Abstract
The purpose of this paper is to describe the role of an instructional sequence and two accompanying computer-based tools in supporting students' developing understandings of statistical data analysis. In doing so, we also take account of the role of the data creation process in supporting students' ability to engage in genuine data analysis. Data is taken from two classroom teaching experiments conducted with middle-grades students (ages twelve and thirteen) in the fall semester of 1998 and 1999. Through analysis of two classroom episodes we document 1) the emergence of the sociomathematical norm of what counts as a mathematical argument in the context of data analysis, and 2) the importance of the data creation process in grounding the students' activity in the context of a problem or question under investigation. These claims are grounded in students' ways of reasoning about data as they made arguments in the course of their analyses.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Bauersfeld, H., Krummheuer, G. and Voigt, J.: 1988, ‘Interactional theory of learning and teaching mathematics and related microethnographical studies’, in H.G. Steiner and A. Vermandel (eds.), Foundations and Methodology of the Discipline of Mathematics Education, Antwerp, Belgium: Proceedings of the Theory of Mathematics Education Conference, pp. 174–188.
Biehler, R.: 1993, ‘Software tools and mathematics education: The case of statistics’, in C. Keitel and K. Ruthven (eds.), Learning from Computers: Mathematics Education and Technology Springer, Berlin, pp. 68–100.
Biehler, R.: 1994, ‘Cognitive technologies for statistics education: Relating the perspective of tools for learning and of tools for doing statistics’, in L. Brunelli and G. Cicchitelli (eds.), Proceedings of the First Scientific Meeting of the International Association for Statistical Education, Universita de Perugia, Perugia, pp. 173–190.
Biehler, R., Rach, W. and Winkelmann, B.: 1988, Computers and Mathematics Teaching: The German Situation and Reviews of International Software, Occasional paper #103. Institute fur Didaktik der Mathematik. University of Bielefeld, Bielefeld, FRG.
Biehler, R. and Steinbring, H.: 1991, ‘Explorations in statistics, stem-and-leaf, boxplots: Concepts, justifications and experience in a teaching experiment’, Der Mathematikunterricht 37(6), 5–32.
Burrill, G.: 1996, ‘Data analysis in the United States: Curriculum projects’, in B. Phillips (ed.), Papers on Statistical Education, Swinburne Press, Hawthorn, Australia.
Burrill, G. and Romberg, T.A. (in press), ‘Statistics and probability for the middle grades: Examples from mathematics in context’, in S.P. Lajoie (ed.), Reflections on Statistics: Agendas for Learning, Teaching, and Assessment in K-12, Erlbaum, Hillsdale, NJ.
Cai, J. and Moyer, J.C.: 1995, Middle School Students' Understanding of Average: A Problem-Solving Approach, Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus, OH.
Cobb, G.W.: 1997, ‘Mere literacy is not enough’, in L.A. Steen (ed.), Why Numbers Count: Quantitative Literacy for Tomorrow's America, College Examination Board, New York.
Cobb, P.: 1999,‘Individual and collective mathematical learning: The case of statistical data analysis’, Mathematical Thinking and Learning, 5–44.
Cobb, P., Perlwitz, M. and Underwood, D.: 1994, ‘Construction individuelle, acculturation mathématique et communauté scolaire’, Revue des Sciences de l'Éducation 20, 41–62.
Cobb, P. and Yackel, E.: 1996, ‘Constructivist, emergent, and sociocultural perspectives in the context of developmental research’, Educational Psychologist 31, 175–190.
Cobb, P., McClain, K. and Gravemeijer, K.: (in press), ‘Learning about statistical covariation’, Cognition and Instruction.
Cobb, P., Stephan, M., McClain, K. and Gravemeijer, K.: 2001, ‘Participating in classroom mathematical practices’, Journal for the Learning Sciences 10(1,2), 113–164.
Cobb, P. and Whitenack, J.W.: 1996, ‘A method for conducting longitudinal analyses of classroom videorecordings and transcripts’, Educational Studies in Mathematics 30, 458–477.
deLange, J., van Reeuwijk, M., Burrill, G. and Romberg, T.: 1993, Learning and Testing Mathematics in Context. The Case: Data Visualization, University of Wisconsin, National Center for Research in Mathematical Sciences Education, Madison, WI.
Doerr, H.M.: 1995, April, An Integrated Approach to Mathematical Modeling: A Classroom Study, Paper presented at the annual meeting of the American Educational Research Association, San Francisco.
Dörfler, W.: 1993, ‘Computer use and views of the mind’, in C. Keitel and K. Ruthven (eds.), Learning from Computers: Mathematics Education and Technology, Springer-Verlag, Berlin, pp. 159–186.
Glaser, B. and Strauss, A.: 1967, The Discovery of Grounded Theory: Strategies for Qualitative Research, Aldine, New York.
Gravemeijer, K., Cobb, P., Bowers, J. and Whitenack, J.: 2000, ‘Symbolizing, modeling, and instructional design,’ in P. Cobb, E. Yackel and K. McClain (eds.), Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design, Lawrence Erlbaum Associates, Mahwah, NJ.
Hancock, C.: in press, ‘The medium and the curriculum: Reflection on transparent tools and tacit mathematics’, in A. diSessa, C. Hoyles, R. Noss and L. Edwards (eds.), Computers and Exploratory Learning, Springer Verlag, Heidelberg, Germany.
Harel, G. and Confrey, J.: 1994, The Development of Multiplicative Reasoning in the Learning of Mathematics, SUNY Press, New York.
Hershkowitz, R. and Schwartz, B.: 1999, ‘The emergent perspective in rich learning environments: Some roles of tools and activities in the construction of sociomathematical norms’, Educational Studies in Mathematics 39, 149–166.
