Skip to main content
Log in

Inferential reasoning and the influence of cognitive conflict

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

This study follows two earlier studies of school students' abilities to draw inferences when comparing two datasets presented in graphical form (Watson and Moritz, 1999; Watson, 2001). Using the same interview protocol with a new sample of 60 students, 20 from each of grades 3,6 and 9, cognitive conflict was introduced in the form of video clips of reasoning expressed by students in the earlier studies. This methodology was intended to mimic the type of argumentation that might take place in the classroom but in a controlled setting where identical arguments could be presented to different students. Interviews were videotaped and analysed in a similar fashion to the earlier studies in order to document change associated with the presentation of cognitive conflict. Change was documented with respect to the levels of observed response for two parts of the protocol and for the use of displayed variation in the graphs. Implications of the methodology for future research and teaching are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  • Australian Education Council: 1991, A National Statement on Mathematics for Australian schools, Curriculum Corporation, Carlton, Vic.

    Google Scholar 

  • Australian Education Council: 1994, Mathematics - A Curriculum Profile for Australian Schools, Curriculum Corporation, Carlton, Vic.

    Google Scholar 

  • Behr, M. and Harel, G.: 1990, ‘Students' errors, misconceptions and cognitive conflict in application of procedures’, Focus on Learning Problems in Mathematics 12(3&4), 75–84.

    Google Scholar 

  • Biehler, R.: 1997, ‘Students' difficulties in practicing computer-supported data analysis: Some hypothetical generalizations from results of two exploratory studies’, in J.B. Garfield and G. Burrill (eds.), Research on the Role of Technology in Teaching and Learning Statistics, International Statistical Institute, Voorburg, The Netherlands, pp. 169–190.

    Google Scholar 

  • Biggs, J.B.: 1992, ‘Modes of learning, forms of knowing and ways of schooling’, in A. Demetriou, M. Shayer and A. Efklides (eds.), Neo-Piagetian Theories of Cognitive Development: Implications and Applications for Education, Routledge, London, pp. 31–51.

    Google Scholar 

  • Biggs, J.B. and Collis, K.F.: 1982, Evaluating the Quality of Learning: The SOLO Taxonomy, Academic Press, New York.

    Google Scholar 

  • Chick, H.L. and Watson, J.M.: 2001, ‘Data representation and interpretation by primary school students working in groups’, Mathematics Education Research Journal 13, 91–111.

    Google Scholar 

  • Driver, R.: 1985, ‘Changing perspectives on science lessons’, in N. Bennett and C. Desforges (eds.), Recent Advances in Classroom Research, Scottish Academic Press, Edinburgh, pp. 58–75.

    Google Scholar 

  • Estepa, A., Batanero, C. and Sanchez, F.T.: 1999, ‘Students' intuitive strategies in judging association when comparing two samples’, Hiroshima Journal of Mathematics Education 7, 17–30.

    Google Scholar 

  • Gal, I., Rothschild, K. and Wagner, D.A.: 1989, April, Which Group is Better? The Development of Statistical Reasoning in Elementary School Children, Paper presented at the meeting of the Society for Research in Child Development, Kansas City.

  • Gal, I., Rothschild, K. and Wagner, D.A.: 1990, April, Statistical Concepts and Statistical Reasoning in School Children: Convergence or Divergence?, Paper presented at the meeting of the American Educational Research Association, Boston.

  • Gal, I. and Wagner, D.A.: 1992, Project STARC: Statistical Reasoning in the Classroom, (Annual Report: Year 2, NSF Grant No. MDR90-50006). Philadelphia, PA: Literacy Research Center, University of Pennsylvania.

    Google Scholar 

  • Goos, M.: 2000, ‘Collaborative problem solving in senior secondary mathematics classrooms’, in J. Bana and A. Chapman (eds.), Mathematics Education beyond 2000 (Proceedings of the 23rd annual conference of the Mathematics Education Research Group of Australasia), MERGA, Perth, Vol. 1, pp. 38–45.

    Google Scholar 

  • Green, D.: 1993, ‘Data analysis:What research do we need?’, in L. Pereira-Mendoza (ed.), Introducing Data Analysis in the Schools: Who Should Teach It?, International Statistical Institute, Voorburg, The Netherlands, pp. 219–239.

    Google Scholar 

  • Kelly, B.A. and Watson, J.M.: 2002, ‘Variation in a chance sampling setting: The lollies task’, in K. Irwin, M. Pfannkuch, B. Barton and M. Thomas (eds.), Mathematics Education in the South Pacific (Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia), MERGA, Auckland, NZ.

    Google Scholar 

  • Konold, C. and Miller, C.: 1994, DataScope® [Computer program], Intellimation Library for the Macintosh, Santa Barbara, CA.

    Google Scholar 

  • Konold, C. and Pollatsek, A.: 2002, ‘Data analysis as the search for signals in noisy processes’, Journal for Research in Mathematics Education 33, 259–289.

    Article  Google Scholar 

  • Konold, C., Pollatsek, A., Well, A. and Gagnon, A.: 1997, ‘Students analyzing data: Research of critical barriers’, in J.B. Garfield and G. Burrill (eds.), Research on the Role of Technology in Teaching and Learning Statistics, International Statistical Institute, Voorburg, The Netherlands, pp. 151–167.

