# TEACHING MATHEMATICS A

## Learning outcomes of the course unit

At the end of the course, the student should have completed the following skills:

To interpret, exemplifying and comparing frequent mistakes and difficulties among students in the various fields of mathematics

To summarize, for the most part, the most common theories developed in mathematics education research

To organize knowledge about basic mathematics, mathematics teaching and learning and epistemology, in order to adequately design classroom teaching activities in an innovative but realistic way

To criticize and produce short learning units and assessment, formative and summative tests, scholastic or and standardized

Understand mathematics education articles and set up a simple empirical research, even in view of any thesis work.

At the end of the course, the student should have completed the following skills:

To interpret, exemplifying and comparing frequent mistakes and difficulties among students in the various fields of mathematics

To summarize, for the most part, the most common theories developed in mathematics education research

To organize knowledge about basic mathematics, mathematics teaching and learning and epistemology, in order to adequately design classroom teaching activities in an innovative but realistic way

To criticize and produce short learning units and assessment, formative and summative tests, scholastic or and standardized

Understand mathematics education articles and set up a simple empirical research, even in view of any thesis work

## Course contents summary

Disciplinary and general education: perspectives on research

in education. Current research topics in International

Mathematics education, with particular attention to Secondary

and High School. The role of epistemology and history in

mathematics education research. Classic topics of disciplinary

research and learning difficulties in arithmetic, geometry,

algebra, analysis, probability and statistics. Knowledge,

skills, benchmarks for the development of key competences

for the citizenship (examples from national and international

development and assessment programs). General research topics,

with particular attention to the national research, for a

scientific approach to Mathematics education: Theory of situation

and Didactical Contract, Didactical transposition (Brousseau,

Sarrazy, D'Amore, Chevallard), Obstacles, Misconceptions,

Conceptual Change (Brousseau, Posner, Strike, Hewson & Gertzog), concept image and concept definition (Tall and Vinner), semiotic and

mathematics education (Frege, Peirce, Duval, Arzarello),

theory of figural concepts and mathematical intuition (Fischbein)

embodiment (Lakoff and Nunez), argumentation and proof

(Boero and Morselli), problem solving (Freudenthal,

Schoenfeld, D'Amore), the role of language in the Learning of mathematics, formative and summative evaluation

(Bolondi), methodologies for teaching mathematics (laboratory,

math discussion, group work, technologies and software),

affect and beliefs (Zan, Di Martino), the role of examples

(Antonini), interdisciplinary approaches to mathematics and physics.

Teacher, researcher, teacher-researcher: training paths and possible professions in mathematics, school and research.

Disciplinary and general education: perspectives on research

in education. Current research topics in International

Mathematics education, with particular attention to Secondary

and High School. The role of epistemology and history in

mathematics education research. Classic topics of disciplinary

research and learning difficulties in arithmetic, geometry,

algebra, analysis, probability and statistics. Knowledge,

skills, benchmarks for the development of key competences

for the citizenship (examples from national and international

development and assessment programs). General research topics,

with particular attention to the national research, for a

scientific approach to Mathematics education: Theory of situation

and Didactical Contract, Didactical transposition (Brousseau,

Sarrazy, D'Amore, Chevallard), Obstacles, Misconceptions,

Conceptual Change (Brousseau, Posner, Strike, Hewson & Gertzog), concept image and concept definition (Tall and Vinner), semiotic and

mathematics education (Frege, Peirce, Duval, Arzarello),

theory of figural concepts and mathematical intuition (Fischbein)

embodiment (Lakoff and Nunez), argumentation and proof

(Boero and Morselli), problem solving (Freudenthal,

Schoenfeld, D'Amore), the role of language in the

Learning of mathematics, formative and summative evaluation

(Bolondi), methodologies for teaching mathematics (laboratory,

math discussion, group work, technologies and software),

affect and beliefs (Zan, Di Martino), the role of examples

(Antonini), interdisciplinary approaches to mathematics and

physics.

Teacher, researcher, teacher-researcher: training paths and

possible professions in mathematics, school and research.

## Teaching methods

Frontal lectures, groupworks, workshops and presentations will The evaluation will take place on the basis of a project

and an oral exam, in which the student will have to show

that he knows basic mathematics and mathematics education

themes and has developed a critical, thoughtful and innovative

attitude towards teaching and learning mathematics

in the secondary school.

Frontal lectures, groupworks, workshops and presentations will

be alternated to promote conceptual understanding but also

communicative skills and to give the student a personal point

of view about the teaching profession and the role of the

researcher , even respectful of the constraints given by disciplinary correctness and knowledge of the fundamental results in mathematics education research.

## Assessment methods and criteria

The evaluation will take place on the basis of a project

and an oral exam, in which the student will have to show

that he knows basic mathematics and mathematics education

themes and has developed a critical, thoughtful and innovative

attitude towards teaching and learning mathematics

in the secondary school.

The evaluation will take place on the basis of a project and an oral exam, in which the student will have to show that he knows basic mathematics and mathematics education themes and has developed a critical, thoughtful and innovative attitude towards teaching and learning mathematics

in the secondary school.