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

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.

[1]  Leslie P. Steffe,et al.  Cognitive Play and Mathematical Learning in Computer Microworlds. , 1994 .

[2]  Leslie P. Steffe,et al.  Schemes of action and operation involving composite units , 1992 .

[3]  Ernst von Glasersfeld,et al.  An Attentional Model for the Conceptual Construction of Units and Number. , 1981 .

[4]  Seymour Papert,et al.  Mindstorms: Children, Computers, and Powerful Ideas , 1981 .

[5]  Leslie P. Steffe,et al.  Individual constructive activity: an experimental analysis , 1999, Cybern. Hum. Knowing.

[6]  John Olive,et al.  Computer Tools for Interactive Mathematical Activity in the Elementary School , 2000, Int. J. Comput. Math. Learn..

[7]  John Olive,et al.  Building a New Model of Mathematics Learning. , 1994 .

[8]  Barry D. Biddlecomb.  Theory-Based Development of Computer Microworlds , 1994 .

[9]  Robert G. Cooper,et al.  The Role Mathematical Transformations and Practice in Mathematical Development , 1991 .

[10]  J. Piaget.  Play, dreams and imitation in childhood , 1951 .

[11]  J. Piaget.  The Child's Conception of Number , 1953 .

[12]  C. Hoyles,et al.  A pedagogy for mathematical microworlds , 1992 .

[13]  F. Wood-Black.  Do you see what I see , 2002 .

[14]  G. Pólya.  Mathematics and Plausible Reasoning , 1958 .

[15]  Leslie P. Steffe,et al.  Symbolizing as a Constructive Activity in a Computer Microworld , 1996 .

[16]  Thomas E. Kieren,et al.  Orthogonal Reflections on Computer Microworlds, Constructivism, Play and Mathematical Understanding , 1994 .

[17]  R. Skemp,et al.  Intelligence, Learning and Action , 1980 .

[18]  Massimo Piattelli-Palmarini,et al.  Language and Learning: The Debate Between Jean Piaget and Noam Chomsky , 1980 .

[19]  Leslie P. Steffe,et al.  Children's counting types: Philosophy, theory, and application , 1983 .