31620 - Didactics of Mathematics 2

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

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) 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) 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;


5) introduction to publishing: overview of the various jobs opened for a mathematician in a publishing house.

In laboratory activities, some "disciplinary" path (also in agreement with the students) 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, role of the proofs, probabilistic thinking.

Readings/Bibliography

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

 

SUGGESTED READINGS

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
Israel, Millan Gasca, Pensare in matematica, Zanichelli 2015

Dedò, Alla ricerca della geometria perduta 1, Alice e Bob 46 (2016)
Di Sieno, Alla ricerca della geometria perduta 2, Alice e Bob 53 (2018)
Dedò, Di Sieno, Laboratorio di matematica: una sintesi di contenuti e metodologie

Castelnuovo, Pentole, ombre, formiche, Utet 2017
Castelnuovo, Didattica della matematica, Utet 2017

Benvenuti, Natalini, Comunicare la matematica: chi, come, dove, quando e, soprattutto, perché?!, Rivista Umi - Matematica, cultura e società, agosto 2017.

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 projects (two group ones and an individual one) and one oral exam.

Projects: implementation of three projects, an individual one and two group ones. Subject and tools for projects will be described during the course, once laboratory topics have been fixed.

Oral exam

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

Second part: written test examination. "Disciplinary" and "didactical" discussion on concepts and topics dealt with 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.

Office hours

See the website of Silvia Benvenuti