The classification of examples used by teachers and the analysis of its relationship with dimensions of instructional explanation

For many years, there have been so many different on how to teach mathematics better. In spite of the differences among them, they are all agreed on the importance of the examples in mathematics education as an instructional tool because people tend to associate the concepts and especially mathematical relations through examples. This situation requires the efficient usage of examples and the explanations carried out by these examples in the classroom. In the studies, the types of examples and various example classifications which these types of examples belong to, have been encountered. However, these classifications are not directly related to the teachers, and they have some deficiencies in some points and there seems to be confusion about these classifications. In the light of these facts, our study aims to fulfill two main goals. The first one is the classification of examples used by teachers, and the second one is to identify the relationship between the instructional explanations and the examples used by teachers. Within this context, the study has been carried out with five mathematics teachers in two different Anatolian High Schools. Accordingly, collecting the data to classify the examples used by teachers took two years and 275 lessons were observed. In addition to these observations, the informal interviews were conducted with teachers before and after the lessons. Moreover, the data were collected only through observations to find out the relationship between the type of examples used by teachers and the dimensions of the instructional explanations in their lessons. For analyzing the data obtained in the research, we benefited from both content analysis and descriptive analysis. The content analysis is used to classify the examples. The descriptive analysis is utilized according to the roof developed by Kinach to identify the dimensions of teachers' instructional explanations developed by Kinach. In accordance with the results of the content analysis, the example codes are created and brought together to form the categories. Furthermore, the accuracy of these categories are checked by applying the Clustering analyze technique. In this thesis, we conclude that the examples used by teachers can be classified into six different categories: start up examples, extreme examples, non-examples, counter examples, improving examples and standard examples. In addition, it is found that the teachers in descriptive and operational dimension use mostly standard and improving examples. Also it is seen that the teachers in descriptive dimension use non-example more in their lesson. Since it has been seen that the teachers prefer the examples which show how to use definitions, rules and relations by various operations more rather than explaining the meanings of these in their lessons, the teachers have been recommended to spend more time for the definitions and the rules and especially to give place to the non-examples as well as the standard examples and improving examples while illustrating the definitions and the rules.