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IES Grant

Title: Understanding and Facilitating Symbolic Learning
Center: NCER Year: 2005
Principal Investigator: Uttal, David Awardee: Northwestern University
Program: Cognition and Student Learning      [Program Details]
Award Period: 3 years Award Amount: $958,346
Type: Development and Innovation Award Number: R305H050059

Purpose: In this project, researchers developed and tested interventions designed to help parents and teachers use symbolic objects, such as manipulatives, more effectively. The ability to understand letters, numbers, and mathematical symbols is critically important to learning in school and teachers often use such objects, commonly called manipulatives, to facilitate children's learning of mathematics. However, the underlying assumption that interacting with manipulatives would improve mathematics learning had not been adequately tested, and there were theoretical reasons to believe that merely interacting with an object that was intended to be a symbol may actually be counterproductive. By the end of this project, researchers aimed to have an intervention that used symbolic objects to support mathematics learning and evidence of this intervention's benefits.

Structured Abstract


Setting: Three elementary schools in the Chicago area are participating. Participating preschool children also live in the greater Chicago area

Sample: The participants include 4-year-olds and students in grades 2 and 4. Participating children are diverse in terms of ethnicity and socioeconomic status. The grade 2 and 4 students attend one of three elementary schools. One school serves a population that is 97 percent African American. A second school serves a population that is very diverse with approximately equal numbers of White, Hispanic, and Asian-American children. The third school serves a population that is approximately 85 percent White.

Intervention: Two types of interventions are being developed. The first is designed to facilitate four-year-olds in understanding the symbolic properties of letters and numbers through simple games using magnetic letters and numbers that parents can play with their child. The second intervention takes place in elementary schools. Teachers will implement instructional methods designed to help children link what they learn with mathematics manipulatives to written versions of the same kind of problems.

Research Design and Methods: The research team is conducting experiments that focus on children's understanding of letters, numbers, and mathematical symbols and the influences of interacting with concrete symbolic objects on this understanding. The researchers use pre-test, post-test designs, and include control groups to ensure that observed improvements are attributable to the newly developed interventions.

Control Condition: Some of the studies rely on a within-subject design, and in those cases, children serve as their own control. In other experiments, children are randomly assigned to control conditions where they complete the same tasks as the experimental children but without the use of concrete symbolic objects.

Key Measures: A variety of assessments of number and letter knowledge are being used. They include standardized tests such as the Test of Early Mathematics Ability (TEMA 3), relevant subscales of the Woodcock-Johnson tests, and simple experimenter-developed measures, such as tests of letter and number recognition and counting.

Data Analytic Strategy: Differences between experimental and control groups are being evaluated using analysis of variance techniques.

Related IES Projects: Learning From Symbolic Objects (R305H020088)

Products and Publications

ERIC Citations:  Find available citations in ERIC for this award here.

Select Publications

Book chapters

Deloache, J.S. (2005). The Pygmalion Problem in Early Symbol Use. In L. Namy (Ed.), Symbol Use and Symbolic Representation: Developmental and Comparative Perspectives (pp. 47–67). Mahwah, NJ: Erlbaum.

Deloache, J.S., and Bloom, M.E. (2010). Of Chimps and Children: Use of Spatial Symbols by Two Species. In F. Dolins, and R. Mitchell (Eds.), Spatial Perception, Spatial Cognition (pp. 486–501). New York: Cambridge University Press.

DeLoache, J.S., and Ganea, P.A. (2007). The Early Growth of Symbolic Understanding and Use: A Tribute to Ann Brown. In J.C. Campione, K.E. Metz, and A.S. Palincsar (Eds.), Children's Learning in the Laboratory and Classroom Contexts: Essays in Honor of Ann Brown (pp. 39–54). Mahwah, NJ: Lawrence Erlbaum and Associates.

DeLoache, J.S., Ganea, P.A., and Jaswal, V.K. (2009). Early Learning Through Language. In J. Colombo, P. McArdle, and L. Freund (Eds.), Infant Pathways to Language: Methods, Models, and Research Directions (pp. 119–140). Mahwah, NJ: Erlbaum.

Uttal, D.H., and O'Doherty, K. (2008). Comprehending and Learning From Visual Representations: A Developmental Approach. In J. Gilbert, M. Reiner, and M. Nakhleh (Eds.), Visualization: Theory and Practice in Science Education (pp. 53–72). New York: Springer.

Uttal, D.H., and O'Doherty, K. (2008). Comprehending and Learning From Visualizations: A Developmental Perspective. In J. Gilbert, M. Reiner, and M. Nakhleh (Eds.), Visualization: Theory and Practice in Science Education (pp. 53–72). New York: Springer.

Uttal, D.H., Liu, L.S., and Deloache, J.S. (2005). Concreteness and Symbolic Development. In L. Balter, and C.S. Tamis-Lemonda (Eds.), Child Psychology: A Handbook of Contemporary Issues (2nd ed., pp. 167–184). New York: Psychology Press.

Journal article, monograph, or newsletter

Deloache, J.S. (2006). Mindful of Symbols. Scientific American Mind, 17(1): 71–75. DeLoache, J.S., and Chiong, C. (2009). Babies and Baby Media. American Behavioral Scientist, 52(8): 1115–1135.

McNeil, N., Uttal, D.H., Jarvin, L., and Sternberg, R.J. (2009). Should You Show Me the Money? Concrete Objects Both Hurt and Help Performance on Mathematics Problems. Learning and Instruction, 19(2): 171–184.

Simcock, G., and DeLoache, J.S. (2006). Get the Picture? The Effects of Iconicity on Toddlers' Reenactment From Picture Books. Developmental Psychology, 42(6): 1352–1357.

Sternberg, R. (2008). Applying Psychological Theories to Educational Practice. American Educational Research Journal, 45(1): 150–165.

Uttal, D.H., and Deloache, J.S. (2006). Learning From Symbolic Objects. APS Observer, 19(5).

Uttal, D. H., Amaya, M., del Rosario Maita, M., Hand, L. L., Cohen, C. A., O'Doherty, K., & DeLoache, J. S. (2013). It works both ways: Transfer difficulties between manipulatives and written subtraction solutions. Child Development Research, 2013.

Uttal, D.H., Gentner, D., Liu, L.L., and Lewis, A.R. (2008). Developmental Changes in Children's Understanding of the Similarity Between Photographs and Their Referents. Developmental Science, 11(1): 156–170.

Uttal, D.H., O'Doherty, K.D., and DeLoache, J.S. (2009). Rethinking the Concrete-Abstract Distinction: The Case of Mathematics Manipulatives. Child Development Perspectives.

Ware, E., Uttal, D.H., Wetter, E.K., and DeLoache, J.S. (2006). Young Children Make Scale Errors When Playing With Dolls. Developmental Science, 9(1): 40–45.

Yuan, L., & Uttal, D. H. (2017). Analogy lays the foundation for two crucial aspects of symbolic development: Intention and correspondence. Topics in Cognitive Science, 9(3), 738–757.