, Volume 47, Issue 3, pp 391–405 | Cite as

Geometry in early years: sowing seeds for a mathematical definition of squares and rectangles

  • Maria G. Bartolini Bussi
  • Anna Baccaglini-Frank
Original Article


In early years schooling it is becoming common to propose activities that involve moving along paths, or programming robots to do so. In order to promote continuity towards the introduction of geometry in primary school, we developed a long-term teaching experiment (with 15 sessions) carried out over 4 months in a first grade classroom in northern Italy. Students were asked to program a robot to move along paths, to pretend to act as robots and to represent the sequence of commands and the resulting paths. In particular, in this teaching experiment, an overarching mathematical aim was to sow the seeds for a mathematical definition of rectangles that includes squares. Within the paradigm of semiotic mediation, we intended to foster the students’ transition from a dynamic perception of paths to seeing paths also as static wholes, boundaries of figures with sets of geometric characteristics. The students’ situated productions were collected and analysed together with the specific actions of the adults involved, aimed at fostering processes of semiotic mediation. In this paper we analyse the development of the situated texts produced by the students in relation to the pivot signs that were the beginnings of an inclusive definition of rectangles.


Teaching Experiment Mathematical Definition Mathematical Meaning Sowing Seed Artefact Sign 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We wish to profusely thank: Roberta Munarini for offering to involve her first grade classroom in the project and for her so active collaboration in the project, together with Federica Baroni; the children in the classes and their parents; Alessandro Ramploud for the intercultural issues included in the paper; our Burmese friends, Thein Lwin and Ko Tar, who, thanks to Giuseppe Malpeli, were able to watch and comment on some of the activities reported in this paper, and initiate a programme of international friendship involving Italian and Burmese children.


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Copyright information

© FIZ Karlsruhe 2014

Authors and Affiliations

  • Maria G. Bartolini Bussi
    • 1
  • Anna Baccaglini-Frank
    • 1
  1. 1.Dipartimento di Educazione e Scienze UmaneUniversità di Modena e ReggioEmiliaItaly

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