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Department of Mathematics and Applications
"Renato Caccioppoli"


Elementary Mathematics from an Advanced Standpoint

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Elementary Mathematics from an Advanced Standpoint

Credits

6

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/04 Complementary Mathematics.

Examination method

Group report and oral exam.

Learning
objectives

The aim of the course is to revisit and frame the main mathematical topics of interest for school teaching in the light of the historical development of mathematics and its current disciplinary structure.

Syllabus

Origin of the various kinds of numbers and the main conceptual turning points in their history. Historical and epistemological motivations for the extensions of number systems: from N to Z to Q to R. Teaching issues relating to the various kinds of numbers and their properties. Algebraic and topological reasons for the passage from Q to R. Infinity in mathematics and at school, potential and actual infinity, infinity in geometry. Reflections on the meanings of algebra, in particular on the links between “elementary” algebra and “abstract” algebra, and on the transition from arithmetic to algebra: algebra as a language. Further topics, varying from year to year, will also be explored in depth.

Expected learning
outcomes

At the end of the course, students must demonstrate that they

  • know and understand the topics of the course and are able to interpret and discuss the content of some research articles on mathematics education;
  • are able to apply the knowledge acquired by reworking their own mathematical knowledge of interest for school teaching in the light of the historical development of mathematics and its current disciplinary structure;
  • are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
  • are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Formal correctness and completeness in the presentation of the topics of the syllabus. Accurate and critical presentation of the contents of papers selected each year.