Using mathematical literature to develop rational number sense

Postgraduate Thesis uoadl:2849561 306 Read counter

Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των Μαθηματικών
Library of the School of Science
Deposit date:
2019-01-31
Year:
2019
Author:
Maris Dimitris
Supervisors info:
Κωσταντίνος Χρήστου - Επίκουρος Καθηγητής (Επιβλέπων) - Παιδαγωγικό Τμήμα Νηπιαγωγών - Πανεπιστήμιο Δυτικής Μακεδονίας
Ξένια Βαμβακούσση - Επίκουρος Καθηγήτρια - Παιδαγωγικών Τμήμα Νηπιαγωγών - Πανεπιστήμιο Ιωαννίνων
Παναγιώτης Σπύρου - Καθηγητής - Αναπληρωτής Καθηγητής - Τμήμα Μαθηματικών - Πανεπιστήμιο Αθηνών
Original Title:
Χρήση της μαθηματικής λογοτεχνίας για την καλλιέργεια της αίσθησης του αριθμού
Languages:
Greek
Translated title:
Using mathematical literature to develop rational number sense
Summary:
The purpose of this study is to investigate if Mathematical Literature can improve the rational number sense. Rational numbers are a cornerstone of mathematics and mathematics education, they are the numbers that help students obtain algebraic reasoning and mediate the transition from the Natural to the Real numbers. Mathematics education research has identified great difficulties in the understanding of rational numbers and has recorded a lot of common errors and misconceptions. Numerous researches that dealt with the difficulties in Rational numbers have pointed out that for these difficulties the pre-existing knowledge of Natural numbers is responsible.
Many researchers have studied the process of moving from the concept of Natural number to the concept of the Rational number and have shown that it is a time consuming and painful process. For this transition, teaching interventions have been designed to either address the difficulties and misconceptions that arise. In the present work an attempt is made to deal with these difficulties and misunderstandings with the use of Mathematical literature.
Mathematical literature refers to the kind of literature that the author draws material from the science of mathematics. Mathematical stories are a type of mathematical literature and can be used to serve various educational purposes. A mathematical story can become a tool for the dissemination of mathematical knowledge and provide meaning to mathematical concepts and processes that appear to students totally unrelated to every day life. A mathematical story can create an appropriate learning environment within the cognitive misconceptions can be addressed.
In this work, i have written a mathematical story that deals with the concept of ordering and density of the Rational numbers in their various representations (decimal numbers and fractions). The story is called "Ταξίδι προς το Μηδέν" and consists of 11 Chapters, a total of 60 pages, which deal with the ordering of decimals, the ordering of fractions, homonymous fractions, the conversion of decimal into fraction and the density of Rational numbers. The story also includes 5 drawings (images) that represent parts of the world of the story that contain decimal numbers and fractions. The setting of the story is a world of numbers where its rules, characters, and character ideas are directly influenced by the mathematical concept of the layout and follow its mathematical principles. All the story unfolds on the axis of the Rational numbers in order for the geometry of the world to contribute to the understanding of the concept of the density of Rational numbers. As far as the plot of the story is concerned, decimal numbers and fractions are "nationals" of Νatural numbers, and earlier knowledge of students about Νatural numbers acquires in the story the meaning of the "power" of the Natural numbers over the decimal numbers and fractions. The basic idea of the plot design is to change students' attitudes towards decimal numbers and fractions by making them "heroes" in a "world of Natural numbers".
For this study, questionnaires were given to 6 students of the 6th Primary, one before the reading of the story and one after, examining the ordering and the density of the Rational numbers, and individual semi-structured interviews, one before the reading of the story, and one after, in order to identify students' attitudes to the Rational numbers. The research questions of this paper concerned whether the writing of a mathematical story and its reading could: 1) help students to cope with known misconceptions in Rational numbers; and 2) improve students' attitudes to Rational numbers and in mathematics in general.
The analysis of the questionnaires and transcripts showed that the story dealt with several misconceptions in the ordering of decimal numbers and fractions, with the direct consequence of improving students' performance in the specific projects in the second questionnaire given to them. In the works on the density of Rational numbers, which is the most difficult concept or the more difficult misconception to correct, there has not been much improvement. Students' attitudes to decimal numbers became more positive and student attitudes for fractions remained neutral. The attitudes of students towards the story and its teaching goals were positive and many students said that they would like to learn mathematics with the help of mathematical stories.
Main subject category:
Science
Keywords:
Mathematical Literature, Rational Numbers, Rational number Ordering, Rational number Density, Rational number misconceptions, Natural Number bias
Index:
Yes
Number of index pages:
2
Contains images:
Yes
Number of references:
85
Number of pages:
146
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