363
Views
2
CrossRef citations to date
0
Altmetric
Articles

Beginner’s mind and the middle years mathematics student

ORCID Icon
Pages 48-66 | Received 17 Aug 2018, Accepted 17 Jul 2019, Published online: 06 Aug 2019

References

  • Berger, J. (1973). Ways of seeing. New York, NY: Viking Press.
  • Boaler, J. (2016). Mathematical mindsets. San Francisco, CA: Jossey-Bass.
  • Brown, L., & Coles, A. (2011). Developing expertise: How enactivism re-frames mathematics teacher development. ZDM Mathematics Education, 43, 861–873. doi: 10.1007/s11858-011-0343-4
  • Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58, 45–75. doi: 10.1007/s10649-005-0808-x
  • Chase, W., & Simon, H. (1973). The mind’s eye in chess. In W. Chase (Ed.), Visual information processing (pp. 215–281). New York, NY: Academic Press.
  • Chi, M. T. H., Feltovich, P., & Glaser, R. (1981). Categorisation and representation of physics problems by experts and novices. Cognitive Science, 5, 121–152. doi: 10.1207/s15516709cog0502_2
  • Chi, M. T. H., & Glaser, R. (1985). Problem solving ability. Washington, DC: ERIC Clearinghouse.
  • Chi, M. T. H., Glaser, R., & Farr, M. J. (1988). The nature of expertise. Hillsdale, NJ: Lawrence Erlbaum.
  • Clark, K., James, A., & Montelle, C. (2014). We definitely wouldn’t be able to solve it all by ourselves, but together … : group synergy in tertiary students’ problem-solving. Research in Mathematics Education, 16(3), 306–323. doi: 10.1080/14794802.2014.950687
  • Coles, A. (2015). On enactivism and language: Toward a methodology for studying talk in mathematics classrooms. ZDM, The International Journal on Mathematics Education, 47, 235–246. doi: 10.1007/s11858-014-0630-y
  • De Groot, A. D. (1978). Thought and choice in chess (2nd English edition). The Hague: Mouton.
  • Dweck, C. (2006). Mindset: The new psychology of success. New York, NY: Ballantine Books.
  • Engeström, Y. (1994). Teachers as collaborative thinkers: Activity-theoretical study of an innovative teacher team. In I. Cargren, G. Handal, & S. Vaage (Eds.), Teachers’ minds and actions: Research on teachers’ thinking and practice (pp. 43–61). Bristol, PA: Farmer.
  • Ericsson, K. A., & Charness, N. (1994). Expert performance. Its structure and acquisition. American Psychologist, 49(8), 725–747. doi: 10.1037/0003-066X.49.8.725
  • Ericsson, K. A., & Lehmann, A. C. (1996). Expert and exceptional performance: Evidence of maximal adaption to task constraints. Annual Review of Psychology, 47, 273–305. doi: 10.1146/annurev.psych.47.1.273
  • Gattegno, C. (1987). The science of education: Part I theoretical considerations. New York, NY: Educational Solutions.
  • Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research (1st ed). Chicago, IL: Aldine.
  • Hewitt, D. (2001). Arbitrary and Necessary: Part 3 Educating awareness. For the Learning of Mathematics, 21(2), 37–49.
  • Lakoff, G., & Núnez, R. E. (2000). Where mathematics come from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.
  • Lester, F. (1994). Musings about mathematical problem-solving research: 1970–1994. Journal for Research in Mathematics Education, 25(6), 660–675. doi: 10.2307/749578
  • Maciejewski, W., & Star, J. R. (2016). Developing flexible procedural knowledge in undergraduate calculus. Research in Mathematics Education, 18(3), 299–316. doi: 10.1080/14794802.2016.1148626
  • Marcou, A. (2008). Coding strategic behaviour in mathematical problem solving. Research in Mathematics Education, 10(1), 99–100. doi: 10.1080/14794800801916929
  • Mason, J. (1994). Researching from the inside in mathematics education: Locating an I-You relationship. Plenary address to Psychology of mathematics education XVII, Lisbon, Spain. Retrieved from https://www.researchgate.net/publication/288975126
  • Mason, J. (2004). Doing ≠ construing and doing + discussing learning: The importance of the structure of attention. Regular lecture at the 10th International Congress of mathematics education, Copenhagen. Retrieved from http://math.unipa.it/~grim/YESS-5/ICME201020Lecture%20Expanded.pdf
  • Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd edition). Harlow: Pearson.
  • Merleau-Ponty, M. (1962). Phenomenology of perception. New York, NY: Routledge.
  • Merriam-Webster Online Dictionary. Retrieved from https://www.merriam-webster.com/
  • Nathan, M. J., & Petrosino, A. (2003). Expert blind spot among preservice teachers. American Educational Research Journal, 40(4), 905–928. doi: 10.3102/00028312040004905
  • Poltoskaia, E., & Savard, A. (2018). Using the relational paradigm: Effects on pupils’ reasoning in solving additive word problems. Research in Mathematics Education, 20(1), 70–90. doi: 10.1080/14794802.2018.1442740
  • Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. Journal of Mathematical Behavior, 22, 405–435. doi: 10.1016/j.jmathb.2003.09.002
  • Romesburg, H. (2001). The life of the creative spirit. Philadelphia, PA: Xlibris Corporation. Retrieved from http://books.google.ca/books?id=–qMPwAACAAJ
  • Stahl, G. G. (2006). Group cognition: Computer support for building collaborative knowledge. Cambridge, MA: MIT Press.
  • Suzuki, S. (1985). Zen mind, beginner’s mind. New York, NY: John Weatherhill, Inc.
  • Tall, D. (2013). How humans learn to think mathematically: Exploring the three worlds of mathematics. New York, NY: Cambridge University Press.
  • Thurston, W. P. (1990). Mathematical education. Notices of the American Mathematical Society, 37, 844–850.
  • Wiley, J. (1998). Expertise as metal set: The effects of domain knowledge in creative problem solving. Memory & Cognition, 26, 716–730. doi: 10.3758/BF03211392

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.