A quasi-experimental case study involving teaching division to low attaining grade 5 learners using variation theory.
Date
2011-05-17
Authors
Samuel, Kerry
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Abstract
This research was a quasi-experimental case study involving the teaching of division to low attaining Grade
5 learners using variation theory. This area of study interested me because as a primary school
mathematics teacher I found that many of my Grade 5, 6 and 7 learners struggled to understand the
concepts of division and successfully solve division problems. I hoped that through this research I would be
able to identify the key areas of difficulty and find ways to assist learners in overcoming these difficulties and
prevent them from occurring in future teaching and learning.
My research involved the entire Grade 5 group of learners at the school where I was teaching. However, the
intervention was conducted with a small sample of six Grade 5 learners that were in my class at the time of
the research.
This research was planned and conducted within the theoretical framework of variation theory. Variation
theory is based on the premise that “we learn from discerning variation, and what varies in our experiences
influences what we learn” (Rowland, 2008, p.153). Accordingly the focus of all teaching, within the
intervention, including all materials and examples was on highlighting variation to promote teaching and
learning.
My research involved a pre-test that was conducted with all Grade 5 learners, an intervention which involved
six low attaining learners, an immediate post-test that was only conducted with the intervention group, and a
delayed post-test that was again conducted with the whole grade. The pre-test was used to establish
common errors across the entire grade and answer the first research question of “What are the specific
features that learners struggle to understand within the concepts and procedures associated with division at
a Grade 5 level?”. I identified a range of errors across the grade and within the intervention group. All errors
corresponded to those highlighted in the literature on division.
The second research question was “How can variation theory be used to devise an intervention to improve
learners’ understanding of the concepts and procedures of division?”. My research and intervention was
based on my application of the principles of variation theory to key division concepts and procedures.
Results suggested that I was able to highlight the variation between quotitive and partitive problems quite
well. For example, I feel that by the end of the intervention learners were able to differentiate between
quotitive and partitive problems, and for the most part solve them appropriately. However, I believe that I
was unable to successfully highlight the variation in problems involving zero. This was illustrated when
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learners were unable to work confidently with and solve problems involving zero. My recommendations
include suggestions as to how this area of teaching could be improved in future.
My final research question, “What are the effects of the intervention on learner performance in this area?”
required me to reflect on the intervention and evaluate its overall success. The results suggested that
overall the intervention had allowed the six learners to close the ‘gap’ to a small degree between themselves
and their peers. This was confirmed by the post-test results where all learners improved on their pre-test
results by on average, 13% in comparison to the non-intervention group which improved by an average of
11.3%. However, I believe there were areas that could have been improved further within the intervention
which might have allowed for a more extensive closing of the gap.