INVESTIGATING PRE-SERVICE MATHEMATICS TEACHERS' CONCEPTIONS OF THE PROPERTY OF COMPLETENESS OF REAL NUMBERS

Year 2024, Volume: 23 Issue: 89, 81 - 96, 09.01.2024

Özgün Şefik , Şenol Dost

https://doi.org/10.17755/esosder.1300987

Abstract

In recent years, the emphasis on concept teaching and conceptual understanding has played a central role in mathematics education curricula. The conceptualization of number systems is important to understand all areas of mathematics. Considering the difficulties experienced in the conceptualization of real numbers, it is seen that students have difficulty in understanding the relationship between real numbers and other number systems. This study aims to investigate pre-service mathematics teachers' conceptions of the property of completeness, which is the most basic element that distinguishes a real number set from other number systems. To this end, the APOS theory, which reveals the mental structures and mechanisms of the individual regarding a concept, was used. Data were collected via semi-structured interviews with three pre-service teachers. The data were analyzed using the descriptive analysis method, and the findings were presented under two themes, which are the epistemology of the concept of the property of completeness of real numbers and the mental structures in the schemas related to the property of completeness of real numbers. The findings revealed that the pre-service teachers' conceptions of the property of completeness of real numbers was mostly at the action level. The study found some mental structures such as the representation of rational numbers on a line, which should be included in the genetic decomposition to be created in the context of the APOS theory regarding the completeness of real numbers.

Keywords

Completeness axiom, conceptual understanding, conception, APOS theory

MATEMATİK ÖĞRETMEN ADAYLARININ GERÇEL SAYILARIN TAMLIK ÖZELLİĞİNE İLİŞKİN KAVRAYIŞLARININ İNCELENMESİ

Abstract

Son yıllarda kavram öğretimi ve kavramsal anlama vurgusu matematik eğitimi müfredatlarında merkezi rol oynamaktadır. Sayı sistemlerinin kavramsallaştırılması matematiğin tüm alanlarının anlaşılması bakımından önemlidir. Gerçel sayıların kavramsallaştırılmasında yaşanan güçlüklere bakıldığında, öğrencilerin gerçel sayıların diğer sayı sistemleriyle olan ilişkilerini anlamakta zorlandıkları görülmektedir. Bu çalışmanın amacı matematik öğretmen adaylarının gerçel sayı kümesini diğer sayı sistemlerinden ayıran en temel unsur olan tamlık özelliğine ilişkin kavrayışlarını incelemektir. Bu amaç doğrultusunda bireyin bir kavrama ilişkin zihinsel yapılarını ve mekanizmalarını ortaya koyan APOS teorisi kullanılmıştır. Çalışmanın verileri üç öğretmen adayıyla yarı-yapılandırılmış görüşmeler yapılarak elde edilmiştir. Veriler betimsel analiz yöntemiyle incelenmiş ve analiz sonucunda bulgular belirlenen iki ana temaya göre, gerçel sayıların tamlık özelliği kavramının epistemolojisi ve gerçel sayıların tamlık özelliğine ilişkin şemalarda yer alan zihinsel yapılar olarak sunulmuştur. Bulgulara bakıldığında öğretmen adaylarının gerçel sayıların tamlık özelliğine ilişkin kavrayışlarının çoğunlukla eylem düzeyinde olduğu görülmüştür. Buna bağlı olarak gerçel sayıların tamlık özelliğine ilişkin APOS teorisi bağlamında oluşturulacak genetik ayrışımda yer alması gereken rasyonel sayıların bir doğru üzerinde temsil edilmesi gibi zihinsel yapılar belirlenmiştir.

Keywords

Tamlık özelliği, kavramsal anlama, kavrayış, APOS teorisi

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