From whole number to real number: Applying Rasch measurement to investigate threshold concepts

Abstract

The developments in mathematics that take place in Grades 7 to 9 constitute critical nodes in a learner’s scholing. One of the major transitions to be made is from whole numbers to real numbers, which involves theunderstanding of rational (and irrational) numbers, and concepts such as ratio, proportion and percent. I hypothesise that ratio is a threshold concept that provides the conceptual gateway to higher order concepts. The research problem is to describe the learning challenges and provide an array of insightsand strategies that will inform teaching. The theory of conceptual fields provides the framework for this research (Vergnaud, 1988). The Rasch measurement model (Rasch, 1960/1980) articulates the qualitative and quantitative aspects of the research. This paper provides an overview of the broader study and reports on an aspect of the data analysis.