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.

Interactive lessons, group work, online activities supported by the Moodle platform. Use of software for innovative teaching.

Learning monitoring: ongoing exercises supported by the use of the Moodle platform. Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/services-students-physical-or-learning-disabilities Students with disabilities, learning disabilities or special education needs can refer to the teacher in charge of the course to define the examination modalities.

Ongoing formative assessment. Final written work followed by oral discussion of a project developed by the student.

A priori analysis of mathematical tasks
Formative assessment
Summative assessment and standardised tests
the specialist knowledge of mathematics teachers
Mathematical competences
Fields of experience
Mathematics and language
Language and learning
Principles of cooperation and mathematical knowledge
Cooperation and implicatures
The language of mathematics as a multimodal and multivariate system
Examples of visual demonstrations
Visual Salience of representations in mathematics
Psychological theories of learning
Sociocultural orientations, Vygotskij
Difficulties in mathematics
Cognitive, metacognitive and non-cognitive aspects
Interpretation of difficulties
Technology in Mathematics Education
Software Dynamic Geometry
Platforms for e-learning

Capacity to critically interpret the main institutional references for the curriculum (National Indications for the first cycle of Education), the mathematical knowledge to be transposed and the related learning theories. Ability to design and evaluate learning paths appropriate to the school grades. Ability to use innovative methodologies and information technology for the design and development of teaching activities. Ability to identify the main problems in the teaching and learning of mathematics in the first cycle of education. Ability to communicate clearly and comprehensively the description and reasons for one's statements and choices. Ability to identify and use materials for teaching design.