'Profound understanding of fundamental mathematics' and mathematical life histories of some teachers teaching mathematics in the intermediate phase in KwaZulu-Natal.

Abstract

This study had two components: 1) Investigating the conceptual understanding of teachers teaching elementary mathematics at primary schools in the province of KwaZulu-Natal, who had been successful in their mathematics modules in the National Professional Diploma in Education (NPDE) teacher upgrading program, and 2) Investigating the influence of their mathematical lifehistories on their understanding and personal philosophies about mathematics. It firstly required the NPDE students from the University of KwaZulu-Natal to complete a questionnaire adapted from the TELT interview schedule used by Liping Ma (1999). This questionnaire was to assess whether these high scoring teachers had an understanding of basic mathematical concepts that could have been regarded as being profound. The second part of the study was designed in order to get these teachers to examine their mathematical life histories and then to look at how their life histories could have influenced their level of understanding. It was found that these teachers were procedurally capable and were aware of the algorithms that could be used to solve the problems posed, but they lacked deep understanding of the concepts and were thus conceptually weak. None of the teachers demonstrated an understanding of the fundamental mathematics concepts that were assessed, that could be regarded as been ‘profound’. The mathematical life history portion of this study revealed that these teachers, having experienced mathematics education very differently due to their Apartheid influenced education, mentioned that there were definite influences that had a marked effect on their outlook on the subject and thus their belief in their ability to do basic/ fundamental mathematics.