Developing kindergartners' reasoning with number using a part-whole schema.

Abstract

The purpose of this study was to investigate the effect of emphasizing a part-whole understanding of number, i.e. the ability to visualize a number as the sum of two smaller numbers, on kindergartners' small number concepts, thinking strategies for the basic facts, and understanding of place value, addition, and subtraction. Explicit attention was given to students' invention and verbalization of their reasoning processes. There were 295 kindergarten students from four schools in the Experimental group, and 150 students from four schools in the Control group. The Experimental group received instruction from an investigator-designed 70-lesson program from October to May, 1993-94. Data were collected from interviews with a sample of 85 students, 59 Experimental and 26 Control. Achievement data were analyzed with independent t-tests. Solution strategies were analyzed with chi-square tests. It was hypothesized that emphasizing reasoning with number using parts and wholes and making connections between models such as dot patterns and ten-frames, oral names, and written symbols would result in superior performance. This hypothesis was verified. The Experimental group performed significantly better than the Control group on all sections of the interview. The mean percent correct on the overall interview for the Experimental group was 77.9, while only 54.0 for the Control group. Findings were similar for all ability groups. The startling result was that the low-ability Experimental group performed better than the average-ability Control group in every category and as well as the high-ability Control group on small numbers and basic facts. The Experimental group also used more advanced thinking strategies, using groups or parts of numbers and automatic recall, whereas the Control group counted-all by ones, guessed, or made no attempt. Overall, this study demonstrated that emphasizing reasoning with number using parts and wholes helped kindergartners gain richer small-number concepts, use more advanced thinking strategies for the basic facts, better understand place value, and become better at problem solving.