cod. 1007189

Academic year 2018/19
2° year of course - First semester
Academic discipline
Matematiche complementari (MAT/04)
Attività formative affini o integrative
Type of training activity
60 hours
of face-to-face activities
6 credits
course unit

Learning objectives

Knowledge and ability to understand: through the lectures held during the course, the student will acquire the methods and knowledge necessary to analyze teaching proposals, curricula and materials for the mathematics of secondary school first and second degree, and identify the design criteria and strengths and weaknesses. He will learn the main concepts, some methods and empirical results of didactic research in mathematics. He will learn the structure of the national indications, of the INVALSI and OECD-PISA frameworks, of the cultural axes. In particular, the student will have to apply the acquired knowledge to the analysis of research articles, textbooks, curricula, and standardized evaluation tests.
Autonomy of judgment
The student must be able to evaluate and critically choose a teaching strategy and evaluate the potential impact of planning decisions and implementation of the teaching action on different types of students.
Communication skills
Through the lectures and the comparison with the teacher, the student acquires the specific vocabulary inherent in the teaching of mathematics as a scientific discipline. It is expected that, at the end of the course, the student is able to transmit, in oral and written form, the main contents of the course, the key ideas for interpreting classroom situations, learning problems and possible solutions. . The student must communicate his / her knowledge with a good balance between precision in the language and exhibition of concrete examples among those analyzed, as well as showing that he has gained his own point of view.
Learning ability
The student who has attended the course will be able to deepen their knowledge in mathematics education through the independent consultation of specialized texts, scientific or popular journals, even outside the topics dealt with strictly in class, in order to deal effectively inclusion in the school world.



Course unit content

Disciplinary and general education: perspectives on research
in education. Current research topics in International
Mathematics education, with particular attention to Secondary
and High School. The role of epistemology and history in
mathematics education research. Classic topics of disciplinary
research and learning difficulties in arithmetic, geometry,
algebra, analysis, probability and statistics. Knowledge,
skills, benchmarks for the development of key competences
for the citizenship (examples from national and international
development and assessment programs). General research topics,
with particular attention to the national research, for a
scientific approach to Mathematics education: Theory of situation
and Didactical Contract, Didactical transposition (Brousseau,
Sarrazy, D'Amore, Chevallard), Obstacles, Misconceptions,
Conceptual Change (Brousseau, Posner, Strike, Hewson & Gertzog), concept image and concept definition (Tall and Vinner), semiotic and
mathematics education (Frege, Peirce, Duval, Arzarello),
theory of figural concepts and mathematical intuition (Fischbein)
embodiment (Lakoff and Nunez), argumentation and proof
(Boero and Morselli), problem solving (Freudenthal,
Schoenfeld, D'Amore), the role of language in the
Learning of mathematics, formative and summative evaluation
(Bolondi), methodologies for teaching mathematics (laboratory,
math discussion, group work, technologies and software),
affect and beliefs (Zan, Di Martino), the role of examples
(Antonini), interdisciplinary approaches to mathematics and
Teacher, researcher, teacher-researcher: training paths and
possible professions in mathematics, school and research.

Full programme

Disciplinary teaching and general teaching: perspectives on research in the educational field. Current research topics in Mathematics Education at the international level, with particular attention to first and second level secondary schools: The role of epistemology and history in mathematics education research. Classical themes of disciplinary research and learning difficulties in arithmetic, geometry, algebra, analysis, probability and statistics. Knowledge, competence, reference frameworks for the development of key competences for the citizen (examples from national and international development and competence assessment programs). General research, with particular attention to research conducted in the national field, for a scientific approach to research in mathematics education: theory of situations, didactic contract, didactic transposition (Brousseau, Sarrazy, D'Amore, Chevallard), obstacles, errors , misconceptions (Brousseau, Posner), theory of figural concepts and intuition in mathematics (Fischbein), concept image and concept definition (Tall and Vinner), semiotics and didactics of mathematics (Duval, Mariotti and Bartolini Bussi, D'Amore, Godino and Font), argumentation and demonstration (Boero and Morselli), problem solving (Brousseau, Schoenfeld, D'Amore), the role of language in the learning of mathematics, formative and summative assessment (Bolondi), methodologies for the teaching of mathematics ( laboratory, mathematical discussion, group work, technologies and software), affects and convictions (Zan, Di Martino), interdisciplinarity between mathematics and physics.
Examples of teaching units on different themes and for different scholastic orders and evaluation tests.


The slides projected during the course in PDF format and all the material used during lessons and laboratory hours are made available to students and shared on the Elly platform. In addition to the shared material, the student can personally deepen some topics addressed during the course by referring to the following texts:
D’Amore, B. (1999). Elementi di Didattica della matematica. Bologna: Pitagora
Baccaglini-Frank, A., Di Martino, P., Natalini, R., Rosolini, G. (2017). Didattica della matematica. Mondadori.
Further teaching materials in English will be provided to students who will require them.

Teaching methods

The course has a weight of 6 CFU, which corresponds to 48 hours of lessons. The teaching activities will be conducted by giving lectures in the classroom. During the lectures the topics of the course are dealt with from a theoretical point of view and with detailed examples. In addition to the teaching methods presented so far, in-depth seminars are organized on the topics of the course. The slides and documents used to support the lessons will be uploaded at the beginning of the course on the Elly platform; To download the slides it is necessary to register for the online course. All shared material is considered an integral part of the teaching material. Non-attending students are reminded to check the available teaching materials and the indications provided by the teacher through the Elly platform, the only communication tool used for direct teacher / student contact. On this platform, on a weekly basis, the topics discussed in class are indicated, which will then form the contents index in preparation for the final exam.

Assessment methods and criteria

The assessment of learning includes an oral test based on questions related to the contents of the course, aimed at assessing understanding and development of skills indicated in the section of objectives. The test consists of four questions that can focus on research results and teaching theories, institutional references, transversal didactic topics addressed during the course. The vote is calculated by assigning to each question an evaluation from 0 to 30 and making the arithmetic average of the individual evaluations, with final rounding up; the test is passed if it reaches a score of at least 18 points. The praise is assigned in the case of reaching the maximum score on each item to which is added the mastery of the disciplinary lexicon.

Other information

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