MATH, MUSIC AND THE PART-WHOLE CONCEPT: LINKING STEFFE AND COBB’S

MODEL OF NUMBER SENSE DEVELOPMENT TO CURRENT MUSIC RESEARCH

Dorothea Arne Steinke

NumberWorks

steinke@rt66.com

This paper proposes that the “gate” concepts between the three stages of Steffe and Cobb’s (1988) 3-Stage model of number understanding can be experienced in music rhythm. The “gate” between Stage 1 and Stage 2, the concept of the equal distance of 1 between neighboring whole numbers, is the same as the equal distance between the steady melody beats of simple children’s songs. The “gate” between Stage 2 and Stage 3, the part-whole concept (the coexistence of all the partitions of a quantity and the whole quantity), is the same as the coexistence of the melody beats (the parts) grouped into the unchanging meter or “big beat” (the whole) of a song. Rauscher et. al. (1997) recent work appears to show that the “equal distance” concept can be assimilated through rhythmic, sequential finger training at a music keyboard. A classroom-based research project is underway to determine whether non-keyboard music instruction targeted to the part-whole concept will significantly improve 2nd- and 3rd-graders’ grasp of that concept.

References

Steffe, L.P. and Cobb, P. (1988). Construction of arithmetical meanings and strategies. New York: Springer-Verlag.

Rauscher, F.H., Shaw, G.L., Levine, L.J., Wright, E.L., Dennis, W.R., and Newcomb, R.L. (1997). Music training causes long-term enhancement of preschool children’s spatial-temporal reasoning. Neurological Research, 19, 2-8.