Key outcomes
The project completed two lines of work, one in the area of biological reasoning about living things (science) and one in the area of numerical estimation (mathematics). Research articles describing the findings of this work are available in the publications section of this abstract.
The completed research in estimation led to the development of several interventions that can be used with preschool and elementary school children. Those new interventions were implemented in classrooms and tested with support from subsequent awards.
In addition, their research has demonstrated that performance on the number line task does relate to performance on other estimation tasks, and does correlate with other arithmetic tasks. They also found that exposing children to linear representations influenced their ability to perform subsequent tasks well (both in preschool and in elementary school). Thus, linear representations seem critical to mathematics performance, and amenable to instruction.
People and institutions involved
IES program contact(s)
Products and publications
Publications:
ERIC Citations: Find available citations in ERIC for this award here.
WWC Review:
Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child development, 79(4), 1016-1031. [WWC Review]
Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games. Child development, 79(2), 375-394. [WWC Review]
Ramani, G. B., & Siegler, R. S. (2011). Reducing the gap in numerical knowledge between low-and middle-income preschoolers. Journal of applied developmental Psychology, 32(3), 146-159. [WWC Review]
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child development, 75(2), 428-444. [WWC Review]
Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games-but not circular ones-improves low-income preschoolers' numerical understanding. Journal of educational psychology, 101(3), 545. [WWC Review]
Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children's numerical development. Developmental science, 11(5), 655-661. [WWC Review]
Select Publications:
Book chapters
Lin, X., Siegler, R.S., and Sullivan, F.R. (2010). Students' Goals Influence Their Learning. In D.D. Preiss, and R.J. Sternberg (Eds.), Innovations in Educational Psychology: Perspectives on Learning, Teaching, and Human Development (pp. 79-104). New York: Springer.
Siegler, R.S., and Araya, R. (2005). A Computational Model of Conscious and Unconscious Strategy Discovery. In R.V. Kail (Ed.), Advances in Child Development and Behavior, Volume 33 (pp. 1-42). Oxford, UK: Elsevier.
Siegler, R.S., and Booth, J.L. (2005). Development of Numerical Estimation: A Review. In J.I.D. Campbell (Ed.), Handbook of Mathematical Cognition (pp. 197-212). Boca Raton, FL: CRC Press.
Siegler, R.S. (2006). Microgenetic Analyses of Learning. In D. Kuhn, and R.S. Siegler (Eds.), Handbook of Child Psychology: Volume 2: Cognition, Perception, and Language (6th ed., pp. 464-510). Hoboken, NJ: Wiley.
Journal articles
Booth, J.L., and Siegler, R.S. (2006). Developmental and Individual Differences in Pure Numerical Estimation. Developmental Psychology, 42(1): 189-201.
Booth, J.L., and Siegler, R.S. (2008). Numerical Magnitude Representations Influence Arithmetic Learning. Child Development, 79(4): 1016-1031.
Laski, E.V., and Siegler, R.S. (2007). Is 27 a Big Number? Correlational and Causal Connections Among Numerical Categorization, Number Line Estimation, and Numerical Magnitude Comparison. Child Development, 76(6): 1723-1743.
Opfer, J.E., and Siegler, R.S. (2004). Revisiting Preschoolers' Living Things Concept: A Microgenetic Analysis of Conceptual Change in Basic Biology. Cognitive Psychology, 49(4): 301-332.
Opfer, J.E., and Siegler, R.S. (2007). Representational Change and Children's Numerical Estimation. Cognitive Psychology, 55(3): 169-195.
Ramani, G.B., and Siegler, R.S. (2008). Promoting Broad and Stable Improvements in Low-Income Children's Numerical Knowledge Through Playing Number Board Games. Child Development, 79(2): 375-394.
Ramani, G.B., and Siegler, R.S. (2011). Reducing the Gap in Numerical Knowledge Between Low- and Middle-Income Preschoolers. Journal of Applied Developmental Psychology, 32(3): 146-159.
Siegler, R.S. (2003). Relations Between Short-Term and Long-Term Cognitive Development. Psychological Science Agenda, 16: 8-10.
Siegler, R.S. (2004). Turning Memory Development Inside Out. Developmental Review, 24(4): 469-475.
Siegler, R.S. (2004). U-Shaped Interest in U-Shaped Development and What it Means. Journal of Cognition and Development, 5(1): 1-10.
Siegler, R.S. (2009). Improving the Numerical Understanding of Children From Low-Income Families. Child Development Perspectives, 3(2): 118-124.
Siegler, R.S., and Booth, J.L. (2004). Development of Numerical Estimation in Young Children. Child Development, 75(2): 428-444.
Siegler, R.S., and Mu, Y. (2008). Chinese Children Excel on Novel Mathematics Problems Even Before Elementary School. Psychological Science, 19(8): 759-763.
Siegler, R.S., and Opfer, J. (2003). The Development of Numerical Estimation: Evidence for Multiple Representations of Numerical Quantity. Psychological Science, 14: 237-243.
Siegler, R.S., and Ramani, G.B. (2006). Early Development of Estimation Skills. APS Observer, 19(5): 34-44.
Siegler, R.S., and Ramani, G.B. (2008). Playing Linear Numerical Board Games Promotes Low-Income Children's Numerical Development. Developmental Science, 11(5): 655-661.
Siegler, R.S., and Ramani, G.B. (2009). Playing Linear Number Board Games, but not Circular Ones, Improves Low-Income Preschoolers' Numerical Understanding. Journal of Educational Psychology, 101(3): 545-560.
Siegler, R.S., and Svetina, M. (2006). What Leads Children to Adopt New Strategies?: A Microgenetic/Cross-Sectional Study of Class Inclusion. Child Development, 77(4): 997-1015.
Siegler, R.S., Thompson, C.A., and Opfer, J. E. (2009). The Logarithmic-to-Linear Shift: One Learning Sequence, Many Tasks, Many Time Scales. Mind, Brain, and Education, 3(3): 143-150.
Related projects
Questions about this project?
To answer additional questions about this project or provide feedback, please contact the program officer.
