Research in both cognitive and educational psychology has explored the effect of different types of external knowledge representations (e.g., manipulatives, graphical/pictorial representations, texts) on a variety of important outcome measures. We place this large and multifaceted research literature into an organizing framework, classifying three categories of external knowledge representations along a dimension of groundedness: (1) idealized, (2) grounded and including only relevant features, and (3) grounded and including irrelevant features. This organizing framework allows us to focus on the implications of these characteristics of external knowledge representations on three important educational outcomes: learning and immediate performance using the target knowledge, the degree to which that knowledge can transfer flexibly, and the interest engendered by the learning materials. We illustrate the framework by mapping a wide body of research from educational and cognitive psychology onto its dimensions. This framework can aid educators by clearly stating what the research literature says about these characteristics of external knowledge representations and how they activate and support the construction of internal knowledge representations. In particular, it will speak to how to best structure instruction using external knowledge representations with different characteristics, depending on the learning objective. Researchers will benefit from the analysis of the current state of knowledge and by the description of what open questions still remain.
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Throughout this paper, we refer to types of representations when discussing different forms, like figures, manipulatives, etc. In contrast, we use kinds of representations when referring to the characteristic categories defined by our framework.
Ainsworth, S. (2006). DeFT: a conceptual framework for considering learning with multiple representations. Learning & Instruction, 16, 183–198.
Alfieri, L., Nokes-Malach, T. J., & Schunn, C. D. (2013). Learning through case comparisons: a meta-analytic review. Educational Psychologist, 48(2), 87–113.
Anderson, J. R., Bothell, D., Byrne, M. D., Douglass, S., Lebiere, C., & Qin, Y. (2004). An integrated theory of mind. Psychological Review, 111(4), 1036–1060.
Baddeley, A. D. (1986). Working memory. Oxford: Oxford University Press.
Baltes, P. B., Staudinger, U. M., & Lindenberger, U. (1999). Lifespan psychology: theory and application to intellectual functioning. Annual Review of Psychology, 50, 471–507.
Barnett, S. M., & Ceci, S. J. (2002). When and where do we apply what we learn? A taxonomy for far transfer. Psychological Bulletin, 128(4), 612–637.
Bassok, M. (1996). Using content to interpret structure: effects on analogical transfer. Current Directions in Psychological Science, 5(2), 54–57.
Bassok, M., & Holyoak, K. J. (1989). Interdomain transfer between isomorphic topics in algebra and physics. Journal of Experimental Psychology. Learning, Memory, and Cognition, 15(1), 153–166.
Belenky, D. M., & Nokes, T. J. (2009). Examining the role of manipulatives and metacognition on engagement, learning, and transfer. The Journal of Problem Solving, 2(2), 102–129.
Belenky, D. M., & Nokes-Malach, T. J. (2012). Motivation and transfer: the role of mastery-approach goals in preparation for future learning. The Journal of the Learning Sciences, 21(3), 399–432.
Belenky, D. M., & Nokes-Malach, T. J. (2013). Mastery-approach goals and knowledge transfer: an investigation into the effects of task structure and framing instructions. Learning and Individual Differences, 25, 21–34.
Braithwaite, D., & Goldstone, R. L. (2013). Integrating formal and grounded representations in combinatorics learning. Journal of Educational Psychology, 105(3), 666–682.
Bransford, J. D., & Schwartz, D. L. (1999). Rethinking transfer: a simple proposal with multiple implications. Review of Research in Education, 24, 61–100.
Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400.
Carey, S. (2000). Science education as conceptual change. Journal of Applied Developmental Psychology, 21(1), 13–19.
Carey, S. (2009). The origin of concepts. Oxford: Oxford University Press.
Catrambone, R., & Holyoak, K. J. (1989). Overcoming contextual limitations on problem-solving transfer. Journal of Experimental Psychology. Learning, Memory, and Cognition, 15(6), 1147–1156.
