68005 - Foundations of Mathematics and Mathematics Teaching

Learning outcomes

At the end of the course the student: - has a thorough and critical knowledge of the basic mathematical contents; - has achieved, in relation to mathematics, a willingness to flexibly integrate his previous and current knowledge; - knows how to control and frame the evolution of basic mathematical knowledge from an epistemological point of view; - will be able to grasp and evaluate the elements of continuity / discontinuity characterizing the mathematical arguments addressed by seeking / recognizing, on the level of reasoning, correctness or fallacy; - will know the emerging themes of the current national and international debate on mathematics education and will be able to outline its recent historical genesis; - knows how to connect the mathematical knowledge acquired with the teaching contents of the discipline proposed in kindergarten and primary school in order to formulate hypotheses of didactic intervention solidly founded from a conceptual point of view; - is able to analyze and interpret some of the aspects of teaching in relation to the teaching / learning of mathematics by detecting any problematic features; - knows how to propose, through a formally correct exposition, the mathematical contents addressed and on them is able to formulate, at a first level, proposals for didactic transposition suitable for pupils of kindergarten or primary school; - knows how to communicate problems, ideas, issues concerning the teaching of mathematics within the peer group or to expert subjects; - knows how to grasp the problems connected with teaching theory and practice in relation to simulated classroom situations, through 'case studies', or experienced through laboratory or internship activities.

Course contents

 Foundations of mathematics and elementary mathematics seen from a superior point of view.

 Mathematics today: elements of maths communication

 Introduction to laboratorial teaching

 A first example of a laboratory: Football Maths 

 Theories of learning/teaching in mathematics

 Main theoretical constructs useful to analyze learning processes

 National Guidelines and main national and international standardized surveys.

 The role of affective factors in the mathematics teaching / learning process

 Mathematical thinking, computational thinking and problem solving

 Errors and difficulties in mathematics


The laboratories attached to the course include the use of ad hoc teaching materials and the preparation of a report. Each laboratory will provide video analysis of teaching situations of Primary School and Nursery School, with the help of theoretical tools studied in depth during the course.

Readings/Bibliography

In addition to slides and materials made available by the teacher, the following reference texts are recommended:

Baccaglini Frank, Di Martino, Natalini, Rosolini, Didattica della matematica, Mondadori Università (2018)

Bolondi, Fandino Pinilla, Metodi e strumenti per l’insegnamento e l’apprendimento della matematica, EdiSES, 2012

Castelnuovo, Pentole, ombre, formiche, Utet 2017

Castelnuovo, Didattica della matematica, Utet 2017

Cazzola, Elementi di didattica della matematica, Pitagora ed.

D’Amore, Matematica per scienze della formazione primaria, Carocci 2017

Dedò, Di Sieno, Laboratorio di matematica: una sintesi di contenuti e metodologie

Israel, Millan Gasca, Pensare in matematica, Zanichelli 2015

Teaching methods

Frontal lectures and laboratory sessions. Group work on case studies.

Assessment methods

Written test

Teaching tools

Online documentation

Office hours

See the website of Silvia Benvenuti