    Google Scholar 

  • Konold, C., Robinson, A., Khalil, K., Pollatsek, A., Well, A., Wing, R. and Mayr, S.: 2002, ‘Students' use of modal clumps to summarize data’, in B. Phillips (ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a statistically literate society, Cape Town, South Africa, International Statistical Institute, Voorburg, The Netherlands.

    Google Scholar 

  • Macbeth, D.: 2000, ‘On an actual apparatus for conceptual change’, Science Education 84, 228–264.

    Article  Google Scholar 

  • Miles, M.B. and Huberman, A.M.: 1994, Qualitative Data Analysis: An Expanded Sourcebook (2nd ed.), Sage, Thousand Oaks, CA.

    Google Scholar 

  • Mokros, J. and Russell, S.J.: 1995, ‘Children's concepts of average and representativeness’, Journal for Research in Mathematics Education 26, 20–39.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics: 2000, Principles and Standards for School Mathematics, thor, Reston, VA.

  • Posner, G.J., Strike, K.A., Hewson, P.W. and Gertzog, W.A.: 1982, ‘Accommodation of a scientific conception: Toward a theory of conceptual change’, Science Education 66, 211–227.

    Google Scholar 

  • Pratt, D.: 2000, ‘Making sense of the total of two dice’, Journal for Research in Mathematics Education 31, 602–625.

    Article  Google Scholar 

  • Reading, C. and Shaughnessy, M.: 2000, ‘Student perceptions of variation in a sampling situation’, in T. Nakahara and M. Kyama (eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4), Hiroshima University, Hiroshima, pp. 89–96.

    Google Scholar 

  • Shaughnessy, J.M.: 1985, ‘Problem-solving derailers; The influence of misconceptions on problem-solving performance’, in E.A. Silver (ed.), Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, Erlbaum, Hillsdale, NJ, pp. 399–415.

    Google Scholar 

  • Shaughnessy, J.M.: 1997, ‘Missed opportunities in research on the teaching and learning of data and chance’, in F. Biddulph and K. Carr (eds.), People in Mathematics Education (Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia), MERGA, Rotorua, NZ, pp. 6–22.

    Google Scholar 

  • Shaughnessy, J.M. and Ciancetta, M.: 2002, ‘Students' understanding of variability in a probability environment’, in B. Phillips (ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a statistically literate society, Cape Town, South Africa, International Statistical Institute, Voorburg, The Netherlands.

    Google Scholar 

  • Shaughnessy, J.M., Watson, J., Moritz, J. and Reading, C.: 1999, April, School Mathematics Students’ Acknowledgement of Statistical Variation, in C. Maher (Chair), There's more to life than centers, Presession Research Symposium, 77th Annual National Council of Teachers of Mathematics Conference, San Francisco, CA.

  • Steffe, L.P.: 1990, ‘Inconsistencies and cognitive conflict: A constructivist's view’, Focus on Learning Problems in Mathematics 12(3&4), 99–109.

    Google Scholar 

  • Strike, K.A. and Posner, G.J.: 1992, ‘A revisionist theory of conceptual change’, in R.A. Duschl and R.J. Hamilton (eds.), Philosophy of Science, Cognitive Psychology and Educational Theory and Practice, State University of New York Press, Albany, NY, pp. 147–176.

    Google Scholar 

  • Tirosh, D., Graeber, A.O. and Wilson, P.S.: 1990, ‘Introduction to special issue’, Focus on Learning Problems in Mathematics 12(3&4), 29–30.

    Google Scholar 

  • Torok, R. and Watson, J.: 2000, ‘Development of the concept of statistical variation: An exploratory study’, Mathematics Education Research Journal 12, 147–169.

    Google Scholar 

  • Watson, J.M.: 2001, ‘Longitudinal development of inferential reasoning by school students’, Educational Studies in Mathematics 47, 337–372.

    Article  Google Scholar 

  • Watson, J.M.: 2002, ‘Creating cognitive conflict in a controlled research setting: Sampling’, in B. Phillips (ed.), Proceedings of the Sixth International Conference on the Teaching of Statistics: Developing a statistically literate society, Cape Town, South Africa, International Statistical Institute, Voorburg, The Netherlands.

    Google Scholar 

  • Watson, J.M. and Moritz, J.B.: 1999, ‘The beginning of statistical inference: Comparing two data sets’, Educational Studies in Mathematics 37, 145–168.

    Article  Google Scholar 

  • Watson, J.M. and Moritz, J.B.: 2000, ‘Developing concepts of sampling’, Journal for Research in Mathematics Education 31, 44–70.

    Article  Google Scholar 

  • Watson, J.M. and Moritz, J.B.: 2001a, ‘The role of cognitive conflict in developing students’ understanding of chance measurement’, in J. Bobis, B. Perry and M. Mitchelmore (eds.), Numeracy and Beyond (Proceedings of the 24th annual conference of the Mathematics Education, Research Group of Australia Incorporated, Vol. 2), MERGA, Sydney, pp. 523–530.

    Google Scholar 

  • Watson, J.M. and Moritz, J.B.: 2001b, ‘Development of reasoning associated with pictographs: Representing, interpreting and predicting’, Educational Studies in Mathematics 48, 47–81.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Watson, J. Inferential reasoning and the influence of cognitive conflict. Educational Studies in Mathematics 51, 225–256 (2002). https://doi.org/10.1023/A:1023622017006

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023622017006

Keywords

Navigation