Chi, M. T. H. (2005). Commonsense misconceptions of emergent processes: why some misconceptions are robust. The Journal of the Learning Sciences, 14(2), 161–199.
Chi, M. T. H. (2009). Active-constructive-interactive: a conceptual framework for differentiating learning activities. Topics in Cognitive Science, 1, 73–105.
Chi, M. T. H., & VanLehn, K. A. (2012). Seeing deep structure from the interactions of surface features. Educational Psychologist, 47(3), 177–188.
Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121–152.
Cordova, D. I., & Lepper, M. R. (1996). Intrinsic motivation and the process of learning: beneficial effects of contextualization, personalization, and choice. Journal of Educational Psychology, 88(4), 715–730.
Cowan, N. (2000). The magical number 4 in short-term memory: a reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24, 87–185.
De Bock, D., Deprez, J., Van Dooren, W., Roelens, M., & Verschaffel, L. (2011). Abstract or concrete examples in learning mathematics? A replication and elaboration of Kaminski, Sloutsky, and Heckler’s study. Journal for Research in Mathematics Education, 42(2), 109–126.
De Corte, E. (2003). Transfer as the productive use of acquired knowledge, skills, and motivations. Current Directions in Psychological Science, 12(4), 142–146.
DeLoache, J. S. (2004). Becoming symbol-minded. Trends in Cognitive Sciences, 8(2), 66–70.
Donaldson, M. (1978). Children’s minds. London: Fontana.
Durik, A. M., & Harackiewicz, J. M. (2007). Different strokes for different folks: how individual interest moderates the effects of situational factors on task interest. Journal of Educational Psychology, 99(3), 597–610.
Dweck, C. (2006). Mindset: the new psychology of success. New York: Random House.
Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014/this issue). Concreteness fading offers the best of both concrete and abstract instruction. Educational Psychology Review.
Garner, R., Gillingham, M. G., & White, S. (1989). Effects of ‘seductive details’ on macroprocessing and microprocessing in adults and children. Cognition and Instruction, 6(1), 41–57.
Gentner, D. (2010). Bootstrapping the mind: analogical processes and symbol systems. Cognitive Science, 34, 752–775.
Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12, 306–355.
Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1–38.
Goldstone, R. L., & Sakamoto, Y. (2003). The transfer of abstract principles governing complex adaptive systems. Cognitive Psychology, 46(4), 414–466.
Goldstone, R. L., & Son, J. Y. (2005). The transfer of scientific principles using concrete and idealized simulations. The Journal of the Learning Sciences, 14(1), 69–110.
Goldstone, R. L., Landy, D. H., & Son, J. Y. (2010). The education of perception. Topics in Cognitive Science, 2(2), 265–284.
Gopnik, A. (1996). The post-Piaget era. Psychological Science, 7(4), 221–225.
Griggs, R. A., & Cox, J. R. (1982). The elusive thematic-materials effect in Wason’s selection task. British Journal of Psychology, 73(3), 407–420.
Harackiewicz, J. M., Barron, K. E., Tauer, J. M., Carter, S. M., & Elliot, A. J. (2000). Short-term and long-term consequences of achievement goals: predicting interest and performance over time. Journal of Educational Psychology, 92(2), 316–330.
Harackiewicz, J. M., Tauer, J. M., Barron, K. E., & Elliot, A. J. (2002). Predicting success in college: a longitudinal study of achievement goals and ability measures as predictors of interest and performance from freshman year through graduation. Journal of Educational Psychology, 94(3), 562–575.
Harp, S. F., & Maslich, A. A. (2005). The consequences of including seductive details during lecture. Teaching of Psychology, 32(2), 100–103.
Harp, S. F., & Mayer, R. E. (1998). How seductive details do their damage: a theory of cognitive interest in science learning. Journal of Educational Psychology, 90(3), 414–434.
Hidi, S., & Harackiewicz, J. M. (2000). Motivating the academically unmotivated: a critical issue for the 21st century. Review of Educational Research, 70(2), 151–179.
