| [N/D] [ITA] | 1st | 1st | 6 |
Educational objectives Depending on the course chosen, these activities contribute to the development of additional disciplinary knowledge and/or transversal skills, the strengthening of critical, communicative, and practical abilities, as well as the enhancement of autonomous learning capabilities. The selection of elective courses must be consistent with the overall educational objectives of the Degree Programme and supports the construction of a more individualized academic or professional profile.
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| 10631688 | Laboratory of classical and modern Physics [PHYS-06/B, PHYS-03/A] [ITA] | 1st | 1st | 9 |
Educational objectives At the end of the course, the student will be able to – Knowledge and understanding: acquire a solid understanding of the main phenomena of classical and modern physics that can be addressed in upper secondary school, as well as the fundamentals of the experimental method, measurement techniques, and statistical data analysis. The student will also become familiar with the main findings of research in physics education, with particular reference to students’ spontaneous interpretative models and the conceptual difficulties documented in the literature, as well as some key stages in the history of physics that help to clarify the epistemic roots of the scientific concepts taught. – Applying knowledge and understanding: observe, describe, and interpret physical phenomena through laboratory activities; carry out measurements; represent and analyze experimental data; and design simple experiments, including those using low-cost materials, interpreting their results within the framework of relevant theoretical models. The student will also be able to design teaching sequences and laboratory activities for upper secondary school based on participatory and inquiry-based approaches, aimed at fostering students’ conceptual change, also through the use of historical‑epistemological perspectives that support the understanding of physical concepts. – Making judgments: develop the ability to critically evaluate experimental results, teaching strategies, and students’ interpretative models, recognizing misconceptions and spontaneous ideas, including in relation to past conceptions that emerged in the historical development of physics, and identifying the most effective ways to help overcome such models toward a scientifically grounded understanding. – Communication skills: communicate clearly, rigorously, and effectively in a didactic context about physical concepts, models, experimental results, and historical‑epistemological references, adapting language and explanatory strategies to the level of upper secondary school and fostering students’ active participation through discussion and reflection on observed phenomena. – Learning skills: acquire methodological, didactic, and historical‑epistemological tools useful for continuous professional development in the field of physics and physics education, developing the ability to integrate findings from educational research, laboratory practice, and historical reflection into future teaching activities.
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| Experiments in Physics [PHYS-06/B] [ITA] | 1st | 1st | 3 |
Educational objectives At the end of the course, the student will be able to – Knowledge and understanding: acquire a solid understanding of the main phenomena of classical and modern physics that can be addressed in upper secondary school, as well as the fundamentals of the experimental method, measurement techniques, and statistical data analysis. The student will also become familiar with the main findings of research in physics education, with particular reference to students’ spontaneous interpretative models and the conceptual difficulties documented in the literature, as well as some key stages in the history of physics that help to clarify the epistemic roots of the scientific concepts taught. – Applying knowledge and understanding: observe, describe, and interpret physical phenomena through laboratory activities; carry out measurements; represent and analyze experimental data; and design simple experiments, including those using low-cost materials, interpreting their results within the framework of relevant theoretical models. The student will also be able to design teaching sequences and laboratory activities for upper secondary school based on participatory and inquiry-based approaches, aimed at fostering students’ conceptual change, also through the use of historical‑epistemological perspectives that support the understanding of physical concepts. – Making judgments: develop the ability to critically evaluate experimental results, teaching strategies, and students’ interpretative models, recognizing misconceptions and spontaneous ideas, including in relation to past conceptions that emerged in the historical development of physics, and identifying the most effective ways to help overcome such models toward a scientifically grounded understanding. – Communication skills: communicate clearly, rigorously, and effectively in a didactic context about physical concepts, models, experimental results, and historical‑epistemological references, adapting language and explanatory strategies to the level of upper secondary school and fostering students’ active participation through discussion and reflection on observed phenomena. – Learning skills: acquire methodological, didactic, and historical‑epistemological tools useful for continuous professional development in the field of physics and physics education, developing the ability to integrate findings from educational research, laboratory practice, and historical reflection into future teaching activities.
