Good errors in mathematics education

References

• Boaler, J. (2013). Ability and mathematics: The mindset revolution that is reshaping education. Forum (chicago, Ill ), 55(1), 143–152.
   Google Scholar
• Borasi, R. (1994). Capitalizing on errors as “springboards for inquiry": A teaching experiment. Journal for Research in Mathematics Education, 25(2), 166–208. doi: 10.2307/749507
   Web of Science ®Google Scholar
• Buchbinder, O., & Zaslavsky, O. (2013). Inconsistencies in students’ understanding of proof and refutation of mathematical statements. In Lindmeier, A. M. & Heinze, A. (Eds.), Proceedings of the 37th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 129–136). Kiel: PME.
   Google Scholar
• Cosmides, L., & Tooby, J. (1992). Cognitive adaptations for social exchange. In J. H. Barkow, L. Cosmides, & J. Tooby (Eds.), The adapted mind: Evolutionary psychology and the generation of culture (pp. 163–228). Oxford: Oxford University Press.
   Google Scholar
• Cosmides, L., & Tooby, J. (1997). Evolutionary psychology: A primer. Santa Barbara: Center for Evolutionary Psychology, University of California. Retrieved from http://www.cep.ucsb.edu/primer.html.
   Google Scholar
• Dweck, C. S. (2006). Mindset: The new psychology of success. New York: Ballantine Books.
   Google Scholar
• Ejersbo, L. R., & Leron, U. (2013). Revisiting the medical diagnosis problem: Reconciling intuitive and analytical thinking. In E. J. Chernoff, & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 215–238). Dordrecht: Springer.
   Google Scholar
• Ejersbo, L. R., Leron, U., & Arcavi, A. (2014). Bridging intuitive and analytical thinking: Four looks at the 2-glass puzzle. For the Learning of Mathematics, 34(3), 2–7.
   Google Scholar
• Evans, J. S. B. T. (2006). The heuristic–analytic theory of reasoning: Extension and evaluation. Psychonomic Bulletin & Review, 13, 378–395. doi: 10.3758/BF03193858
   PubMed Web of Science ®Google Scholar
• Evans, J. S. B. T., & Frankish, K. (Eds.). (2009). In two minds: Dual processes and beyond. Oxford: Oxford University Press.
   Google Scholar
• Geary, D. (2002). Principles of evolutionary educational psychology. Learning and Individual Differences, 12, 317–345. doi: 10.1016/S1041-6080(02)00046-8
   Web of Science ®Google Scholar
• Gigerenzer, G. (2005). I think, therefore I err. Social Research, 72(1), 1–24.
   Web of Science ®Google Scholar
• Gigerenzer, G., Todd, P. M., & The ABC Research Group. (1999). Simple heuristics that make us smart. Oxford: Oxford University Press.
   Google Scholar
• Gilovich, T., Griffin, D., & Kahneman, D. (2002). Heuristics and biases: The psychology of intuitive Judgment. Cambridge: Cambridge University Press.
   Google Scholar
• Kahneman, D. (2002). Maps of bounded rationality: A perspective on intuitive judgment and choice. Nobel Prize Lecture. In T. Frangsmyr (Ed.), Les Prix Nobel (pp. 416–499). Stockholm: Nobel Foundation. Retrieved from https://www.nobelprize.org/uploads/2018/06/kahnemann-lecture.pdf
   Google Scholar
• Kahneman, D. (2011). Thinking, fast and slow. New York: Farrar, Straus and Giroux.
   Google Scholar
• Leron, U., & Hazzan, O. (2006). The rationality debate: Application of cognitive psychology to mathematics education. Educational Studies in Mathematics, 62(2), 105–126. doi: 10.1007/s10649-006-4833-1
   Google Scholar
• Leron, U., & Hazzan, O. (2009). Intuitive vs. Analytical thinking: Four perspectives. Educational Studies in Mathematics, 71, 263–278. doi: 10.1007/s10649-008-9175-8
   Web of Science ®Google Scholar
• Loibl, K., & Leuders, T. (2019). How to make failure productive: Fostering learning from errors through elaboration prompts. Learning and Instruction, 62, 1–10. doi: 10.1016/j.learninstruc.2019.03.002
   Web of Science ®Google Scholar
• Manalo, E., & Kapur, M. (2018). The role of failure in promoting thinking skills and creativity: New findings and insights about how failure can be beneficial for learning. Thinking Skills and Creativity, 30(special issue), 1–6. doi: 10.1016/j.tsc.2018.06.001
   Google Scholar
• Mercier, H., & Sperber, D. (2017). The enigma of reason: A new theory of human understanding. Cambridge: Harvard University Press.
   Google Scholar
• Papert, S. (1980). Mindstorms: Children, computers and powerful ideas. New York: Basic Books.
   Google Scholar
• Samuels, R., Stich, S., & Tremoulet, P. D. (1999). Rethinking rationality: From bleak implications to darwinian modules. In K. Korta, E. Sosa, & X. Arrazola (Eds.), Cognition, agency and rationality ( Philosophical Studies Series, Vol. 79, pp. 21–62). Dordrecht: Springer.
   Google Scholar
• Simms, V. (2016). Review of Jo Boaler: Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. Research in Mathematics Education, 18(3), 317–320. doi: 10.1080/14794802.2016.1237374
   Web of Science ®Google Scholar
• Smith, J. P., diSessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: A constructivist analysis of knowledge in transition. Journal of the Learning Sciences, 3(2), 115–163. doi: 10.1207/s15327809jls0302_1
   Google Scholar
• Stanovich, K. E. (2011). Rationality and the reflective mind. Oxford: Oxford University Press.
   Google Scholar
• Stanovich, K. E., & West, R. F. (2000). Individual differences in reasoning: Implications for the rationality debate. Behavioral and Brain Sciences, 23, 658–659.
   Web of Science ®Google Scholar