Hidi, S., & Renninger, K. A. (2006). The four-phase model of interest development. Educational Psychologist, 41(2), 111–127.
Holyoak, K. J. (2005). Analogy. In K. J. Holyoak & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (pp. 117–142). Cambridge: Cambridge University Press.
Holyoak, K. J., & Koh, K. (1987). Surface and structural similarity in analogical transfer. Memory & Cognition, 15(4), 332–340.
Inhelder, B., & Piaget, J. (1958). The growth of logical thinking: from childhood to adolescence. New York: Basic Books.
Johnson-Laird, P. N., Legrenzi, P., & Legrenzi, M. S. (1972). Reasoning and a sense of reality. British Journal of Psychology, 63(3), 395–400.
Kalyuga, S. (2007). Expertise reversal effect and its implications for learner-tailored instruction. Educational Psychology Review, 19, 509–539.
Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38(1), 23–31.
Kaminski, J. A., & Sloutsky, V. M. (2012). Representation and transfer of abstract mathematical concepts in adolescence and young adulthood. In V. F. Reyna, S. B. Chapman, M. R. Dougherty, & J. Confrey (Eds.), The adolescent brain: learning, reasoning, and decision making (pp. 67–93). Washington, DC: American Psychological Association.
Kaminski, J. A., & Sloutsky, V. M. (2013). Extraneous perceptual information interferes with children’s acquisition of mathematical knowledge. Journal of Educational Psychology, 105(2), 351–363.
Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2008). The advantage of abstract examples in learning math. Science, 320, 454–455.
Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2013). The cost of concreteness: the effect of nonessential information on analogical transfer. Journal of Experimental Psychology. Applied, 19(1), 14–29.
Keil, F. C. (1981). Children’s thinking: what never develops? Cognition, 10, 159–166.
Keil, F. C. (1989). Concepts, kinds and cognitive development. Cambridge: MIT Press.
Kemp, C. (2012). Exploring the conceptual universe. Psychological Review, 119(4), 685–722.
Koedinger, K. R., & Nathan, M. J. (2004). The real story behind story problems: effects of representations on quantitative reasoning. The Journal of the Learning Sciences, 13(2), 129–164.
Koedinger, K. R., Alibali, M. W., & Nathan, M. J. (2008). Trade-offs between grounded and abstract representations: evidence from algebra problem solving. Cognitive Science, 32, 366–397.
Koedinger, K. R., Corbett, A. T., & Perfetti, C. (2012). The knowledge-learning-instruction framework: bridging the science–practice chasm to enhance robust student learning. Cognitive Science, 36, 757–798.
Kotovsky, K., Hayes, J. R., & Simon, H. A. (1985). Why are some problems hard? Evidence from Tower of Hanoi. Cognitive Psychology, 17, 248–294.
Langley, P., Laird, J. E., & Rogers, S. (2009). Cognitive architectures: research issues and challenges. Cognitive Systems Research, 10, 141–160.
Lehman, S., Schraw, G., McCrudden, M. T., & Hartley, K. (2007). Processing and recall of seductive details in scientific text. Contemporary Educational Psychology, 32, 569–587.
Magner, U. I. E., Schwonke, R., Aleven, V., & Popescu, O. (2014). Triggering situational interest by decorative illustrations both fosters and hinders learning in computer-based learning environments. Learning & Instruction, 29, 141–152.
Markman, A. B., & Dietrich, E. (2000). In defense of representation. Cognitive Psychology, 40, 138–171.
Marley, S. C., Levin, J. R., & Glenberg, A. B. (2010). What cognitive benefits does an activity-based reading strategy afford young Native American readers? The Journal of Experimental Psychology, 78, 395–417.
Martin, T., & Schwartz, D. L. (2005). Physically distributed learning: adapting and reinterpreting physical environments in the development of fraction concepts. Cognitive Science, 29, 587–625.
Mayer, R. E., & Moreno, R. (2003). Nine ways to reduce cognitive load in multimedia learning. Educational Psychologist, 38(1), 43–52.
