The course is the last course devoted to mathematics and its teaching and learning.
Issues for reflection "on" mathematics, from cognitive, didactic, and historical-epistemological points of view, are proposed and analysed with the aim of broadening the knowledge and vision of mathematics, offering tools for the analysis of learning processes and for the construction of didactic activities in the first cycle school.
Course Content - Last names M-Z
The course is the last course devoted to mathematics and its teaching and learning.
Issues for reflection "on" mathematics, from cognitive, didactic, and historical-epistemological points of view, are proposed and analysed with the aim of broadening the knowledge and vision of mathematics, offering tools for the analysis of learning processes and for the construction of didactic activities in the first cycle school.
Donaldson, M. Come ragionano i bambini. Springer 2010.
Sabena, C., Ferri, F, Martignone, F, Robotti, E. Insegnare e apprendere la matematica nella scuola dell’infanzia e primaria. Mondadori Università 2019.
Zan, R. I problemi di matematica, Carocci 2016.
Zan, R. Difficoltà in matematica. Osservare, interpretare, intervenire. Springer 2007.
Materials provided by the teachers (during the course on Moodle Platform).
- Donaldson, M. Come ragionano i bambini. Springer 2010.
- Sabena, C., Ferri, F, Martignone, F, Robotti, E. Insegnare e apprendere la matematica nella scuola dell’infanzia e primaria. Mondadori Università 2019.
- Zan, R. I problemi di matematica, Carocci 2016.
- Zan, R. Difficoltà in matematica. Osservare, interpretare, intervenire. Springer 2007.
- Materials provided by the teachers (during the course on Moodle Platform).
Learning Objectives - Last names A-L
Concerning the subjects addressed in the course, students must show:
- to interpret correctly the emerging innovation processes in education
- to interpret teaching-learning processes in Mathematics and frame them in their epistemological and didactic context.
- developing an adequate, original and creative mathematical thinking regarding the topics of the course and in particular in view of the effects in education
- understanding some results of current research in mathematics education relating to the development of basic mathematical concepts
- applying some results of current research in mathematics education to observe and interpret students’ processes, errors and difficulties, and to design teaching activities
- understanding, producing, comparing and evaluating argumentation at different levels of formalization
- understanding the value of generating argumentations, conjecturing, posing, and solving problems
- to possess communicative skills, by using correctly mathematical language, both in peer-to-peer relationships and in simulating teaching-learning situations;
- to show good skills to learn autonomously and personally and to deepen the subjects developed in the course
Learning Objectives - Last names M-Z
Concerning the subjects addressed in the course, students must show:
- to interpret correctly the emerging innovation processes in education
- to interpret teaching-learning processes in Mathematics and frame them in their epistemological and didactic context
- developing an adequate, original and creative mathematical thinking regarding the topics of the course and in particular in view of the effects in education
- understanding some results of current research in mathematics education relating to the development of basic mathematical concepts
- applying some results of current research in mathematics education to observe and interpret students’ processes, errors and difficulties, and to design teaching activities
- understanding, producing, comparing and evaluating argumentation at different levels of formalization
- understanding the value of generating argumentations, conjecturing, posing, and solving problems
- to possess communicative skills, by using correctly mathematical language, both in peer-to-peer relationships and in simulating teaching-learning situations
- to show good skills to learn autonomously and personally and to deepen the subjects developed in the course.
Prerequisites - Last names A-L
Fundamental prerequisites are both basic knowledge and algorithmic skills, useful to deeply understand the issues analysed in the course, and developed in:
- the mathematics courses for basic education planned for the first and second year in the Degree in Primary teacher education
- any pre-academic teaching, which is supposed to be followed with seriousness and commitment.
Strong motivations towards the teaching, a positive attitude toward mathematics and the awareness of the importance of mathematical education in training to a conscious and active citizenship are indispensable.
Prerequisites - Last names M-Z
Fundamental prerequisites are both basic knowledge and algorithmic skills, useful to deeply understand the issues analysed in the course, and developed in:
- the mathematics courses for basic education planned for the first and second year in the Degree in Primary teacher education
- any pre-academic teaching, which is supposed to be followed with seriousness and commitment.
Strong motivations towards the teaching, a positive attitude toward mathematics and the awareness of the importance of mathematical education in training to a conscious and active citizenship are indispensable.
Teaching Methods - Last names A-L
Lecture-style instruction, participated lessons, teacher-led discussions.
Through the student reception, topics chosen by students will be discussed and deepen in individual way and any question can be posed to the teacher.
The course is also connected to a mathematics laboratory with mandatory attendance.
