Experimenting a MIF on Quantum Mechanics for pre-service teacher training

1. Experimenting a MIF on Quantum Mechanics for pre-service teacher training M Michelini, R Ragazzzon, L Santi, A Stefanel Research Unit in Physics Education, Udine University

2. Quantum Mechanics (QM) constitutes the cultural reference paradigm and theoretical foundation for the present description of the microscopic phenomena (Hadzidaki et al. 2000). Its implications are very important in many branches of sciences that investigate nature. It is, therefore, important that the cultural baggage of a well-informed citizen includes those methodological elements, that constitute the "quantum-mechanical way of thinking”. (Sakurai, 1985) Müller, Wieser (2002)

3. Many works have been made on QM teaching in the high school and at the university (special issues: Am. J. P. 2002; Phys. Educ. 2000). aspects to be treated there is no consensus on lay-out to be adopted • provide the cultural contents of quantum theory, • show its potential for unifying the understanding of microscopic phenomena • highlight the interconnection between its formalism and its physical meaning.

4. In this context arises the problem of teacher training, which furthermore adds cultural formation issues to the educational ones. The knots on the strategies to be adopted in the teacher training and on the supporting materials needed for teaching innovation are completely unsolved (Pospiech 2000 b). The lack of specific disciplinary knowledge in QM of many teachers (and future teachers) enhances such problems.

5. Within the framework of the SeCiF and FFC National Research Projects • we developed : • a web site with the materials for work and study for teaching QM in secondary school • (This environment targets teachers and teacher trainers) • a Formative Intervention Module (MIF) for teacher training about the subject. Spiegare e Capire in Fisica (SeCiF) Explaining and understanding in Physics and Fisica come Formazione Culturale (FFC) Physics as a Cultural Formation are two of the relevant national Project financed by Ministerium respectively for the period 1999-2000 and the period 2001-2003. The materials developed in SeCiF by Italian community are available at the url: . The research groupe partecipating to the FFC project are those in the universities of Bologna, Milano Statale, Milano Bicocca, Napoli, Palermo, Pavia, Roma, Torino, Udine.

6. The environment translates the didactic proposal produced in previous research (Ghirardi, Grassi, Michelini 1995; Michelini et al. 2000; Michelini et al. 2001) with indications on: • It also provides: • suggestions and examples on how to operate in the classroom context, local common computer software and/or java applets on the web for modeling and simulations, • examples of worksheets for pupils, designed according to what has emerged from previous researches (Martongelli et. Al. 2001), • experiment presentations and reports on previous sperimentations in school. Lay-out, approach, strategy and methods, prerequisite map educational path and contents

7. In the context of the biannual postgraduate Specialization School for Secondary teaching (SSIS) a MIF on QM has been organized: 3 cts per year (about 30 hours). The MIF sperimentation has been running for 2 years (academic years 01/02 and 02/03) and 22 teachers in training (student-teacher from now on) have been involved.

8. The MIF in QM is organized in terms of a critical overview of the basic ideas of the theory: the concepts related to the formalism their consequences. It is structured in a modular way through: 1) A critical discussion of the quantum theory foundation; 2) a discussion of the reasons of the crisis in classical physics through crucial experiments in lab activities; 3) A study on three different approaches presented in FFC project; 4) A detailed analysis in operative terms of the educational proposal developed in Udine (Ghirardi, Grassi, Michelini 1995; Michelini et al. 2000; Michelini et al. 2001), supported by lab activities on optical physics; 5) Planning educational path and eventual implementation in the school.

9. 1) The first point consists of an overview of QM foundations, in the light of different interpretations. Dirac’s formalism for simple systems has been used to give formal basis good enough to discuss the fundamental ideas and the structure of the theory. • In simple contexts, like the one of particles with spin ½, several basically questions have been discussed: • the physical meaning of state vector • macrorealism and the problem of measure • projection postulate and the interpretation problems it opens • Zeno’s effect • problems concerning the completeness of quantum theory • locality-non locality and Bell’s theorem. It has so been possible to give the necessary instruments to develop an autonomous capacity to analyze the other educational proposals.

10. 2) The discussion of the most important experiments aim to highlight the interpretative problems presented and is run using the proposals of activities which can be done in a didactic lab (i.e. Franck and Hertz experiment, the photoelectric effect, the diffraction of the electrons). Their discussion by the conceptual point of view stresses some of the principal changes necessary for a phenomenological interpretative theory.

11. 3) The study of the three different approaches developed in the national FFC project regards • their critical analysis • identification of the possible integration with the Udine approach • both on the cultural level (Roma , Milano) on the level of the rigorous theoretical analysis (like the one proposed as an alternative approach with the Feynman paths integral (Torino).

12. 4) Phase 4 is crucial to allow the student-teachers to master the conceptual setting and to translate it into professional skill. A strategy of the type PEC (prevision-hypothesis, experiment and results comparison) is used in the context of the educational proposal to be analyzed. This one itself is characterized by a development of the concepts in simple specific contexts, such as that one of polarization phenomenology. This is easily studied with quantitative experiments and its phenomenological laws can be reinterpreted as probabilistic laws.

13. In a first step the superposition principle is discuss qualitatively, in a conceptual environment where the photons interact with ideal polaroids and birefringent crystals. An iconographic representation of the properties that can be associated with the photons has been used. This has been seen as a very powerful teaching tool (Michelini et al. 2001)

14. The students then recognize the quantumechanical state as been represented as a vector. The superposition principle arises from the moment we express such vector as a linear combination of two orthogonal vectors, associated with states characterized by mutually exclusive properties. Its physical meaning emerges from the comparison with the classical point of view. Finally the linear operators-observables association is proposed, determining the aspectation value of a physical observable (in the specific case the polarization). The results obtained in the case of polarization can be generalized to systems which possess more than two accessible states.

