KidCode is email-based software designed to supplement the National Council of Teachers of Mathematics (NCTM) elementary curriculum standards by addressing the need to develop conceptual links between concrete mathematical activities and mathematics as a language. It provides children with the opportunity to explore mathematics as one of many symbol systems that have been built for the purposes of communication. We designed a sequence of four two-person games centered on the theme of codes and secret messages and conducted formative evaluation of the games.
By pairing tools for the creation of codes and authoring of coded messages with a full featured email messaging system, KidCode enables children to gain experience with many kinds of symbolic representations. Message authoring can consist of text, graphics, and even animations. Similarly, with KidCode children can advance from an understanding of symbolic representation of object/noun type entities for text and simple pictures to coded representations of spatial relationships and, finally, to representation of operator actions. Our work provides an example of how mathematics instruction can be based on the use of email software to structure cooperative interactions among elementary aged students.
For formative studies, we crafted materials of paper and poster board with varied examples at different levels of difficulty that could be used for multiple rounds of play. These materials were used throughout the research period in evaluations with three adults and twenty children in the first through fourth grades (ages 5-10 yrs.) from a wide range of socioeconomic backgrounds. As the research progressed, the materials were revised or expanded in order to address issues that arose during the evaluation sessions. Some of the games were modified considerably after observing children play the games. Our research suggests that, taken together, the games improve the children's facility with symbolic processing.
In this paper we describe one of the KidCode games - Rebus - in detail. We explain how formative evaluation based on paper materials was used to test design ideas for the KidCode software and develop a sequence of games to scaffold children's understanding of symbol systems and that would work effectively in an electronic mail context. The figure on the cover page shows the email inbox from a screen dump of a Macromedia Director2 prototype of the software. The bus icon indicates a Rebus game message.
The ideas for KidCode arose out of studies of educational research that indicate that children's difficulty with mathematics in school arises from the failure to develop conceptual links between mathematics as a symbol system and mathematical concepts that can be used to describe the physical world. (e.g. Ginsburg, 1989, Goldman et. al., 1997) Whereas the development of mathematical thinking in young children and skill in basic counting and arithmetic can be quite advanced when posed in real world settings, their application in school math has seemed limited and often, resistant to further development.
Research on children's mathematics thinking has shown that understanding of basic mathematical concepts generally developed well before children's facility with symbolic representation. Preschool children, who cannot yet read are usually quite competent in using mental math to solve simple arithmetic problems requiring addition and subtraction. However, young elementary aged children have generally not developed an ability to use symbols. Few first graders are able to read upon entering school and their experience with symbolic processing is very limited. Nevertheless, until recently they have been required to use to use symbols to represent relatively abstract mathematical ideas.
The result of emphasizing symbolic math before the children develop competence with symbolic processing has been negative. This is where children begin to view school math as separate and unrelated to anything in their experience. Failure to develop children's facility with symbolic representations has the result that many children in early elementary grades develop misconceptions about school math as a nonsensical system of symbol manipulation. In studies of children who perform poorly in mathematics at school, it was found that the same children could solve problems with ease if they were presented in context and without recourse to paper and pencil. ( Ginsburg 1984, 1997) Related research has shown that children's performance on mathematical problem solving tasks actually declined after a few years of schooling. Children upon entering school showed good insight relating arithmetic to real situations but by the ages of 9 or 10 were trying to solve word problems by resorting to superficial strategies such as "guess the operation" or "find the numbers and add". (e.g. Carpenter et. al. 1993)____________________