Original Research

Proportional reasoning as a threshold to numeracy at university: A framework for analysis

Pam Lloyd, Vera Frith
Pythagoras | Vol 34, No 2 | a234 | DOI: https://doi.org/10.4102/pythagoras.v34i2.234 | © 2013 Pam Lloyd, Vera Frith | This work is licensed under CC Attribution 4.0
Submitted: 14 June 2013 | Published: 10 October 2013

About the author(s)

Pam Lloyd, Numeracy Centre, Academic Development Programme, University of Cape Town, South Africa
Vera Frith, Numeracy Centre, Academic Development Programme, University of Cape Town, South Africa


There is a generally acknowledged need for students to be quantitatively literate in an increasingly quantitative world. This includes the ability to reason critically about data in context. We have noted that students experience difficulty with the application of certain mathematical and statistical concepts, which in turn impedes progress in the development of students’ critical reasoning ability. One such concept, which has the characteristics of a threshold concept, is that of proportional reasoning. The main focus of this article is a description of the development of a framework using an adapted phenomenographic approach that can be used to describe students’ experiences in the acquisition of the concept of comparing quantities in relative terms. The framework has also helped to make explicit the elements that constitute a full understanding of the requirements for the proportional comparison of quantities. Preliminary results from using the framework to analyse students’ responses to assessment questions showed that many students were challenged by proportional reasoning. When considering the notion of the liminal space that is occupied en route to a full understanding of a threshold concept, about half of the students in the study were at the preliminal stage of understanding the concept and very few were at the threshold.


proportional reasoning; proportional comparison; threshold concepts; quantitative literacy; academic numeracy


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