Teaching Methods - Last names M-Z
Lecture-style instruction, participated lessons, teacher-led discussions.
Through the student reception, topics chosen by students will be discussed and deepen in individual way and any question can be posed to the teacher.
The course is also connected to a mathematics laboratory with compulsory attendance.
Further information - Last names A-L
Although not mandatory, class attendance is strongly recommended, because of the relevance of relational aspects in teaching-learning processes both with other students and with the teacher.
Teaching takes advantage of MOODLE platform, which is obligatory for all students and can be particularly useful for students having motivated difficulties in attending classes with regularity.
During the course, the student reception is encouraged for any discussion on mathematical topics and for any individual in-depth analysis
Further information - Last names M-Z
Although not mandatory, class attendance is strongly recommended, because of the relevance of relational aspects in teaching-learning processes both with other students and with the teacher.
Teaching takes advantage of MOODLE platform, which is obligatory for all students and can be particularly useful for students having motivated difficulties in attending classes with regularity.
During the course, the student reception is encouraged for any discussion on mathematical topics and for any individual in-depth analysis.
Type of Assessment - Last names A-L
Written exam, followed by an oral exam.
Although it is impossible to make a strict separation between the two types, it is possible to state that subjects of particular examination of the written exam are all the skills required between the objectives with particular regard to the basic knowledge of the topics addressed and those of the type operational and problem-solving applications and modeling of problem situations, while the subject of particular examination of the oral examination is all the skills required between the objectives with particular regard to linguistic and communicative skills and the ability to discuss the topics in a critical and informed manner.
In order to pass the exam, it is necessary at all stages to demonstrate to possess all basic elementary knowledge which are taught in primary school.
Type of Assessment - Last names M-Z
Written exam, followed by an oral exam.
Although it is impossible to make a strict separation between the two types, it is possible to state that subjects of particular examination of the written exam are all the skills required between the objectives with particular regard to the basic knowledge of the topics addressed and those of the type operational and problem-solving applications and modeling of problem situations, while the subject of particular examination of the oral examination is all the skills required between the objectives with particular regard to linguistic and communicative skills and the ability to discuss the topics in a critical and informed manner.
In order to pass the exam, it is necessary at all stages to demonstrate to possess all basic elementary knowledge which are taught in primary school.
Course program - Last names A-L
History of Mathematics:
- Examples from history of mathematics of positional and non-positional systems and various multiplication algorithms (Egyptian multiplication, Lattice or gelosia multiplication, criss-cross multiplication). Egyptian division
- Leonardo Pisano, the Liber Abbaci and the spread of the Hindu-Arabic numeral system through the Latin West during the 13th century. The flourishing of abacus schools and abacus treatises.
- Early calculating instruments: Genaille-Lucas rulers and Napier bones.
Didactic of Mathematics:
- The notion of didactical contract
- The affective factors (beliefs, attitude, emotion) in mathematics learning and teaching
- Conceptual and procedural knowledge
- The mathematical laboratory.
- The theory of semiotic mediation and the use of artefacts
- Figural concepts and the Van Hiele Model for the learning and teaching of geometry
- The principles of counting (Gelman and Gallistel).
- The argumentation in mathematics: conjecturing, producing argumentation, proving
- Different models of mathematical problems: "Problemi a righe" versus "Problemi a quadretti", "Variation problems"
- The INVALSI test and problems taken from "Rally matematico transalpino"
Course program - Last names M-Z
History of Mathematics:
- Examples from history of mathematics of positional and non-positional systems and various multiplication algorithms (Egyptian multiplication, Lattice or gelosia multiplication, criss-cross multiplication). Egyptian division
- Leonardo Pisano, the Liber Abbaci and the spread of the Hindu-Arabic numeral system through the Latin West during the 13th century. The flourishing of abacus schools and abacus treatises.
- Early calculating instruments: Genaille-Lucas rulers and Napier bones.
Didactic of Mathematics:
- The notion of didactical contract
- The affective factors (beliefs, attitude, emotion) in mathematics learning and teaching
- Conceptual and procedural knowledge
- The mathematical laboratory.
- The theory of semiotic mediation and the use of artefacts
- Figural concepts and the Van Hiele Model for the learning and teaching of geometry
- The principles of counting (Gelman and Gallistel).
- The argumentation in mathematics: conjecturing, producing argumentation, proving
- Different models of mathematical problems: "Problemi a righe" versus "Problemi a quadretti", "Variation problems"
- The INVALSI test and problems taken from "Rally matematico transalpino".
Sustainable Development Goals 2030 - Last names A-L