CREATING DIAGRAMS FOR PROBLEM-SOLVING IN MATHEMATICS: IS IT WORTH THE EFFORT?
DOI:
https://doi.org/10.20319/pijss.2018.41.690699Keywords:
Probability, Diagrams, Mental Effort, Cognitive Load, Problem-SolvingAbstract
Diagrams are ubiquitous in mathematics instruction. This investigation examines whether the mental effort – often referred to as cognitive load – that is required to construct and use a diagram in order to solve a problem is associated with success in arriving at accurate problem solutions. In this article, data from a series of experiments that were conducted during the past decade are re-analyzed to compare the self-rated effort of being trained to use a diagram with subsequent problem-solving performance, relative to interventions in which participants were trained to use only equations to solve the same word problems. The results demonstrate that the mental effort invested in diagram training is not uniformly beneficial across all types of mathematics problems. Specifically, diagram training is more efficacious for conditional-probability word problems than for joint- and total-probability word problems. Of particular note is the repeated finding that training in how to use Venn diagrams causes worse performance for undergraduates solving total-probability problems.
References
Atkinson, R. K. and Derry, S. J. and Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70, 181-214. https://doi.org/10.3102/00346543070002181
Beitzel, B. D., & Staley, R. K. (2011, April). Sometimes they are effective: Using external representations to help solve probability word problems. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
Beitzel, B. D., & Staley, R. K. (2015). The efficacy of using diagrams when solving probability word problems in college. The Journal of Experimental Education, 83, 130-145. https://doi.org/10.1080/00220973.2013.876232
Beitzel, B. D., Boss, R. C., & Gonyea, N. E. (2015, April). Diagrams may not be your friend: Empirically discriminating their problem-solving efficacy. Poster presented at the annual meeting of the American Educational Research Association, Chicago, IL.
Beitzel, B. D., Gonyea, N. E., & Staley, R. K. (2013, April). The more the merrier? An investigation of multiple external representations on problem-solving performance. Poster presented at the annual meeting of the American Educational Research Association, San Francisco, CA.
Beitzel, B. D., Gonyea, N. E., & Staley, R. K. (2014). Illusions of using a diagram: An investigation of two types of mathematical representations. Poster presented at the annual meeting of the American Educational Research Association, Philadelphia, PA.
Beitzel, B. D., Staley, R. K., & DuBois, N. F. (2011). When best intentions go awry: The failures of concrete representations to help solve probability word problems. Educational Research Quarterly, 34(3), 3-14.
Beitzel, B. D., Staley, R. K., Holmes, M. S., & Snow, A. L. (2017, April). The eyes have it: Examining a physiological measure of cognitive load. Poster presented at the annual meeting of the American Educational Research Association, San Antonio, TX.
Committee on the Undergraduate Program in Mathematics. (2015). Curriculum guide to majors in the mathematical sciences. Washington, DC: The Mathematical Association of America.
Conference Board of the Mathematical Sciences. (2012). The mathematical education of teachers II. Providence, Rhode Island: American Mathematical Society.
Cooper, J. L., Sidney, P. G., & Alibali, M. W. (2018). Who benefits from diagrams and illustrations in math problems? Ability and attitudes matter. Applied Cognitive Psychology, 32, 24-38. https://doi.org/10.1002/acp.3371
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555
Hart, S. G. and Staveland, L. E. (1988). Development of NASA-TLX (Task Load Index): Results of empirical and theoretical research. In Hancock, Peter A. and Meshkati, Najmedin (Eds.), Human mental workload (pp. 139-183). Amsterdam: North-Holland Press. https://doi.org/10.1016/S0166-4115(08)62386-9
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
Renkl, A., & Atkinson, R. K. (2003). Structuring the transition from example study to problem solving in cognitive skill acquisition: A cognitive load perspective. Educational Psychologist, 38, 15-22. https://doi.org/10.1207/S15326985EP3801_3
Sedlmeier, P., & Gigerenzer, G. (2001). Teaching Bayesian reasoning in less than two hours. Journal of Experimental Psychology: General, 130, 380-400 https://doi.org/10.1037/0096-3445.130.3.380
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