28409 - Teaching of Mathematics 1

Academic Year 2021/2022

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Physics (cod. 9245)

    Also valid for Second cycle degree programme (LM) in Mathematics (cod. 5827)

Learning outcomes

At the end of the course, the student: - knows the main results of international research in didactics of mathematics; - is able to handle concrete learning situations in the teaching-learning process of math in secondary school; - is able to use, manage, criticize several different tools for didactics; - is able to use this knowledge to develop effective teaching materials that can be experienced in the classroom.

Course contents

The course integrates a theoretical part, of critical analysis of the methodologies developed in math education research and in the history of mathematics, with laboratory activities, designing and developing mathematics teaching methodologies for building activities and, more generally, a mathematics curriculum consistent with the goals set by national guidelines.

The first part has as the aim to contextualize the teaching-learning process both from the institutional and the research point of view and point out the complexity and the various facets of this process, highlighting the the role of the teacher, conceptual, epistemological, linguistic and didactic nodes in teaching and learning mathematics. Furthermore the theoretical framework will aim to provide reading lenses of the disciplinary topics that will be studied in depth in the laboratories.
In particular, the following issues will be pursued:

1) theories of learning / teaching in mathematics: the common sense model; macroterories of learning: behaviorism, cognitivism, constructivism; consequences of the various macro-stories on didactic models; personality theories: emotional intelligence, multiple intelligences, cooperative learning;

2) the role of affective factors in the mathematics teaching/learning process: finding negative emotions; beyond the purely cognitive; need for new observation tools; the central role of the teacher; compromise of correct answers; from reproductive thinking to productive thought; rethinking the role of time and error;

3) institutional context: National Guidelines. This analysis wats to combine the skills and contents there described with those acquired in the first level degree;

4) basics of didactics of mathematics: the didactic triangle, the didactic contracts and the theory of learning situations;

5) study of teaching processes and math learning using technology, with particular attention to new digital technologies, analyzing the potential and criticality of the use of technological tools for teaching and learning math.

1) institutional context: Invalsi, OECD-Pisa framework. This analysis wats to combine the skills and contents there described with those acquired in the first level degree;

2) basics of didactics of mathematics: images and models, conflicts and misconceptions, semiotics and the theory of representations, components of mathematical learning;

3) mathematical thinking, computational thinking and problem solving: mathematical competence and problem solving; the definition of problem; Gestalt studies on problem solving: perception as a structured totality, studies on visual perception, interest in productive thinking, studies on chimpanzees, the definition of functional fixity, insight and productive/binding anxiety; from studies on chimpanzees to the definition of the resolution phases of a problem, how learning works; problem vs exercise; problem solving in the classroom; school problem vs real problem; the narrative dimension; the context-demand link; indications for the formulation of a problem; rethink the problem solving activity; why do problem solving; mathematical thinking and computational thinking; keywords of computational thinking; computational thinking in the school; the game of imitation;

4) mathematics education and evolutionary dyscalculia: the development of numerical skills (sense of numbers, counting development, subitizing); evolutionary dyscalculia (definition, characteristics, the dyscalculic brain, comorbidity, genetics); the psychological effects; the diagnosis; rehabilitation; didactics; compensatory tools and dispensatory measures;

5) elements of communication of mathematics: what mathematics is NOT; how the public idea of mathematics is formed; prejudices; social danger of mathematical illiteracy; the trades of the mathematician;

6) introduction to publishing - narrative and scholastic: narrative/non-fiction versus school; what a book is: physical and formal structure; outline of typography: characters, styles, spaces, layout; editorial rules; school publishing: overview of the various jobs opened for a mathematician in a publishing house.

In laboratory activities, after an introduztion to laboratory tecniques, some "disciplinary" path will be described in a vertical approach. The analysis will be dealt with in the design and development of teaching and learning activities of mathematics mainly focused on the use of new technologies. This will also give the opportunity to experience firsthand some teaching methods and to analyze some textbooks. Among the possible laboratories: non-euclidean geometries, mathematics and arts, geometry of transformations, symbol sense and algebraic thought, concept of function, role of the proofs, probabilistic thinking.

The detailed and complete teaching program will be published on Virtuale at the end of the lessons.


During the course, teaching material will be provided through the e-learning platform Virtuale. The material consist in slides / presentations, research articles, digital textbooks, work materials (tutorials, group work papers, research questionnaires, student protocols, ...).


  • 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.
  • Benvenuti, Natalini, Comunicare la matematica: chi, come, dove, quando e, soprattutto, perché?!, Rivista Umi - Matematica, cultura e società, agosto 2017.
  • Castelnuovo, Pentole, ombre, formiche, Utet 2017.
  • Castelnuovo, Didattica della matematica, Utet 2017.
  • D'Amore, Elementi di didattica della matematica, Pitagora 1999.
  • Dedò, Alla ricerca della geometria perduta 1, Alice e Bob 46 2016.
  • Dedò, Di Sieno, Laboratorio di matematica: una sintesi di contenuti e metodologie, https://arxiv.org/pdf/1211.2159.pdf
  • Di Sieno, Alla ricerca della geometria perduta 2, Alice e Bob 53, 2018.
  • Israel, Millan Gasca, Pensare in matematica, Zanichelli 2015.

Teaching methods

The course consists of: ex-cathedra lectures, critical analysis of texts and articles, laboratories or small group activities, cooperative learning and microteaching activities, co-design, collective discussion and peer-to-peer evaluation.

Assessment methods

Realization of two projects (one for each module) and a oral exam.


Implementation of two projects (one for each module). Subject and tools for projects will be described during the course, and published on the IOL platform of the course.

Oral exam

First part: presentation of the projects carried out and discussion over them from a didactical point of view.

Second part: "Disciplinary" and "didactical" oral discussion on concepts and topics covered during the course. In this part the following abilities will be evaluated: the level of understanding the concepts and themes discussed in the course, the ability to analyze such a theme or concept from a didactical point of view, recognizing delicate points for understanding; the ability to place such a topic or concept in a broad educational and cultural perspective and within a learning path.

The final mark will take into account in equal parts the project (realization, presentation and discussion) and the oral discussion "disciplinary" and "didactical" on concepts and topics covered during the course.


It is compulsory to register on Almaesami.

Teaching tools

All the materials will be posted on Virtuale.

Office hours

See the website of Alessia Cattabriga


Quality education

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.