Learning objectives
At the end of the course, the student should have completed the following skills:
To interpret, exemplifying and comparing frequent mistakes and difficulties among students in the various fields of mathematics
To summarize, for the most part, the most common theories developed in mathematics education research
To organize knowledge about basic mathematics, mathematics teaching and learning and epistemology, in order to adequately design classroom teaching activities in an innovative but realistic way
To criticize and produce short learning units and assessment, formative and summative tests, scholastic or and standardized
Understand mathematics education articles and set up a simple empirical research, even in view of any thesis work
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
physics.
Teacher, researcher, teacher-researcher: training paths and
possible professions in mathematics, school and research.
Teaching methods
Frontal lectures, groupworks, workshops and presentations will
be alternated to promote conceptual understanding but also
communicative skills and to give the student a personal point
of view about the teaching profession and the role of the
researcher , even respectful of the constraints given by disciplinary correctness and knowledge of the fundamental results in mathematics education research.
Assessment methods and criteria
The evaluation will take place on the basis of a project and an oral exam, in which the student will have to show that he knows basic mathematics and mathematics education themes and has developed a critical, thoughtful and innovative attitude towards teaching and learning mathematics
in the secondary school.
