Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των ΜαθηματικώνLibrary of the School of Science
Author:
Sofianopoulou Angeliki
Supervisors info:
Πόταρη Δέσποινα, Καθήγητρια, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Στρατηγικές απαρίθμησης αντικειμένων και συλλογισμοί σε έργα χωρικά, αριθμητικά και γεωμετρικά
Translated title:
Counting strategies of objects and reasoning in spatial, numerical and geometrical tasks
Summary:
In the present study we investigated the ways of reasoning and the strategies suggested by students of 4th and 5th grade to counting activities of mathematical objects, in connection with the examination of multiplicative relationships and patterns. The study was conducted with three students for each grade, with high achievement in school mathematics. It was implemented in three phases – personal interviews with each student. The participants engaged in spatial, numerical and geometrical activities. The counting strategies and the types of errors expressed by students in the spatial activity were categorized with the use of the models proposed by Anghileri and Finesilver respectively, while the categorization to the other activities was configured by the answers of the students. Through the results, the combination of multiplicative and additive relationships proved the predominant way of counting. In total, 5th grade students suggested more strategies of grouping objects in the spatial activity, which depended heavily on the use of the concept of divisor. In most activities, their visual representation played the principal role to the emergence of multiplicative relationships expressed by students, something that did not happen in the case of numerical patterns. Similarities were noticed in the treatment of the different activities related to the counting strategies, the types of errors and the semiotics.
Main subject category:
Science
Keywords:
multiplicative thinking, pattern, counting, semiotic means, visual representation
