Mathematics Education
A.Y. 2024/2025
Learning objectives
The main objective of the course is to introduce the theoretical and applicative aspects of the Didactics of mathematics, with particular attention to the context of secondary school. To this end, some results of national and international research in mathematics teaching, national indications and reference frameworks for the evaluation of skills, criteria underlying the design and implementation of educational activities in mathematics for secondary school, tools for analyzing difficulties and teaching strategies oriented to the enhancement of excellence or inclusion in mathematics will be presented. Students will develop skills in design of didactical activities and analysis of the criticalities of learning processes.
Expected learning outcomes
The students must be able to design teaching activities and evaluation tests for secondary school students, based on the results and theoretical frameworks of the research in mathematics teaching presented in the course and on the national indications for the curricula. They must also have developed analytical skills, in particular to be able to critically analyze mathematics textbooks and other teaching resources and analyze research data with some quantitative and qualitative techniques. At the same time, they will have to acquire communication skills, arguing their choices and exposing their knowledge with a good balance between precision in language and discussion of concrete examples.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
CHAPTER 1: RESEARCH IN MATHEMATICS TEACHING Disciplinary teaching and general didactics: different perspectives on research in the didactic field. Current research topics in Didactics of mathematics at an international level, with particular attention to secondary school of first and second degree. In particular, the following topics will be addressed. The role of epistemology and history in the research in mathematics teaching. Knowledge, competence, frameworks for the development of key competences for the citizen (examples from national and international programmes for the development and assessment of competence). Research strands that allow to adopt a scientific approach to research in mathematics teaching: theory of didactical situations, didactic contract, didactic transposition (Brousseau, Chevallard), obstacles, errors, misconceptions (Brousseau), theory of figural concepts and intuition in mathematics (Fischbein), concept image/concept definition (Tall and Vinner), semiotics and didactics of mathematics (Duval, Radford, Godino and Font), argumentation and proof (Boero and Morselli, Toulmin, Balacheff), problem solving (Brousseau, Schoenfeld), the role of language in the learning of mathematics, formative and summative evaluation (Bolondi), methodologies for teaching mathematics (laboratory, mathematical discussion, group work, technologies and software, method of varied research), affect and beliefs (Zan, Di Martino), interdisciplinarity between mathematics and physics.
CHAPTER 2: FROM RESEARCH TO CLASSROOM TEACHING
Examples of teaching units on different topics and for different school orders and assessment tests.
Analysis of students' protocols.
Analysis of textbooks.
CHAPTER 2: FROM RESEARCH TO CLASSROOM TEACHING
Examples of teaching units on different topics and for different school orders and assessment tests.
Analysis of students' protocols.
Analysis of textbooks.
Prerequisites for admission
The course has as prerequisites the basic knowledge of the courses of Analysis, Geometry, Physics, Probability and Statistics relevant for the teaching of mathematics in the middle and high school, as indicated in the guidelines of the national Italian curricula.
Teaching methods
The course has a weight of 6 CFU, which corresponds to 42 hours of lessons. The teaching activities will be conducted favoring lectures and group activities conducted in laboratory mode. During the lectures the topics of the course are addressed from a theoretical point of view and with detailed examples. The slides and documents used to support the lessons will be uploaded at the end of each lesson on the Ariel platform. All material shared on the platform is considered an integral part of the teaching material. Non-attending students are reminded to check the available teaching material and the indications provided by the teacher through the Ariel platform, a communication tool used for direct teacher / student contact in addition to e-mail communications. On this platform are indicated the topics addressed in class that will then constitute the index of the contents in view of the preparation for the final exam. There are also hours of exercise with an educational tutor for the design of educational activities and the analysis of textbooks and experimentation protocols, which are functional to the writing of the project and the preparation of the oral exam.
Teaching Resources
The slides projected during the course in PDF format and all the material used during the lessons (presentations, articles, evaluation tests, questionnaires and research protocols, examples of teaching units) are made available to students and shared on the Ariel platform. In addition to the shared material, the student can personally deepen some topics addressed during the course by referring to the following recommended texts:
D'Amore, B. (1999). Elementi di Didattica della matematica. Bologna: Pitagora
Baccaglini-Frank, A., Di Martino, P., Natalini, R., Rosolini, G. (2017). Didattica della matematica. Mondadori.
D'Amore, B. (1999). Elementi di Didattica della matematica. Bologna: Pitagora
Baccaglini-Frank, A., Di Martino, P., Natalini, R., Rosolini, G. (2017). Didattica della matematica. Mondadori.
Assessment methods and Criteria
The assessment of learning involves the delivery and discussion of a project (design of teaching activities / evaluation tests) and an oral test based on questions related to the contents of the course, aimed at evaluating understanding and the development of skills indicated in the objectives section. The oral exam consists of four questions, two related to the project - further than the presentation - and two others that can focus on research results and didactic theories, institutional references, transversal didactic themes addressed during the course. The grade is calculated by assigning to the presentation of the project delivered with the two questions and to each of the theoretical questions an evaluation from 0 to 30 and carrying out the arithmetic average of the three individual evaluations, with final rounding up. The test is passed if it reaches a score of at least 18 points. 30 cum laude is assigned in the case of reaching the maximum score on each item, to which is added the mastery of the disciplinary lexicon and a personal deepening and rielaboration.
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 6
Laboratories: 12 hours
Lessons: 35 hours
Lessons: 35 hours
Professors:
Bini Giulia Giovanna, Branchetti Laura
Shifts:
Educational website(s)
Professor(s)
Reception:
By appointment
Online, Microsoft Teams