# Mathematical

**Topics:**Mathematics, Problem solving, Mathematics education

**Pages:**21 (7079 words)

**Published:**June 20, 2013

Hamsa Venkat 1 Mellony Graven 2 Erna Lampen 1 Patricia Nalube 1 1 Marang Centre for Mathematics and Science Education, Wits University hamsa.venkatakrishnan@wits.ac.za; christine.lampen@wits.ac.za; patricia.nalube@wits.ac.za 2 Rhodes University

m.graven@ru.ac.za

In this paper we consider the ways in which the Mathematical Literacy (ML) assessment taxonomy provides spaces for the problem solving and reasoning identified as critical to mathematical literacy competence. We do this through an analysis of the taxonomy structure within which Mathematical Literacy competences are assessed. We argue that shortcomings in this structure in relation to the support and development of reasoning and problem solving feed through into the kinds of questions that are asked within the assessment of Mathematical Literacy. Some of these shortcomings are exemplified through the questions that appeared in the 2008 Mathematical Literacy examinations. We conclude the paper with a brief discussion of the implications of this taxonomy structure for the development of the reasoning and problem‐solving competences that align with curricular aims. This paper refers to the assessment taxonomy in the Mathematical Literacy Curriculum Statement (Deparment of Education (DOE), 2007).

Mathematical Literacy was introduced as a new subject in the post-compulsory Further Education and Training (FET) curriculum in 2006. Its introduction made a mathematically-oriented subject – either Mathematics or Mathematical Literacy – compulsory for all FET learners. The curriculum statement for Mathematical Literacy defines the subject in the following terms: Mathematical Literacy provides learners with an awareness and understanding of the role that mathematics plays in the modern world. Mathematical Literacy is a subject driven by life-related applications of mathematics. It enables learners to develop the ability and confidence to think numerically and spatially in order to interpret and critically analyse everyday situations and to solve problems. (DOE, 2003, p. 9) This definition alongside the broader description of the new subject’s aims in this document places emphasis on the need to develop life-oriented competences for a range of everyday situations in which mathematical reasoning and mathematical tools can be brought to bear productively to aid informed decision making and problem solving. Situational reasoning relating to the identification and selection of salient features of the context is therefore required alongside and integrated with mathematical reasoning.

Pythagoras, 70, 43-56 (December 2009)

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Critiquing the Mathematical Literacy assessment taxonomy

Within this definition, we highlight two features that the broader literature suggests are central to the notion of mathematical literacy1 that is promoted in the South African rhetoric: firstly, the need for the reasoning that is implicated within the need to “think numerically and spatially” and to “interpret” and “critically analyse everyday situations”; and secondly, the need for “problem solving”. Both of these aspects have significant bodies of literature associated with them in the field of mathematics education – some focused on the teaching and learning of mathematics, and some specific to discussions of mathematical literacy. Olkin and Schoenfeld (1994), focusing on mathematics, describe problem solving in terms of “confronting a novel situation and trying to make sense of it” (p. 43). Steen, a leading advocate of what he terms “quantitative literacy” comments that centrally what quantitatively literate citizenship requires is “a predisposition to look at the world through mathematical eyes … and to approach complex problems with confidence in the value of careful...

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