The enactive roots of STEM: Rethinking educational design in mathematics

Educational Psychology Review

Volumn 27, Issue 3, 2015, Pages 371-389

  Hutto, Daniel D ^a   Kirchhoff, Michael D ^a   Abrahamson, Dor ^b  

^a UNIVERSITY OF WOLLONGONG   (Australia)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Attentional anchor; Ecological dynamics; Enactivism; Mathematics

Indexed keywords

EID: 84943390999     PISSN: 1040726X     EISSN: 1573336X     Source Type: Journal    
DOI: 10.1007/s10648-015-9326-2     Document Type: Review

References (104)

1. Abrahamson, D. (2009). Embodied design: constructing means for constructing meaning. Educational Studies in Mathematics, 70(1), 27–47. [Electronic supplementary material at http://edrl.berkeley.edu/publications/journals/ESM/Abrahamson-ESM/]. doi: 10.1007/s10649-008-9137-1
2. Abrahamson, D. (2012a). Discovery reconceived: product before process. For the Learning of Mathematics, 32(1), 8–15.
3. Abrahamson, D. (2012c). Mathematical Imagery Trainer - Proportion (MIT-P) IPhone/iPad application (Terasoft): iTunes. Retrieved from https://itunes.apple.com/au/app/mathematical-imagery-trainer/id563185943.
4. Abrahamson, D., & Lindgren, R. (2014). Embodiment and embodied design. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (2nd ed., pp. 358–376). Cambridge: Cambridge University Press.
5. Abrahamson, D., & Sánchez-García, R. (2014). Learning is moving in new ways: an ecological dynamics view on learning across the disciplines. Paper presented at the BEmbodied cognition in educationsymposium (A. Bakker, M. F. van der Schaaf, S. Shayan, & P. Leseman, Chairs), Freudenthal Institute for Science and Mathematics Education, University of Utrecht, The Netherlands.
6. Abrahamson, D., & Trninic, D. (2015). Bringing forth mathematical concepts: signifying sensorimotor enactment in fields of promoted action. In D. Reid, L. Brown, A. Coles, & M.-D. Lozano (Eds.), Enactivist methodology in mathematics education research [Special issue]. ZDM, 47(2), 295–306.
7. Abrahamson, D., Trninic, D., Gutiérrez, J. F., Huth, J., & Lee, R. G. (2011). Hooks and shifts: a dialectical study of mediated discovery. Technology, Knowledge and Learning, 16(1), 55–85.
8. Abrahamson, D., Gutiérrez, J. F., Charoenying, T., Negrete, A. G., & Bumbacher, E. (2012). Fostering hooks and shifts: tutorial tactics for guided mathematical discovery. Technology, Knowledge and Learning, 17(1–2), 61–86.
9. Abrahamson, D., Lee, R. G., Negrete, A. G., Gutiérrez, J. F. (2014). Coordinating visualizations of polysemous action: values added for grounding proportion. In F. Rivera, H. Steinbring, & A. Arcavi (Eds.), Visualization as an epistemological learning tool [Special issue]. ZDM–The international Journal on Mathematics Education, 46(1), 79–93.
10. Aguilera, M., Bedia, M. G., Santos, B. A., & Barandiaran, X. E. (2013). The situated HKB model: how sensorimotor spatial coupling can alter oscillatory brain dynamics. Frontiers in Computational Neuroscience, 7(117), 1–15.
11. Bamberger, J. (2011). The collaborative invention of meaning: a short history of evolving ideas. Psychology of Music, 39(1), 82–101.
12. Barab, S., Zuiker, S., Warren, S., Hickey, D., Ingram-Goble, A., Kwon, E.-J., & Herring, S. C. (2007). Situationally embodied curriculum: relating formalisms and contexts. Science Education, 91, 750–782.
13. Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: artefacts and signs after a Vygotskian perspective. In L. D. English, M. G. Bartolini Bussi, G. A. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (2nd ed., pp. 720–749). Mahwah: Lawrence Erlbaum Associates.
14. Behr, M. J., Harel, G., Post, T., & Lesh, R. (1993). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–333). NYC: Macmillan.
15. Boutin, A., Blandin, Y., Massen, C., Heuer, H., & Badets, A. (2014). Conscious awareness of action potentiates sensorimotor learning. Cognition, 133(1), 1–9.
