Original Research

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

Caroline Long, Tim Dunne, Hendrik de Kock
Pythagoras | Vol 35, No 2 | a240 | DOI: https://doi.org/10.4102/pythagoras.v35i2.240 | © 2014 Caroline Long, Tim Dunne, Hendrik de Kock | This work is licensed under CC Attribution 4.0
Submitted: 07 August 2013 | Published: 12 December 2014

About the author(s)

Caroline Long, Centre for Evaluation and Assessment, Faculty of Education, University of Pretoria, South Africa
Tim Dunne, Department of Statistical Sciences, University of Cape Town, South Africa
Hendrik de Kock, Independent consultant, South Africa


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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.

Keywords

Taxonomy; Assessment; Curriculum; Mathematics

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Surette Van Staden, Puleng Motsamai
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doi: 10.4102/pythagoras.v38i1.367