Early numerical representations and the natural numbers: Is there really a complete disconnect?

The proposal of Rips et al. is motivated by discontinuity and input claims. The discontinuity claim is that no continuity exists between early (nonverbal) numerical representations and natural number. The input claim is that particular experiences (e.g., cardinality-related talk and object-based activities) do not aid in natural number construction. We discuss reasons to doubt both claims in their strongest forms.

[1]  Stacy B. Ehrlich The preschool achievement gap: Are variations in teacher input associated with differences in number knowledge? , 2007 .

[2]  Linda Whealton Suriyakham Input effects on the development of the cardinality principle: Does gesture count? , 2007 .

[3]  Kristin Denton,et al.  Children's Reading and Mathematics Achievement in Kindergarten and First Grade. , 2002 .

[4]  G. Duncan,et al.  School readiness and later achievement. , 2007, Developmental psychology.

[5]  Robert L. Goldstone,et al.  How abstract is symbolic thought? , 2007, Journal of experimental psychology. Learning, memory, and cognition.

[6]  Susan Carey,et al.  One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles , 2007, Cognition.

[7]  Nancy C. Jordan,et al.  Development of calculation abilities in young children. , 1992, Journal of experimental child psychology.

[8]  Patrick W Thompson,et al.  Concrete materials and teaching for mathematical understanding , 1994 .

[9]  Eric A. Jenkins,et al.  How Children Discover New Strategies , 1989 .

[10]  D. Everett Cultural Constraints on Grammar and Cognition in Pirahã , 2005, Current Anthropology.

[11]  Patrick W Thompson,et al.  Research into Practice: Concrete Materials and Teaching for Mathematical Understanding. , 1994 .

[12]  Janellen Huttenlocher,et al.  Preschool children's mathematical knowledge: The effect of teacher "math talk.". , 2006, Developmental psychology.

[13]  Kelly S. Mix,et al.  Surface similarity and label knowledge impact early numerical comparisons , 2008 .

[14]  S. Carey Bootstrapping & the origin of concepts , 2004, Daedalus.