Browsing by Author "Long, Caroline"

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    Meeting 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, Elsie
    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.
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    Proficiency in the multiplicative conceptual field: using Rasch measurement to identify levels of competence
    (Taylor & Francis, 2010) Long, Caroline; Dunne, Tim; Craig, Tracy S
    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 problem 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.
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    A small-scale investigation into teachers' access to the regulating principles underlying the "new mathematics" curriculum in the Junior Primary phase
    (1995) Long, Caroline; Ensor, Paula
    This research project focuses on the "new primary mathematics" curriculum that has been implemented in the schools in the Western Cape over the past six years. The specific question I addressed was, 'What access do teachers have to the regulating principles underpinning the 'new primary mathematics' curriculum". The term "regulating principles" is drawn from the work of Paul Dowling (1993;98). In terms of this research, the regulating principles are the theoretical underpinnings to the new curriculum, which include substantially a theory of learning. I explore access to the regulating principles through semi-structured interviews with six teachers, who have implemented this new approach with different degrees of success, as measured in their own terms. I also investigate the official Teachers' Guide for Mathematics (Cape Education Department, 1993) for explicitness of theoretical underpinnings. An analysis of the teachers' guide indicated that the regulatory principles were not made explicit and the research indicates that the teachers in my sample have restricted access to these principles. I conclude that teachers who have little access to the regulating principles are constructed as a subordinate voice in relation to teacher educators, and must of necessity rely on procedure for their practice and be subject to external validation. This raises questions as to the successful implementation of the curriculum, in that it limits access by teachers to the educational debates surrounding theories of knowledge and theories of learning, and so inhibits teacher involvement in curriculum implementation. It also limits the ability of teachers to interrogate their own practice.