Abstract
A study into the mathematics-related interactions and developing attitudes of young children during the transition period between pre-school and school is reported. Transcripts of interactions during a six-week observation period in one of two preschool sites are coded according to the classifications defined within a theoretical framework. Two separate episodes of construction play were analysed and one of these is used to examine the mathematical nature of the children’s interactions within an emerging model of autonomous learning. The results of the analysis indicate that access to self-regulatory social relations is very closely linked to the accessibility of mathematical meanings.
Similar content being viewed by others
References
Abelson, R. (1979). Differences between belief systems and knowledge systems.Cognitive Science, 3, 355–366.
Arthur, L., Beecher, B., Dockett, S., Farmer, S., & Richards, E. (1993).Programming and planning in early childhood settings. Sydney: Harcourt & Brace.
Bandura, A. (1986).Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, NJ: Prentice-Hall.
Bishop, A. J. (1988).Mathematical enculturation. Kluwer: Dordrecht.
Bredekamp, S. (1986).Developmentally appropriate practice. Washington DC: National Association for the Education of Young Children.
Bronfenbrenner, U. (1979).The ecology of human development: Experiments by nature and design. Cambridge, MA: Harvard University Press.
Brown, A. (1982). Learning and development: The problems of compatibility, access and induction.Human Development, 25, 91–104.
Case, R. (1980). Implications of neo-Piagetian theory for improving the design of instruction. In J. Kirby & J. Biggs (Eds.),Cognition, development and instruction (pp. 161–186). New York: Academic Press.
Chapman, A. (1993). Language and learning in school mathematics: A social semiotic perspective.Issues in Educational Research, 3(1), 35–46.
Cobb, P. (1985). Two children’s anticipations, beliefs, and motivations.Educational Studies in Mathematics, 16, 111–126.
Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s acts while engaged in mathematical problem solving. In D. B. McLeod & V. A. Adams (Eds.),Affect and mathematical problem solving: A new perspective (pp. 2–19). New York: Springer-Verlag.
Corno, L. (1993). The best-laid plans: Modern conceptions of volition and educational research.Educational Researcher, 22(2), 14–21.
Covington, M. (1984). The self-worth theory of achievement motivation: Findings and implications.The Elementary School Journal, 85, 5–20.
Davies, B. (1993).Shards of glass: Children reading and writing beyond gendered identities. Sydney: Allen & Unwin.
Dienes, Z. P. (1970). Some basic processes involved in mathematics learning. In C. Schminke & W. Arnold (Eds.),Mathematics is a verb (pp. 29–33). Illinois: Dryden Press.
Ellerton, N. F. (1987). A window into children’s perceptions of mathematics. In W. Caughey (Ed.),From now to the future (pp. 64–70). Melbourne: Mathematics Association of Victoria.
Ellerton, N. F., & Clements, M. A. (1994).Fostering mathematical attitudes and appreciation Adelaide: Australian Association of Mathematics Teachers.
Erlwanger, S. H. (1975). Case studies of children’s conceptions of mathematics.Journal of Children’s Mathematical Behavior, 1(2), 157–283.
Everingham, C. E. (1994).Motherhood and modernity. Sydney: Allen & Unwin.
Fennema, E., & Peterson, P. (1985). Autonomous learning behaviour: A possible explanation of gender-related differences in mathematics. In L. C. Wilkinson & C. Marrett (Eds.),Gender influences in classroom interaction (pp. 17–35). Orlando: Academic Press.
Gold, R. (1987).The description of cognitive development: Three Piagetian themes. Oxford: Clarendon Press.
Graham, S. (1984). Teacher feelings and student thoughts: An attributional approach to affect in the classroom.Elementary School Journal, 85, 91–104.
Halliday, M. A. K. (1978).Language as a social semiotic. The social interpretation of language and meaning. Baltimore, MD: University Park Press.
Hirsch, E. S. (1974).The block book. Washington: National Association for the Education of Young Children.
Kamii, C. (1982).Number in preschool and kindergarten: Educational implications of Piaget’s theory. Washington: National Association for the Education of Young Children.
Lave, J., & Wenger, E. (1991).Legitimate peripheral participation: Situated learning. Cambridge: Cambridge University Press.
Lean, G., Clements, M. A., & Del Campo, G. (1990). Linguistic and pedagogical factors affecting children’s understanding of arithmetic word problems: A comparative study.Educational Studies in Mathematics, 21, 165–191.
Lewis, H. (1990).A question of values. San Francisco: Harper & Row.
Macmillan, A. (1991).Gender-related differences in the mathematical problem solving of five-year old children. Unpublished Masters Dissertation. Geelong: Deakin University.
