THERE. TEACHING OF MATHEMATICS 1 AND 2 WITH LABORATORY

Module MATHEMATICS TEACHING 2

The course aims to provide basic knowledge of arithmetic, algebra and logic and to develop students’ command of formal mathematical language, enabling them to communicate mathematical knowledge clearly and accurately to primary school pupils. The workshop component allows students to explore theoretical ideas through practical tasks, exercises, cooperative activities and simulations. It also aims to develop their communication skills so that they can support primary school pupils in learning abstract concepts.

Knowledge and understanding. By the end of the course, students will know the fundamental concepts of elementary arithmetic and algebra (numeral systems, operations and their properties, divisibility, prime numbers, fractions and rational numbers, and initial forms of algebraic generalisation) and understand their logical organisation: definitions, statements, properties and justifications. They will also know the basic elements of formal mathematical language — connectives, quantifiers and the truth value of a statement — and the main theoretical perspectives in mathematics education relevant to understanding learning in primary school.

Applying knowledge and understanding. Students will be able to solve problems in elementary arithmetic and algebra, providing reasons for the procedures they use. They will be able to design and conduct workshops for primary school pupils, identifying the mathematical content that can emerge from a resource, a game or a problem situation. They will be able to recognise and analyse pupils’ recurring errors, interpreting them as evidence of an ongoing learning process rather than simply as shortcomings.

Making judgements. Students will be able to assess the correctness of a statement and the validity of their own and others’ arguments. They will be able to critically compare different representations and solution strategies for the same problem, recognising that teaching choices influence what pupils learn.

Communication skills. Students will be able to use accurate mathematical language while expressing abstract concepts in ways appropriate to primary school pupils’ age, without introducing inaccuracies that could become obstacles in later years. They will be able to lead mathematical discussions in the classroom, encouraging pupils to formulate conjectures and assess them collectively.

Learning skills. Students will acquire tools for independently continuing their mathematical and professional development, including the ability to consult mathematics education literature, national curriculum guidelines and resources for designing activities.

The course adopts a predominantly workshop-based approach, with students taking an active role. Activities include exploring problems and games, using materials, working in small groups and participating in whole-class discussions. Reflection on mathematical content and teaching choices builds on these experiences and is supported by sessions that consolidate and formalise the underlying concepts.

No specific prerequisites are required beyond basic school mathematics. The course will revisit the content starting from the fundamentals.

Attendance is not compulsory but is strongly recommended. The educational value of the course lies primarily in direct participation in workshops, games and group discussions, experiences that independent study of the materials alone cannot fully replace.

• Numbers and operations: numeral systems, place value, properties of operations, divisibility, fractions and decimals.

• Logic and argumentation: statements, connectives, quantifiers and sets; examples, counterexamples and justification of reasoning.

• Early algebraic thinking: patterns, generalisation, unknowns and equations through problems and games.

• Games and strategies: analysing rules, formulating conjectures and developing strategies; connections between games, algorithms and proofs.

• Mathematics education in primary school: activities involving materials and representations, whole-class discussion, the role of errors and attempts, and the design of workshop-based learning sequences.

Reference texts:

• D’Amore, B. (2023). Elementi di didattica della matematica. Bonomo Editore.

• Castelnuovo, E. (2008). L’officina matematica. Ragionare con i materiali. Edizioni La Meridiana.

Further reading:

• Brousseau, G. (1997). Theory of Didactical Situations in Mathematics. Kluwer Academic Publishers.

• Radford, L. (2021). The Theory of Objectification. A Vygotskian Perspective on Knowing and Becoming in Mathematics Teaching and Learning. Brill Sense.

Resources and materials:

• OILER: https://www.oiler.education — learning sequences, games and mathematics teaching resources, with particular reference to Zermelo, BUL, Robinson and Pitagoras.

• Additional materials will be provided during the course.

Assessment consists of an oral examination on the course content. The examination may include discussion of an portfolio of activities and reflections developed during the course. Assessment will focus on understanding mathematical concepts, the ability to reason and justify claims, and the ability to connect course content with teaching choices for primary school.

The following questions are illustrative only and do not constitute an exhaustive list of possible examination questions:

• What distinguishes an example from a proof? Explain the role of a counterexample.

• How could you explain to a pupil why 1/3 is greater than 1/4?

• Choose a game discussed during the course and examine its mathematical content and possible classroom applications.