Educational Psychology Review

, Volume 29, Issue 1, pp 11–25 | Cite as

Using Relational Reasoning to Learn About Scientific Phenomena at Unfamiliar Scales

  • Ilyse Resnick
  • Alexandra Davatzes
  • Nora S. Newcombe
  • Thomas F. Shipley
Review Article

Abstract

Many scientific theories and discoveries involve reasoning about extreme scales, removed from human experience, such as time in geology and size in nanoscience. Thus, understanding scale is central to science, technology, engineering, and mathematics. Unfortunately, novices have trouble understanding and comparing sizes of unfamiliar large and small magnitudes. Relational reasoning is a promising tool to bridge the gap between direct experience and phenomena at extreme scales. However, instruction does not always improve understanding, and analogies can fail to bring about conceptual change, and even mislead students. Here, we review how people reason about phenomena across scales, in three sections: (a) we develop a framework for how relational reasoning supports understanding extreme scales; (b) we identify cognitive barriers to aligning human and extreme scales; and (c) we outline a theory-based approach to teaching scale information using relational reasoning, present two successful learning activities, and consider the role of a unified scale instruction across STEM education.

Keywords

Size and scale Relational reasoning Analogy Progressive alignment Corrective feedback 

References

  1. Ainsworth, S. E. (1999). The functions of multiple representations. Computers & Education, 33, 131–152.CrossRefGoogle Scholar
  2. Alexander, P. A., & the Disciplined Reading and Learning Research Laboratory. (2012). Reading into the future: competence for the 21st century. Educational Psychologist, 47, 259–28.CrossRefGoogle Scholar
  3. Alexander, P. A., Jablansky, S., Singer, L. M., & Dumas, D. (2016). Relational reasoning: what we know and why it matters. Policy Insights from the Behavioral and Brain Sciences, 3(1), 36–44. doi:10.1177/2372732215622029.CrossRefGoogle Scholar
  4. American Association for the Advancement of Science (AAAS). (1993). Benchmarks for science literacy. New York: Oxford University Press.Google Scholar
  5. Barth, H. C., & Paladino, A. M. (2011). The development of numerical estimation: evidence against a representational shift. Developmental Science, 14(1), 125–135. doi:10.1111/j.1467-7687.2010.00962.x.CrossRefGoogle Scholar
  6. Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42, 189–201. doi:10.1037/0012-1649.41.6.189.CrossRefGoogle Scholar
  7. Booth, J. L., & Siegler, R. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016–1031.CrossRefGoogle Scholar
  8. Brown, D., & Clement, J. (1989). Overcoming misconceptions via analogical reasoning: abstract transfer versus explanatory model construction. Instructional Science, 18, 237–261.CrossRefGoogle Scholar
  9. Brown, S., & Salter, S. (2010). Analogies in science and science teaching. Advanced Physiological Education, 34, 167–169. doi:10.1152/advan.00022.2010.CrossRefGoogle Scholar
  10. Bueti, D., & Walsh, V. (2009). The parietal cortex and the representation of time, space, number and other magnitudes. Philosophical Transactions of the Royal Society B, 364, 1831–1840.CrossRefGoogle Scholar
  11. Callanan, M. A., & Markman, E. M. (1982). Principles of organization in young children’s natural language hierarchies. Child Development, 53, 1093–1101.CrossRefGoogle Scholar
  12. Cantlon, J. F., Platt, M. L., & Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Science, 13, 83–91.CrossRefGoogle Scholar
  13. Carpenter, T. P., & Moser, J. M. (1983). The acquisition of addition and subtraction concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  14. Clary, R. M., & Wandersee, J. H. (2009). Tried and true: How Old? Tested and trouble-free ways to convey geologic time. ScienceScope, 33(4), 62–66.Google Scholar
