Ateneo - UPO

Critical analysis of the main teaching methods developed in the research in mathematics education and in the history of mathematics, also related to the role of the teacher and to the conceptual, epistemological, linguistic and didactic nodes involved in teaching and learning mathematics. Development of the knowledge identified by literature as necessary for teaching.
Design and development of mathematics teaching methods: illustration, starting from the main theoretical frameworks used in mathematics education, of the principles and methods for designing activities and more generally a mathematics curriculum coherent with the goals set by National Guidelines for first and second level secondary school. Study of the teaching and learning processes of mathematics mediated by
technologies, with particular care to new digital technologies. Analysis of the potentiality and criticality of the use of technological tools for the teaching and learning of mathematics.

DIDATTICA DELLA MATEMATICA di Roberto Natalini, Anna Baccaglini-Frank, Pietro Di Martino, Giuseppe Rosolini. Mondadori
INSEGNARE E APPRENDERE MATEMATICA di Cristina Sabena, Franca Ferri, Francesca Martignone, Elisabetta Robotti. Mondadori
Notes given by the teachers

Ability to interpret behaviors and competences of the students and implement appropriate teaching paths, taking into account the results of research.

Some elements of logic. Number systems. Integers. Divisibility and primes. Greatest commun divisor. Euclid's algorithm. Least common multiple. Congruences and rest classes. Divisibility criteria. Rational and real numbers. Approximations. Percentages. Mathematical modeling: first degree problems. Equations and inequalities.
Analytical geometry: Cartesian plane, lines and parabolas. Linear systems.
Real functions of real variable, graphs, links between graph and analytical expression. Trigonometric functions and periodic phenomena. Examples of exponential and logarithmic growths. Composition of functions. Intersections between curves. Limits and continuity.
Derivativs. Continuity and derivability. Derivatives of elementary functions and graphical representations. Increasing and decreasing functions, Minima and maxima of a function. Applications of derivativs. Discussion of examples based on functions of particular interest in applications.
Primitives of a function. Integrals. The fundamental theorem of integral calculus. Applications of the integrals.

Lectures, workshops, online activities, personalized tutoring sessions

Learning monitoring: ongoing exercises supported by the use of the Moodle platform.

Ongoing evaluation activities (online). Final written work followed by oral discussion of a project developed by the student.

A priori analysis of mathematical tasks
The INVALSI tests
Examples of mathematical problems of various kinds
Mathematics and language
Language and learning: denotational theory and instrumental theory
Principles of cooperation and mathematical knowledge
Inclusive and exclusive use of words.
Linguistic acts and propositions.
Cooperation and implications.
The language of mathematics as a multimodal and multivariate system
Examples of visual demonstrations
Visual salience of mathematical representations
Psychological theories on learning
Behaviorism, cognitivism
Constructivism
Contemporary radical constructivism
The APOS model by Dubinsky
Socio-cultural guidelines, Vygotsky
The research by Anna Sfard
The difficulties in mathematics
Cognitive, metacognitive and non-cognitive aspects
Interpretation of difficulties
Technology in Mathematical Education
Micromondi for geometry
Platforms for e-learning

Ability to critically interpret mathematical knowledge and related learning theories, also identifying their potential and limits. Ability to design and evaluate appropriate learning paths for students. Ability to use innovative methodologies and information technology for the design and development of educational activities. Ability to communicate clearly and completely the description and motivation of one's own statements and choices. Ability to identify and use materials for educational design.