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Using Relational Reasoning to Learn About Scientific Phenomena at Unfamiliar Scales

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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.

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References

  • Ainsworth, S. E. (1999). The functions of multiple representations. Computers & Education, 33, 131–152.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • American Association for the Advancement of Science (AAAS). (1993). Benchmarks for science literacy. New York: Oxford University Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Booth, J. L., & Siegler, R. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016–1031.

    Article  Google Scholar 

  • Brown, D., & Clement, J. (1989). Overcoming misconceptions via analogical reasoning: abstract transfer versus explanatory model construction. Instructional Science, 18, 237–261.

    Article  Google Scholar 

  • Brown, S., & Salter, S. (2010). Analogies in science and science teaching. Advanced Physiological Education, 34, 167–169. doi:10.1152/advan.00022.2010.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Callanan, M. A., & Markman, E. M. (1982). Principles of organization in young children’s natural language hierarchies. Child Development, 53, 1093–1101.

    Article  Google Scholar 

  • Cantlon, J. F., Platt, M. L., & Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Science, 13, 83–91.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • de Havia, M. D., & Spelke, E. S. (2010). Number-space mapping in human infants. Psychological Science, 21, 653–660.

    Article  Google Scholar 

  • 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 

  • Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and numerical magnitude. Journal of Experimental Psychology: General, 122, 371–396.

    Article  Google Scholar 

  • 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 

  • Duit, R. (1991). On the role of analogies and metaphors in learning science. Science Education, 30, 1241–1257.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Eames, C. & Eames, R. (1968). Powers of Ten [Motion picture]. USA: IBM.

  • Ellis, A. K., & Fouts, J. T. (2001). Interdisciplinary curriculum: the research base. Music Educators Journal, 87, 22–27.

    Article  Google Scholar 

  • Friedman, A., & Brown, N. R. (2000). Reasoning about geography. Journal of Experimental Psychology. General, 129, 193–219.

    Article  Google Scholar 

  • Galilei, G. (1638). Two new sciences. Madison, WI: University of Wisconsin Press.

    Google Scholar 

  • Gentner, D. (1982). Are scientific analogies metaphors? In D. S. Miall (Ed.), Metaphor: Problems and perspectives (pp. 106–132). Brighton, England: Harvester Press Ltd.

  • Gentner, D. (1983). Structure-mapping: a theoretical framework for analogy. Cognitive Science, 7, 155–170.

    Article  Google Scholar 

  • 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).

  • Gentner, D., & Gunn, V. (2001). Structural alignment facilitates the noticing of differences. Memory and Cognition, 29(4), 565–577.

  • Gentner, D., & Holyoak, K. J. (1997). Reasoning and learning by analogy: introduction. American Psychologist, 52, 32–34.

    Article  Google Scholar 

  • Gentner, D., & Namy, L. (1999). Comparison in the development of categories. Cognitive Development, 14, 487–513.

  • Gentner & Namy. (2006). Analogical Processes in Language Learning. Association for Psychological Science, 15(6).

  • 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.

  • Glynn, S. (1995). Conceptual bridges: using analogies to explain scientific concepts. Science Teacher, 62, 24–27.

    Google Scholar 

  • Goldstone, R. L. (1994). The role of similarity in categorization: Providing a groundwork. Cognition, 52, 125–157.

  • Halford, G. S. (1993) Children’s understanding: the development of mental models. Erlbaum. [DBB, DG, arGSH].

  • Hawkins, D. (1978), Critical barriers to science learning, Outlook, 29.

  • Huang, C., & Huang, M. (2012). The scale of the universe 2. Copyright: Cary and Michael Huang. Retrieved from http://htwins.net/scale2/.

  • Hummel, J. E., & Holyoak, K. J. (2003). A symbolic-connectionist theory of relational inference and generalization. Psychological Review, 110, 220–264.

    Article  Google Scholar 

  • Huttenlocher, J., Hedges, L., & Prohaska, V. (1988). Hierarchical organization in ordered domains: Estimating the dates of events. Psychological Review, 95, 471–484.

    Article  Google Scholar 

  • Huttenlocher, J. E., Hedges, L. V., & Vevea, J. L. (2000). Why do categories affect stimulus judgment? Journal of Experimental Psychology. General, 129, 220–241.

    Article  Google Scholar 

  • James, W. (1890). The principles of psychology. New York, NY: Henry Holt.

    Book  Google Scholar 

  • Jones, M. G., & Taylor, A. R. (2009). Developing a sense of scale: looking backward. Journal of Research in Science Teaching, 46(4), 460–475.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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 

  • Kotovsky, L., & Gentner, D. (1996). Comparison and categorization in the development of relational similarity. Child Development, 67, 2797–2822.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Landy, D., Silbert, N., & Goldin, A. (2013). Estimating large numbers. Cognitive Science, 37, 775–799.

