Pathways to Number: Children's Developing Numerical Abilities

By Jacqueline Bideaud; Claire Meljac et al. | Go to book overview

7
Number Conservation: Distinguishing Quantifier From Operator Solutions

Linda Tollefsrud-Anderson University of Wisconsin Barron County Center

Robert L. Campbell IBM T. J. Watson Research Center

Prentice Starkey University of California at Berkeley

Robert G. Cooper Jr. San Jose State University

Ever since its introduction by Piaget and Szeminska ( 1941), conservation of number has been one of the most widely researched topics in cognitive development, yet debate continues about this developmental issue. Conflicting definitions of conservation have led to conflicting ways of assessing it. Conflicts about how to assess conservation have led, in turn, to theoretical disputes like the question of small number conservation. We reconsider here the nature of number conservation and the appropriate methods for assessing it. We present refinements in method that make it easier to determine how children are solving conservation tasks. Specifically, we recommend ways to distinguish solutions based on reasoning about the transformation from solutions based on counting or matching. Being able to make these distinctions should help us to understand the developmental transition from nonconserver to conserver.


WHAT CONSERVATION IS AND IS NOT

We define conservation as the ability to know what does and does not change a given quantity. Conservation of number involves the application of a number reasoning principle or operator ( Gelman, 1972) to the task: specifically, the principle that number does not change when nothing is added or subtracted. In its insistence on transformations and reasoning about them, our definition agrees

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