Effects of perceptually rich manipulatives on preschoolers' counting performance: established knowledge counts.

Educators often use concrete objects to help children understand mathematics concepts. However, findings on the effectiveness of concrete objects are mixed. The present study examined how two factors-perceptual richness and established knowledge of the objects-combine to influence children's counting performance. In two experiments, preschoolers (N = 133; Mage = 3;10) were randomly assigned to counting tasks that used one of four types of objects in a 2 (perceptual richness: high or low) × 2 (established knowledge: high or low) factorial design. Findings suggest that perceptually rich objects facilitate children's performance when children have low knowledge of the objects but hinder performance when children have high knowledge of the objects.

[1]  Christopher Ricks,et al.  To J.S. , 2014 .

[2]  Robert L. Goldstone,et al.  Connecting instances to promote children's relational reasoning. , 2011, Journal of experimental child psychology.

[3]  Zsófia Osváth,et al.  DOI: 10 , 2011 .

[4]  Vladimir M. Sloutsky,et al.  Transfer of Mathematical Knowledge: The Portability of Generic Instantiations , 2009 .

[5]  Nicole M. McNeil,et al.  Should you show me the money? Concrete objects both hurt and help performance on mathematics problems , 2009 .

[6]  Jennifer A. Kaminski,et al.  The effect of concreteness on children’s ability to detect common proportion , 2009 .

[7]  Robert L. Goldstone,et al.  ' s personal copy Simplicity and generalization : Short-cutting abstraction in children ’ s object categorizations , 1997 .

[8]  Vladimir M Sloutsky,et al.  The Advantage of Abstract Examples in Learning Math , 2008, Science.

[9]  Linda Jarvin,et al.  When Theories Don't Add Up: Disentangling he Manipulatives Debate , 2007 .

[10]  Vladimir M. Sloutsky,et al.  Do Children Need Concrete Instantiations to Learn an Abstract Concept , 2006 .

[11]  Sandra R Waxman,et al.  Mother-child conversations about pictures and objects: referring to categories and individuals. , 2005, Child development.

[12]  Nicole M. McNeil,et al.  Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations. , 2005, Child development.

[13]  B. Ambridge,et al.  The structure of working memory from 4 to 15 years of age. , 2004, Developmental psychology.

[14]  Margaret Anne Defeyter,et al.  Acquiring an understanding of design: evidence from children's insight problem solving , 2003, Cognition.

[15]  Robert L. Goldstone,et al.  The transfer of abstract principles governing complex adaptive systems , 2003, Cognitive Psychology.

[16]  P. Bloom,et al.  How specific is the shape bias? , 2003, Child development.

[17]  Linda B. Smith,et al.  How children know the relevant properties for generalizing object names , 2002 .

[18]  Susan C. Levine,et al.  Quantitative Development in Infancy and Early Childhood , 2002 .

[19]  David M. Sobel,et al.  Causal learning mechanisms in very young children: two-, three-, and four-year-olds infer causal relations from patterns of variation and covariation. , 2001, Developmental psychology.

[20]  Larissa K. Samuelson,et al.  Children's attention to rigid and deformable shape in naming and non-naming tasks. , 2000, Child development.

[21]  J. Deloache Dual representation and young children's use of scale models. , 2000, Child development.

[22]  R. Siegler,et al.  Conscious and unconscious strategy discoveries: a microgenetic analysis. , 1998, Journal of experimental psychology. General.

[23]  F. Paas,et al.  Cognitive Architecture and Instructional Design , 1998 .

[24]  C. Sophian Beyond competence: The significance of performance for conceptual development , 1997 .

[25]  L. Markson,et al.  Evidence against a dedicated system for word learning in children , 1997, Nature.

[26]  J. Deloache,et al.  Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics , 1997 .

[27]  Nancy K. Mack Confounding whole-number and fraction concepts when building on informal knowledge. , 1995 .

[28]  James W. Stigler,et al.  The Learning Gap: Why our Schools are Failing and What We can Learn from Japanese and Chinese Education. , 1993 .

[29]  Jacob Cohen,et al.  THINGS I HAVE LEARNED (SO FAR) , 1990 .

[30]  Karen Wynn,et al.  Children's understanding of counting , 1990, Cognition.

[31]  Linda B. Smith,et al.  The importance of shape in early lexical learning , 1988 .

[32]  K. Fuson Children's Counting and Concepts of Number , 1987 .

[33]  E. Markman,et al.  Young children's inductions from natural kinds: the role of categories and appearances. , 1987, Child development.

[34]  Robert S. Siegler,et al.  A featural analysis of preschoolers' counting knowledge. , 1984 .

[35]  R. Gelman,et al.  Preschoolers' counting: Principles before skill , 1983, Cognition.

[36]  C. Gallistel,et al.  The Child's Understanding of Number , 1979 .

[37]  Morton Friedman The Manipulative Materials Strategy: The Latest Pied Piper?. , 1978 .

[38]  M. Scheerer,et al.  Problem Solving , 1967, Nature.

[39]  R. Adamson Functional fixedness as related to problem solving; a repetition of three experiments. , 1952, Journal of experimental psychology.

[40]  N. Maier Reasoning in humans. II. The solution of a problem and its appearance in consciousness. , 1931 .

[41]  L. Witmer The Montessori Method , 1914, The Psychological clinic.