  • 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.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Markman, A. B., & Gentner, D. (1993a). Structural alignment during similarity comparisons. Cognitive Psychology, 25, 431–467.

  • Markman, A. B., & Gentner, D. (1993b). Splitting the differences: A structural alignment view of similarity. Journal of Memory and Language, 32, 517–535.

  • Markman, A. B., & Gentner, D. (1996). Commonalities and differences in similarity comparisons. Memory and Cognition, 24, 235–249.

    Article  Google Scholar 

  • Markman, A. B., & Gentner, D. (1997). The effects of alignability on memory. Psychological Science, 8, 363c367.

  • Medin, D. L., Goldstone, R. L., & Gentner, D. (1993). Respects for similarity. Psychological Review, 100(2), 254–278.

  • Miller & Brewer. (2010). Misconceptions of Astronomical Distances. International Journal of Science Education, 32(12).

  • 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 

  • 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.

    Article  Google Scholar 

  • Orgill, M., & Bodner, G. (2004). What research tells us about using analogies to teach chemistry. Chemistry Education Research and Practice, 5, 15–32.

    Article  Google Scholar 

  • 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 

  • Petcovic & Ruhf. (2008). Geoscience conceptual knowledge of preservice elementary teachers: results from the geoscience concept inventory. Journal of Geoscience Education, 56(3), 251–260.

    Article  Google Scholar 

  • 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 

  • 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.

  • 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.

  • Resnick, I., Newcombe, N. S., & Shipley, T. F. (2016). Dealing with big numbers: Representation and understanding of magnitudes outside of human experience. Cognitive Science.

  • Riebeek, H. (2010, June). Global Warming. Retrieved from: http://earthobservatory.nasa.gov/Features/GlobalWarming/.

  • Schmidt, W. H., Houang, R., & Cogan, L. (2002). A coherent curriculum: The case of mathematics. American Educator, 26.

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • Shipley, T. F., & Zacks, J. (2008). Understanding events: from perception to action. New York: NY, Oxford University Press.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Siegler, R. S., & Lortie-Forgues, H. (2014). An integrative theory of numerical development. Child Development Perspectives, 8, 144–150.

    Article  Google Scholar 

  • Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14.

  • 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.

    Article  Google Scholar 

  • Simons, P. R. J. (1984). Instructing with analogies. Journal of Educational Psychology, 76, 513–527.

    Article  Google Scholar 

  • Stevens, A., & Coupe, P. (1978). Distortions in judged spatial relations. Cognitive Psychology, 10, 422–437.

    Article  Google Scholar 

  • Thagard, P. (1992). Analogy, explanation, and education. Journal of Research in Science Teaching, 29, 537–544.

    Article  Google Scholar 

  • Thompson, C., & Opfer, J. (2010). How 15 hundred is like 15 cherries: Effect of progressive alignment on representational changes in numerical cognition. Child Development.

  • Thompson, C. A., & Siegler, R. S. (2010). Linear numerical magnitude representations aid children’s memory for numbers. Psychological Science, 21, 1274–1281.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Walsh, V. (2003). A theory of magnitude: common cortical metrics of time, space and quantity. TRENDS in Cognitive Sciences, 7(11).

  • Wheeling Jesuit University. (2004). Geologic time activity. Copy right 1997-2004 by Wheeling Jesuit University/NASA-supported Classroom of the Future.

  • Zacks, J. M., & Tversky, B. (2001). Event structure in perception and conception. Psychological Bulletin, 127, 3–21.

    Article  Google Scholar 

  • Zook, K. B. (1991). Effects of analogical processes on learning and misrepresentation. Educational Psychology Review, 3, 41–72.

    Article  Google Scholar 

  • Zook, K. B., & DiVesta, F. J. (1991). Instructional analogies and conceptual misrepresentations. Journal of Educational Psychology, 83, 246–252.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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Acknowledgments

This research was supported by the National Science Foundation Grants SBE-0541957 and SBE-1041707 which support the NSF funded Spatial Intelligence Learning Center and the Institute of Education Sciences Grant R305B130012 as part of the Postdoctoral Research Training Program in the Education Sciences.

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Authors and Affiliations

  1. School of Education, University of Delaware, 211C Willard Hall, Newark, DE 19716, USA

    Ilyse Resnick

  2. Department of Earth and Environmental Sciences, Temple University, Philadelphia, PA, 19122, USA

    Alexandra Davatzes

  3. Department of Psychology, Temple University, Philadelphia, PA, 19122, USA

    Nora S. Newcombe & Thomas F. Shipley

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  1. Ilyse Resnick
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  4. Thomas F. Shipley
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Correspondence to Ilyse Resnick.

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Resnick, I., Davatzes, A., Newcombe, N.S. et al. Using Relational Reasoning to Learn About Scientific Phenomena at Unfamiliar Scales. Educ Psychol Rev 29, 11–25 (2017). https://doi.org/10.1007/s10648-016-9371-5

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