Geometry in early years: sowing seeds for a mathematical definition of squares and rectangles
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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.
KeywordsTeaching Experiment Mathematical Definition Mathematical Meaning Sowing Seed Artefact Sign
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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