Mathematics, curriculum and assessment: The role of taxonomies in the quest for coherence

Authors: Caroline Long, Tim Dunne and Hendrik de Kock

Bloom’s taxonomy is one of the taxonomies most frequently used for assessment, curriculum design and defining goals for instructional activities. However, it does not provide adequate feedback to teachers on how to improve or direct instructional activities; and neither does it fully relate to the assessment terms in the mathematics curriculum.

Coherence in the language used for mathematics assessment is needed for curriculum design and assessment; and to enable teachers to translate educational objectives into classroom activities and assessment tasks. In addition, a coherent framework is needed for qualifications and educational institutions to be universally recognised and evaluated.

In order to select an appropriate taxonomy, a few aspects need to be taken into consideration:

Firstly, the difficulty of assigning mathematics items to one particular mathematics category; and the additional difficulty of assigning an item to a cognitive category, since this will be influenced by what the learner already knows.

A second consideration is that the categories in the taxonomy must align with teaching and learning; since feedback from a particular category should provide information to the teacher about needs and interventions.

This paper discusses and compares six taxonomies in respect of their suitability. These are: Bloom’s original taxonomy (1956); Bloom’s revised taxonomy (2002); TIMSS (1995/99); TIMSS (2003); TIMSS (2007/11); RNCS (2002) & CAPS (2011)

Finally Usiskin’s (2012) taxonomy is discussed. He proposes that, for a full understanding of concepts, five dimensions are necessary: The skills-algorithm dimension; the property-proof dimension; the use-application dimension; the representation-metaphor dimension; and the history-culture dimension. Dimension five, however, is difficult to assess using test items, and was subsequently not used in this study.

The study found that a two-way matrix with a variation of Bloom’s revised taxonomy on the one axis and Usiskin’s four dimensions on the other axis provided an alternative to current taxonomies; was more directly applicable to mathematics; and provided the necessary coherence when reporting results.

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