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IES Grant

Title: A Multidisciplinary Study of Analogical Transfer in Children's Mathematical Learning
Center: NCER Year: 2003
Principal Investigator: Holyoak, Keith Awardee: University of California, Los Angeles
Program: Cognition and Student Learning      [Program Details]
Award Period: 2 years Award Amount: $300,715
Goal: Exploration Award Number: R305H030141

Mathematics education in the United States does not enable a substantial number of students to meet state achievement standards for proficiency in mathematics, and many school systems lack effective programs for teaching students to think conceptually about novel or difficult problems. Research suggests that analogical reasoning plays an important yet little understood role in teaching mathematical thinking and learning. The researchers in this project are using both previous studies of typical U.S. classroom activities and laboratory experiments to study the instructional use of analogy as a mechanism for enhancing children's learning. The purpose of this project is to explore ways to improve children's learning of mathematics through teachers' use of analogy in instruction.

Structured Abstract

As a first step, the research team is analyzing videotapes of 25 mathematics lessons from a randomly selected sample of eighth-grade American classrooms to examine how mathematics teachers currently use analogies in their teaching, and how students rely on analogies in their learning. Based on those analyses, the researchers are then carrying out four experiments in which middle school students are randomly assigned to view videotaped mathematics lessons reflecting various aspects of the use of analogy in instruction. In the first study, students will be tested before and after they watch videotapes in which the teacher either uses an analogy explicitly while teaching a lesson about dividing fractions, or leaves the analogy unmentioned. The second experiment is designed to investigate the effects of students watching a student who is involved in developing a relevant analogy for solving a problem, and the third experiment is the same except for the addition of interviews designed to investigate what students have learned about the analogy involved. The fourth experiment is designed to examine student learning of different kinds of analogies. In all four experiments students are tested immediately after watching the videotape and after a period of time, to see what they have learned and how well they have retained it. If the use of analogies improves student learning, the researchers will develop workshops for teachers in the participating schools on the use of analogies in teaching mathematics.

Project Website:


Book chapter

Holyoak, K.J. (2005). Analogy. In K.J. Holyoak, and R.G. Morrison (Eds.), The Cambridge Handbook of Thinking and Reasoning (pp. 117–142). New York: Cambridge University Press.

Holyoak, K.J. (2008). Relations in Semantic Memory: Still Puzzling After all These Years. In M.A. Gluck, J.R. Anderson, and S.M. Kosslyn (Eds.), Memory and Mind: A Festschrift for Gordon H. Bower (pp. 141–158). Mahwah, NJ: Lawrence Erlbaum Associates Publishers.

Holyoak, K.J., and Morrison, R.G. (2005). Thinking and Reasoning: A Reader's Guide. In K.J. Holyoak, and R.G. Morrison (Eds.), The Cambridge Handbook of Thinking and Reasoning (pp. 1–9). New York: Cambridge University Press.

Richland, L.E., Bjork, R.A., and Linn, M.C. (2007). Instruction. In F. Durso, R. Nickerson, S. Dumais, S. Lewandowsky and T. Perfect (Eds.), Handbook of Applied Cognition (2nd ed., pp. 555–583). New Jersey: Wiley and Sons, Ltd.

Journal article, monograph, or newsletter

Richland, L.E., Holyoak, K.J., and Stigler, J.W. (2004). Analogy use in Eighth-Grade Mathematics Classrooms. Cognition and Instruction, 22(1): 37–60.

Richland, L.E., Morrison, R.G., and Holyoak, K.J. (2006). Children's Development of Analogical Reasoning: Insights From Scene Analogy Problems. Journal of Experimental Child Psychology, 94(3): 249–271.

Richland, L.E., Zur, O., and Holyoak, K.J (2007). Cognitive Supports for Analogy in the Mathematics Classroom. Science, 316: 1128–1129.


Morrison, R.G., Doumas, L.A.A., and Richland, L.E. (2006). A Computational Account of Children's Analogical Reasoning: Balancing Inhibitory Control in Working Memory and Relational Representation. In R. Sun and N. Miyake (Eds.), Proceedings of the 28th Annual Conference of the Cognitive Science Society (pp. 635–640). Mahwah, NJ: Erlbaum.

Richland, L.E., Morrison, R.G., and Holyoak, K.J. (2004). Developmental Change in Analogical Reasoning: Evidence From a Picture Mapping Task. In K. Forbus, D. Gentner, and T. Regier (Eds.), Proceedings of the 26th Annual Conference of the Cognitive Science Society (pp. 1149–1154). Mahwah, NJ: Erlbaum.

Richland, L.E., Zur, O., and Holyoak, K.J. (2005). Cross-Cultural Differences in Use of Comparisons: Imagery and Visual Cues. In B.G. Bara, L. Barsalou, M. Bucciarelli (Eds.), Proceedings of the 27th Annual Conference of the Cognitive Science Society (pp. 1149–1154). Mahwah, NJ: Erlbaum.