Complexity, Emergence and Embodied Cognition in Education

Roberto Araya Schulz

doi:10.24310/innoeduca.2017.v3i2.3020

Authors

Roberto Araya Schulz Universidad de Chile Chile http://orcid.org/0000-0002-9359-5378

DOI:

https://doi.org/10.24310/innoeduca.2017.v3i2.3020

Keywords:

effective complexity, information, emergence, embodiment, mathematics education

Abstract

Complexity and emergence are core notions for understanding and improving learning. On one hand, with complex concepts students struggle and learning becomes very difficult. On the other hand, emergence phenomena looks like magic or cognitive illusions, they seem to rely on extra qualities not included in the subjacent phenomena. Can the teacher simplify complex notions without changing them? In order to do that, we argue complexity and emergency are not exclusively inherent to objects or phenomena. They also depend on the perceptual, motor and cognitive system of the student. Thus, if the teacher helps to connect notions and phenomena to students' innate and embodied knowledge, then these notions become less complex and the emergent phenomenon loses its magic: it becomes logically connected to the subjacent phenomena. In this paper we present empirical evidence of the effect on students understanding due to the connection stablished in two core curriculum mathematical concepts that are considered very challenging.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Author Biography

Roberto Araya Schulz, Universidad de Chile

Investigador Asociado

References

Araya, R. (2000). Inteligencia Matemática. Editorial Universitaria.

Araya, R. (2000b) A.I., Máquinas que Piensan y Matemáticas. Interview to John Casti. Artes y Letras, El Mercurio. http://www.iing.cl/docs/Araya_EntrevistaCasti.doc

Araya, R. (2006) Complexity and Emergence are Embodied and Observer Dependent Notions but are not Arbitrary. Presentación Congreso Universidad Diego Portales.

Araya, R.; Calfucura, P., Jiménez, A.; Aguirre, C.; Palavicino, M.; Lacourly, N.; Soto-Andrade, J. & Dartnell, P. (2010) The Effect of Analogies on Learning to Solve Algebraic Equations. Pedagogies: An International Journal. Special Issue The teaching of Algebra. Volume 5, Issue 3.

Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D.C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113, 447-455.

Baum, E. (2004) What is Thought? Mit Press.

Baron-Cohen, S.(1997) Mindblindness: An Essay on Autism and Theory of Mind. Mit Press.

Bossomaier, T., Snyder, A. (2004). Absolute pitch accesible to everyone by turning off part of the brain. Organised Sound 9 (2): 181-189.

Casti, John. (2000) Five More Golden Rules. John Wiley & Sons.

Chaitin (1974) Information-Theoretic Computational Complexity. IEEE Transactions on Information Theory IT-20 pp. 10-15

Cosmides, L. Tooby, J.(1996) Are Humans Good Intuitive Statisticians After All? Rethinking Some Conclusions from the Literature on Judgment Under Uncertainty Cognition 58, pp. 1-73

Dennett, Daniel. (2005) Sweet Dreams: Philosophical Obstacles to a Science of Consciousness. MIT Press.

Dennett, Daniel. (2017) From Bacteria to Bach and Back. The evolution of Minds. Mit Press.

Fruteau, C., Voelkl, B., van Dammea, E., Noe, R. (2009) Supply and demand determine the market value of food providers in wild vervet monkeys. PNAS, vol. 106, no. 29. 12007—12012

Geary, D. (2007). Educating the evolved mind: Conceptual foundations for an evolutionary educational psychology. In J.S. Carlson, & J.R.

Levin (Eds.), Educating the evolved mind (Vol. 2, pp. 1–99). Greenwich, CT: Information Age.

Gell-Mann, M. (2000) The Quark and the jaguar, Adventures in the simplex and the complex

Gell-Mann, M. (1995) What Is Complexity? Complexity, Vol. 1, no.1

Gigerenzer, G., Todd, P., & the ABC Research Group (1999). Simple Heuristics that Makes Us Smart. Oxford University Press.

Gigerenzer, G. (2000); Adaptive Thinking. Rationality in the Real World. Oxford University Press.

Hadamard, J.(1945) The Mathematician´s Mind: The Psychology of Invention in the Mathematical Field. Princeton University Press.

Holland, J. (1998). Emergence Addison Wesley.

Inoue, S., Matsuzawa, T. (2007) Working memory of numerals in chimpanzees. Current Biology Vol. 17, Issue 23, pR1004–R1005, 4 December 2007

Jiménez, A., Araya, R. (2013) Comparación de Tres Metodologías para el Aprendizaje de Fracciones. XVII Jornadas Educación Matemática.

Kolmogorov, A. (1968) Logical basis for information theory and probability theory, IEEE Trans. Inform. Theory, vol. IT-14, pp. 662-664.

Lakoff, G. & Johnson, M. (1980). Metaphors we live by. The University of Chicago Press.

Lakoff, George & Johnson, Mark. (1999). Philosophy in the Flesh: the Embodied Mind and its Challenge to Western Thought. Basic Books.

Lakoff, G., Núñez, R. (2000). Where Mathematics come from: How the embodied mind brings mathematics into being. Basic Books.

Mercier, H., Sperber, D. (2017) The Enigma of Reason. Harvard University Press. Cambridge.

Obersteoner, A., Van Dooren, V,. Van Hoof, J., Verschaffel, L. (2013) The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction 28 (2013) 64--72

Pinker, S. (2002) The Blank Slate: The Modern Denial of Human Nature. Viking.

Povinelli, D. (2000) Folk Physics for Apes: The Chimpanzee´s Theory of How the World Works. Oxford University Press.

Rieke, F., Warland, D., van Steveninck, R-, Bialek, W. (1997) Spikes: Exploring the Neural Code. The MIT Press.

Siegler, R. (1996). The Emerging Mind: The Process of Change in Children´s Thinking. Oxford University Press.

Siegler, R., Araya, R. (2005) A Computational Model of Conscious and Unconscious Strategy Discovery. Advances in Child Development and Behavior, 33.

Siegler, R. & Stern, E. (1998) Conscious and Unconscious Strategy Discoveries: A Microgenetic Analysis’ Journal of Experimental Psychology: General´ Vol. 127, No. 4, pp.377-397.

Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y.,

Thompson, L., & Wray, J. (2010). Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE #2010-4039). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from whatworks.ed.gov/ publications/practiceguides.

Siegler, B., Braithwaite, D. (2017) Numerical Development. Annu. Rev. Psychol. 2017. 68:187–213

Simon, H. (1996) The Science of the Artificial. Mit Press.

Sloman, S., Fernbach, P. (2017) The Knowledge Illusion. Why we Never Think Alone. Rverhead Books. N.Y.

Snyder, A., Bossomaier, T., Mitchell, J. (2004). Concept Formation: “Object” Attributes Dynamically Inhibited from Conscious Awareness. Journal of Integrative Neurosciences., Vol. 3, No. 1 (2004) 31-46.

Solso, R. (1994).Cognition and the Visual Arts. Mit Press.

Soto-Andrade, J. (2006) Un monde dans un grain de sable : métaphores et analogies dans l’àprentissage des mathématiques. Annales de Didactique et de Sciences Cognitives, vol. 11, pp. 123-147.