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master degree course in MATHEMATICS

Course year 2
Teaching units Unit Matematiche elementari da un punto di vista superiore
Advanced Theoretical Studies (lesson)
  • TAF: Compulsory subjects, characteristic of the class SSD: MAT/04 CFU: 6
Teachers: Michela MASCHIETTO
Exam type oral
Evaluation final vote
Teaching language Italiano
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The course concerns the development of mathematics through the study of the tools that were used to represent mathematical objects, to solve practical and theoretical problems, and that are available now for mathematics education at secondary school level. From an educational point of view, the use of instruments is considered within the methodology of mathematics laboratory.

Admission requirements

Basic Algebra, calculus and geometry courses.

Course contents

Mechanical tools for tracing curves: compass (Euclide, Nicomede, Descartes), conic section drawers, curve drawers. Mechanical tools for geometrical transformations: pantographs, tridimensional genesis. mechanical tools for perspective drawings: perpectographs. Tools for perspective drawings. The role of tools in the development of mathematics: Euclide, Descartes, Desargues. Kempe Theorem. Tools for mathematics education: dynamic geometry environment, graphic calculators, IWB. Mathematics laboratory: historical and institutional aspects. Methodological elements: epistemological and historical analysis Exploration of mathematical machines. Mathematics laboratory sessions with mathematical machines.

Teaching methods

Lectures, use of IWB and dynamic geometry software, activities to be performed in mathematics laboratory methodology.

Assessment methods

Oral exam consisting in: exploration of a mathematical machine, construction of the animation of that machine with dynamic geometry software, questions about the analysis of educational tasksa and the course content.

Learning outcomes

1)Knowledge and understanding:
a) To know essential elements of the historical phenomenology of mathematics with tools
b) To know different approaches to study curves and geometrical transformation.
c) To understand different forms of thought characterizing the interlink between development of mathematics and construction of instruments.
d) To understand the connections between all the approaches that are presented.
2) Applying knowledge and understanding:
a) Applying knowledge in order to analyze historical and mathematical texts.
b) Applying knowledge to analyze tools and/or their simulations by DGS Applying knowledge to construct simulations of some tools by DGS
3) Making judgments:
a) To evaluate and compare tools and mathematical approaches in a autonomous way
4) Communicating skills:
a) Skill to communicate with an appropriate language, in an oral and/or written form.
b) Skill to structure a talk on the relationship between mathematics and instruments.
5) Learning skills:
Skill to list, schematize and elaborate acquired notions. Skill to deepen some subjects connected to the course.


Bartolini Bussi, M.G. & Maschietto, M. (2006). Macchine matematiche dalla storia alla scuola. Collana Convergenze. Milano: Springer.
Per alcuni strumenti, si veda il sito

Sulla pagina del portale moodle relativa all’insegnamento di MEPVS sono disponibili lezione dopo lezione (e nel rispetto dei diritti d’autore):
- le dispense utilizzate dal docente nel corso delle lezioni frontali;
- le schede descrittive degli strumenti esplorati durante le lezioni frontali e nel lavoro di gruppo, con le relative animazioni;
- articoli di approfondimento.