28409 - Teaching of Mathematics 1

Academic Year 2023/2024

  • Docente: Andrea Maffia
  • Credits: 6
  • SSD: MAT/04
  • Language: Italian
  • 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: - possesses the main results of international research in mathematics education; - is able to manage concrete classroom situations in the teaching-learning process of mathematics in secondary school; - is able to use, manage, and critically criticize various software tools for teaching; - is able to use this knowledge to develop effective teaching materials to be tested in the classroom.

Course contents

AND METHODOLOGIES: National Indications for the first and second cycle secondary school: concept of competence, mathematical competence and European reference framework, purpose of teaching mathematics, structure and contents of the National Indications for the first cycle, the Profile of the student and the National Indications for the Licei and the Guidelines for Technical and Vocational Institutes. Educational software. Geogebra Institute and Geogebra platform. GeoGebra software: features, peculiarities (see also section on demonstration-argumentation).

ELEMENTS OF MATHEMATICS EDUCATION: The minimal didactic system: Chevallard's triangle; didactic transposition, social context and institutional constraints, the noosphere. Didactic contract: origin and main aspects; "captain's age" effect, need for formal justification and formal delegation clause, Topaze effect, situation theory and structure of an a-didactic situation, the devolution and belief paradox.

ARGUMENTATION AND DEMONSTRATION Haley-Hoyles research. The function of demonstration in mathematics and mathematics teaching. Understanding and convincing. Demonstration as object and process. Demonstration as an argumentative form. The social, temporal and spatial dimensions of demonstration. The definition of theorem as a triad. The stages of producing a theorem and students' difficulties. Enunciation and demonstration as process and as product. Cognitive unit. Geogebra and the beginnings of demonstration. Basic features of Geogebra and their educational function. Difference between artifact and tool. The theory of semiotic mediation. The microworld. Vision and visualization.

DOING MATHEMATICS TODAY: ELEMENTS OF COMMUNICATING MATHEMATICS. What mathematics is NOT; how the public idea of mathematics is formed; prejudices; social danger of mathematical illiteracy; the professions of the mathematician. Story telling. Careful reading of Benvenuti-Natalini article in bibliography (attached to slides) recommended. Mention of the gender problem.

INTRODUCTION TO LABORATORY TEACHING. What is a laboratory; elements of a laboratory teaching; a new mode?; before the laboratory: the training of the teacher/entertainer; during the laboratory: the role of rigor; during the laboratory: the role of error; during the laboratory: the role of discussion; after the laboratory: evaluation. Careful reading of the Dedò-Di Sieno article in the bibliography (attached to the slides) is recommended.

THEORIES OF LEARNING/TEACHING IN MATHEMATICS. Macro theories of learning: behaviorism, cognitivism, constructivism; consequences of the various macro theories on teaching models; personality theories: emotional intelligence, multiple intelligences, cooperative learning.

THE ROLE OF AFFECTIVE FACTORS IN MATHEMATICS TEACHING. Responding to negative emotions; Beyond the purely cognitive; need for new observational tools; Di Martino study (autobiographical phrases and themes); the central role of the teacher; Di Paola study (on future teachers); correct answer compromise; from reproductive thinking to productive thinking; rethinking the role of time and error.


  • 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

Lecture, critical analysis of texts and articles, individual or small group workshop activities, cooperative learning and microteaching, co-design, collective discussion and peer-to-peer evaluation.

Assessment methods

The final examination consists of a project and an oral test.


The topic and how to carry out the project will be clarified in class and posted on the Virtual Platform [https://virtuale.unibo.it/] of teaching.

Oral test

Part I: presentation and discussion from a teaching perspective of the realized project.
Part II: "disciplinary" and "didactic" discussion of concepts or topics covered during the course. This part will assess the student's level of understanding of the concepts and themes covered in the course; the student's ability to analyze such a theme or concept from a didactic point of view, knowing how to recognize its sensitive points for understanding; and the student's ability to place the treatment of such a theme or concept in a broad educational and cultural perspective and within a didactic path.

The final outcome will take into account in equal parts the project (implementation, presentation and discussion) and the "disciplinary" and "didactic" oral discussion of concepts and themes covered during the course.

Registration is required on the digital platform Almaesami

Teaching tools

All materials will be published on the digital platform Virtuale [https://virtuale.unibo.it/]

Office hours

See the website of Andrea Maffia