Conceptualization of function as a covariation through the periodicity with 11th-grade students of high school

Postgraduate Thesis uoadl:2961933 1 Read counter

Κατεύθυνση Διδακτική και Μεθοδολογία των Μαθηματικών
Library of the School of Science
Deposit date:
Xylas Nikolaos
Supervisors info:
Ψυχάρης Γεώργιος, Επίκουρος καθηγητής, τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Νοηματοδότηση της έννοιας της συνάρτησης ως συμμεταβολής μέσω της περιοδικότητας από μαθητές Β΄ Λυκείου
Translated title:
Conceptualization of function as a covariation through the periodicity with 11th-grade students of high school
In the present research, we study the concepts of function as covariation and
periodicity. We investigate the concepts in the context of modeling activities by
utilizing authentic situations, model simulation, and digital tools with 11th-grade
students of high school. At first, students studied a physical model - which describes a
periodic phenomenon- and empirically recognized the variation of physical quantities
and the characteristics of their periodicity. After that, they modeled the realistic
situation in the digital environment of Geogebra while their goal was to investigate, to
experiment and finally to develop the meanings of the two concepts. Alongside, in our
study, we investigate the contribution of the available manipulative and digital tools
to the meaning of the periodic covariation. The episodes are analyzed based on the
theoretical framework of Mathematical Working Spaces of the three dimensions: the
instrumental, the semiotic, and the discursive. By analyzing our data, we conclude
that the students had a progressive construction regarding the meaning of the two
concepts in the different working spaces. Furthermore, the students developed
conceptual connections in both the transition from one space to another and into the
same space. In the end, they utilized the available tools in combination with the use of
symbols and representations developed their original meanings.
Main subject category:
Function, Covariation, Periodicity, Authentic Situations , Mathematical Working Spaces, Physical and Digital tools
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Διπλωματική εργασία Ξυλάς Νικόλαος.pdf
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