Meeting the requirements of both classroom-based and systemic assessment of mathematics proficiency: The potential of Rasch measurement theory

Abstract

The 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.

Beyond test scores: A framework for reporting mathematics assessment results to enhance teaching and learning

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A standards-based approach for reporting assessment results in South Africa

“…Yet, studies based on the latent-theory model show that it is more difficult to improve from a score of, say, 80% to 85% than from 20% to 25% even though the interval (5%) is the same in both cases (Bond & Fox, 2007;Dunne et al, 2012). Fourth, reporting performance against seven levels (DBE, 2012) could compromise the accuracy of information and meaningfulness of associated reports.…”

“…Issues of whether ANA results are recorded, reported and disseminated in ways that make their meaning understandable so that they can be utilised optimally by targeted users have aroused growing interest into the role that LSAS in general and ANAs in particular, can play in improving the quality of teaching and learning in schools (Hoadley & Muller, 2014;Kanjee & Moloi, 2014). Reporting assessment results in raw scores such as percentage correct responses has received sharp criticism regarding its utility value as well as its lack of measurement accuracy and consistency (Braun & Kanjee, 2007;Bond & Fox, 2007;Dunne et al, 2012).…”

Exploring Grade Nine Geometry Spatial Mathematical Reasoning in the South African Annual National Assessment

“…The systemic assessments are administered at international, regional and national levels for different functions (Dunne et al, 2012). Ideally, data from international systemic assessments such as TIMSS evaluates the performance of a country's curriculum globally (Kellaghan et al, 2009;Resnick & Schantz, 2017).…”