Secondary school teachers' pedagogical content knowledge of some common students' errors and misconceptions in sets

Abstract

The study investigated teachers' pedagogical content knowledge of common students' errors and misconceptions in sets. Five mathematics teachers from one Lesotho secondary school were the sample of the study. Questionnaires and interviews were used for data collection. The results show that teachers were able to identify the following students' errors: (i) writing an empty set as {0} instead of { }; (ii) treating the repeating elements of the union of two sets as distinct and (iii) treating an infinite set as a finite set. Teachers were not able to identify the errors where students (i) treated infinity as a number; (ii) said that the members of countable infinite sets cannot be compared and (iii) that curly brackets are used only when listing the members of a set. The identified errors were associated with some misconceptions. Depending on the nature of the students' tasks teachers' strategies and explanations of dealing with the errors and misconceptions were inclined towards calling on procedural knowledge. Only a few cases of conceptual knowledge were noted. Implications for teaching are proposed.