### Browsing by Department "ADP: Numeracy Centre"

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- ItemOpen AccessMeeting the requirements of both classroom-based and systemic assessment of mathematics proficiency: the potential of Rasch measurement theory(AOSIS, 2012) Dunne, Tim; Long, Caroline; Craig, Tracy S; Venter, ElsieThe challenges inherent in assessing mathematical proficiency depend on a number of factors, amongst which are an explicit view of what constitutes mathematical proficiency, an understanding of how children learn and the purpose and function of teaching. All of these factors impact on the choice of approach to assessment. In this article we distinguish between two broad types of assessment, classroom-based and systemic assessment. We argue that the process of assessment informed by Rasch measurement theory (RMT) can potentially support the demands of both classroom-based and systemic assessment, particularly if a developmental approach to learning is adopted, and an underlying model of developing mathematical proficiency is explicit in the assessment instruments and their supporting material. An example of a mathematics instrument and its analysis which illustrates this approach, is presented. We note that the role of assessment in the 21st century is potentially powerful. This influential role can only be justified if the assessments are of high quality and can be selected to match suitable moments in learning progress and the teaching process. Users of assessment data must have sufficient knowledge and insight to interpret the resulting numbers validly, and have sufficient discernment to make considered educational inferences from the data for teaching and learning responses.
- ItemOpen AccessProportional reasoning as a threshold to numeracy at university: a framework for analysis(AOSIS, 2013) Lloyd, Pam; Frith, VeraThere 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.