Kaput, J.J.: 1994, ‘The representational roles of technology in connecting mathematics with authentic experience’, in R. Biehler, R.W. Scholz, R. Strasser and B. Winkelmann (eds.), Didactics ofMathematics as a Scientific Discipline, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 379–397.
Konold, C., Pollatsek, A., Well, A. and Gagnon, A.: in press, ‘Students analyzing data: Research of critical barriers,’ Journal of Research in Mathematics Education.
Lampert, M.: 1990, ‘When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching’, American Educational Research Journal 27(1), 29–63.
Lajoie, S.P.: in press, ‘Reflections on a statistics agenda for K-12’, in S.P. Lajoie (ed.), Reflections on Statistics: Agendas for Learning, Teaching, and Assessment in K-12, Erlbaum, Hillsdale, NJ.
Lajoie, S.P. and Romberg, T.A.: in press, ‘Identifying an agenda for statistics instruction and assessment in K-12’, in S.P. Lajoie (ed.), Reflections on Statistics: Agendas for Learning, Teaching, and Assessment in K-12, Erlbaum, Hillsdale, NJ.
Lehrer, R. and Romberg, T.: 1996, ‘Exploring children's data modeling’, Cognition and Instruction 14, 69–108.
Lipson, K. and Jones, P.: 1996, ‘Statistics: Towards the 21st century’, in Phillips, B. (ed.), Papers on Statistical Education, Swinburne Press, Hawthorn, Australia.
McClain, K., Cobb, P. and Gravemeijer, K.: 2000, ‘Supporting students' ways of reasoning about data’, in Burke, M. (ed.), Learning mathematics for a new century, (2001 Yearbook of the National Council of Teachers of Mathematics), NCTM, Reston, VA.
McGatha, M., Cobb, P. and McClain K.: 1999, April, An Analysis of Student's Initial Statistical Understandings, Paper presented at the annual meeting of the American Educational Research Association, Montreal.
Meira, L.: 1998, ‘Making sense of instructional devices: The emergence of transparency in mathematical activity’, Journal for Research in Mathematics Education 29, 121–142.
Mokros, J. and Russell, S.: 1995, ‘Childrens' concepts of average and representativeness’, Journal for Research in Mathematics Education 26(1), 20–39.
Moore, David S.: 1996, ‘New pedagogy and new content: The case of statistics’, in Phillips, B. (ed.), Papers on Statistical Education Swinburne Press, Hawthorn, Australia.
National Council of Teachers of Mathematics: 2000, Standards 2000, NCTM, Reston, VA.
National Council of Teachers ofMathematics [NCTM].: 1989, Curriculum and Evaluation Standards for School Mathematics, NCTM, Reston, VA.
National Council of Teachers of Mathematics [NCTM].: 1991, Professional Standards for Teaching Mathematics, NCTM, Reston, VA.
Pea, R.D.: 1993, ‘Practices of distributed intelligence and designs for education’, in G. Solomon (ed.), Distributed Cognitions, Cambridge University Press, New York, pp. 47–87.
Pollatsek, A., Lima, S. and Well, A.D.: 1981, ‘Concept or computation: Students’ understanding of the mean’, Educational Studies in Mathematics 12, 191–204.
Roth, W-M. and McGinn, M.K.: 1998, ‘Inscriptions: Towards a theory of representing as social practice’, Review of Educational Research 68, 35–59.
Shaughnessy, J.M.: 1992, ‘Research on probability and statistics: Reflections and directions,’ in D. Grouws (ed.), Handbook of Research on the Teaching and Learning of Mathematics, Macmillan, New York, pp. 465–494.
Shaughnessy, J.M., Garfiled, J. and Greer, B.: 1996, ‘Data handling’, in Bishop, A.J., Clements, K., Keitel, C., Kilpatrick, J. and Laborde, C. (eds.), International Handbook of Mathematics Education, Kluwer Academic Publishers, Dordrecht, The Netherlands, Part 1, 205–237.
Simon, M.A. and Blume, G.W.: 1996, ‘Justification in the mathematics classroom: A study of prospective elementary teachers’, Journal of Mathematical Behavior 15, 3–31.
Strauss, S. and Bichler, E.: 1988, ‘The development of children's concepts of the arithmetic mean', Journal for Research in Mathematics Education 19(1), 64–80.
Thompson, P.W.: 1994, ‘The development of the concept of speed and its relationship to concepts of speed', in G. Harel and J. Confrey (eds.), The Development of Multiplicative Reasoning in the Learning of Mathematics, SUNY Press, NY, pp. 179–234.
Thompson, P. and Saldanha, L.: 2000, To understand Post Counting Numbers and Operations, White paper prepared for the National Council of Teachers of Mathematics.
Tzou, C.: 2000, Learning About Data Creation, Paper presented at the annual meeting of the American Educational Research Association, New Orleans.
von Glaserfeld, E.: 1995, Radical Constructivism: AWay of Knowing and Learning, Falmer Press, Washington, DC.
Wilensky, U.: 1997, ‘What is normal anyway? Therapy for epistemological anxiety', Educational studies on Mathematics 33, 171–202.
Voigt, J.: 1995, ‘Thematic patterns of interaction and sociomathematical norms', in P. Cobb and H. Bauersfeld (eds.), The Emergence of Mathematical Meaning: Interaction in Classroom Cultures, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 163–202.
Yackel, E. and Cobb, P.: 1996, ‘Sociomathematical norms, argumentation and autonomy in mathematics’, Journal for Research in Mathematics Education 27(4), 458–477.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
McClain, K., Cobb, P. Supporting Students' Ability to Reason about Data. Educational Studies in Mathematics 45, 103–129 (2001). https://doi.org/10.1023/A:1013874514650
Issue Date:
DOI: https://doi.org/10.1023/A:1013874514650