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 their previous and current knowledge; - knows how to control and frame the evolution of basic mathematical knowledge from an epistemological point of view; - is 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 educational interventions solidly grounded 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 problematic features; - knows how to propose, through a formally correct exposition, the mathematical contents addressed and 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 experts; - 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

Mathematical literacy and its components; affective factors in the process of teaching/learning mathematics; didactical contract; a-didactical situations.


Mathematical laboratory; fields of experience; mistakes and errors in mathematics; mathematical discussion; the mathematics teachers as mediator; the role of artifacts.


The development of number sense and the four basic arithmetical operations; intuitive models in the case of operations.

Concept image and concept definition for geometrical shapes; figural  concepts.

Early algebra as teaching approach to arithmetic; learning the meaning of the equivalence symbol.

Readings/Bibliography

The course is mainly based on the following books:

• Sabena, Ferri, Martignone, Robotti, Insegnare e apprendere matematica nella scuola dell'infanzia e primaria, Mondadori Università 2019
• Baccaglini Frank, Di Martino, Natalini, Rosolini, Didattica della matematica, Mondadori Università 2018
• Castellini, Giberti, Lemmo, Maffia, Attivazione: Laboratori di matematica per la scuola del primo ciclo, Libreria Univeristaria 2023

Additional material is provided via the e-learning platform Virtuale. Accessing the platform is necessary.

Teaching methods

Lectures; workshops; case studies in couples or small groups; collective discussion about problems

Assessment methods

The final written exam consists of 20 multiple-choice questions and one open-ended question. The test duration is 1h30.


Each multiple-choice question contributes 1 point to the final score; each open-ended question contributes 10 points.


Each correct multiple-choice question is worth one point, and there is no penalty for an incorrect answer. At least 12 out of 20 closed-ended questions must be answered correctly for the exam to be considered satisfactory overall.


The evaluation of the open-ended question is based primarily on the quality of the argument and the relevance and accuracy of the references to the course content, as well as on the clarity of the presentation.

Teaching tools

The slides used in classes and other supplementary materials are provided via the platform "Virtuale".

Office hours

See the website of Andrea Maffia