Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των ΜαθηματικώνLibrary of the School of Science
Author:
Nasiopoulou Elpida
Supervisors info:
Δ. Πόταρη (Επιβλέπουσα), Καθηγήτρια ΕΚΠΑ
Θ. Ζαχαριάδη, Καθηγητής ΕΚΠΑ
Κ. Π. Χρήστου, Επικ. Καθηγητής Πανεπιστήμιο Δυτικής Μακεδονίας
Original Title:
Διερεύνηση της κατανόησης του πραγματικού αριθμού στη μετάβαση από τους ρητούς αριθμούς από μαθητές και εκπαιδευτικούς
Translated title:
Investigating students' and teachers' understanding of real numbers in the transition from rational numbers
Summary:
The present work aims to cover the literature concerning the concept of irrational numbers, as the key-concept in the introduction of real numbers.
In the literature review of Mathematics Education, the idea that rational numbers are dense but cannot cover every point on the continuous real number line is proved to be naturally difficult, leading to epistemological and cognitive obstacles. It is also highlighted that the concept of irrational numbers is essential in the transition from rational to the set of real numbers, therefore demands careful teaching, in order to properly develop the concept of number in general.
In conclusion, tasks including number representations and deep knowledge that definitions of irrational numbers are equivalent, consequently lead to richer problem-solving strategies and enhance abstract thinking. Moreover, such activities disclose the coherence of Mathematics.
The goal of teaching real numbers by building a coherent arithmetical system could be organized by blending the empirical activity of measurement and its reasonable adjustment.
Main subject category:
Science
Keywords:
irrational number, rational number, real number, transition to real number, teaching real number
Number of references:
215
