepts.Comment: 6 pages, 8 figures, presented at International Symposium on Interdisciplinary Research, Education, and Communication: IDREC 2012 in the Context of The 3rd International Multi-Conference on Complexity, Informatics and Cybernetics, March 25th - 28th, 2012, Orlando, Florida,US

Measures of radioactivity: a tool for understanding statistical data analysis

A learning path on radioactivity in the last class of high school is presented. An introduction to radioactivity and nuclear phenomenology is followed by measurements of natural radioactivity. Background and weak sources are monitored for days or weeks. The data are analyzed in order to understand the importance of statistical analysis in modern physics.Comment: 3 pages, 2 figures, Twelfth International Symposium Frontiers of Fundamental Physics (FFP12), Udine 21-23 November 201

Seeing How Fitting Process Works

A common problem in teaching Physics in secondary school is due to the gap in terms of difficulty between the physical concepts and the mathematical tools which are necessary to study them quantitatively. Advanced statistical estimators are commonly introduced only a couple of years later than some common physical topics, such as e.g. the electronic circuit analysis. Filling this gap with alternative methods appears to be opportune, in order to let the students reach a full comprehension of the issue they are facing with. In this work we use a smartphone camera and GeoGebra to propose a visual method for understanding the physical meaning of a fitting process. The time constant of an RC circuit is estimated by fitting the discharge curve of a capacitor visualized on the screen of an oscilloscope.Comment: 6 pages, 3 figures, presented at the 20th edition of the Multimedia in Physics Teaching and Learning Workshop MPTL20, September 9-11, 2015, Munich, German

Active learning in pre-service science teacher education

We report a course on teaching in physics lab for teachers enrolled in Formative Active Training, which actually allows to obtain the teacher qualification in Italy. The course was designed with the purpose of showing in practice what means active learning in physics and how effective activities can be realized in practice. Two different type of teachers attended to the course, a small group, with physics or mathematics degree, for teacher qualification in secondary school of second grade (age 14-19) and a more numerous group for qualification in secondary school of first grade (age 11-14), usually with a different science degree such as biology, environmental sciences and so on. We compare this training in physics lab between the two groups and with other experiences we performed in previous years in pre-service education and updating courses for teachers in-service.Comment: 8 pages, 5 figures, 4 tables, presented to ICPE-EPEC 2013 The International Conference on Physics Education PRAHA, CZECH REPUBLIC August 5-9, 2013 to appear in the ICPE-EPEC 2013 Conference Proceeding

An empirical study on a learning path on wave physics focused on energy

We describe an extracurricular learning path on waves focused on energy transfer. The advantages of introducing mechanical waves by using the Shive wave machine and laboratory activities are presented. Laboratories are realized by inquiry, i.e. students explore waves behavior in qualitative way, guess what can happen and suddenly test their hypothesis. Recently, we presented some disciplinary knots that arise usually in empirical investigation, according to the Model of Educational Reconstruction and discussed methodological choices made in designing the learning path and preliminary result about its realization with few, interested and talented pupils. We report the second year of this learning path performed with the same students that are introduced to more complex topics such as analogy in wave phenomena and resonance. Laboratories are described with particular attention for the energy transformation. We designed the activities in order to propose a complementary experience compared to what was done in class. Despite resonance is a relevant phenomenon which runs through almost every branch of physics, many students have never studied it. Yet, resonance is one of the most striking and unexpected phenomenon in all physics and it easy to observe but difficult to understand. Students performed activities in laboratory on several resonant systems. Our purpose was to outline how it is possible to tune a system or a device in order to obtain resonance and an efficient energy transfer from different physical systems, such as a mechanical one and an electrical one. This year, the final task was to analyze different natural phenomena in order of choosing one suitable for energy transfer. We present our considerations on the students' learning process and on the possibility of extend a similar path in a classroom.Comment: 10 pages, 7 figures, presented to The World Conference on Physics Education (WCPE), July 1-6, 2012, Istanbu

Promoting Multimedia in Physics Teaching Through the Flipped Classroom in Pre-Service Education

A flipped classroom was introduced in pre-service education in order to promote MM and the quality of their use in the teaching and learning process in laboratory. The course, Physics Lab Didactics, promoted active learning through the direct experience of young teachers. The flipped classroom approach was presented and discussed with the aim of clarifying the teaching process and in-training teachers were invited to explore how to implement this methodology in a class after their experience. Different open source or free software were proposed (Audacity, Algodoo, GeoGebra and Tracker) with some examples of their use in physics teaching. The discussion on their implementation as tools in physics laboratory was postponed to the last lesson of the course. This pilot study shows a great potentiality of the flipped classroom in pre-service education and it indicates that the use of MM in laboratory learning process can be improved following this approach.Comment: 8 pages, 8 figures, presented at the 20th edition of the Multimedia in Physics Teaching and Learning Workshop MPTL20, September 9-11, 2015, Munich, German

Seeing and interacting with the invisible: A powerful tool for the learning of science

In order to describe natural phenomena, science develops sophisticated models that use mathematical and formal languages which seem, and often are, very far from common experience. When a phenomenon is not accessible to our senses, its description is indirect and understanding can be difficult for those who are not trained to understand the consequences of formal languages used by scientists. When one succeed to obtain a direct visualization of a phenomenon inaccessible to senses, it is possible to get a deeper understanding since a very effective channel of learning is involved. A wider and more profound result in learning process can be obtained if the physical system utilized for visualization enables direct interaction with the phenomenon. From the infrared vision to cosmic rays, from the magnetic field to the flow of energy, many phenomena can be suitable for building systems that allow capturing a greater awareness of the physical world. Some examples of such systems are given for relevant topics in physics and for mathematical tools. They were designed for a summer school for students in the last years of high school or for deepening laboratories addressed to talented students in secondary school, but with some attention it is possible to adapt them to other cases like high school classes or undergraduate students.Comment: 13 pages, 16 figures, 2 tables, presented at the 10th Conference of the European Science Education Research Association (ESERA), 2-7 September 2013, Nicosia, Cypru