### EXPLORING PRE-SERVICE MATHEMATICS TEACHERS’ UNDERSTANDINGS OF COUNTABILITY AND INFINITY IN WEBQUEST BASED LEARNING ENVIRONMENT

#### Abstract

Infinity concept is difficult to understand because of its nature. Even if the concept of infinity doesn’t directly take part in mathematics curriculum, it takes place on many topics such as lines, planes, sets, irrational numbers, limit, differentiation, and integration. The present study examined pre-service mathematics teachers’ understandings of infinity and countability concepts in WebQuest based learning environment. Twenty-nine pre-service teachers participated at the study. Data were collected through a questionnaire developed by the researchers and semi-structured interviews. Qualitative data were analyzed by using phenomenology research method. The findings of this study revealed that pre-service teachers generally defined infinite sets as the sets whose elements continue infinitely. They inclined to define countable sets as bounded sets, finite sets, and the sets with known elements. Whereas most of the students stated countable finite sets and countable infinite sets were existent, they also expressed uncountable finite sets and uncountable infinite sets were non-existent. They used natural numbers set as an example for the countable infinite sets. This research presented some implications for teacher education programme in the light of obtained findings.

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