From learner algebraic misconceptions to reflective educator : three cycles of an action research project.
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Date
2010
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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.
Description
Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2010.
Keywords
Algebra--Study and teaching (Secondary)--South Africa., Mathematical ability., Action research in education--South Africa., Theses--Education.