15. 5) The planning of educational paths and the eventual implementation in the school is the most important part of the MIF. In this phase the student-teachers prepared the experiments to be carried out in school activities and supporting materials (worksheets and tests). They realized educational projects from the SeCiF materials and from the notes, according to the grid proposed in an other research (Marucci et al. 2001) and working with the supervisor (an experienced high-school teacher) and the professor responsible for education in physics at the university. There are two kinds of didactical projects: didactical paths and real packages. 8 of the student-teacher realized didactical project on QM implemented in school. Afterwards we analyze 6 implemented path that are included in the final reports discussed in the state exam of the end of the SSIS course.

16. 3. Methods To evaluate the effectiveness of the MIF and how it has so far influenced the planning and teaching competencies of the student teachers we analyzed the reports of the proposal developed and implemented in the class. These were compared with similar reports prepared by the students without using the contents of the following research (in the following we refer to the two kinds of reports as “MIF reports” and “non-MIF reports”, respectively). The projects have been analyzed on the basis of three grids: “elements grid”, “evaluation grid”, “experimentation grid”.

17. The “elements grid” can gather the different aspects of the project, the particular attention given to them by the student teachers and in particular find out the dynamic of the teaching-learning process.

18. The “evaluation grid” has been developed in the FFC research. It is focused on the planning competencies of the student-teachers in implementing educational paths and teaching sequences.

19. The “experimentation grid” gives the opportunity to find out and characterize the elements present in the student teachers reports on the projects implementation in the school.

20. A score has been given to each grid component: 3 – good performance; 2 – intermediate performance; 1 – unsatisfactory performance; 0 – component absent. The results obtained by each student in the different components have been summed up and the average has been calculated for each category. Finally the average of the results of each student-teacher has been worked out.

21. 4. REPORTS ANALYSIS The analysis consists of two parts. The first one is more focussed on the elements of the teacher professionality in the context of the didactical innovation related to the subject. The second one concerns more methological, strategically and contents elements of the specific topic

22. the MIF reports are more focused on the strategies and on the materials and tools used. Figure 1: average evaluation of the “elements grid” categories

23. there is an improvement in the planning abilities of the student-teachers, above all, with reference to the general presentation of the teaching projects, the consciousness of the methodology used, the pertinence and variety of the references. Figure 2. Average evaluation of the “evaluation grid” categories”

24. The student-teachers paths are not so different to those subjected in the supporting materials. The main differencies are: • particular attention to the knot of the passage from the macroscopic analysis (classic) of real experiments to the microscopic one (quantistic) in ideal situations. In two cases information tools are used to facilitate the above-mentioned passage. • nobody uses the experiments with birefringent crystals to complete the exploration of the hypothesis started with polaroid, that is a basic knot when we recognize the active role that polaroid plays in the interaction with photons (Michelini et al. 2001, Ghirardi 1997). • Regarding formalism, all student-teachers propose the association state-vector. Three of them included it in the description of the phenomenology as a qualitative representation.

25. The weight give to quantum indeterminism and indeterminacy principle (discussed only in half of the cases), discussion about the physical meaning of the superposition principle (2/6); Finally, the historical development of the QM and the wave and particle models of light are mentioned in two of the didactical paths. Nobody suggest to deepen some topics developed in the other parts of the MIF.

26. Respect to the contents The six student-teachers, five of which didn’t receive a previous specific training about QM, showed in this field the same knowledge as those that traditionally belong to the maths or engineering courses. conceptual difficulties on following aspects: a) Distinction from property and state of a photon with that given property b) Explication of the elements that lead to the association with a vector of all the information available on a system prepared in a defined physical state.

27. A better evaluation of the first two categories in non-MIF reports comes from a greater cooperation in the planning phase with the in-service teacher who received them in their school. The major attention given to the activity is counterbalanced referring to MIF reports by the deep analysis of the tests and partially by the working sheets given to the students. Figure 3. Average evaluation of the “experimentation grid” categories

28. As indirect evaluation of the MIF we have briefly analyzed some elements common to all the paths that are implemented in school. In table 4 are shown the contents aims of the tests ande the frequency occurance They map the elements included in the didactical paths

29. The majority of students understood and known the phenomenology of the photons interaction with polaroid (from 70% to 90%) and the phenomenology of birefringence (about 70%). Most pupils understood the meaning of mutually exclusive properties, while not all of them understood the concept of incompatible properties. The role played by the formalism, at least at a first level, has been widely recognized (70% at least). Never the less there are difficulties in overcoming the specific phenomenological context.

30. Some final rimarks on MIF efectiveness. Many student-teachers (in most of 50% of cases) implemented in the schools personal proposals on QM teaching In the MIF reports the student-teachers showed better project skills then they show in non MIF reports, are also more focused on the student’s learning and on the materials and tools used. Furthermore they discussed quantum mechanical issues and other topics which were well known to them with the same competence. These results are coherent with the results of the classroom implementations that showed a significant learning curve. This shows the effectiveness of the used teacher training strategies that integrate physical knowledge with teaching proposals.

31. Good project skills and knowledge of the subject, shown by the reports by the results of the school sperimentations, emerges in relation to the aspects supported with adequate material. • This highlights the importance of supporting the teacher training with material designed to aid the educational planning. • This material has to be flexible enough to guarantee the transfer capability, that is the ability to use physical and educational knowledge to construct proposals that differ significantly to the ones object of the formation. • The limited transfer capacity, demonstrated by the student-teachers (and by the student) shows the necessity to adopt in the future more flexible strategies where the cultural context of reference is completely integrated with the educational proposals.