Abstract:
A challenge encountered when monitoring mathematics teaching and learning at high school
is that taxonomies such as Bloom’s, and variations of this work, are not entirely adequate
for providing meaningful feedback to teachers beyond very general cognitive categories
that are difficult to interpret. Challenges of this nature are also encountered in the setting of
examinations, where the requirement is to cover a range of skills and cognitive domains. The
contestation as to the cognitive level is inevitable as it is necessary to analyse the relationship
between the problem and the learners’ background experience. The challenge in the project
described in this article was to find descriptive terms that would be meaningful to teachers.
The first attempt at providing explicit feedback was to apply the assessment frameworks
that include a content component and a cognitive component, namely knowledge, routine
procedures, complex procedures and problem solving, currently used in the South African
curriculum documents. The second attempt investigated various taxonomies, including those
used in international assessments and in mathematics education research, for constructs that
teachers of mathematics might find meaningful. The final outcome of this investigation was
to apply the dimensions required to understand a mathematical concept proposed by Usiskin
(2012): the skills-algorithm, property-proof, use-application and representation-metaphor dimension.
A feature of these dimensions is that they are not hierarchical; rather, within each of the
dimensions, the mathematical task may demand recall but may also demand the highest level
of creativity. For our purpose, we developed a two-way matrix using Usiskin’s dimensions on
one axis and a variation of Bloom’s revised taxonomy on the second axis. Our findings are that
this two-way matrix provides an alternative to current taxonomies, is more directly applicable
to mathematics and provides the necessary coherence required when reporting test results to
classroom teachers. In conclusion we discuss the limitations associated with taxonomies for
mathematics.
