Project Activities
As a first step, the research team analyzed videotapes of 25 mathematics lessons from a randomly selected sample of 8th-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 then completed four experiments in which middle school students were randomly assigned to view videotaped mathematics lessons reflecting various aspects of the use of analogy in instruction. In the first study, students were 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 investigated the effects of students watching a student who is involved in developing a relevant analogy for solving a problem. The third experiment was the same except for the addition of interviews designed to investigate what students have learned about the analogy involved. The fourth experiment examined student learning of different kinds of analogies. In all four experiments students were 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.
Key outcomes
Through an analysis of the TIMSS video data, the research team was able to identify substantive differences in the ways in which US, Japanese, and Hong Kong teachers used analogies during instruction. While all teachers used analogies during instruction in eighth-grade mathematics classrooms, US teachers did not systematically use the same supportive cues as Asian teachers. These supportive cues are associated with student engagement in the deep conceptual processing that analogical instruction can support. The descriptive research identified the following three components of the most effective instructional use of analogies: 1. using a very familiar source, 2. making the source visually available during the solution of the target, and 3. making use of comparative gesture and visual imagery.
These findings were then used to design a series of experiments in order to elucidate the processes underlying students’ learning from analogies. The first experiment tested the hypothesis that more highly supported analogies were more successful at promoting conceptual understanding and transfer – this conclusion was supported in the experiments completed at UCLA and UCI. A second series of experiments was conducted in order to examine developmental differences in children’s analogical reasoning ability, with an eye to using this knowledge in future instructional research with children of different ages. They found that younger children (3- to 7-year-olds) were affected both by distraction and relational complexity, whereas older children (13- to 14-year-olds) were affected only by relational complexity. These findings will be used by this team in building future instructional tools that use analogies to support the acquisition of mathematical concepts.
People and institutions involved
IES program contact(s)
Products and publications
Publications:
ERIC Citations: Find available citations in ERIC for this award here.
Select Publications:
Book chapters
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 articles
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.
Proceedings
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&nddash;640). Mahwah, NJ: Erlbaum.
Richland, L.E., Morrison, R.G., and Holyoak, K.J. (2004). Developmental Change in nalogical 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.
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