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A follow-up assessment of a second-grade problem-centered mathematics project

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Abstract

Five second-grade classes in two schools participated in a project that was generally compatible with a constructivist theory of knowing. At the end of the school year, the students in these classes and their peers in six non-project classes in the same schools were assigned to ten textbook-based third-grade classes on the basis of reading scores. The two groups of students were compared at the end of the third-grade year on a standardized achievement test and on instruments designed to assess their conceptual development in arithmetic, their personal goals in mathematics, and their beliefs about reasons for success in mathematics. The levels of computation performance on familiar textbook tasks were comparable, but former project students had attained more advanced levels of conceptual understanding. In addition, they held stronger beliefs about the importance of working hard and being interested in mathematics, and about understanding and collaborating. Further, they attributed less importance to conforming to the solution methods of others.

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References

  • Addison-Wesley Mathematics Teacher's Resource Book, Book 3: 1987, Addison-Wesley, Menlo Park, CA.

  • Barnes, D.: 1976,From Communication to Curriculum, Penguin, New York.

    Google Scholar 

  • Bartolini Bussi, M. B.: 1991, “Social interaction and mathematical knowledge”. In F. Furinghetti (ed.),Proceedings of the Fifteenth Conference of the International Group for the Psychology of Mathematics Education, Program Committee of the 15th PME Conference, Genoa, Italy, pp. 1–16.

  • Bauersfeld, H.: 1980, “Hidden dimensions in the so-called reality of a mathematics classroom”,Educational Studies in Mathematics 11, 23–41.

    Google Scholar 

  • Bauersfeld, H.: 1988, “Interaction, construction, and knowledge: Altemative perspectives for mathematics education”. In T. Cooney and D. Grouws (eds.),Effective Mathematics Teaching, National Council of Teachers of Mathematics/Lawrence Erlbaum, Reston, VA, pp. 27–46.

    Google Scholar 

  • Bishop, A. J.: 1985, “The social construction of meaning — A significant development for mathematics education?”,For the Learning of Mathematics 5(1), 24–28.

    Google Scholar 

  • Bishop, A. J.: 1988,Mathematical Enculturation: A Cultural Perspective on Mathematics Education, Kluwer, Dordrecht.

    Google Scholar 

  • Blumer, H.: 1969,Symbolic Interactionism: Perspectives and Method, Prentice Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Brousseau, G.: 1984, “The crucial role of the didactical contract in the analysis and construction of situations in teaching and learning mathematics”. In H. G. Steiner (ed.),Theory of Mathematics Education (Occasional paper 54), IDM, Bielefeld, pp. 110–119.

    Google Scholar 

  • Bruner, J.: 1986,Actual Minds, Possible Worlds, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Carpenter, T. P. Fennema, E., Peterson, P. L., Chiang, C., and Loef, M.: 1989, “Using knowledge of children's mathematics in press thinking in classroom teaching: An experimental study”,American Educational Research Journal 26, 499–532.

    Google Scholar 

  • Carpenter, T. P. and Moser, J. M.: 1984, “The acquisition of addition and subtraction concepts in grades one through three”,Journal for Research in Mathematics Education 15, 179–202.

    Google Scholar 

  • Cobb, P. and Wheatley, G.: 1988, “Childen's initial understandings of ten”,Focus on Learning Problems in Mathematics 10(3), 1–28.

    Google Scholar 

  • Cobb, P., Wood, T., and Yackel, E.: 1991a, “A constructivist approach to second grade mathematics”. In E.von Glasersfeld (ed.),Constructivism in Mathematics Education, Kluwer, Dordrecht, pp. 157–176.

    Google Scholar 

  • Cobb, P., Wood, T. and Yackel, E.: 1991b, “Analogies from the philosophy and sociology of science for understanding classroom life”,Science Education 75, 23–44.

    Google Scholar 

  • Cobb, P., Wood, T., and Yackel, E.: in press-a, “Discourse, mathematical thinking, and classroom practice”. In E. Forman, N. Minick, and A. Stone (eds.),Contexts for Learning: Sociocultural Dynamics in Children's Development, Oxford University Press, Oxford.

  • Cobb, P., Wood, T., and Yackel, E.: in press-b, “Learning and interaction in classroom situations”,Educational Studies in Mathematics.

  • Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., and Perlwitz, M.: 1991, “Assessment of a problem-centered second grade mathematics project”,Journal for Research in Mathematics Education 22, 3–29.

    Google Scholar 

  • Cobb, P., Yackel, E., and Wood, T.: 1988, “Curriculum and teacher development: Psychological and anthropological perspectives”. In E. Fennema, T. P. Carpenter, and S. J. Lamon (eds.),Integrating Research on Teaching and Learning Mathematics, Wisconsin Center for Educational Research, University of Wisconsin-Madison, Madison, WI, pp. 92–131.