  15. Clement, J. (1993). Using bridging analogies and anchoring intuitions to deal with students’ preconceptions in physics. Journal of Research in Science Teaching, 30, 1241–1257.CrossRefGoogle Scholar
  16. Cohen Kadosh, R., Lammertyn, J., & Izard, V. (2008). Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology, 84, 132–147.CrossRefGoogle Scholar
  17. Coulter, G. A., & Grossen, B. (1997). The effectiveness of in-class instructive feedback versus after-class instructive feedback for teachers learning direct instruction teaching behaviors. Effective School Practices, 16, 21–34.Google Scholar
  18. de Havia, M. D., & Spelke, E. S. (2010). Number-space mapping in human infants. Psychological Science, 21, 653–660.CrossRefGoogle Scholar
  19. de Jong, T., Ainsworth, S., Dobson, M., van der Hulst, A., Levonen, J., Reimann, P., Sime, J., van Someren, M., Spada, H., & Swaak, J. (1998). Acquiring knowledge in science and math: the use of multiple representations in technology based learning environments. In M. W. Van Someren, P. Reimann, H. Bozhimen, & T. de Jong (Eds.), Learning with multiple representations (pp. 9–40). Amsterdam: Elsevier.Google Scholar
  20. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and numerical magnitude. Journal of Experimental Psychology: General, 122, 371–396.CrossRefGoogle Scholar
  21. Delgado, C., Stevens, S., Shin, N., Yunker, M., & Krajcik, J. (2007). The development of Students’ conceptions of size. New Orleans, LA: National Association of Research in Science Teaching.Google Scholar
  22. Duit, R. (1991). On the role of analogies and metaphors in learning science. Science Education, 30, 1241–1257.Google Scholar
  23. Dumas, D., Alexander, P. A., & Grossnickle, E. M. (2013). Relational reasoning and its manifestations in the educational context: a systematic review of the literature. Educational Psychology Review, 25, 391–427.CrossRefGoogle Scholar
  24. Eames, C. & Eames, R. (1968). Powers of Ten [Motion picture]. USA: IBM.Google Scholar
  25. Ellis, A. K., & Fouts, J. T. (2001). Interdisciplinary curriculum: the research base. Music Educators Journal, 87, 22–27.CrossRefGoogle Scholar
  26. Friedman, A., & Brown, N. R. (2000). Reasoning about geography. Journal of Experimental Psychology. General, 129, 193–219.CrossRefGoogle Scholar
  27. Galilei, G. (1638). Two new sciences. Madison, WI: University of Wisconsin Press.Google Scholar
  28. Gentner, D. (1982). Are scientific analogies metaphors? In D. S. Miall (Ed.), Metaphor: Problems and perspectives (pp. 106–132). Brighton, England: Harvester Press Ltd.Google Scholar
  29. Gentner, D. (1983). Structure-mapping: a theoretical framework for analogy. Cognitive Science, 7, 155–170.CrossRefGoogle Scholar
  30. Gentner, D., & Gentner, D. R. (1983). Flowing waters or teeming crowds: Mental models of electricity. In D. Gentner & A. L. Stevens (Eds.), Mental models (pp. 99–129). Hillsdale, NJ: Lawrence Erlbaum Associates. (Reprinted in M. J. Brosnan (Ed.), Cognitive functions: Classic readings in representation and reasoning. Eltham, London: Greenwich University Press).Google Scholar
  31. Gentner, D., & Gunn, V. (2001). Structural alignment facilitates the noticing of differences. Memory and Cognition, 29(4), 565–577.Google Scholar
  32. Gentner, D., & Holyoak, K. J. (1997). Reasoning and learning by analogy: introduction. American Psychologist, 52, 32–34.CrossRefGoogle Scholar
  33. Gentner, D., & Namy, L. (1999). Comparison in the development of categories. Cognitive Development, 14, 487–513.Google Scholar
  34. Gentner & Namy. (2006). Analogical Processes in Language Learning. Association for Psychological Science, 15(6).Google Scholar
  35. Gentner, D., Loewenstein, J., & Hung, B. (2007). Comparison facilitates children's learning of names for parts. Journal of Cognition and Development, 8(3), 285–307.Google Scholar
  36. Glynn, S. (1995). Conceptual bridges: using analogies to explain scientific concepts. Science Teacher, 62, 24–27.Google Scholar
  37. Goldstone, R. L. (1994). The role of similarity in categorization: Providing a groundwork. Cognition, 52, 125–157.Google Scholar