16. Brown, M. C., McNeil, N. M., & Glenberg, A. M. (2009). Using concreteness in education: real problems, potential solutions. Child Development Perspectives, 3, 160–164.
17. Bruner, J. S. (1960). The process of education: a searching discussion of school education opening new paths to learning and teaching. New York: Vintage.
18. Carey, S. (2011). Précis of The origin of concepts. Behavioral and Brain Sciences, 34, 113–167.
19. Carruthers, P. (2011). Opacity of mind. New York: Oxford University Press.
20. Chahine, I. C. (2013). The impact of using multiple modalities on students’ acquisition of fractional knowledge: An international study in embodied mathematics across semiotic cultures. The Journal of Mathematical Behavior, 32(3), 434–449.
21. Chemero, T. (2009). Radical Embodied Cognitive Science. Cambridge,MA: The MIT Press.
22. Chow, J. Y., Davids, K., Button, C., Shuttleworth, R., Renshaw, I., & Araújo, D. (2007). The role of nonlinear pedagogy in physical education. Review of Educational Research, 77(3), 251–278.
23. Davids, K. (2012). Learning design for nonlinear dynamical movement systems. The Open Sports Sciences Journal, 5(Suppl. 1), 9–16.
24. Davids, K., Button, C., & Bennett, S. (2008). Dynamics of skill acquisition. Campaign: Human Kinetics.
25. Davids, K., Araújo, D., Vilar, L., Renshaw, I., & Pinder, R. A. (2013). An ecological dynamics approach to skill acquisition: Implications for development of talent in sport. Talent Development and Excellence, 5, 21–34.
26. Davis, P. J., & Hersh, R. (1981). The mathematical experience. Boston: Birkhauser.
27. de Freitas, E., & Sinclair, N. (2012). Diagram, gesture, agency: theorizing embodiment in the mathematics classroom. Educational Studies in Mathematics, 80(1–2), 133–152.
28. diSessa, A. A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. The Journal of the Learning Sciences, 13(1), 77–103.
29. Dreyfus, H., & Dreyfus, S. (1986). Mind over machine. New York: The Free Press.
30. Dreyfus, H. L., & Dreyfus, S. E. (1999). The challenge of Merleau-Ponty’s phenomenology of embodiment for cognitive science. In G.Weiss & H. F. Haber (Eds.), Perspectives on embodiment: the intersections of nature and culture (pp. 103–120). New York: Routledge.
31. Duijzer, C. (2015). How perception guides cognition: Insights from embodied interaction with a tablet application for proportions – an eye-tracking study. Utrecht: Utrecht University.
32. Ferrara, F. (2014). How multimodality works in mathematical activity: young children graphing motion. International Journal of Science and Mathematics Education, 12(4), 917–939.
33. Fischer, U., Moeller, K., Bientzle, M., Cress, U., & Nuerk, H.-C. (2011). Sensori-motor spatial training of number magnitude representation. Psychonomic Bulletin & Review, 18(1), 177–183.
34. Fodor, J. A. (1975). The language of thought. Cambridge: Harvard University Press.
35. Fodor, J. A. (2003). Hume variations. Oxford: Oxford University Press.
36. Fodor, J. A. (2007). The revenge of the given. In B. McLaughlin & J. Cohen (Eds.), Contemporary debates in philosophy of mind (pp. 105–116). Oxford: Blackwell.
37. Fodor, J. A., & Pylyshyn, Z. (2015). Minds without meanings. Cambridge: MIT Press.
38. Gallagher, S. (2005). How the body shapes the mind. Oxford: Oxford University Press.
39. Gerofsky, S. (2011). Seeing the graph vs. being the graph: gesture, engagement and awareness in schoolmathematics. In G. Stam & M. Ishino (Eds.), Integrating gestures (pp. 245–256). Amsterdam: John Benjamins.
40. Gibson, J. J. (1977). The theory of affordances. In R. Shaw & J. Bransford (Eds.), Perceiving, acting and knowing: toward an ecological psychology (pp. 67–82). Hillsdale: Lawrence Erlbaum Associates.
41. Ginsburg, C. (2010). The intelligence of moving bodies: a somatic view of life and its consequences. Santa Fe: AWAREing Press.