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| Modern Physics [PHYS-03/A] [ITA] | 1st | 1st | 6 |
Educational objectives At the end of the course, the student will be able to – Knowledge and understanding: acquire a solid understanding of the main phenomena of classical and modern physics that can be addressed in upper secondary school, as well as the fundamentals of the experimental method, measurement techniques, and statistical data analysis. The student will also become familiar with the main findings of research in physics education, with particular reference to students’ spontaneous interpretative models and the conceptual difficulties documented in the literature, as well as some key stages in the history of physics that help to clarify the epistemic roots of the scientific concepts taught. – Applying knowledge and understanding: observe, describe, and interpret physical phenomena through laboratory activities; carry out measurements; represent and analyze experimental data; and design simple experiments, including those using low-cost materials, interpreting their results within the framework of relevant theoretical models. The student will also be able to design teaching sequences and laboratory activities for upper secondary school based on participatory and inquiry-based approaches, aimed at fostering students’ conceptual change, also through the use of historical‑epistemological perspectives that support the understanding of physical concepts. – Making judgments: develop the ability to critically evaluate experimental results, teaching strategies, and students’ interpretative models, recognizing misconceptions and spontaneous ideas, including in relation to past conceptions that emerged in the historical development of physics, and identifying the most effective ways to help overcome such models toward a scientifically grounded understanding. – Communication skills: communicate clearly, rigorously, and effectively in a didactic context about physical concepts, models, experimental results, and historical‑epistemological references, adapting language and explanatory strategies to the level of upper secondary school and fostering students’ active participation through discussion and reflection on observed phenomena. – Learning skills: acquire methodological, didactic, and historical‑epistemological tools useful for continuous professional development in the field of physics and physics education, developing the ability to integrate findings from educational research, laboratory practice, and historical reflection into future teaching activities.
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| 10628961 | Foundations of Complementary Mathematics [MATH-01/B] [ITA] | 1st | 2nd | 9 |
Educational objectives General objectives Addressing the study of varied mathematical content, favoring an "extensive" approach that highlights the links between content and other parts of mathematics and science, with particular attention to the historical evolution of concepts and their placement in a cultural frame that may help the future mathematics teacher to integrate the educational role of teaching mathematics more closely with that of other subjects. Specific objectives Knowledge and understanding: At the end of the course, students who have passed the exam will have the basic knowledge and methodological tools to place mathematics teaching in a wider cultural context that enriches its educational value. Apply knowledge and understanding: At the end of the course, students who have passed the exam will be able to face the reading and understanding of the general parts of mathematical articles of historical and cultural relevance, in particular of the nineteenth century (in one of the foreign languages known to the student or in the translation into Italian) and to compare the methods used by their authors with those of contemporary mathematics which they learned about during their three-year degree studies. They will be able to appreciate the didactic value of a historical approach to mathematics and to apply it to the planning of didactic teaching paths in the school. They will have developed a critical and informed attitude towards the applications of mathematics to social sciences and the modeling of complex systems. Critical and judgmental skills: The student will receive the necessary bases to appreciate the historical development of the main concepts relating to the foundations of non-Euclidean geometry, differential and projective geometry, the idea of function and the calculation of probabilities and the relationships between the topics covered in this course and those covered in other courses (of the three-year degree, in particular the History of Mathematics course, and of the master's degree, such as the course of Elementary Mathematics from a higher point of view and that of Fundamentals of Mathematics, Real Analysis and Differential Geometry). Communication skills: Ability to expose the contents in the oral part of the verification and to summarize the knowledge acquired in the development of the topic proposed in the written test. Particular attention will be devoted to developing the ability to communicate correctly, even if incomplete, a non-elementary mathematical content by relying on digital tools, heuristic analogies, examples and significant and illuminating exercises and to critically address the siege of available information. online or in libraries. Learning ability: the knowledge acquired will allow the student to develop a critical attitude, attentive to the historical and conceptual development, of mathematical ideas and their cultural value, also in relation to the other sciences and society.