    Google Scholar 

  • Cobb, P., Yackel, E., and Wood, T.: 1989, “Young children's emotional acts while doing mathematical problem solving”. In D. B. McLeod and V. M. Adams (eds.),Affect and Mathematical Problem Solving: A New Perspective, Springer-Verlag, New York, pp. 117–148.

    Google Scholar 

  • Cobb, P., Yackel, E., and Wood, T.: 1982, “A constructivist altemative to the representational view of mind in mathematics education”,Journal for Research in Mathematics Education,23(1), 2–33.

    Google Scholar 

  • Cobb, P., Yackel, E., Wood, T., and McNeal, B.: 1992, “Mathematics as procedural instructions and mathematics as meaningful activity: The reality of teaching for understanding”. In R.B. Davis and C.A. Maher (eds.),Schools, Mathematics and the World of Reality, Allyn and Bacon, Needham Heights, MA, pp. 119–133.

    Google Scholar 

  • Confrey, J.: 1986, “A critique of teacher effectiveness research in mathematics education”,Journal for Research in Mathematics Education 17, 347–360.

    Google Scholar 

  • Confrey, J.: 1990a, “What constructivism implies for teaching”. In R. B. Davis, C. A. Maher, and N. Noddings (eds.),Constructivist Views on the Teaching and Learning of Mathematics (Journal for Research in Mathematics Education Monograph No. 4), National Council of Teachers of Mathematics, Reston, VA, pp. 107–122.

    Google Scholar 

  • Confrey, J.: 1990b, “Student conceptions, representations, and the design of software”. InDesign for Learning Apple Computer, External Research, Cupertino, CA, pp. 55–62.

    Google Scholar 

  • Kamii, C. and de Clark, G.: 1985,Young Children Reinvent Arithmetic: Implications of Piaget's Theory, Teachers College Press, New York.

    Google Scholar 

  • Kaput, J. J.: 1991, “Notations and representations as mediators of constructive processes”. In E.von Glasersfeld (ed.),Constructivism in Mathematics Education, Kluwer, Dordrecht, pp. 53–74).

    Google Scholar 

  • 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, 29–63.

    Google Scholar 

  • McNeal, B.: 1991,The Social Context of Mathematical Development. Unpublished doctoral dissertation, Purdue University, West Lafayette, IN.

  • Mead, G. H.: 1934,Mind, Self, and Society, University of Chicago Press, Chicago.

    Google Scholar 

  • Mehan, H.: 1979,Learning Lessons, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Minick, N.: 1989, “Mind and activitty in Vygotsky's work: An expanded frame of reference”,Cultural Dynamics 2, 162–187.

    Google Scholar 

  • Newman, D., Griffin, P., and Cole, M.: 1989,The Construction Zone: Working for Cognitive Change in School, Cambridge University Press, Cambridge.

    Google Scholar 

  • Nicholls, J., Cobb, P., Wood, T., Yackel, E., and Patashnik, M.: 1990, “Dimensions of success in mathematics: Individual and classroom differences”,Journal for Research in Mathematics Education 21, 109–122.

    Google Scholar 

  • Perret-Clermont, A. N.: 1980,Social Interaction and Cognitive Development in Children, Academic Press, New York.

    Google Scholar 

  • Piaget, J.: 1971,Biology and Knowledge, University of Chicago Press, Chicago.

    Google Scholar 

  • Piaget, J.: 1980,Adaptation and Intelligence: Organic Selection and Phenocopy, University of Chicago Press, Chicago.

    Google Scholar 

  • Richards, J.: 1991, “Mathematical discussions”. In E.von Glasersfeld (ed.),Constructivism in Mathematics Education, Kluwer, Dordrecht, pp. 13–52.

    Google Scholar 

  • Rogoff, B.: 1990,Apprenticeship in Thinking: Cognitive Development in Social Context, Oxford University Press, Oxford.

    Google Scholar 

  • Rorty, R.: 1983, “Method and morality”. In N. Haan, R. N. Bellah, and P. Robinson (eds.),Social Science as Moral Inquiry, Columbia University Press, New York, pp. 155–176.

    Google Scholar 

  • Saxe, G. B.: 1991,Culture and Cognitive Development: Studies on Mathematical Understanding, Lawrence Erlbaum, Hillsdale, NJ.

    Google Scholar 

  • Schütz, A.: 1962,The Problem of Social Reality, Martinus Nijhoff, The Hague.

    Google Scholar 

  • Silver, E. A.: 1986, “Using conceptual and procedural knowledge: A focus on relationships”. In J. Hiebert (ed.),Conceptual and Procedural Knowledge: The Case of Mathematics, Lawrence Erlbaum, Hillsdale, NJ, pp. 181–198.

