From learner algebraic misconceptions to reflective educator : three cycles of an action research project.

Abstract

This was a qualitative study carried out with one grade 8 multicultural, multiethnic, mathematics class. This research study began with the idea of finding out whether the learners home language (especially Zulu Xhosa) could be linked to algebraic misconceptions. The 40 learners (participants) in my study had just been introduced to algebra. I chose the school and participants through “convenience sampling”. This made sense since I am an educator at this particular school. I had explained the meaning of the word "variable" in depth. The concepts "like terms" and "unlike terms" had been explained. The index laws for multiplication and division of the same bases had been discussed. It was within this context that the algebra worksheet was given to the learners, in the first cycle. I examined the algebra errors made by the grade 8 learners after marking the worksheets. I linked the errors to past literature on algebraic misconceptions as well as to Bernard's (2002b) error classification list. The conclusion was that the learners were making common errors which were not affected by their home language. I spent time on reflection since the outcome was not exactly what I had anticipated (that is, I had harboured strong suspicions that English second language learners would commit more algebraic errors than the English home language learners). I then considered a possible link between culture and algebraic misconceptions. Videotaped lessons were used for this purpose. However, observations of these videotaped lessons did not produce much data. I honestly could not reach a conclusion. This formed the second cycle of my action research. Prompted by the obvious lack of interaction in the video recordings from my teaching, I changed my focus to what I, the teacher, did during the lessons, and how these actions may or may not have supported some of the algebraic misconceptions. I reflected on my teaching method and recognized the need to change to a more interactive teaching style. I needed to give the learners the space to think for themselves. I would merely facilitate where necessary. In the third cycle, I drew up a set of problems which matched the new teaching style (interactive teaching).The lessons during which the new set of problems were discussed and solved, were videotaped. These videotaped lessons were analyzed and a completely different picture emerged. The learners were absolutely responsive and showed a side of them that I had not seen before! This study came to be an action research study because I went through three cycles of reflecting, planning, acting and observing and then reflecting, re-planning, further implementation, observing and acting etc.