Teachers’ multimodal functioning in relation to the concept of average

Mathematics Education Research Journal - Tập 9 - Trang 205-224 - 1997
Rosemary A. Callingham1
1Department of Education, Community and Cultural Development, Tasmania

Tóm tắt

Average is a concept encountered in a wide variety of situations. In this paper, responses of 136 pre- and in-service teachers to a series of graded questions about average are analysed. The theoretical model used as the basis of the analysis is the SOLO Taxonomy with multimodal functioning developed by Biggs and Collis (1991). Information presented in graphical form requiring respondents to compare data sets induced responses in ikonic and concrete symbolic modes, demonstrating multimodal functioning. These responses are mapped onto a model of problem solving proposed by Collis and Romberg (1990). Cycles of response in relation to the concept of average are proposed.

Tài liệu tham khảo

Australian Education Council, (1991).A national statement on mathematics for Australian schools. Carlton, VIC: Author. Berenson, S. B., Friel, S., & Bright, G. (1993, April).Elementary teachers’ fixations on graphical features to interpret statistical data. Paper presented at the annual meeting of the American Educational Research Association, Atlanta, GA. Biggs, J. B., & Collis, K. F. (1982).Evaluating the quality of learning: The SOLO Taxonomy. New York: Academic Press. Biggs, J. B., & Collis, K. F. (1991). Multi-modal learning and the quality of intelligent behaviour. In H. Rowe (Ed.),Intelligence: Reconceptualisation and measurement. Hillsdale, NJ: Lawrence Erlbaum. Bright, G. W., Berenson, S. B., & Friel, S. (1993).Teachers’ knowledge of statistics pedagogy. Paper presented at the annual meeting of the Research Council for Diagnostic and Prescriptive Mathematics, Melbourne. Callingham, R. A., Watson, J. M., Collis, K. F., & Moritz, J. B. (1995). Teacher attitudes towards chance and data. In B. Atweh & S. Flavel (Eds.),Galtha (pp. 143–150). Darwin: Mathematics Education Research Group of Australasia. Campbell, K. J., Watson, J. M., & Collis, K. F. (1992). Volume measurement and intellectual development.Journal of Structural Learning, 11(3), 279–298. Collis, K. F., & Biggs, J. B. (1991). Developmental determinants of qualitative aspects of school learning. In G. T. Evans (Ed.),Learning and teaching cognitive skills. Melbourne: Australian Council for Education Research. Collis, K. F., & Romberg, T. A. (1990). “The standards”: Theme and assessment. In K. Milton & H. McCann (Eds.),Mathematical turning points—Strategies for the 1990s (pp. 173–189). Hobart: Australian Association of Mathematics Teachers. Cox, C., & Mouw, J. T. (1992). Disruption of the representativeness heuristic: Can we be perturbed into using correct probabilistic reasoning?Educational Studies in Mathematics, 23, 163–178. Fischbein, E. (1990) Training teachers for teaching statistics. In A. Hawkins (Ed.),Training teachers to teach statistics. Voorburg: International Statistical Institute. Gal, I. (1992).Reaching out: Some issues and dilemmas in expanding statistics education. InProceedings of the August 1992 International Statistics Institute Roundtable on Teaching Data-analysis. Canada: Bishop University. Greer, B., & Ritson, R., (1993).Teaching data handling within the Northern Ireland mathematics curriculum: Report on survey in schools. Unpublished manuscript, School of Psychology, Queens University, Belfast. Lamborn, S. D., & Fischer, K. W. (1988). Optimal and functional levels in cognitive development: The individual’s developmental range. Newsletter of the InternationalSociety for the Study of Behavioural Development, 2(14), 1–4. Lidster, S. T., Pereira-Mendoza, L., Watson, J. M., & Collis, K. F. (1996, November).What’s fair for Grade 6? Paper presented at the Annual Conference of the Australian Association for Research in Education, Hobart. Mokros, J. R., & Russell, S. J. (1992).Children’s concepts of average and representativeness. (Working Paper 4-92). Cambridge, MA: TERC. National Council of Teachers of Mathematics. (1989).Curriculum and evaluation standards for school mathematics. Reston, VA: Author. Pollatsek, A., Lima, S., & Well, A. D. (1981). Concept or computation: Students understanding of the mean.Educational Studies in Mathematics, 12, 191–204. Russell, S. J., & Mokros, J. R. (1991). What’s typical? Children’s and teachers’ ideas about average. In D. Vere-Jones (Ed.),Proceedings of the 3rd International Conference on Teaching Statistics. Vol. 1. School and General Issues, (pp. 307–313) Voorburg: International Statistical Institute. Russell, S. J. (1990). Issues in training teachers to teach statistics in the elementary school: A world of uncertainty. In A. Hawkins (Ed.),Training teachers to teach statistics. Voorburg: International Statistical Institute. Watson, J. M., Campbell, K. J. & Collis, K. F. (1993). Multimodal functioning in understanding fractions.Journal of Mathematical Behaviour, 12, 45–62. Watson, J. M., Collis, K. F., Callingham, R. A., & Moritz, J. B., (In press.) A model for assessing higher order thinking in statistics.Educational Research and Evaluation. Watson, J. M., Collis, K. F., & Moritz, J. B. (1995).The development of concepts associated with sampling in Grades 3, 5, 7 and 9. Paper presented at the Annual Conference of the Australian Association for Research in Education, Hobart.