Claudio Bernardi, Annalisa Cusi, Alessandro Gambini Nicoletta Lanciano, Marta Menghini, Enrico Rogora
Content and methods for mathematics education:
Elementary mathematics from a higher standpoint. Curriculum construction.
Pre-service and in-service teacher training (in the university, at school and in residential courses).
Definitions and proof:
Rigor vs. intuition in teaching and learning mathematics. The use of manipulatives and geometric software, the role of perception, of movement, of visual proofs, of problem solving and mathematization strategies; van Hiele’s levels of geometrical thought.
The teaching of three-dimensional geometry (for children, students, adults):
experiences in small, little and big space. The link with other subjects: astronomy, archeo-astronomy, cultural astronomy, and art.
The use of 3D software in upper secondary school.
Foundations of mathematics:
Mathematical logic. Pathological classes of functions (such as additive discontinuous functions and everywhere surjective functions). Mathematical logic in education: different kinds of proofs, paradoxes; the role of examples and counterexamples.
History of mathematics education:
History of teaching geometry. The Roman School of didactics of mathematics. The development of intuitive geometry. Chief characters, as Guido and Emma Castelnuovo, Federigo Enriques, … The influence on teaching of developments in mathematics.
History of mathematics:
The development of mathematics during the XIXth century in the context of the development of science and society, with particular emphasis on Italy. Mathematics in Italy from Risorgimento to the second world wide wars: the reasons for its rise and its decline; mathematics in Rome; the Italian school of algebraic geometry; the spread of Lie’s idea in Italy and its influences on the Italian school of algebraic geometry; the leaders of the community of Italian mathematicians (Brioschi, Cremona, Volterra and Severi). Descriptive and projective geometry in the university courses and in schools.
Large scale assessment:
Investigating multidimensional IRT models, Rasch model and their application in the educational field. Construction of standardized tests for the measurement of difficulties in learning in mathematics.
Learning Difficulties in Mathematics:
Developing effective teaching strategies for preventing and/or addressing learning difficulties of students of different ages, in particular of children who are at risk of being diagnosed with developmental dyscalculia, or who have been diagnosed with the condition. Combining perspectives from cognitive psychology and mathematics education. Investigating how technology-enhanced learning can foster the development of different mathematical abilities, from early numerical abilities in pre-schoolers, to geometric and algebraic thinking in secondary school students manifesting persistent learning difficulties in mathematics.
Non-Euclidean geometry in math education:
Investigating a "comparative geometry" that combines plane and sphere concepts from primary to secondary or tertiary education. Such an approach can develop mathematical, logical and spatial competences in various fields.