Sources Of Developmental Change Research Articles

Intuitive proportion judgment in number-line estimation: Converging evidence from multiple tasks

How children’s understanding of numerical magnitudes changes over the course of development remains a key question in the study of numerical cognition. In an ongoing debate about the source of developmental change, some argue that children maintain and access different mental representations of number, with evidence coming largely from common number-line estimation tasks. In contrast, others argue that a theoretical framework based on psychophysical models of proportion estimation accounts for typical performance on these tasks. The current study explored children’s (n=71) and adults’ (n=27) performance on two number-line tasks: the “number to position” (or NP) task and the inverse “position to number” (or PN) task. Estimates on both tasks are consistent with the predictions of the proportion estimation account and do not support the hypothesis that a fundamental shift in mental representations underlies developmental change in numerical estimation and, in turn, mathematical ability. Converging evidence across the tasks also calls into question the utility of bounded number-line tasks as an evaluation of mental representations of number.

The development of numerical estimation: evidence against a representational shift

How do our mental representations of number change over development? The dominant view holds that children (and adults) possess multiple representations of number, and that age and experience lead to a shift from greater reliance upon logarithmically organized number representations to greater reliance upon more accurate, linear representations. Here we present a new theoretically motivated and empirically supported account of the development of numerical estimation, based on the idea that number-line estimation tasks entail judgments of proportion. We extend existing models of perceptual proportion judgment to the case of abstract numerical magnitude. Two experiments provide support for these models; three likely sources of developmental change in children's estimation performance are identified and discussed. This work demonstrates that proportion-judgment models provide a unified account of estimation patterns that have previously been explained in terms of a developmental shift from logarithmic to linear representations of number.

The prehistory of discovery: precursors of representational change in solving gear system problems.

Microgenetic research has identified 2 different types of processes that produce representational change: theory revision and redescription. Both processes have been implicated as important sources of developmental change, but their relative status across development has not been addressed. The current study investigated whether (a) the process of representational change undergoes developmental change itself or (b) different processes occupy different niches in the course of knowledge acquisition. College, 3rd-, and 6th-grade students solved gear system problems over 2 sessions. For all grades, discovery of the physical principles of the gear system was consistent with theory revision, but discovery of a more sophisticated strategy, based on the alternating sequence of gears, was consistent with redescription. The results suggest that these processes may occupy different niches in the course of acquiring knowledge and that the processes are developmentally invariant across a broad age range.

Sources of developmental change in children's word-problem performance.

This study was designed to examine the roles of domain-specific and general information-processing skills in developmental change in children's performance on arithmetic word problems. In 2 studies, arithmetic knowledge, processing time, memory, reading skill, and word-problem performance were measured in 8- to 12-year-olds (N = 120 in Study 1 and N = 155 in Study 2). Word-problem performance was predicted by arithmetic knowledge (times and errors in solving simple addition and subtraction problems) and by general information-processing skills (reading and processing time and, to a lesser extent and less consistently, memory). Results are discussed in relation to the factors that contribute to word-problem skill.

Sources of developmental change in children's word-problem performance.

Sources of developmental change in children's word-problem performance.

Mothers of Vulnerable and Normal Infants: More Alike than Different

The implications of a research project comparing personality development in firsttime mothers of vulnerable and normal infants are discussed. The mothers exhibited changes across time in anxiety and self-sentiment; these time differences suggest that parenthood can be a source of developmental change. Few significant differences between mothers of vulnerable and normal infants were found, implying that during the early months of an infant's life, mothers of vulnerable and normal children were more alike than different. Since the mothers were showing changes across time, this period appears to be an appropriate time for parent intervention, including possible mains treaming of the mother.