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Garden of Constants, The Ohio State University 

Overview

Many cognitive models assume that concepts are represented in a psychological similarity space, with conceptual referents appearing as values along a (multi-) dimensional continua. From this assumption, children's concepts are interesting because their initial similarity space appears to be distorted in ways that are not scientifically or mathematically correct (e.g., judging plants to be more similar to rocks than to animals, or judging 100 to be closer to 1000 than 1), but do make sense evolutionarily. For example, to a hungry animal, the difference between 1 and 10 pieces of food is more important than the difference between 101 and 110 pieces of food. By conceptualizing development as a change in underlying similarity space, we can make quite specific predictions about the properties of information that will lead to conceptual change, how quickly and broadly conceptual change will occur, and what factors will lead to transfer to new types of problems. We apply this approach to several families of concepts, including numerical and biological concepts.

Representations and Representational Change

Representational change and transfer:

Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237 - 243. [pdf]

Opfer, J. E., & Siegler, R. S. (2007). Representational change and children's numerical estimation. Cognitive Psychology, 55, 169-195. [pdf]

Thompson, C. A., & Opfer, J. E. (2010). How 15 hundred is like 15 cherries: Effect of progressive alignment on representational changes in numerical cognition. Child Development, 81, 1768-1786. [pdf]

Numerical Cognition

Development of the mental number line:

Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237 - 243. [pdf]

Opfer, J. E., & Siegler, R. S. (2007). Representational change and children's numerical estimation. Cognitive Psychology, 55, 169-195. [pdf]

Siegler, R. S., Thompson, C. A., & Opfer, J. E. (2009). The logarithmic-to-linear shift:  One learning sequence, many tasks, many time scales. Mind, Brain, and Education, 3, 143 - 150. [pdf]

Categorization, Analogy, and Induction

Generalization over similarities between objects and object relations. Role of analogy in conceptual change:

Opfer, J. E., & Siegler, R. S. (2004). Revisiting preschoolers' living things concept: A microgenetic analysis of conceptual change in basic biology. Cognitive Psychology, 49, 301-332. [pdf] 

Opfer, J. E., & Bulloch, M. J. (2007). Causal relations drive young children's induction, naming, and categorization. Cognition, 105, 207-217. [pdf]

 

Bulloch, M. J., & Opfer, J. E. (2009). What makes relational reasoning smart? Revisiting the relational shift in cognitive development. Developmental Science, 12, 114 - 122. [pdf]

Animacy and biological reasoning

Animacy and conceptual change in biology:

Gelman, S. A., & Opfer, J. E. (2002). Development of the animate-inanimate distinction. In U. Goswami (Ed.), Blackwell Handbook of Childhood Cognitive Development (pp. 151 - 166). Oxford, UK: Blackwell. [pdf]

Nehm, R., Beggrow, E. P., Opfer, J. E., & Ha, M. (2012). Reasoning about natural selection: Diagnosing contextual competency in evolutionary reasoning using the ACORNS instrument. American Biology Teacher, 74, 92-98. [pdf]

Opfer, J. E., Nehm, R., & Ha, M. (2012). Cognitive foundations for science assessment design: Knowing what students know about evolution. Journal of Research in Science Teaching, 49, 744-777. [pdf]