Taxonomy matters : cognitive levels and types of mathematical activities in mathematics examinations

We argue that there are intrinsic difficulties in using the Subject Assessment Guidelines for Mathematics (SAGM) for evaluating the standard of a South African matriculation mathematics examination and for determining how it aligns with the curriculum. Our argument has two prongs. First, the SAGM taxonomy conflates cognitive level with type of mathematical activity; we contend that such a conflation leads to problems in assessing the complexity of the examination item. Second, the SAGM taxonomy provides no space for important mathematical activities such as justification and conjecturing despite the promotion of these activities in key curriculum documents (Department of Education, 2003). This absence may obscure weak alignment of the examination and the curriculum. These arguments are illustrated through examples taken from the 2008 Department of Education (DOE) and Independent Examination Board (IEB) Grade 12 Mathematics examination papers. We also examine other well-known taxonomies in order to discern those aspects of a taxonomy which may be useful for evaluation and alignment. We conclude with the construction of a matrix that could provide an appropriate taxonomy for the South African matriculation Mathematics examination. It has activities on one axis and levels of complexity on the other.