42. Goldstone, R. L., Landy, D. H., & Son, J. Y. (2009). The education of perception. Topics in Cognitive Science, 2(2), 265–284.
43. Howison, M., Trninic, D., Reinholz, D., & Abrahamson, D. (2011). The mathematical imagery trainer: from embodied interaction to conceptual learning. In G. Fitzpatrick, C. Gutwin, B. Begole, W. A. Kellogg, & D. Tan (Eds.), Proceedings of the annual meeting of The association for computer machinery special interest group on computer human interaction: Bhuman factors in computing systems (CHI 2011) (pp. 1989–1998). Vancouver: ACM Press.
44. Hutto, D. D., & Myin, E. (2013). Radical enactivism. Cambridge: The MIT Press.
45. Hutto, D. D., & Sánchez-García, R. (2014). Choking RECtified: embodied expertise beyond Dreyfus. Phenomenology and the Cognitive Sciences, 1–23. doi: 10.1007/s11097-014-9380-0
46. Hutto, D. D., Kirchhoff, M. D., Myin, E. (2014). Extensive enactivism: Why keep it all in? Frontiers in Human Neuroscience, 1–11. DOI: 10.3389/fnhum.2014.00706.
47. Ingold, T. (2000). The perception of the environment: essays on livelihood, dwelling, and skill (2nd ed.). London: Routledge.
48. Karplus, R., Pulos, S., & Stage, E. K. (1983). Proportional reasoning of early adolescents. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 45–89). New York: Academic Press.
49. Kelso, J. A. S. (1984). Phase transitions and critical behavior in human bimanual coordination. American Journal of Physiology: Regulatory, Integrative and Comparative, 246(6), R1000–R1004.
50. Kelso, J. A. S. (1995). Dynamic patterns: the self-organization of brain and behavior. Cambridge: MIT Press.
51. Kelso, J. A. S., & Engstrøm, D. A. (2006). The complementary nature. Cambridge: MIT Press.
52. Kirsh, D. (2010). Thinking with external representations. AI & Society, 25, 441–454.
53. Kirsh, D., & Maglio, P. (1994). On distinguishing epistemic from pragmatic action. Cognitive Science, 18(4), 513–549.
54. Kostrubiec, V., Zanone, P.-G., Fuchs, A., Kelso, J. A. S. (2012). Beyond the blank slate: routes to learning new coordination patterns depend on the intrinsic dynamics of the learner – experimental evidence and theoretical model. Frontiers in Human Neuroscience, 6. doi: 10.3389/fnhum.2012.00222.
55. Laurence, S., & Margolis, E. (2007). Linguistic Determinism and the Innate Basis of Number. In P. Carruthers et al. (eds.), The Innate Mind, vol. 3: Foundations and the Future (Oxford University Press), pp. 139–169.
56. Lee, R. G., Hung, M., Negrete, A. G., Abrahamson, D. (2013). Rationale for a ratio-based conceptualization of slope: results from a design-oriented embodied-cognition domain analysis. Paper presented at the annual meeting of the American Educational Research Association (Special Interest Group on Research in Mathematics Education), San Francisco, April 27 - May 1.
57. Liao, C., & Masters, R. S. (2001). Analogy learning: a means to implicit motor learning. Journal of Sports Sciences, 19, 307–319.
58. Loader, P. (2012). The epistemic/pragmatic dichotomy. Philosophical Explorations: An International Journal for the Philosophy of Mind and Action, 15(2), 219–232.
59. Marghetis, T., & Núñez, R. l. (2013). The motion behind the symbols: a vital role for dynamism in the conceptualization of limits and continuity in expert mathematics. Topics in Cognitive Science. doi:10.1111/tops.12013.
60. Nemirovsky, R. (2003). Three conjectures concerning the relationship between body activity and understanding mathematics. In R. Nemirovsky, M. Borba, N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the twenty seventh annual meeting of the international group for the psychology of mathematics education Vol. 1 (pp. 105–109). Honolulu: OH: Eric Clearinghouse for Science, Mathematics, and Environmental Education.
61. Newell, K.M., & Ranganathan, R. (2010). Instructions as constraints in motor skill acquisition. In I. Renshaw, K. Davids, & G. J. P. Savelsbergh (Eds.), Motor learning in practice: a constraints-led approach (pp. 17–32). Florence: Routledge.
