Future teachers’ reflections on mathematical errors made in their teaching practice

Abstract

AbstractThis study answers the following research questions: 1) What types of mathematical errors do future teachers identify when they reflect on their practice? and 2) Which levels of development of the didactic suitability assessment competence for the “errors” component can be inferred when they reflect on their practice? To answer these questions, we explain the Didactic Suitability Criteria construct and describe the associated training cycle structure in the theoretical and methodological framework sections. We followed a qualitative research methodology that mainly consists of thematic analysis. The study conducted allows finding inductive categories of types of mathematical errors, such as error in the task instructions, error of proposition, procedural error, error in the representation, error in the definition and error in the argument. It also enables establishing levels of development of the didactic suitability assessment competence of future teachers for the “errors” component. The main conclusion of this research is the importance of the context to decide what a mathematical error is. The need to further examine the notion of mathematical error in the training of future mathematics teachers is also stressed. Another conclusion is the development of a rubric that allows for more accurate and deeper reflections of future teachers on the errors made.