Investigating Proportional Reasoning in a University Quantitative Literacy Course

Abstract

The ability to reason with proportions is known to take a long time to develop and to be difficult to learn. We regard proportional reasoning (the ability to reason about quantities in relative terms) as a threshold concept for academic quantitative literacy. Our study of the teaching and learning of proportional reasoning in a university quantitative literacy course for law students consisted of iterative action research, in which we introduced various teaching interventions and analysed students' written responses to assessment questions requiring students to explain their reasoning in situations that call for proportional reasoning. For this analysis we used a modified phenomenographic method to develop and refine a framework to code the responses. This enabled us to broadly describe the responses in terms of the concept of the liminal space that a student must traverse in coming to a full understanding of a threshold concept, and to further define the liminal space to facilitate finer description of students' responses. Our latest analysis confirmed that many university students cannot reason with proportions, that this kind of thinking is difficult to learn, and that it takes more time than is available in a one-semester course. The context and structure of the questions have a marked effect on students' ability to apply proportional reasoning successfully. The fraction of students who were classified as 'at or over the threshold' (i.e., fairly competent at proportional reasoning) after instruction ranged between 8% for the most difficult question and 48% for the easiest. Vera Frith is the coordinator of the Numeracy Centre, a unit within the Centre for Higher Education Development at the University of Cape Town. Her primary interests are the quantitative literacy development of university students and the appropriate curriculum for this purpose.Pam Lloyd is a quantitative literacy lecturer in the Numeracy Centre at the University of Cape Town and is responsible for the course for law students. She is interested in researching her own practice in order to improve teaching and learning.

The National Benchmark Quantitative Literacy Test for Applicants to South African Higher Education

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Resolución de Tipos de Problemas y Niveles del Razonamiento Proporcional en Formación Inicial de Profesores de Matemática

“…En el ámbito de la enseñanza superior y específicamente en la formación de profesores, se observa un mayor interés en el desarrollo de investigaciones relativas al estudio del conocimiento matemático y didáctico considerado necesario para enseñar la proporcionalidad (Lo, 2004;Rivas, Godino y Castro, 2012). Existen evidencias empíricas que el razonamiento proporcional sigue M siendo problemático para muchos estudiantes universitarios (Harries y Botha, 2013;Frith y Lloyd, 2016;Ben-Chaim, Ilany y Keret, 2012). Otros estudios corroboran los resultados de que estudiantes de pregrado e incluso docentes, tienen problemas en los temas de razón, proporción y fracciones reductoras (Çalışıcı, 2018;Bingölbali y Özmantar, 2010;Kaplan, İşleyen y Öztürk, 2011;Ekawati, Lin y Yang, 2018).…”

Analysis the proportional reasoning abilities of senior high school students in solving mathematical problems

“…Şen & Güler (2017) mengatakan bahwa tingkat keterampilan penalaran proporsional siswa masih rendah sebelum diberikan pengajaran strategi pemecahan masalah. Frith & Lloyd (2016) meneliti bahwa hanya 40% hingga 50% dari siswanya yang mampu mengatasi dengan baik pertanyaan yang memiliki rasio yang mudah dikenali, sehingga perlu pengajaran tentang penalaran proporsional.…”