Evaluating mathematical cretivity using multiple solutions tasks

Postgraduate Thesis uoadl:2766591 471 Read counter

Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των Μαθηματικών
Library of the School of Science
Deposit date:
2018-06-03
Year:
2018
Author:
Gridos Panagiotis
Supervisors info:
Αθανάσιος Γαγάτσης, Καθηγητής, Τμήμα Επιστημών της Αγωγής, Πανεπιστήμιο Κύπρου
Ζαχαριάδης Θεοδόσιος, Καθηγητής, Τμήμα Μαθηματικών, Ε.Κ.Π.Α
Πόταρη Δέσποινα, Καθηγήτρια, Τμήμα Μαθηματικών, Ε.Κ.Π.Α
Original Title:
Ανάπτυξη μαθηματικής δημιουργικότητας διαμέσου προβλημάτων πολλαπλών λύσεων στη Γεωμετρία
Languages:
Greek
Translated title:
Evaluating mathematical cretivity using multiple solutions tasks
Summary:
Further to the rest areas of mathematics, geometry can be used to discover and develop different ways of thinking. Due to this, the study of understanding the learning and teaching of geometry can only be multi-dimensional. The present thesis presents such an analysis of the understanding of geometry learning. The four dimensions which are proposed are: (a) Geometrical figure apprehension; (b) spatial ability; (c) mathematical creativity; and (d) the ability to produce multiple solutions in geometry problems.
Several studies have shown the important role of multiple solution tasks in the development of geometric thinking and especially in the development of creative thinking. This research studies the performance of high school students in multiple solution geometry problems. The three dimensions of mathematical creativity, namely, fluency, flexibility and originality are examined. Towards this, students are asked to solve 4 classical geometrical problems which are subjected to different solutions. In two of them, the shape is provided, while this not the case for the other two and subsequently we assume that that the conditions are totally different. In addition, the research aims at exploring the relationship of understanding the geometric shape with the production of multiple solutions to a geometric problem. The sample of the survey consisted of 149 high school students from 5 schools in the prefecture of Attica, of whom 147 took part in a written test and 2 in an oral interview. The results of the research reinforce our hypothesis that the fluency and flexibility of the students in their solutions is enhanced when the shape is given to the problem. At the same time, research supports the view that originality does not seem to be influenced by whether or not the shape is given, as it is more inherent in and more closely related to creativity. The similarity analysis in the number of student’s solutions resulted in three groups: (a) a zero - fluency ability group; (b) a low – fluency and flexibility ability group; and (c) a group of high fluency and flexibility, with the first two groups gathering the largest number of students, a situation which, from the qualitative data, seems to be varying. Finally, it seems that the connection of the four types of geometric figure apprehension (perceptual, sequential, discursive, and operative) is a prerequisite for high levels of creativity in geometry.
Main subject category:
Science
Other subject categories:
Education - Sport science
Keywords:
Mathematical creativity, multiple solution tasks in geometry, geometrical figure apprehension, spatial ability.
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
81
Number of pages:
133
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