Towards validation of a rational number instrument: An application of Rasch measurement theory

Venkat and Spaull (2015) reported that 79% of 401 South African Grade 6 mathematics teachers showed proficiency of content knowledge below Grade 6–7 level in a Southern and East African Consortium for Monitoring Educational Quality (SACMEQ) 2007 mathematics teacher test. Universities recruit and receive students from some of these school where these teachers are teaching. In the previous years of teaching first-year students in the mathematics module in the Foundation Phase teacher development programme, we noticed that each cohort of prospective teachers come with knowledge bases that are at different levels. These classes, of students’ with varied mathematics knowledge, are difficult to teach unless you have some idea of their conceptual and procedural gaps. This varied knowledge base is greatly magnified in the domain of rational numbers in which they are expected to be knowledgeable and confident in order to teach and lay a good foundation in future teaching. An instrument, functioning as a diagnostic and baseline test for the 2015 first-year Foundation Phase cohort, was constructed at the university level in the fractions-decimals-percentages triad. This instrument aimed at gauging the level of students’ cognitive understanding of rational numbers as well as evaluating the validity of the instrument that was used to elicit their mathematical cognition. All the participants admitted into the Foundation Phase teacher training programme were tested on 93 items comprising multiple choice, short answer and constructed response formats. That elicited both conceptual and procedural understanding.