SONSUZ SAYI KÜMELERİ IŞIĞINDA İLKÖĞRETİM ÖĞRENCİLERİNİN SONSUZLUK ALGI VE YANILGILARININ BELİRLENMESİ

Year 2012, Issue: 33, 122 - 133, 01.12.2012

Serkan Narlı Pınar Narlı

Abstract

Sonsuzluk, gerçek ve potansiyel sonsuzluk olmak üzere ikiye ayrılmaktadır. Eski zamanlardan beri, potansiyel sonsuzluğun matematiksel sonsuzluk olduğu kabul edilmektedir. Sayı kümeleri ise, matematiksel sonsuzluğu içeren kavramların başında gelir. Bu yüzden, sayı kümeleri, sonsuzluk fikrinin belirlenmesinde kullanılabilir. Diğer taraftan, bu kümelerin tam olarak algılanabilmesi için öğrencilerde sonsuzluk fikrinin bulunması gerekir. Bu bağlamda bu çalışmanın amacı, öğrencilerin sonsuzluk fikrine ne derece sahip olduklarını, okulun öğrencilere sonsuzluk fikrini kazandırıp kazandıramadığını ve öğrencilerin bu konudaki yanılgılarını, sayı kümeleri ile ilişkilendirerek belirlemeye çalışmaktır. Bu amaçla 13-14 yaş arası İlköğretim öğrencilerinden, 131 öğrencinin görüşleri açık uçlu anket ile toplanmış ve bunların 10’u ve 3 ilköğretim öğretmeni ile yarı yapılandırılmış görüşme yapılmıştır. Sonuçta öğrencilerin sahip oldukları sonsuzluk fikirlerinde kişisel deneyimlerin yattığı ve formal eğitimin buna fazla yardım etmediği görülmüştür. Ayrıca öğrencilerin kümelerin sonsuz olup olmamasını belirlemede, sezgisel yollarla, tümevarımsal süreç ve başka bir küme ile karşılaştırma yöntemlerini kullandıkları tespit edilmiştir.  Sonsuz kümelerin karşılaştırılmasında da literatürde bahsedilen bazı yanılgıların bulunduğu anlaşılmıştır.

Keywords

Sonsuz kümeler, matematik eğitimi, sayı kümeleri, denklik

DETERMINATION OF PRIMARY SCHOOL STUDENTS’ PERCEPTIONS AND MISCONCEPTIONS OF INFINITY USING INFINITE NUMBER SET

Abstract

Infinity has divided into two componenets, the actual and potential infinity. Potential infinity has been considered as mathematical infinity for a long time. Number sets is one of the concepts involving mathematical infinity. Therefore, numer sets can be used to determine perception of infinity. On the other hand, students must have some perception of infinity to perceive this sets exactly. In this context, the aim of this study is threefold: to investigate primary school students’ perception of infinity concept, to determine to what extent schooling is successful in the attainment of the concept of infinity, and to investigate their misconceptions of the concept of infinity by associating it with number sets. Data collected through open-ended questionnaires administered to 131 primary school students aged 13-14 and semi-structured interviews conducted with ten of these students and three primary mathematics teachers. Results indicated that students’ personal experiences mainly determined their concept of infinity and that formal education had minimal effects. Also, it was determined that there were two methods which intuitively used by students to decide whether a given set is finite or infinite: induction process and comparing the given set with another set. Students’ also displayed some misconceptions about the comparison of infinite sets.

Keywords

Infinity sets, matematics education, number sets, equality

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