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.
Highlights
Usiskin (2005) highlighted the critical mathematical developments that take place during the “transition years”, most notably the transition from whole number1 to real number
The overall result is a conceptual system of enormous power and flexibility (Skemp, 1971, p. 226). It is this structure of number systems, where aspects of the system, for example the fraction notation used for both fraction and ratio, deceptively alike and yet subtly different, that is the Rubicon for most learners of mathematics as they make the transitions from whole numbers to rational numbers and to real numbers
A secondary analysis of the Trends in International Mathematics and Science Study (TIMSS) 1999 and 2003 results investigating only the items which fell into the domain ratio, proportion and percent, showed that in general South African Grade 8 learners do not have an operational understanding of this domain; they are not able to solve problems in which these concepts are embedded
Summary
The developments in mathematics that take place in Grades 7 to 9 constitute critical nodes in a learner’s schooling. One of the major transitions to be made is from whole numbers to real numbers, which involves the understanding 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 insights and 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
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
