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Original Research

Proportional reasoning ability of school leavers aspiring to higher education in South Africa

Vera Frith, Pam Lloyd

Pythagoras; Vol 37, No 1 (2016), 10 pages. doi: 10.4102/pythagoras.v37i1.317

Submitted: 19 November 2015
Published:  03 December 2016


The ability to reason about numbers in relative terms is essential for quantitative literacy, which is necessary for studying academic disciplines and for critical citizenship. However, the ability to reason with proportions is known to be difficult to learn and to take a long time to develop. To determine how well higher education applicants can reason with proportions, questions requiring proportional reasoning were included in one version of the National Benchmark Test as unscored items. This version of the National Benchmark Test was taken in June 2014 by 5 444 learners countrywide who were intending to apply to higher education institutions. The multiple choice questions varied in terms of the structure of the problem, the context in which they were situated and complexity of the numbers, but all involved only positive whole numbers. The percentage of candidates who answered any particular question correctly varied from 25% to 82%. Problem context and structure affected the performance, as expected. In addition, problems in which the answer was presented as a mathematical expression, or as a sentence in which the reasoning about the relative sizes of fractions was explained, were generally found to be the most difficult. The performance on those questions in which the answer was a number or a category (chosen as a result of reasoning about the relative sizes of fractions) was better. These results indicate that in learning about ratio and proportion there should be a focus on reasoning in various contexts and not only on calculating answers algorithmically.

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Author affiliations

Vera Frith, Centre for Higher Education Development, University of Cape Town, South Africa
Pam Lloyd, Centre for Higher Education Development, University of Cape Town, South Africa


Proportional reasoning; quantitative literacy; school-leavers; higher education


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1. The quantitative literacy of South African school-leavers who qualify for higher education
Robert Prince, Vera Frith
Pythagoras  vol: 38  issue: 1  year: 2017  
doi: 10.4102/pythagoras.v38i1.355

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