    Google Scholar 

  • Sinclair, H.: 1990, “Learning: The interactive recreation of knowledge”. In L. P. Steffe and T. Wood (eds.),Transforming Children's Mathematics Education: International Perspectives, Lawrence Erlbaum, Hillsdale, NJ, pp. 19–29.

    Google Scholar 

  • Smith, E. and Confrey, J.: 1991,Understanding Collaborative Learning: Small-Group Work on Contextual Problems Using a Multi-Representational Software Tool. Paper presented at AERA annual meeting, Chicago, April.

  • Steffe, L. P.: 1987,Principles of Mathematical Curriculum Design in Early Childhood Teacher Education. Paper presented at AERA annual meeting, Washington, DC, April.

  • Steffe, L. P., Cobb, P. (with E. von Glasersfeld):. 1988,Construction of Arithmetical Meanings and Strategies, Springer-Verlag, New York.

    Google Scholar 

  • Steffe, L. P., von Glasersfeld, E., Richards, J., and Cobb, P.: 1983,Children's Counting Types: Philosophy, Theory and Applications, Praeger Scientific, New York.

    Google Scholar 

  • Streeck, J.: 1979, “Sandwich. Good for you”. In J. Dittman (ed.),Arbeiten zur Konversationsanalyse: Neimeyer, Tübingen, pp. 235–257.

    Google Scholar 

  • Thompson, P.: 1985, “Experience, problem solving, and learning mathematics: Considerations in developing mathematical curricula”. In E. A. Silver (ed.),Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, Lawrence Erlbaum, Hillsdale, NJ, pp. 189–236.

    Google Scholar 

  • Treffers, A.: 1987,Three dimensions: A Model of Goal and Theory Description in Mathematics Instruction—The Wiskobas Project, Reidel, Dordrecht.

    Google Scholar 

  • Voigt, J.: 1985, “Patterns and routines in classroom interaction”,Recherches en Didactique des Mathématiques 6, 69–118.

    Google Scholar 

  • Voigt, J.: 1989, “The social constitution of the mathematics province-A microethnographical study in classroom interaction”,The Quarterly Newsletter of the Laboratory of Comparative Human Cognition 11(1/2), 27–34.

    Google Scholar 

  • von Glasersfeld, E.: 1984a, “An introduction to radical constructivism”. In P. Watzlawick (ed.),The Invented Reality, Norton, New York, pp. 17–40.

    Google Scholar 

  • von Glasersfeld, E.: 1984b, “Thoughts about space, time, and the concept of identity”. InBook-Conference, First Installment, Princelet Editions Living Books, Zurich, pp. 21–36

    Google Scholar 

  • von Glasersfeld, E.: 1990a, “Constructivism in mathematics education: Why some like it radical”. In R. B. Davis, C. A. Maher, and N. Noddings (eds.),Constructivist Views on the Teaching and Learning of Mathematics (Journal for Research in Mathematics Education Monograph No. 4), National Council of Teachers of Mathematics, Reston, VA, pp. 19–30.

    Google Scholar 

  • von Glasersfeld, E.: 1990b, “Environment and communication”. In L. P. Steffe and T. Wood (eds.),Transforming Children's Mathematics Education: International Perspectives, Lawrence Erlbaum, Hillsdale, NJ, pp. 30–38.

    Google Scholar 

  • Wood, T., Cobb, P., and Yackel, E.: 1990, “The contextual nature of teaching: Mathematics and reading instruction in one second-grade classroom”,Elementary School Journal 90, 497–514.

    Google Scholar 

  • Wood, T., Cobb, P., and Yackel, E.: 1991, “Change in teaching mathematics: A case study”,American Educational Research Journal 28(3), 587–616.

    Google Scholar 

  • Wood, T., Cobb, P., and Yackel, E.: 1992, “Change in learning mathematics: Change in teaching mathematics”. In H. Marshall (ed.),Redefining Student Learning: Roots of Educational Change, Ablex, Norwood, NJ.

    Google Scholar 

  • Wood, T. and Yackel, E.: 1990, “The development of collaborative dialogue within small group interactions”. In L. P. Steffe and T. Wood (eds.),Transforming Children's Mathematics Education: International Perspectives, Lawrence Erlbaum, Hillsdale, NJ.

    Google Scholar 

  • Yackel, E., Cobb, P., and Wood, T.: 1991, “Small group interactions as a source of learning opportunities in second grade mathematics”,Journal for Research in Mathematics Education 22(5), 390–408.

    Google Scholar 

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Cobb, P., Wood, T., Yackel, E. et al. A follow-up assessment of a second-grade problem-centered mathematics project. Educ Stud Math 23, 483–504 (1992). https://doi.org/10.1007/BF00571469

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