Repeating Decimals and Irrational Numbers on the Number Line: Through the Lens of Pre-Service and In-Service Mathematics Teachers

Abstract

Abstract: The purpose of the study is to examine how pre-service and in-service mathematics teachers locate repeating decimals and irrational numbers on the number line. The participants of the study included 274 pre-service and 106 in-service mathematics teachers. Data were collected through a written questionnaire including four open-ended questions. In the questionnaire, preservice and in-service teachers were asked to determine whether the given numbers 0.444…,√2, 𝜋 and e can be located on the number line, they cannot be located on the number line or they do not have exact places on the number line. Additionally, they were asked to justify their responses to each of the questions in the questionnaire. Open coding was performed while analysing data. Findings indicated that while majority of the participants stated that given repeating decimal, i.e. 0.444…, can be located on the number line, for the given irrational numbers, i.e. √2, 𝜋 and e, only small number of participants considered that they can be located on the number line. The main sources of the consideration that the given numbers do not have an exact place or they cannot be located on the number line were identified as approximation, infinity, irrationality and uncertainty in the justifications.