Children's invented symbol systems: Exploring parallels between music and mathematics.

Abstract

This is a short report of an exploratory study linking children's invented mathematical notations and music notations. Ten 8-year-old children participated in the study. Prior research in music notations has indicated that children have a variety of symbols at their disposal, and their choice of symbols depends on the entity they are trying to capture. This was also the case for notations of tessellations. Although there were similarities found between the use of symbols in the two domains, a consideration of the intended reader did not appear to be a contributing factor in designing mathematical notations. This research note describes the first of four phases of the research comparing children's invented notations for mathematics and music. The overall aims of the research are to explore the authentic connections between music and mathematics in terms of notations, as well as form and transformations, and to adapt methodologies used in researching children's music cognition to address parallel situations in mathematics. There is much to learn from the research on music notations in advancing our understanding of mathematics notations. A diverse body of research indicates that children use a rich and varied repertoire of symbols and strategies in notating rhythm sequences and melodies. They notate with pictures or icons, letters and words, numbers, lines and squiggles and crosses, music symbols, and color to create engaging systems of recording the music they (Bamberger, 1982; Davidson & Colley, 1986; Davidson & Scripp, 1988; Davidson, Scripp, & Welsh, 1988; Smith, 1989; Upitis, 1987, 1990a) and compose (Borstad, 1989; Upitis, 1990b, 1992). In an examination of the research on children's music notations, three other features consistently emerge. The first is that children are more likely to engage in exploring and using music notations when they are involved in making something that they value as real—perhaps composing a piece that others will in a class concert (Upitis, 1992). Second, research on music notations indicates the importance of the intended or imagined reader. Children are less likely to use music symbols if they know that the person who will be reading their notation is not fluent in standard notation (Upitis, 1990a, 1992). Finally, research indicates that when children truly embrace an idea, they make it a part of their world, using the idea to see the everyday phenomena in new ways (Hodgkin, 1985). Thus, children who become musicians and composers may hear the music in the pattern on a sweater or in a mosaic (Upitis, 1990b).