  38. Halford, G. S. (1993) Children’s understanding: the development of mental models. Erlbaum. [DBB, DG, arGSH].Google Scholar
  39. Hawkins, D. (1978), Critical barriers to science learning, Outlook, 29. Google Scholar
  40. Huang, C., & Huang, M. (2012). The scale of the universe 2. Copyright: Cary and Michael Huang. Retrieved from http://htwins.net/scale2/.
  41. Hummel, J. E., & Holyoak, K. J. (2003). A symbolic-connectionist theory of relational inference and generalization. Psychological Review, 110, 220–264.CrossRefGoogle Scholar
  42. Huttenlocher, J., Hedges, L., & Prohaska, V. (1988). Hierarchical organization in ordered domains: Estimating the dates of events. Psychological Review, 95, 471–484.CrossRefGoogle Scholar
  43. Huttenlocher, J. E., Hedges, L. V., & Vevea, J. L. (2000). Why do categories affect stimulus judgment? Journal of Experimental Psychology. General, 129, 220–241.CrossRefGoogle Scholar
  44. James, W. (1890). The principles of psychology. New York, NY: Henry Holt.CrossRefGoogle Scholar
  45. Jones, M. G., & Taylor, A. R. (2009). Developing a sense of scale: looking backward. Journal of Research in Science Teaching, 46(4), 460–475.CrossRefGoogle Scholar
  46. Jones, M. G., Tretter, T., Taylor, A., & Oppewal, T. (2008). Experienced and novice teachers’ concepts of spatial scale. International Journal of Science Education, 30(3), 409–429.CrossRefGoogle Scholar
  47. Kamrin, M. A., Katz, D. J., & Walter, M. L. (1995). Reporting on risk. A Journalist’s handbook. Ann Arbor: Michigan sea grant college program, 1994 (2nd ed.). Los Angeles: Foundation for American Communications and National Sea Grant College Program.Google Scholar
  48. Kaufman, D. R., Patel, V. L., & Magder, S. A. (1996). The explanatory role of spontaneously generated analogies in reasoning about physiological concepts. International Journal of Science Education, 18, 369–386.CrossRefGoogle Scholar
  49. Kay, R. H., & LeSage, A. (2009). A strategic assessment of audience response systems used in higher education. Australian Journal of Educational Technology, 25(2), 235-249.Google Scholar
  50. Kokinov, B., & French, R. M. (2003). Computational models of analogy making. In L. Nadel (Ed.), Encyclopedia of cognitive science (pp. 113–118). London: MacMillan.Google Scholar
  51. Kotovsky, L., & Gentner, D. (1996). Comparison and categorization in the development of relational similarity. Child Development, 67, 2797–2822.CrossRefGoogle Scholar
  52. Kozma, R., Chin, E., Russell, J., & Marx, N. (2000). The role of representations and tools in the chemistry laboratory and their implications for chemistry learning. Journal of the Learning Sciences, 9(3), 105–144.CrossRefGoogle Scholar
  53. Lamon, S. (1994). Ratio and proportion: cognitive foundations in unitizing and norming. In G. J. Harel Confrey (Ed.), The development of multiplicative reasoning in the learning of mathematics (pp. 89–120). Albany, NY: State University of New York Press.Google Scholar
  54. Landy, D., Silbert, N., & Goldin, A. (2013). Estimating large numbers. Cognitive Science, 37, 775–799.Google Scholar
  55. Landy, D., Charlesworth, A., & Ottmar, E. (2014). Cutting in line: discontinuities in the use of large numbers in adults. Proceedings of the 36th Annual Conference of the Cognitive Science Society. Quebec City, Quebec: Cognitive Science Society.Google Scholar
  56. Laski, E., & Siegler, R. (2007). Is 27 a Big number? correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison. Child Development, 78(6), 1723–1743.CrossRefGoogle Scholar
  57. Libarkin, J. C., Anderson, S. W., Dahl, J., Beilfuss, M., & Boone, W. (2005). Qualitative analysis of college Students’ ideas about the earth: interviews and open-ended questionnaires. Journal of Geoscience Education, 53(1), 17–26.CrossRefGoogle Scholar
  58. Libarkin, J. C., Kurdziel, J. P., & Anderson, S. W. (2007). College student conceptions of geological time and the disconnect between ordering and scale. Journal of Geoscience Education, 55, 413–422.CrossRefGoogle Scholar