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| 10628495 | Teaching of mathematics [MATH-01/B] [ITA] | 1st | 2nd | 6 |
Educational objectives General aims: The successful student will be able to deal with arguments concerning the teaching of the mathematics in secondary schools. Specific aims: Knowledge and understanding: The successful student will have acquired basic notions about didactical theories and will know possible different approaches to specific mathematical topics. The successful student will know a suitable framework for the main concepts of several mathematical topics, having caught up a good familiarity with fundamental aspects, as the connection between various fields of the mathematics. Applying knowledge and understanding: The successful student will be able to discuss traditional didactic choices. S/he will be able to prepare lectures and exercises to teach mathematics taking in due account some solutions to several teaching problems. S/he will be able to use a dynamic geometry software in an education context. Critical and judgmental skills: The successful student will be familiar with mathematical methods. S/he will have reflected on known mathematical contents; s/he knows how to tackle questions about the teaching of mathematics in a critical way. S/he will be able to discuss the role of software at an educational level. Communication skills: The successful student will be able to present subjects and arguments in the oral test, and to explain to other people what s/he learned. Learning skills: The acquired knowledge will allow to study more specialized subjects. The student will be motivated to extend his/her knowledge.
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| 10629297 | FOUNDAMENTALS OF MATHEMATICS [MATH-01/B] [ITA] | 1st | 2nd | 6 |
Educational objectives General aims: to acquire basic knowledge and skills in axiomatic set theory and to be able to apply them in various contexts, including teaching. Specific aims: Knowledge and understanding: The successful student will have acquired basic notions and results in mathematical logic: axioms and main results of the theory ZF; ordinal numbers; the axiom of choice; cardinal numbers; paradoxes in several areas of mathematics. Applying knowledge and understanding: The successful student will be able to solve exercises and problems referring to the topics covered and to application in other mathematical areas. S/he will perform computations with ordinal numbers and cardinal numbers; s/he is familiar with mathematical translations of the notion of infinity. S/he will be able to apply her/his knowledge in an education context. Critical and judgmental skills: The successful student will be familiar with mathematical rigor and formalism. S/he will have reflected on known mathematical contents; s/he knows how to tackle questions about the foundations of mathematics in a critical way. S/he will be able to discuss the role of intuition and rigor in teaching mathematics in different situations. Communication skills: The successful student will be able to present subjects and arguments in the oral test, and to explain what s/he learned. Learning skills: The acquired knowledge will allow to study more specialized subjects. The student will be motivated to extend the acquired knowledge.
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| [N/D] [ITA] | 2nd | 1st | 6 |
Educational objectives Depending on the course chosen, these activities contribute to the development of additional disciplinary knowledge and/or transversal skills, the strengthening of critical, communicative, and practical abilities, as well as the enhancement of autonomous learning capabilities. The selection of elective courses must be consistent with the overall educational objectives of the Degree Programme and supports the construction of a more individualized academic or professional profile.
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| AAF1778 | Scientific English [N/D] [ITA] | 2nd | 1st | 4 |
Educational objectives To provide students with the basic linguistic skills needed to deal with written and oral scientific communication.
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| AAF1044 | Training [N/D] [ITA] | 2nd | 1st | 6 |
Educational objectives Compulsory curricular internship at school institutions.
