The coherence of theory and measurement:the application of the Rasch measurement model to the investigation of ratio, and related concepts.(symposium1919)

Author(s):

Caroline Long

Conference:

ECER 2009

Network:

9. Assessment, Evaluation, Testing and Measurement

Format:

Symposium Paper

Session Information

09 SES 09 A, Rasch Measurement in Educational Contexts (Part 2)

Symposium. Continued from 09 SES 08 A

Time:

2009-09-30

10:30-12:00

Room:

HG, HS 50

Chair:

Sarah Howie

Discussant:

Eugenio Gonzalez

Contribution

The theme of this conference includes the coherence of theory and empirical research in establishing evidence for inferences and actions concerning educational practice. This paper describes an application of the Rasch model (Rasch, 1960/80) where theory and measurement are used interactively to provide greater understanding of the mathematical concepts fractions, ratio, proportion and percent (FRPP). I hypothesise that these are ‘threshold concepts’ that provide the conceptual gateway to higher mathematics (Meyer & Land, 2005). In order to locate the Rasch model in the current research context, I highlight some features of current research domains namely educational measurement and sociocognitive perspectives. Educational measurement is generally thought of as empirical (with some theoretical underpinning), 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 a fine grained analysis of a particular aspect of learning or development, or to comprehend in depth the development of a mathematical topic such as ratio. Important considerations for researching mathematics are firstly, that concepts are located as an interrelated array, described as a ‘conceptual field’ (Vergnaud, 1983, 1988). Secondly, it is necessary to describe cognitive development using a framework that refers to a conceptual analysis of the mathematical domain (Vergnaud, 1994). Mathematical progress can be gauged against this mathematical framework. Against the background of the current research context, and the mathematical considerations, the application of the Rasch model, using both ConQuest and RUMM software, illustrates the integration of both theoretical analyses and empirical research, and the dialectical relationship of qualitative and quantitative methodologies. The theoretical component required an investigation of the mathematical structures inherent in these concepts. The empirical component consisted of designing a test instrument using selected items adapted from TIMSS 2003 (Mullis et al., 2004), and administering the test to 330 learners in Grades 7, 8 and 9 at two schools differing in socio-economic status. Learners from a range of proficiency levels were interviewed on items at graded difficulty level in order to provide greater understanding of the learner’s cognitive processes and of the construct. The interplay of theory and measurement contributes to both the further development of theory and improvement of the measuring instrument.... ...continued in methodology...

Method

..... I propose that Rasch measurement provides the basis for a coherent model based on sound principles of measurement, while at the same time giving serious consideration to the theoretical construct being measured. Critique of both educational measurement and the Rasch measurement model challenges the theoretical elaboration underpinning educational measurement and the level of inference that can be made as a result of both theoretical sophistication and measurement design.

Expected Outcomes

References

Callingham, R. & Bond, T. (2006). Research in Mathematics Education and Rasch Measurement. Mathematics Education Research Journal, 18(2), 1-10. Humphry, S. M. (2005). Maintaining a common arbitrary unit in social measurement. Perth: Murdoch University. Martin, M. O., Mullis, I. V. S. & Chrostowski, S. J. (Eds.). (2004). TIMSS 2003 Technical Report. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College. Meyer, J. H. F. & Land, R. (2005). Threshold concepts and troublesome knowledge (2): Epistemological considerations and a conceptual framework for teaching and learning. Higher Education, 49, 373-388. Michell, J. (2008). Is psychometrics pathological science? Measurement, 6, 7-24. Mislevy, R. J. (2008). How Cognitive Science challenges the Education Measurement Tradition. Maryland: University of Maryland. 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. Usiskin, Z. (2005). The importance of the transition years, Grades 7-10, in school mathematics. UCSMP Newsletter. Vergnaud, G. (1983). Multiplicative structures. In R. L. a. M. Landau (Ed.), Acquisition of mathematics concepts and processes (pp. 127-174). New York: Academic Press. 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.

Author Information

Caroline Long

Centre for Evaluation and Assessment, University of Pretoria

Johannesburg

235

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