The course offers an analysis of the main models of mathematics teaching-learning and the main theoretical frameworks that provide classical references for research in mathematics education. Specifically, students should achieve the following objectives: - Awareness of epistemological principles, research methodologies and research questions that characterize theories in mathematics education - Know how to design teaching activities, based on one or more theories in mathematics education for all the domains of the National Indications. - Know how to analyze students’ protocols based on the theoretical frameworks discussed in class to identify the cognitive processes underlying the teaching-learning of mathematics, recognize the causes of students' difficulties and identify possible interventions to overcome them. - Analyze, in the light of one or more theories, textbooks, artifacts, educational software, etc. to identify their potential and limitations. - Know how to rigorously use terminology specific to mathematics education in applications of theories in research contexts and teaching-learning practices.
Course Prerequisites
Mathematical knowledge and compentencies developed in the "laurea triennale" in mathematics. The course is not recommended for students of the "laurea triennale".
Teaching Methods
Lectures and general discussions, group work and discussions, case studies, project work, in-depth seminars. For some lectures, students will be required to read in advance the material that will then be discussed in class. The course requires regular attendance.
Assessment Methods
Oral test. The test consists of an interview designed to ascertain knowledge of the topics covered in the course. This test is aimed at verifying the degree of understanding of the theoretical topics carried out in class, clarity of exposition but also the ability to apply these notions in concrete situations. For this reason, the student will be required to have a substantial understanding of all the theory presented, which can be verified both through questions on specific topics and through the proposal of problems, analysis of protocols, and didactic design concerning the course topics; the students will have recourse to theoretical and methodological tools introduced in class. The questions will be articulated on variable difficulty to establish the degree of depth in the acquisition of these skills The formulation of the mark will be obtained by considering the overall breadth and depth of learning, as well as the clarity of the exposition and the skills demonstrated in dealing with the different situations concerning the teaching-learning of mathematics proposed during the test.
Texts
Articles from scientific journals, chapters from textbooks, and other working materials provided by the lecturer.
Contents
Teaching-learning Mathematics models: - transmissive program - the progressive program - the cultural-historical approach. Moreover, we will analyse the main tenets of theoretical frameworks which provide the classical conceptual background for research in Mathematics Education and investigate how some of the ideas developed within these theories have informed research studies in Mathematics Education. More specifically, we will focus on: - Piaget's studies on cognitive development, mental models and mental images, misconceptions, frame and script - Fischbein’s studies on intuition - Vygotsky's studies about higher psychic functions - the Theory of Semiotic Mediation - the Theory of Objectification - Duval's semio-cognitive approach - the Theory of Didactical Situations - Tall and Vinner concept image and concept definition
