Session Information
09 SES 06 C, Assessment of Competencies and Attitudes in Mathematics Classrooms
Paper Session
Contribution
The question asked by governments and education departments around the world is how to improve achievement in mathematics across the school population in order to prepare learners for greater participation in the economy. Large-scale international studies and national systemic studies provide information at the level of education systems by aggregation of results, and offer some insight into current grade-specific outcomes at school and classroom levels. However the translation of large-scale and systemic results into coherent policy at the curriculum level, or information at the teaching and learning site in the classroom is less clear.
In this research study into rational number and proportional reasoning, we ask "How can the extant implicit and local ideas of learners be transformed into mathematics concepts and theorems that can be generalised to many classes of problems?” The theory of conceptual fields (Vergnaud, 1988, 1994), best attends to the essential features of mathematics by making explicit the structural links across concepts, and by tracing the filiations and thresholds along the mathematical path from early arithmetic to advanced mathematics. The development along a mathematical path requires analysis of both problem situations, in which the desired concepts and theorems of the curriculum are embedded, and the observation of the current concepts-in-action and theorems-in-action with which students engage the problem situations. The concepts-in-action and theorems-in-action provide the malleable building blocks, which teachers may use to help learners transform current thinking into generalizable concepts and actions.
The theoretical tools required for the analysis of problem situations and the analysis of learner responses are provided by Vergnaud’s explication of the multiplicative conceptual field (1983), Parker and Leinhardt’s analysis of the percent concept (1995), and other mathematics education literature providing insight into elements such as proportional reasoning.
The need for a specific theory of mathematics education assessment has been proposed by Webb (1992) as a response to the complexity inherent in both mathematics itself, and to the multiple paths to attaining proficiency. One of the purposes of this paper is to exhibits the potential of a model, drawing on the theory of conceptual fields and applying a Rasch analysis, to provide diagnostic insights into the plausible mathematical development of individual learners.
Method
Expected Outcomes
References
Mullis, I. V. S., Martin, M. O., Smith, T. A., Garden, R. A., Gregory, K. D., Garden, R.A.,, Gonzalez, E. J., et al. (2003). TIMSS Assessment Frameworks and Specifications 2003. Chestnut Hill, MA: International Study Centre, Boston College. Parker, M., & Leinhardt, G. (1995). Percent: A privileged proportion. Review of Educational Research, 65(4), 421-481. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. (Expanded edition (1980) with foreword and afterword by B.D. Wright, (1980) Chicago: The University of Chicago Press. ed.). Copenhagen: Danish Institute for Educational Research. Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades. Hillsdale, NJ: National Council of Teachers of Mathematics. Vergnaud, G. (1994). Multiplicative conceptual field: what and why? In G. Harel & J. Confrey (Eds.), Multiplicative reasoning (pp. 41-59). Albany: State University of New York. Webb, N. L. (1992). Assessment of student’s knowledge of mathematics: Steps toward a theory. In D. A. Grouws (Ed.), NCTM Handbook of Research on Mathematics Teaching and Learning. (pp. 661-683). New York: Macmillan Publishing Company.
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