Mayer, R. E., Heiser, J., & Lonn, S. (2001). Cognitive constraints on multimedia learning: when presenting more material results in less understanding. Journal of Educational Psychology, 93(1), 187–198.
Mayer, R. E., Griffiths, E., Jurkowitz, I. T. N., & Rothman, D. (2008). Increased interestingness of extraneous details in a multimedia science presentation leads to decreased learning. Journal of Experimental Psychology. Applied, 14(4), 329–339.
McDaniel, M. A., Finstad, K., Waddill, P. J., & Bourg, T. (2000). The effects of text-based interest on attention and recall. Journal of Educational Psychology, 92(3), 492–502.
McLaren, I. P. L., Wood, K., & McLaren, R. P. (2013). Naïve physics—the wrong theory? Paper presented at the 35th Annual Meeting of the Cognitive Science Society, Berlin, Germany.
McNeil, N. M., & Fyfe, E. R. (2012). “Concreteness fading” promotes transfer of mathematical knowledge. Learning and Instruction, 22, 440–448.
McNeil, N. M., & Jarvin, L. (2007). When theories don’t add up: disentangling the manipulatives debate. Theory Into Practice, 46, 309–316.
McNeil, N. M., & Uttal, D. H. (2009). Rethinking the use of concrete materials in learning: perspectives from development and education. Child Development Perspectives, 3(3), 137–139.
McNeil, N. M., Uttal, D. H., Jarvin, L., & Sternberg, R. J. (2009). Should you show me the money? Concrete objects both hurt and help performance on mathematics problems. Learning and Instruction, 19, 171–184.
Mevarech, Z., & Stern, E. (1997). Interaction between knowledge and contexts on understanding abstract mathematical concepts. Journal of Experimental Child Psychology, 65, 68–95.
Mitchell, M. (1993). Situational interest: its multifaceted structure in the secondary school mathematics classroom. Journal of Educational Psychology, 85(3), 424–436.
Moreno, R. (2006). Learning in high-tech and multimedia environments. Current Directions in Psychological Science, 15(2), 63–67.
Moreno, R., & Mayer, R. E. (2004). Personalized messages that promote science learning in virtual environments. Journal of Educational Psychology, 96(1), 165–173.
Moreno, R., Ozogul, G., & Reisslein, M. (2011). Teaching with concrete and abstract visual representations: effects on students’ problem solving, problem representations, and learning perceptions. Journal of Educational Psychology, 103(1), 32–47.
Nokes, T. J. (2009). Mechanisms of knowledge transfer. Thinking & Reasoning, 15(1), 1–36.
Nokes, T. J., & Belenky, D. M. (2011). Incorporating motivation into a theoretical framework for knowledge transfer. In J. P. Mestre & B. H. Ross (Eds.), Psychology of learning and motivation: vol. 55. Cognition in education (pp. 109–135). San Diego: Academic.
Nunes, T., Schliemann, A. H., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.
Paivio, A., Clark, J. M., & Khan, M. (1988). Effects of concreteness and semantic relatedness on composite imagery ratings and cued recall. Memory & Cognition, 16(5), 422–430.
Park, B., Moreno, R., Seufert, T., & Brünken, R. (2011). Does cognitive load moderate the seductive details effect? A multimedia study. Computers in Human Behavior, 27, 5–10.
Petersen, L. A., & McNeil, N. M. (2013). Effects of perceptually rich manipulatives on preschoolers’ counting performance: established knowledge counts. Child Development, 84(3), 1020–1033.
Pugh, K. J., & Bergin, D. A. (2006). Motivational influences on transfer. Educational Psychologist, 41(3), 147–160.
Richland, L. E., Stigler, J. W., & Holyoak, K. J. (2012). Teaching the conceptual structure of mathematics. Educational Psychologist, 47(3), 189–203.
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: an iterative process. Journal of Educational Psychology, 93(2), 346–362.
