Unit:
Τομέας Μαθηματικών και ΠληροφορικήςΒιβλιοθήκη Δημοτικής Εκπαίδευσης
Author:
Σκαφτούρου Ευφροσύνη
Dissertation committee:
Επιβλέπουσα : Μπούφη Ανδρονίκη.Καθηγήτρια ΠΤΔΕ, ΕΚΠΑ
Εξεταστική Επιτροπή : Νάκας Αθανάσιος .Ομότιμος Καθηγητής ΠΤΔΕ,ΕΚΠΑ
Μπαραλής Γεώργιος.Αναπλ.Καθηγητής ΠΤΔΕ,ΕΚΠΑ
Βουδούρη Αγγελική.Καθηγήτρια ΠΤΔΕ,ΕΚΠΑ
Βρεττός Ιωάννης.Καθηγητής ΠΤΔΕ,ΕΚΠΑ
Μπαμπάλης Θωμάς.Αναπλ.Καθηγητής ΠΤΔΕ,ΕΚΠΑ
Καλαβάσης Φραγκίσκος.Καθηγητής Πανεπιστημίου Αιγαίου
Original Title:
Μαθηματικοποίηση των εξηγήσεων στό μάθημα των μαθηματικών: ο ρόλος των συμβόλων
Translated title:
Μαθηματικοποίηση των εξηγήσεων στο μάθημα των μαθηματικών : ο ρόλος των συμβόλων
Summary:
The doctoral dissertation studies the way in which an instructional
sequence could incorporate the fractional symbols used by students in order
to promote the development of a mature fractional understanding based on
children informal knowledge. Cognitively and didactically, fractions are
among the most complex concepts of the elementary school curriculum.
Despite research efforts, there is still great dissatisfaction with regard to the
levels of understanding of how to support students, so that they construct
fractions in a meaningful way. Therefore, the main purpose of the dissertation
is to contribute to meeting this need by focusing on the study of the role of
symbolic representations and their contribution to the understanding of
fractions. The dissertation places the deep understanding of fractions in the
context of proportionality and its central questions concern the learning
objectives and the design of appropriate supportive learning tools to develop
understanding of fractions in the context of proportionality.The theory of Realistic Mathematics Education and the Emergent
Perspective guided the study of the research questions. The research
methodology chosen is the methodology of the Design Research. The basic
methodological tool of the Design Research is the conduction of a three-phase
classroom experiment. The first phase of the experiment included the
construction of a hypothetical trajectory for teaching and learning fractions
in the context of proportionality based on the starting points of the classroom
the experiment was conducted and on the review of the relatively small
literature concerning the intertwinement of fractions and proportional
thinking. The path of equipartitioning and the path of proportional situations
in situations of fair sharing were considered capable of supporting the
progressive mathematization of fractions in the context of proportionality in
a E class of a primary school in downtown Athens with 23 pupils (10 boys and
13 girls). The experimentation in the classroom (second phase) lasted 2 ½months (January - March 2005 : 40 lessons) and concerned didactic decisions
on the basis of students’ progress of and in relation to the means of support
for the promotion of classroom mathematical development. The
retrospective analysis of the experiment (third phase) suggested that despite
its limited impact, the design study of the dissertation could contribute to the
research literature. It clarifies to a certain extent degree some of the
knowledge and skills students need to have in order to understand fractions
in the context of proportionality and describes a plan to support them in
order to develop understanding. In particular, it determines means of support
for students' learning and illustrates why and how they could be effective
Main subject category:
Mathematics
Other subject categories:
Mathematics
Keywords:
progressive mathematization; teaching fractions in the context of
proportionality; the fraction in a ratio relation; the fraction as a rate; theory
of Realistic Mathematics Education; Emergent Perspective; Design Research;
teaching classroom experiment; path of equipartition; path of proportional
situations; improvement of the quality of Mathematical Education
File:
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Διδακτορικό Σκαφτούρου Ευφροσύνης.pdf
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