62. Núñez, R. E., Edwards, L. D., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39, 45–65.
63. Olson, D. R. (1994). The world on paper. Cambridge: Cambridge University Press.
64. Petrick, C. J., & Martin, T. (2011). Hands up, know body move: learning mathematics through embodied actions. Austin: University of Texas at Austin.
65. Piaget, J. (1968). Genetic epistemology (E. Duckworth, trans.). New York: Columbia University Press.
66. Piaget, J. (1970). Structuralism (C. Maschler, trans.). New York: Basic Books.
67. Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s conception of geometry (E. A. Lunzer, trans.) (E. A. Lunzer, trans.). New York: Basic Books.
68. Presmeg, N. C. (2006). Research on visualization in learning and teaching mathematics: emergence from psychology. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: past, present, and future (pp. 205–235). Rotterdam: Sense Publishers.
69. Prinz, J. (2002). Furnishing the mind: concepts and their perceptual basis. Cambridge: MIT Press.
70. Radford, L. (2013). Three key concepts of the theory of objectification: knowledge, knowing, and learning. In L. Radford (Ed.), Theory of objectification: knowledge, knowing, and learning [Special issue]. REDIMAT - Journal of Research in Mathematics Education, 2(1), 7–44.
71. Reed, E. S., & Bril, B. (1996). The primacy of action in development. In M. L. Latash & M. T. Turvey (Eds.), Dexterity and its development (pp. 431–451). Mahwah: Lawrence Erlbaum Associates.
72. Reinholz, D., Trninic, D., Howison, M., & Abrahamson, D. (2010). It’s not easy being green: embodied artifacts and the guided emergence of mathematical meaning. In P. Brosnan & D. Erchick (Eds.), Proceedings of the thirty-second annual meeting of the north-american chapter of the international group for the psychology of mathematics education (PME-NA 32) Vol. VI, Ch. 18: technology (pp. 1488–1496). Columbus: PME-NA.
73. Renshaw, I., Chow, J. Y., Davids, K., & Hammond, J. (2010). A constraints-led perspective for understanding skill acquisition and game play. Physical Education & Sport Pedagogy, 15(2), 117–137.
74. Rick, J. (2012). Proportion: a tablet app for collaborative learning. In H. Schelhowe (Ed.), Proceedings of the 11th Annual Interaction Design and Children Conference (IDC 2012) (Vol. BDemo Papers, pp. 316–319). Bremen, Germany: ACM-IDC.
75. Roth, W.-M. (2010). Incarnation: radicalizing the embodiment of mathematics. For the Learning of Mathematics, 30(2), 8–17.
76. Roth, W.-M. (2015). Excess of graphical thinking: movement, mathematics and flow. For the Learning of Mathematics, 35, 1–7.
77. Roth, W-M., & Thom, J. S. (2009). Bodily experience and mathematical conceptions: from classical views to a phenomenological reconceptualization. In L. Radford, L. Edwards, & F. Arzarello (Eds.), Gestures and multimodality in the construction of mathematical meaning [Special issue]. Educational Studies in Mathematics, 70(2), 175–189.
78. Rotman, B. (2000). Mathematics as sign: writing, imagining, counting. Stanford: Stanford University Press.
79. Schmandt-Besserat, D. E. (1992). Before writing Vol. 1: from counting to cuneiform. Austin: University of Texas Press.
80. Schneider, B., Bumbacher, E., & Blikstein, P. (2015). Discovery versus direct instruction: learning outcomes of two pedagogical models using tangible interface. In T. Koschmann, P. Häkkinen, & P. Tchounikine (Eds.), Exploring the material conditions of learning: opportunities and challenges for CSCL,B the proceedings of the Computer Supported Collaborative Learning (CSCL) conference. Gothenburg: ISLS.
81. Schwartz, D. L., & Martin, T. (2006). Distributed learning and mutual adaptation. In Harnad, S., & Dror, I. E. (Eds.), Distributed cognition [Special issue]. Pragmatics & Cognition, 14(2), 313–332.
82. Sfard, A. (1994). Reification as the birth of metaphor. For the Learning of Mathematics, 14(1), 44–55.
83. Sfard, A. (2002). The interplay of intimations and implementations: generating new discourse with new symbolic tools. The Journal of the Learning Sciences, 11(2&3), 319–357.
