Knowledge of Flexible Mental Computation of Pre-Service Elementary Mathematics Teachers Upon Entry to University

This study sets out to determine the knowledge of flexible mental computation of pre-service elementary mathematics teachers when enrolling at university. Knowledge of the existing flexible mental computation skills of pre-service teachers could inform teacher educators’ preparation for teaching by determining the algorithms that pre-service teachers are unable to calculate. Such knowledge could also inform teacher educators as to why pre-service teachers are unable to calculate the algorithms. The study produced a domain-specific instrument in the form of a diagnostic test that teacher educators could adopt in their teaching to elicit pre-service teachers’ knowledge, a gap that this study aims to bridge. A diagnostic test comprising 21 items was administered by the researcher to 51 year-one pre-service teachers who agreed to participate in the study. Findings of the study indicate that the majority of the pre-service teachers who participated in the study have a limited understanding of the magnitude of numbers, of basic number facts, of the relationship between numbers and of the relationship between basic operations to calculate flexibly. The argument of the study is that teacher educators’ instruction would be relevant and successful if focused on the cognitive needs of pre-service teachers and the mathematical concepts that they are going to teach. Therefore, this study recommends that teacher educators establish pre-service teachers’ knowledge prior to instruction for relevance and for the success of teaching.