Ross, B. H. (1987). This is like that: the use of earlier problems and the separation of similarity effects. Journal of Experimental Psychology. Learning, Memory, and Cognition, 13, 629–639.
Ross, B. H. (1989). Distinguishing types of superficial similarities: different effects on the access and use of earlier problems. Journal of Experimental Psychology. Learning, Memory, and Cognition, 15(3), 456–468.
Sansone, C., & Harackiewicz, J. M. (2000). Intrinsic and extrinsic motivation: the search for optimal motivation and performance. San Diego: Academic.
Schalk, L., Saalbach, H., & Stern, E. (2011). Designing learning materials to foster transfer of principles. Paper presented at the 33rd Annual Conference of the Cognitive Science Society, Austin, TX.
Schiefele, U. (1991). Interest, learning, and motivation. Educational Psychologist, 3 & 4, 299–323.
Schneider, M., Rittle-Johnson, B., & Star, J. R. (2011). Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental Psychology, 47(6), 1525–1538.
Schnotz, W. (2005). An integrated model of text and picture comprehension. In R. E. Mayer (Ed.), The Cambridge handbook of multimedia learning (pp. 49–69). Cambridge: Cambridge University Press.
Schweppe, J., & Rummer, R. (2014). Attention, working memory, and long-term memory in multimedia learning: An integrated perspective based on process models of working memory. Educational Psychology Review, in press.
Singley, M. K., & Anderson, J. R. (1989). Transfer of cognitive skill. Cambridge: Harvard University Press.
Sloutsky, V. M., Kaminski, J. A., & Heckler, A. F. (2005). The advantage of simple symbols for learning and transfer. Psychonomic Bulletin & Review, 12(3), 508–513.
Son, J. Y., & Goldstone, R. L. (2009). Contextualization in perspective. Cognition and Instruction, 27(1), 51–89.
Staub, F. C., & Stern, E. (1997). Abstract reasoning with mathematical constructs. International Journal of Educational Research, 27(1), 63–75.
Stenning, K. (2002). Seeing reason: image and language in learning to think. New York: Oxford University Press.
Sweller, J. (1988). Cognitive load during problem solving: effects on learning. Cognitive Science, 12, 257–285.
Sweller, J., van Merrienboer, J. J. G., & Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251–296.
Taatgen, N. A. (2013). The nature and transfer of cognitive skills. Psychological Review, 120(3), 439–471.
Thorndike, E. L., & Woodworth, R. S. (1901). The influence of improvement in one mental function upon the efficiency of other functions. Psychological Review, 8, 247–261.
Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: a new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18, 37–54.
Vosniadou, S., & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching. Learning & Instruction, 14(5), 445–451.
Walkington, C. (2013). Using adaptive learning technologies to personalize instruction to student interests: the impact of relevant contexts on performance and learning outcomes. Journal of Educational Psychology, 105(4), 932–945.
Walkington, C., Petrosino, A., & Sherman, M. (2013). Supporting algebraic reasoning through personalized story scenarios: how situational understanding mediates performance. Mathematical Thinking and Learning, 15(2), 89–120.
Wason, P. C., & Shapiro, D. (1971). Natural and contrived experience in a reasoning problem. Quarterly Journal of Experimental Psychology, 23, 63–71.
Winkielman, P., Schwarz, N., Fazendeiro, T., & Reber, R. (2003). The hedonic marking of processing fluency: implications for evaluative judgment. In J. Musch & K. C. Klauer (Eds.), The psychology of evaluation: affective processes in cognition and emotion (pp. 189–217). Mahwah: Erlbaum.
Yarlas, A. S., & Gelman, R. (1998). Learning as a predictor of situational interest. Paper presented at the Annual Conference of the American Educational Research Association, San Diego, CA, USA.
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Belenky, D.M., Schalk, L. The Effects of Idealized and Grounded Materials on Learning, Transfer, and Interest: An Organizing Framework for Categorizing External Knowledge Representations. Educ Psychol Rev 26, 27–50 (2014). https://doi.org/10.1007/s10648-014-9251-9
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