Design and Use of Computer Tools for Interactive Mathematical Activity (TIMA)

Abstract

Our guiding principle when designing the TIMA was to create computer tools that we could use to achieve our goals when teaching children. The design of the TIMA took place in the context of a constructivist teaching experiment with 12 children that extended over a three-year period. Three different TIMA were designed and used in the teaching experiment: Toys, Sticks, and Bars. These tools were designed to provide children contexts in which they could enact their mathematical operations of unitizing, uniting, fragmenting, segmenting, partitioning, disembeding, iterating and measuring. As such, they are very different from the drill and practice or tutorial software that are prevalent in many elementary schools. We provide examples of how the TIMA were used by children to engage in cognitive play and, through interactions with a teacher/researcher and other children, transform that play into independent mathematical activity with a playful orientation. The role of the teacher in provoking perturbations that could lead eventually to accommodations in the children's mathematical schemes was critical in the use of the TIMA as learning tools.

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References

Balacheff

(1998). Paper prepared for the conference on Technology and the NCTM Standards 2000. Arlington, VA: Eisenhower National Clearinghouse.

Biddlecomb

(1994). Theory-based development of computer microworlds. Journal of Research in Childhood Education, 8(2), 87–98.

Bowers

(1997). Analyzing students' learning with computer-based microworlds: Do you see what I see? In Dossey

J. A.

Swafford

J. O.

Parmantie

, & Dossey

A. E.

(Eds.), Proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education. Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Cooper

R. G.

(1991). The role of mathematical transformations and practice in mathematical development. In Steffe

L. P.

(Ed.), Epistemological foundations of mathematical experience (pp. 102–123). New York: Springer-Verlag.

Hoyles

(1998). Lessons we have learnt: Effective technologies for effective mathematics. Paper prepared for the conference on Technology and the NCTM Standards 2000. Arlington, VA: Eisenhower National Clearinghouse.

Hoyles

, & Noss

(1992). A pedagogy for mathematical microworlds. Educational Studies in Mathematics, 23, 31–57.

Kieren

(1994). Orthogonal reflections on computer microworlds, constructivism, play and mathematical understanding. Journal of Research in Childhood Education, 8(2), 132–141.

NCTM (2000). Principals and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

Olive

(1994). Building a new model of mathematical learning. Journal of Research in Childhood Education, 8(2), 162–173.

10.

Olive

(2000). Computer tools for interactive mathematical activity in the elementary school. International Journal of Computers for Mathematical Learning, 5, 241–262.

11.

Olive

, & Steffe

(1994). TIMA: Bars. Acton, MA: William K. Bradford.

12.

Papert

(1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.

13.

Piaget

(1962). Play, dreams, and imitation in childhood. New York: Norton.

14.

Piaget

(1980). The psychogenesis of knowledge and its epistemological significance. In Piattelli-Palmarini

(Ed.), Language and learning: The debate between Jean Piaget and Noam Chomsky (pp. 23–34). Cambridge, MA: Harvard University Press.

15.

Piaget

, & Szeminska

(1952). The child's conception of number. London: Routledge & Kegan Paul.

16.

Polya

(1954). Mathematics and plausible reasoning. Princeton, NJ: Princeton University Press.

17.

Skemp

R. R.

(1979). Intelligence, learning, and action. New York: John Wiley & Sons.

18.

Steffe

L. P.

(1992). Schemes of action and operation involving composite units. Learning and Individual Differences, 4(3), 259–309.

19.

Steffe

L. P.

(1994). Children s construction of meanings for arithmetical words. In Tirosh

(Ed.), Implicit and explicit knowledge: An educational approach (pp. 131–169). New Jersey: Ablex.

20.

Steffe

L. P.

(1999). Individual constructive activity: An experimental analysis. Cybernetics and Human Knowing, 6(1), 17–31.

21.

Steffe

, & Olive

(1996). Symbolizing as a constructive activity in a computer microworld. Educational Computing Research. 14(2), 113–138.

22.

Steffe

L. P.

, & Wiegel

H. G.

(1994). Cognitive play and mathematical learning in computer microworlds. Journal of Research in Childhood Education, 8(2), 117–131.

23.

Steffe

L. P.

von Glasersfeld

Richards

, & Cobb

(1983). Children's counting types philosophy, theory, and application. New York: Praeger Scientific.

24.

von Glasersfeld (1981). An attentional model for the conceptual construction of units and number. Journal for Research in Mathematics Education. 12, 83–94.