Middle school students' conceptualization of infitiny

When mathematics curriculum is examined, one can see that the concept of infinity is closely related to the concepts of natural numbers, rational numbers, line and line segments, and limit. It plays an important role especially in the formation of the number concept and its development. Understanding the concept of infinity is also necessary for learning advanced concepts such as limit, derivative, integral and infinite sets. However, not much is known about how students understand the concept of infinity. In order to help students learn the concept of infinit, one should first uncover students' current conceptualizations and understandings of this concept. Motivated from the lack of previous research on this topic, this study aims to identify middle school students' (5th, 6th, 7th and 8th graders) conceptualization and understanding of infinity. With this aim in mind, an open ended test including questions related to the concept of infinity, big numbers, infinity in numerical context, limit and infinite sets is given to the participants and clinical interviews have been conducted. The sample of the study consisted of 5th, 6th, 7th and 8th graders from three middle schools in the city center of Kocaeli in the academic year 2012-2013. The data collected trough the test and clinical interviews were analyzed using content analysis method. A coding manual with categories and subcategories were constructed based on the responses of the participants to the test questions. A similar method was used to analyze the data of clinical interviews. Results of the study revealed that the participants defined infinity as 'without an end', 'in progress' and 'never lasting' and perceived infinity 'as a process that never ends'. It is also found that the participants had three different perceptions of infinity namely mathematical, phsyical and affective. The analyses based on big numbers revealed that the participants defined numbers which were very big and whose values were indeterminite as infinite. The analyses of the responses related to the questions about infinity in a numerical context and limit revealed that the participants demonstrated a conceptualization of static infinity for infinite sets and a conceptualization of potential infinity for limit context. When natural number and even natural numbers sets were compared, the participants thought that the methods used for comparing finite sets could also be used for infinite sets, and they used similar methods to compare infinite sets. The discussion section of this study included the comparison of the findings of current study with those of the previous studies and some suggestions have been made as educational implications and for future studies. Key words: Infinity, big numbers, infinite numbers, limit, infinite sets, middle school students.