Abstract:
The concept of pattern recognition lies at the heart of numerous deliberations concerned with new
mathematics curricula, because it is strongly linked to improved generalised thinking. However none of
these discussions has made the deceptive nature of patterns an object of exploration and
understanding. Yet there is evidence showing that pattern recognition has both positive and negative
effects on learners’ development of concepts. This study investigated how pattern recognition was both
illuminating and illusionary for Grade 11 learners as they factorised quadratic trinomials. Psillos’s fourconditions
model was used to judge the reasonableness of learners’ generalisations in six selected
examples. The results show that pattern recognition was illuminating in the first three examples where
learners made use of localised pattern recognition. In one example, pattern recognition was coincidental
but not beneficial in terms of conceptual understanding. In the last two examples localised pattern
recognition was at the centre of learner confusion as they failed to extend its application beyond the
domain of the examples that generated the pattern. Learners’ confusion with pattern recognition could
be attributed to teachers’ failure to meet four important conditions for good generalisations. Results
from this study confirm earlier studies showing that abduced generalisations developed out of a few
localised instances might be illuminating at first but might not provide the best explanation when
extended beyond the localised domain. Further studies are needed that assist in developing patternaware
teachers.