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| 10627087 | Elementary mathematics from a higher point of view [MATH-01/B] [ITA] | 2nd | 1st | 6 |
Educational objectives Educational goals General aims: Revision of the developments of the basic subjects of school teaching (geometry, arithmetic, analysis) in the light of the knowledge acquired in the first years of the university. Specific aims: Knowledge and understanding: at the end of the lecture course the successful student has acquired the basic notions related to the geometry of Euclid, and to alternative theories - from non-Euclidean geometries to theories expressly conceived for teaching. He will know the methods used to measure geometric figures. He is able to retrace the extensions of numerical systems, from natural to complex numbers, and their properties. He is able to compare the approach to the limit concept through sequences and through functions. To apply knowledge and understanding: at the end of the lecture course the student is able to recognize the validity of a proof in Euclidean geometry, and is able to compare proofs in different axiomatic systems. He knows some classical results related to the foundations of algebra and analysis and is able to develop them according to different points of view. Critical skills and judgment: the student revisits the development of the basic subjects of school teaching (geometry, arithmetic, analysis) as a whole, analysing them from a critical point of view and in the light of the knowledge acquired in the first years of the university. Capacity of communication: the student is able to expose the contents during the oral examination, during the discussions in the class, and in the deepening of some points of the subject that he will expose in one of the lessons. Capacity of learning: The student is able to compare different theories and approaches for the introduction of the various topics, and is able to make choices in the school curriculum.
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| 10628526 | SPACE AND SHAPE [MATH-01/B] [ITA] | 2nd | 1st | 6 |
Educational objectives Know and understand some issues and problems that fall within the field of study of mathematics, physical science and nature. Learn how to look, recognize and enhance links with the sciences and their history, artefacts and places in cities. To experiment through the example lived in first person, diversified and active methods of teaching-learning, in which body and movement in the environment are also instruments of knowledge. Enhance the concrete operation linked to thinking and designing active teaching materials. Apply teaching-pedagogical knowledge in the implementation of educational projects. Empower students with respect to the co-construction of their knowledge. Learning outcomes - Acquired knowledge: Recognizing the knowledge of scientific knowledge of artefacts and places in the city. Having had the experience of reading scientific texts (direct texts of scientists, or of history of science or of epistemological character), asking questions also in relation to the involvement of science in the history of an era, in the culture and history of societies, in gender and intercultural problems. To know and understand the methodological and didactic aspects of the proposed experiences and the activities carried out in the course, in relation to the scientific topics addressed. Upon completion of the course the student will have an advanced knowledge of research aspects in the fields of the sciences, such as the steps from the description to the following schematization, to the quantification and research of the causes of an observed phenomenon. He will also have developed historical and epistemological knowledge in the field of science. [Descriptor of Dublin n. 1]. The skills acquired will concern a greater ability to work in a group, to formulate questions with clear language, to reflect on their own learning and their difficulties and uncertainties, to analyze the educational aspects from the point of view of different disciplines involved in educational actions and training. It will have integrated modes of use of one's own body and of one's own sensory capacities among the tools of knowing. [Descriptor of Dublin n. 2]. The transversal competences acquired concern critical and judgmental skills, enhanced by participation in reflection and laboratory activities and the ability to ask questions and use an indicative method. [Descriptor of Dublin n. 3]. The intermediate activities of the course and the final ones in the form of the "Science Stands" organized by the students autonomously, also in groups, and presented to specialists and non-special beneficiaries, will allow to use display skills, choice of questions, materials and problems relevant, also on the basis of the age of the recipients, and to put in place a posteriori evaluation capacity of the proposed actions, from a multidisciplinary point of view. [Descriptor of Dublin n. 4]. To have acquired metareflection capacity on one's own and others' way of dealing with new content and issues related to scientific disciplines, and to face uncertainties and difficulties in understanding so that the student is more able to continue the study independently in the course of the life and deepen the scientific and specific themes of design in education and critically address, with the perspective of complexity, materials related to scientific disciplines. [Descriptor of Dublin n. 5]. Learning outcomes - Acquired skills: students who have passed the exam will be able to conceive, plan and evaluate educational interventions and projects through museum visits and in significant anthropic and nature spaces, and to select and discard relevant information to the topics studied in formal and informal contexts
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| AAF1027 | [N/D] [ITA] | 2nd | 2nd | 29 |
Educational objectives The final exam for the attainment of the Master's Degree consists in the preparation and discussion, in front of a special commission, of an individual written paper (possibly in English), prepared by the student under the supervision of at least one teacher.
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