Annarosa Serpe

An algebraic approach to Lidstone polynomials

Abstract A new definition of Lidstone polynomials [G.L. Lidstone, Note on the extension of Aitken’s theorem (for polynomial interpolation) to the Everett types, Proc. Edinb. Math. Soc. 2 (2) (1929) 16–19] is proposed; this is a Hessemberg determinantal form. The algebraic approach provides an elementary proof of the main recursive properties of Lidstone polynomials.

Archimedes in Secondary Schools: A Teaching Proposal for the Math Curriculum

The aim is to propose, at various levels in secondary schools, Archimedes’ idea for calculating π using the computer as programming tool. In this way, it will be possible to remember the work of one of the greatest geniuses in history and, at the same time, carry out an interdisciplinary project, particularly relevant to the current debate on the Math curriculum.

Archimedes and Caustics: A Twofold Multimedia and Experimental Approach

In this work we present a twofold educational approach to the reflective properties of surfaces, starting from the historical context of Archimedes “burning mirrors”. The properties of the emerging surface known as “caustic” of a given smoothly shaped mirror are illustrated by an interactive multimedia. An experimental device is also proposed to visualize the geometrical principles underlying the formation of caustics. The proposed didactical trail is intended also to contextualize the figure and work of Archimedes in a perspective tightly linked to modern technology, so to collect young learners’ interest.

KidSmart: an essential tool for mathematical education in nursery schools

This paper is part of a wide debate and critical reflection on the use of ICT in nursery schools, and focuses on the use of station KidSmart in the classroom to enhance scientific learning within the logical-mathematic field. The study is organized as follows: after presenting the institutional setting within which ICT has been introduced in Italian nursery schools, some considerations are made on the essential characteristics of mathematical education and on the relationship with physical reality through the mediation of ICT, highlighting in particular the pedagogic-educational value of ludic-experiental activities in an early learning context. After that, the characteristics of the KidSmart station are introduced, and some interesting results of the action-research experience aimed at scientifically controlling the conditions and introductory procedures of KidSmart in the field of experience ‘exploring, knowing and planning’ are given. Related conclusions round off this work.