Malone, T. W., & Lepper, M. (1987). Making learning fun. In R. E. Snow & M. J. Farr (Eds.),Aptitude, learning and instruction Vol. 3: Conative and affective process analysis (pp. 223–253). London: Lawrence Erlbaum.
Mandler, G. (1975).Mind and emotion. New York: Wiley.
Mandler, G. (1984).Mind and body: Psychology of emotion and stress. New York: Norton.
Mandler, G. (1989). Affect and learning: Causes and consequences of emotional interactions. In D. B. McLeod & V. A. Adams (Eds.),Affect and mathematical problem solving: A new perspective (pp. 3–19). New York. Springer-Verlag.
Mannigel, D. (1992).Young children as mathematicians: Theory and practice for teaching mathematics. Wentworth Falls: Social Science Press.
McLeod, D. B. (1991). Research on affect in mathematics education: A reconceptualisation. In D. A. Grouws (Ed.),Handbook of research on mathematics teaching and learning (pp. 575–596). New York: Macmillan.
McLeod, D. B., & Adams, V. A. (Eds.). (1989).Affect and mathematics problem solving: A new perspective (pp. 3–19). New York: Springer-Verlag.
Mellin-Olsen, S. (1987).The politics of mathematics education. Dordrecht: Kluwer.
Nespor, J. (1987). The role of beliefs in the practice of teaching.Journal of Curriculum Studies, 19, 317–328.
Newman, M. A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. In M. A. Clements & J. Foyster (Eds.),Research in Mathematics Education in Australia,1, 239–258.
Nicholls, J. (1976). When a scale measures more than its name denotes: The case of the test anxiety scale for children.Journal of Clinical and Consulting Psychology, 44, 976–985.
Nicholls, J. (1983). Conceptions of ability and achievement motivation: A theory and its implications for education. In S. Paris, G. Olson & H. Stevenson (Eds.),Learning and motivation in the classroom (pp. 211–237). Hillsdale, NJ: Lawrence Erlbaum.
Nicholls, J. (1984). Conceptions of ability and achievement motivation. In R. Ames & C. Ames (Eds.),Research on motivation in education Vol. 1: Student motivation (pp. 39–73). New York: Academic Press.
Nisbett, R., & Ross, L. (1980).Human inference: Strategies and shortcomings of social judgement. Englewood Cliffs, NJ: Prentice-Hall.
Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct.Review of Educational Research, 62(3), 307–332.
Pateman, N. A. (1989).Teaching mathematics—A tantalising enterprise. Geelong: Deakin University Press.
Pengelly, H. (1990). Mathematical learning beyond the activity. In L. P. Steffe & T. Wood (Eds.),Transforming children’s mathematics education (pp. 357–376). New Jersey: Lawrence Erlbaum Associates.
Snow, C. E. (1983). Literacy and language: Relationships during the preschool years.Harvard Educational Review, 53(2), 165–89.
Steffe, L. P., & Cobb, P. (1988).The construction of arithmetical meanings and strategies. New York: Springer-Verlag.
Steffe, L. P., Cobb, P., & Wood, T. (1989). Young children’s emotional acts while engaged in mathematical problem solving. In D. B. McLeod & V. A. Adams (Eds.),Affect and mathematical problem solving (pp. 117–148). New York: Springer-Verlag.
Stipek, D. (1993).Motivation to learn: From theory to practice (2nd Ed). Boston: Allyn & Bacon.
Stodolski, S. (1988).The subject matters. Chicago: University of Chicago Press.
Stone, J. (1993). Caregiver and teacher language—Responsive or restrictive?Young Children, 48(4), 12–18.
von Glasersfeld, E. (1984). An introduction to radical constructivism. In P. Watzliwick (Ed.),The invented reality (pp. 17–40). New York: Norton.
Walkerdine, V. (1988).The mastery of reason: Cognitive development and the production of rationality. London: Routledge
Walkerdine, V. (1990).School girl fictions. London: Verso.
Weiner, B. (1986).An attributional theory of motivation and emotion. New York: Springer-Verlag.
Weiner, G. (1993). The gendered curriculum developing a post-structuralist feminist analysis.Australian Education Researcher, 21(1), 63–86.
Wertsch, J. V. (1985).Culture, communication and cognition: Vygotskian perspectives. Cambridge: Cambridge University Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Macmillan, A. Children thinking mathematically beyond authoritative identities. Math Ed Res J 7, 111–131 (1995). https://doi.org/10.1007/BF03217280
Issue Date:
DOI: https://doi.org/10.1007/BF03217280