  59. Lourenco, S. F., & Longo, M. R. (2011). Origins and development of generalized magnitude representation. In S. Dehaene & E. M. Brannon (Eds.), Space, time and number in the brain: Searching for the foundations of mathematical thought (pp. 225–244). London: Elsevier.CrossRefGoogle Scholar
  60. Markman, A. B., & Gentner, D. (1993a). Structural alignment during similarity comparisons. Cognitive Psychology, 25, 431–467.Google Scholar
  61. Markman, A. B., & Gentner, D. (1993b). Splitting the differences: A structural alignment view of similarity. Journal of Memory and Language, 32, 517–535.Google Scholar
  62. Markman, A. B., & Gentner, D. (1996). Commonalities and differences in similarity comparisons. Memory and Cognition, 24, 235–249.CrossRefGoogle Scholar
  63. Markman, A. B., & Gentner, D. (1997). The effects of alignability on memory. Psychological Science, 8, 363c367.Google Scholar
  64. Medin, D. L., Goldstone, R. L., & Gentner, D. (1993). Respects for similarity. Psychological Review, 100(2), 254–278.Google Scholar
  65. Miller & Brewer. (2010). Misconceptions of Astronomical Distances. International Journal of Science Education, 32(12).Google Scholar
  66. National Research Council. (2011). A framework for K-12 science education (Committee on a conceptual framework for new K-12 science education standards. Board on science education, DBASSE). Washington, DC: The National Academies Press.Google Scholar
  67. Opfer, J. E., Siegler, R. S., & Young, C. J. (2011). The powers of noise-fitting: reply to Barth and Paladino. Developmental Science, 14, 1194–1204.CrossRefGoogle Scholar
  68. Orgill, M., & Bodner, G. (2004). What research tells us about using analogies to teach chemistry. Chemistry Education Research and Practice, 5, 15–32.CrossRefGoogle Scholar
  69. Pashler, H., Bain, P., Bottge, B., Graesser, A., Koedinger, K., McDaniel, M., & Metcalfe, J. (2007). Organizing instruction and study to improve student learning (NCER 2007-2004). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ncer.ed.gov.Google Scholar
  70. Petcovic & Ruhf. (2008). Geoscience conceptual knowledge of preservice elementary teachers: results from the geoscience concept inventory. Journal of Geoscience Education, 56(3), 251–260.CrossRefGoogle Scholar
  71. Resnick, I., Atit, K., & Shipley, T. F. (2012). Teaching geologic events to understand geologic time. In K. A. Kastens & C. A. Manduca (Eds.), Earth and mind II: a synthesis of research on thinking and learning in the geosciences: geological society of america special paper 486. Boulder, Colorado: The Geological Society of America, Inc.Google Scholar
  72. Resnick, I., Davatzes. A., & Shipley, T. F. (2013). Using analogy to improve understanding of large magnitudes. Poster presented at the Improving Middle School Science Instruction Using Cognitive Science Conference, Washington D.C.Google Scholar
  73. Resnick, I., Jordan, N. C., Hansen, N., Rajan, V., Rodrigues, J., Siegler, R. S., & Fuchs, L. (2016). Developmental growth trajectories in understanding of fraction magnitude from fourth through sixth grade. Developmental Psychology.Google Scholar
  74. Resnick, I., Newcombe, N. S., & Shipley, T. F. (2016). Dealing with big numbers: Representation and understanding of magnitudes outside of human experience. Cognitive Science.Google Scholar
  75. Riebeek, H. (2010, June). Global Warming. Retrieved from: http://earthobservatory.nasa.gov/Features/GlobalWarming/.
  76. Schmidt, W. H., Houang, R., & Cogan, L. (2002). A coherent curriculum: The case of mathematics. American Educator, 26.Google Scholar
  77. Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology. Human Perception and Performance, 36(5), 1227–1238. doi:10.1037/a0018170.CrossRefGoogle Scholar
