Caroline Long

Applying Rasch Measurement in Mathematics Education Research: Steps towards a Triangulated Investigation into Proficiency in the Multiplicative Conceptual Field.

Educational measurement is generally thought of as empirical, quantitative, and large-scale, whose purpose is to monitor educational systems. Sociocognitive studies, on the other hand, are associated with small-scale, theoretical, and qualitative studies, the purpose of which is to conduct fine-grained analysis of learning or teaching, or to comprehend in depth the development of a mathematical topic. This article describes an application of the Rasch model in mathematics education in which theory and measurement are used interactively to provide greater understanding of a constellation of mathematical concepts within the multiplicative conceptual field. It is affirmed here that Rasch measurement provides the basis for a coherent research model based on principles of measurement, while giving consideration to the theoretical construct. Challenges to educational measurement demand that researchers provide substantive theoretical models to support, firstly, educational measurement and, secondly, the level of inference that can be made from the measurement outcomes.

Proficiency in the multiplicative conceptual field : using Rasch measurement to identify levels of competence

Abstract In the transition years, Grades 7 to 9, the shift from natural numbers to rational numbers and the associated multiplicative concepts prove challenging for many learners. The new concepts, operations and notation must be mastered if the student is to thereafter rise to meet the challenges of algebra and more advanced and powerful mathematics. The multiplicative conceptual field (MCF) groups together such concepts as fraction, ratio, rate, percentage and proportion, all of which are related yet subtly distinct from one another, each with its own challenges. Rasch analysis allows us to compare the difficulty of mathematical problems located within the MCF while, on the same scale, locating the degree to which individual learners have mastered the necessary skill set. Such location of problems and learners on the same unidimensional scale allows for fine-grained analysis of which aspects of the problems being analysed make one problrm more difficult than another. Simultaneously the scale gives the teacher clear evidence of which students have mastered which concepts and skills and which have not, thereby allowing more targeted assistance to the class and individual learners. This paper illustrates the process involved in such analysis by reporting on results located within a larger study. It is suggested that implementing Rasch analysis within the school classroom on appropriately designed assessment instruments would provide clarity for the teacher on the locations of difficulty within the problems used in the assessment and the relative degree to which individual learners are achieving success at mastering the targeted concepts.

Enabling and Constraining Conditions of Professional Teacher Agency: The South African Context.

The South African people have a history of resistance to domination, injustice and inequality. It is therefore surprising that there has been an increase in social inequality, since the start of political democracy in 1994. Recently, the five teachers’ unions refused to administer the Annual National Assessments. This action indicates some resistance to domination. In this article, we will first explore the concept of professional teacher agency in the light of teaching, both as a profession and as a vocation constrained by prior experience and social context. Second, we will draw on the current assessment context to outline its problems and perspectives, and consider within this context the enabling and constraining conditions for teacher agency. Third, we will discuss how assessment as a tool for monitoring teacher performance may impede the conditions for quality education. Finally, we would like to propose that the delivery of a good quality education requires adopting a teacher education model which supports agency, and in which the design of diagnostic assessments is locally responsive.

Understanding Monitoring Systems in Different Contexts: A Focus on Curriculum Development, Teacher Agency and Monitoring Systems

The monitoring of education systems to improve teaching and learning has not yielded the results expected in some countries. Two fundamental problems identified by Bennett and Gitomer (2009), for the situation in the United States, are firstly, that there are significant consequences for teachers should their classes perform poorly in system wide tests, and secondly that many current monitoring programmes have little educational value.

A Comparative Investigation of South Africa's High-Performing Learners on Selected TIMSS Items Comprising Multiplicative Concepts.

South Africa participated in TIMSS from 1995 to 2015. Over these two decades, some positive changes have been reported on the aggregated mathematics performance patterns of South African learners. This paper focuses on the achievement patterns of South Africa’s high-performing Grade 9 learners (n = 3378) in comparison with similar subsamples of learners from Australia (n = 6581) and England (n = 3439) whose education systems are regarded as comparable. The aim of this study is to describe the relative strengths and weaknesses of these learners with reference to a selected subset of the TIMSS-2011 items comprising multiplicative concepts. The focus is on a specific though important content subdomain, the multiplicative conceptual field, which is considered a crucial learning area at this phase of schooling. The percentage correct scores were compared. In addition a Rasch analysis was applied to render both item difficulty and person proficiency on a single scale. In particular, the research outcome shows that this subset of South African Grade 9 students is able to solve routine problems, but lacks proficiency when it comes to application-type or reasoning-type problems. The Australian and English subsets show comparable strengths across all three problem types. We conclude that the factors determining performance include mathematical difficulty. However, where radically different outcomes across the three countries emerge, such differences may be explained by country-specific curricula implementation.

An Application of the Rasch Measurement Theory to an Assessment of Geometric Thinking Levels

The purpose of this study is to apply the Rasch model to investigate both the Van Hiele theory for geometric development and an associated test. In terms of the test, the objective is to investigate the functioning of a classic 25-item instrument designed to identify levels of geometric proficiency. The dataset of responses by 244 students (106 for a pre-test and 138 for a post-test) of whom 76 sat both the pre-test and the post-test. The summary item statistics do not show statistically discernible differences between observed and expected scores under the Rasch model (chi-square statistic). The Rasch analysis confirms to a strong extent the Van Hiele theory of geometric development. The study identifies some problematic test items as they only require knowledge of a specific aspect of geometry instead of testing geometric reasoning. In terms of the Van Hiele theory, the Rasch analyses identified as problematic some items about class inclusion, an issue that has also been raised in other studies.