formula and so that they consciously experiment with alternative representations when asked to solve a mathematics problem. Only a more extensive longitudinal study that includes children's teachers could determine the full impact of KidCode on more general mathematics learning.
Paper prototypes used in this work have resulted in substantial improvements in the design of the KidCode software at very early stages of development. Because we were able to revise quickly and make significant alterations in our initial conceptions, we were able to completely revise many of the games in response to children's interactions with one another and the materials. Moreover, we were able to evaluate and construct the sequence of games to provide good scaffolding to support the children's developing understanding.
We also found that the interaction model of electronic mail works well to structure a series of interactions as a two person game involving a coder and decoder. Occasionally we cautioned a player not to try to peek at a partner's work in progress, but found that the children quickly adapted to the nature of the communication as turn taking that yielded new information with each turn. We also discovered that a few important questions can only be resolved by evaluation of the software. Not surprisingly, most of these questions pertain to the nature of computer mediated interaction. Working with paper materials, children sat together in a room and could monitor one another's reactions in a direct way. To sustain this level of engagement for young children we may wish to incorporate features not normally associated with electronic mail such as audio or video annotations. The effectiveness of the online help system as a sole source of instruction and the degree to which the media supports engaging interaction will guide our research and software development as we proceed in the next phase of this work.
L. J. Bricker, Tanimoto, S. L. Rothenberg, A. I., D.C. Hutama and Wong, T. H. "Multiplayer Activities that Develop Mathematical Coordination". CSCL '95 Proceedings, Lawrence Erlbaum Associates, Inc. New Jersey. 1995.
T. P.Carpenter, Ansell, E., Franke, M. L., Fennema, E. , & Weisbeck, L. "Models of problem-solving: A study of kindergarten children's problem solving processes". Journal for Research in Mathematics, 24( 5), 1993. pp. 428-441.
J. S. DeLoache. "Rapid change in the symbolic functioning of very young children". Science, 238, 1987. pp 1556-1557.
D. C. Edelson, O'Neill, D. K., Gomez, L. M. and D'Amico, L. "A Design for Effective Support of Inquiry and Collaboration". CSCL '95 Proceedings, Lawrence Erlbaum Associates, Inc. New Jersey. 1995.
H. P. Ginsburg, Children's Arithmetic. ( Second edition.), PRO-ED, Inc., Austin, TX, 1989.
H. P. Ginsburg. "Mathematics Learning Disabilities: A View From Developmental Psychology". Journal of Learning Disabilities, 30( 1), 1997. pp. 20-33.
S. R. Goldman, Hasselbring, Ted S. and The Cognition and Technology Group at Vanderbilt. Achieving "Meaningful Mathematics Literacy for Students with Learning Disabilities". Journal of Learning Disabilities, 30( 2), 1997. pp. 198-208.
S. Goldman and J. N. Moschkovich. "Environments for Collaborating Mathematically". CSCL '95 Proceedings, Lawrence Erlbaum Associates, Inc. New Jersey. 1995.
S. Goldman and J. N. Moschkovich et al. MMAP Web site. http://www.irl.org/mmap/MMAPinfo.html
B. Greer. "The Two Faces of Mathematics". Journal of Structural Learning, Vol. 10, 1989. pp 79-82.
C. Gutwin, Stark, G. and Greenberg, S. "Support for Workspace Awareness in Educational Groupware". CSCL '95 Proceedings, Lawrence Erlbaum Associates, Inc. New Jersey. 1995.
M. Guzdial, Turns, J., Rappin T. and Carlson D. Collaborative Support for Learning in Complex Domains. CSCL '95 Proceedings, Lawrence Erlbaum Associates, Inc. New Jersey. 1995.
Harrison Fox & Co., Nanny M., and Mohl, B. Top Secret Decoder. Houghton Mifflin Interactive. 1996.
National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics, 1989.
J. Nielsen. "Iterative User-Interface Design". Computer, Vol. 26, No. 11, Nov. 1993. pp 32-41.