Pre-Service Mathematics Teachers’ Concept Definitions and Examples Regarding Sets

Abstract

The purpose of this study is to reveal the concept definitions and examples of pre-service elementary mathematics teachers regarding sets. In this context, students' formal definitions, personal definitions and examples in sets were investigated. Concept of equal sets, subsets, union, intersection, compliment, and difference were considered as basic concepts of sets in this study. The participants of the study consisted of 79 freshmen studying in the department of elementary mathematics teacher training at a state university of Turkey. The study adopted qualitative research approach and is a sample of a case study. The data of the study was collected from Definition Knowledge Form for Sets and unstructured interviews. The results of the study indicated that most of the pre-service teachers had difficulty in giving notational definitions and daily-life examples while they gave successfully verbal definitions of the basic concepts in sets. It was revealed that verbal definitions, notational definitions, prototype examples with schema, symbols and operational properties were parts of some pre-service teachers' concept images. Furthermore, some pre-service teachers confused equal sets with equivalent sets and difference with symmetric difference. They also did not consider the universal set in defining the compliment. It was found that most of the preservice teachers had difficulty in expressing their thoughts using mathematical language throughout the study.

An Investigation of Mathematics Teachers' Specialized Content Knowledge Related to Basic Concepts about Sets

“…Başka bir ifadeyle, öğretmenlerin derinlemesine matematiksel açıklamalar getirmekten ziyade matematikle uğraşan herhangi bir bireyin cevap verebileceği genel bir matematik bilgisi ile açıklamalar yaptıkları ve de çoğunlukla yanlış açıklamalar verdikleri tespit edilmiştir. Yapılan araştırmalarda da "Kümelerde Temel Kavramlara" ilişkin matematik öğretmen adaylarının, kavramsal öğrenmeleri gerçekleştirmedikleri ve kavramların formal tanımını yapmada zorlandıkları görülmektedir (Doruk ve Çiltaş, 2020;Fischbein ve Baltsan, 1999;Speer vd., 2015;Zehir vd., 2008). Yapılan bu araştırmada, öğretmenlerin "Küme, Evrensel Küme, Sonsuz Küme" ve "Eşit Küme" kavramlarına yönelik sahip oldukları hatalı ya da eksik bilgileri aşağıdaki gibi ifade edebiliriz:…”