Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των ΜαθηματικώνLibrary of the School of Science
Author:
Perivolari Aliki-Iliana
Supervisors info:
Ψυχάρης Γιώργος, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών ΕΚΠΑ
Πόταρη Δέσποινα, Καθηγήτρια, Τμήμα Μαθηματικών ΕΚΠΑ
Ζαχαριάδης Θεοδόσιος, Ομότιμος Καθηγητής, Τμήμα Μαθηματικών ΕΚΠΑ
Original Title:
Ο ρόλος της συνέργειας της δίπλωσης χαρτιού και της χρήσης ψηφιακών εργαλείων στη νοηματοδότηση της υποθετικής πρότασης και της απόδειξης
Translated title:
The role of the synergy of paper folding and the use of digital tools in the conceptualization of conditional statement and proof
Summary:
This research paper discusses the contribution of the combined use of two artefacts of different nature to the conceptualization of meanings related to the generation of conditional statements and their proof. The construction of such meanings is a complex process that needs to overcome the difficulties students face related to the formal process of mathematical proof. The main research hypothesis is that the potential synergy that can occur between two artefacts, a manipulative and a digital one, can promote the evolution of initial personal meanings linked to the individual's experience of working with an artefact, into mathematical and de-contextualised meanings that are central to the understanding of the conditional statement. The theory of Mathematical Working Spaces combined with the Theory of Semiotic Mediation construct a theoretical lens for analyzing the research data. This research draws these data from the work of two groups of 10th grade students on three construction-proving problems in Euclidean Geometry context, using the manipulative artefact of paper folding and the digital artefact Geometer's Sketchpad. The results of the analysis highlight the particular contribution of the synergy of these two artefacts in the formation and validation of conjectures, in understanding the logical dependencies between hypotheses and the conclusion of a conditional statement, and finally in proving it through the conceptualization of signs and processes in the two working spaces and the creation of connections between them.
Main subject category:
Science
Keywords:
Synergy, paper folding, DGE, conditional statement, proof