  78. Semken, S., Dodick, J., Ben-David, O., Pineda, M., Bueno Watts, N., & Karlstrom, K. (2009). Timeline and time scale cognition experiments for a geological interpretative exhibit at Grand Canyon. Proceedings of the National Association for Research in Science Teaching, Garden Grove, California.Google Scholar
  79. Sharpe, T. L., Lounsbery, M., & Bahls, V. (1997). Description and effects of sequential behavior practice in teacher education. Research Quarterly for Exercise and Sport, 68, 222–232.CrossRefGoogle Scholar
  80. Shipley, T. F., & Zacks, J. (2008). Understanding events: from perception to action. New York: NY, Oxford University Press.CrossRefGoogle Scholar
  81. Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428–444. doi:10.1111/j.1467-8624.2004.00684.x.CrossRefGoogle Scholar
  82. Siegler, R. S., & Lortie-Forgues, H. (2014). An integrative theory of numerical development. Child Development Perspectives, 8, 144–150.CrossRefGoogle Scholar
  83. Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14.Google Scholar
  84. Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273–296. doi:10.1016/j.cogpsych.2011.03.001.CrossRefGoogle Scholar
  85. Simons, P. R. J. (1984). Instructing with analogies. Journal of Educational Psychology, 76, 513–527.CrossRefGoogle Scholar
  86. Stevens, A., & Coupe, P. (1978). Distortions in judged spatial relations. Cognitive Psychology, 10, 422–437.CrossRefGoogle Scholar
  87. Thagard, P. (1992). Analogy, explanation, and education. Journal of Research in Science Teaching, 29, 537–544.CrossRefGoogle Scholar
  88. Thompson, C., & Opfer, J. (2010). How 15 hundred is like 15 cherries: Effect of progressive alignment on representational changes in numerical cognition. Child Development.Google Scholar
  89. Thompson, C. A., & Siegler, R. S. (2010). Linear numerical magnitude representations aid children’s memory for numbers. Psychological Science, 21, 1274–1281.CrossRefGoogle Scholar
  90. Trend, R. D. (2001). Deep time framework: a preliminary study of UK primary teachers’ conceptions of geological time and perceptions of geoscience. Journal of Research in Science Teaching, 38(2), 191–221.CrossRefGoogle Scholar
  91. Tretter, T. R., Jones, M. G., Andre, T., Negishi, A., & Minogue, J. (2006). Conceptual boundaries and distances: Students’ and experts’ concepts of the scale of scientific phenomena. Journal of Research in Science Teaching, 43(3), 282–319.CrossRefGoogle Scholar
  92. Vosniadou, S., & Mason, L. (2012). Conceptual change induced by instruction: a complex interplay of multiple factors. In K. Harris, S. Graham, & T. Urdan (Eds.), Handbook of educational psychology (2nd ed., pp. 221–246). Washington, DC: American Psychiatric Association.Google Scholar
  93. Walsh, V. (2003). A theory of magnitude: common cortical metrics of time, space and quantity. TRENDS in Cognitive Sciences, 7(11).Google Scholar
  94. Wheeling Jesuit University. (2004). Geologic time activity. Copy right 1997-2004 by Wheeling Jesuit University/NASA-supported Classroom of the Future.Google Scholar
  95. Zacks, J. M., & Tversky, B. (2001). Event structure in perception and conception. Psychological Bulletin, 127, 3–21.CrossRefGoogle Scholar
  96. Zook, K. B. (1991). Effects of analogical processes on learning and misrepresentation. Educational Psychology Review, 3, 41–72.CrossRefGoogle Scholar
  97. Zook, K. B., & DiVesta, F. J. (1991). Instructional analogies and conceptual misrepresentations. Journal of Educational Psychology, 83, 246–252.CrossRefGoogle Scholar
  98. Zook, K. B., & Maier, J. M. (1994). Systematic analysis of variables that contribute to the formation of analogical misconceptions. Journal of Educational Psychology, 86, 589–699.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Ilyse Resnick
    • 1
  • Alexandra Davatzes
    • 2
  • Nora S. Newcombe
    • 3
  • Thomas F. Shipley
    • 3
  1. 1.School of EducationUniversity of DelawareNewarkUSA
  2. 2.Department of Earth and Environmental SciencesTemple UniversityPhiladelphiaUSA
  3. 3.Department of PsychologyTemple UniversityPhiladelphiaUSA

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