68016 - Didactics of Mathematics with Elements of Statistics

Learning outcomes

At the end of the course, the student: - knows the main contributions of research in Didactics of Mathematics related to some of its founding and privileged themes (problem solving, difficulties in mathematics, mathematics and language, ...) and some research contributions in the 'neighboring' disciplines (psychology, cultural anthropology, neuroscience, ... ) that have more directly investigated the problems of mathematics teaching/learning; - can make use of the knowledge acquired to formulate proposals for educational intervention or to elaborate, in the light of the outcomes of research, working hypotheses and/or investigation/research in classroom situations; - is able to make use of the appropriate tools of observation of teaching activities, proposing interpretative hypotheses of any difficulties detected and formulating compensatory intervention plans aimed at overcoming the critical areas in the area of mathematics teaching/learning; - knows how to propose reflections pertinent to the activities observed/performed by placing them in relation to his or her educational path and knows how to communicate them by making use of specific professional language proper to the teaching of mathematics and the directly 'bordering' disciplines; - moves with good mastery and critical attention to the tools available to the teaching profession: bibliographical, technical, computer science; - knows the basic concepts of descriptive statistics and understands the meaning and value of its tools and methods; - is able to apply methods and tools of statistics finalizing them to the study of phenomena through appropriate activities of organization, synthesis, presentation, interpretation and critical analysis of data; - is able to use said methods and tools to foster, from a didactic point of view and in relation to kindergarten and elementary school pupils, an initial cognitive and critical approach to statistics by implementing simple investigation projects that, starting from data collection, lead, in succession, to their organization, representation, processing, and interpretation.

Course contents

Part one: theory recalls
Ø Indicazioni Nazionali for the first cycle: what they tell us about mathematics.
Ø Introduction to probability calculation: the difference between certain and probable, chance and its quantification. Compound events and tree diagrams.
Ø Introduction to statistics: methods of data collection, organization, and presentation. Frequencies, position indices, dispersion indices.
Ø Mathematical modeling: the quantitative description of the world around us.
Ø Analysis of teaching experiences, textbooks, and questions from Invalsi tests.
For the purpose of the exam, it is also advisable to take a look at the materials:
Ø from https://www.problemi.xyz/
Ø from the M@t.abel project, available online at http://www.scuolavalore.indire.it/superguida/matabel/

Readings/Bibliography

In addition to handouts, slides, materials provided by the lecturer, the following texts are recommended.
For a general reference to all topics in mathematics education:
Bolondi, Fandino Pinilla, Metodi e strumenti per l’insegnamento e l’apprendimento della matematica, EdiSES 2012

For personal insights (and therefore NOT required for the exam).

Castelnuovo, Pentole, ombre, formiche, Utet 2017
Castelnuovo, Didattica della matematica, Utet 2017
Cazzola, Matematica per scienze della formazione primaria, Carocci 2017
D’Amore, Elementi di didattica della matematica, Pitagora ed.
Dedò, Di Sieno, Laboratorio di matematica: una sintesi di contenuti e metodologie

Teaching methods

Lectures+laboratory

Assessment methods

written examination

Teaching tools

Materials made available on Virtuale

Office hours

See the website of Alessandro Gambini