The course addresses main issues involved in the teaching and learning of mathematics from a psycho-pedagogical point of view. The course introduces the most important "theories" giving a general overview of the research in mathematics education. The course also proposes issues studied in mathematics education with respect to specific content for secondary school.
The topics addressed are contained in various books and research papers that are given to the students by the instructor. The following titles are amongst the proposed books:
- Bartolini Bussi, M. & Maschietto, M. (2006) Macchine Matematiche: dalla storia alla scuola. Springer
- Brousseau, G. (2008) Ingegneria didattica ed Epistemologia della Matematica. Pitagora Editrice Bologna.
- Castelnuovo, E. (2008). L’Officina mat3matica. Edizioni la meridiana.
- Mariotti, M. (2005). La geometria in classe. Riflessioni sull’insegnamento e apprendimento della geometria. Pitagora Editrice.
- Sfard, A. (2009). Psicologia del pensiero matematico. Erickson.
- Zan, R. (2007). Difficoltà in Matematica Osservare, Intepretare, Intervenire. Springer.
Learning Objectives
The competencies that the course aims to develop in its participants are to:
• Read and understand research papers in mathematics education
• Read and use secondary school textbooks in a critical manner;
• Learn to consciously choose digital learning environments
• Analyze whether they are appropriate for the mediation of particular mathematical concepts,
• Be able to design activities within digital learning environments,
• Be able to use dynamic geometry environments;
• Analyze students' activities through video analysis and/or analysis of transcripts.
Prerequisites
none
Teaching Methods
in class discussion, critical reading of papers and book chapters, traditional teacher-led classes, analysis of students' protocols
Type of Assessment
Students' final grade is given by the following items:
30% Final hand in of a "diary" held during the course;
30% Critical reading of (and in-class participation to) discussions on the proposed papers;
30% Critical reading and presentation of a book amongst the titles proposed;
10% Analysis of the didactical potential of a software or analysis of a secondary school textbook.
Course program
The main themes of the course are the following:
• Theories:
• Piaget and constructivism in mathematics education;
• The Theory of Didactical Situations;
• ygotsky and the socio-cultural approach. Artifacts and knowledge. The notion of Semiotic Mediation;
• Sfard and the Theory of “commognition”;
“Reppresentations” and “semiotic registers”;
• Mathematizing the idea of space
• Figural concepts,
• Dynamic geometry as a microworld and tool of semiotic mediation,
• Visualization;
Algebra: Algebra as a symbolic system;
• ome studies on the notion of limit to introduce “concept image” and “concept definition”;
• Argumentation and proof (in geometry and in algebra);
• Mathematical learning difficulties;
• Assessment and INVALSI.