84. Shayan, S., Abrahamson, D., Bakker, A., Duijzer, C., & van der Schaaf, M. (2015). The emergence of proportional reasoning from embodied interaction with a tablet application: an eye-tracking study. In L. Gómez Chova, A. López Martínez, & I. Candel Torres (Eds.), Proceedings of the 9th international technology, education, and development conference (INTED 2015) (pp. 5732–5741). Madrid: IATED.
85. Shea, N. (2011). Acquiring a new concept is not explicable-by-content. Behavioral and Brain Sciences, 34(3), 148–149.
86. Siegler, R. S. (2006). Microgenetic analyses of learning. In D. Kuhn & R. S. Siegler (Eds.), Handbook of child psychology 6 ed., Vol. 2, cognition, perception, and language (pp. 464–510). Hoboken: Wiley.
87. Sinclair, N., & Gol Tabaghi, S. (2010). Drawing space: mathematicians’ kinetic conceptions of eigenvectors. Educational Studies in Mathematics, 74(3), 223–240.
88. Smith, L. B., & Gasser, M. (2005). The development of embodied cognition: six lessons from babies. Artificial Life, 11, 13–30.
89. Starra, A., Libertus, M. E., & Brannona, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences of the United States of America, 110(45), 18116–18120.
90. Stevens, R., & Hall, R. (1998). Disciplined perception: learning to see in technoscience. In M. Lampert & M. L. Blunk (Eds.), Talking mathematics in school: studies of teaching and learning (pp. 107–149). New York: Cambridge University Press.
91. Stoate, I., & Wulf, G. (2011). Does the attentional focus adapted by swimmers affect their performance? Journal of Sport science & Coaching, 6(1), 99–108.
92. Strauss, A. L., & Corbin, J. (1990). Basics of qualitative research: grounded theory procedures and techniques. Newbury Park: Sage Publications.
93. Thelen, E., & Smith, L. B. (1994). A dynamic systems approach to the development of cognition and action. Cambridge: MIT Press.
94. Thelen, E., & Smith, L. B. (2006). Dynamic systems theories. In R. M. Lerner (Ed.), Handbook of child psychology (Theoretical models of human development, Vol. 1, pp. 258–312). Hoboken: Wiley.
95. Thompson, E. (2007). Mind in life: biology, phenomenology, and the sciences of mind. Cambridge: Harvard University Press.
96. Trninic, D., & Abrahamson, D. (2012). Embodied artifacts and conceptual performances. In K. Thompson, M. J. Jacobson, & P. Reimann (Eds.), Proceedings of the 10th international conference of the learning sciences: future of learning (ICLS 2012) Vol. 1 (pp. 283–290). Sydney: University of Sydney/ISLS.
97. Uttal, D. H., & O’Doherty, K. (2008). Comprehending and learning from visual representations: a developmental approach. In J. Gilbert, M. Reiner, & M. Nakhleh (Eds.), Visualization: theory and practice in science education (pp. 53–72). New York: Springer.
98. van Dijk, L., Withagen, R., & Bongers, R. M. (2015). Information without content: a Gibsonian reply to enactivists’ worries. Cognition, 134, 210–214.
99. Van Dooren, W., De Bock, D., & Verschaffel, L. (2010). From addition to multiplication … and back. The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction, 28(3), 360–381.
100. Varela, F., Thompson, E. & Rosch, E. (1991). The embodied mind: cognitive science and human experience. Cambridge, MA: The MIT Press.
101. von Glasersfeld, E. (1983). Learning as constructive activity. In J. C. Bergeron & N. Herscovics (Eds.), Proceedings of the 5th annual meeting of the North American group for the psychology of mathematics education (Vol. 1, pp. 41–69). Montreal: PME-NA.
102. Wittmann, M. C., Flood, V. J., & Black, K. E. (2013). Algebraic manipulation as motion within a landscape. Educational Studies in Mathematics, 82(2), 169–181.
103. Wulf, G., & Su, J. (2007). An external focus of attention enhances golf shot accuracy in beginners and experts. Research Quarterly for Exercise and Sport, 78, 384–389.
104. Zarghami, M., Saemi, E., & Fathi, I. (2012). External focus of attention enhances discus throwing performance. Kinesiology, 44(1), 47–51.