Teacher candidates' online math journals: a search for pedagogical surprise

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Palabras clave:

Pedagogical Surprise, Pedagogical Insight, Mathematical Surprise, Teacher Education, Online Education

Resumen

Surprise and insight are an integral part of doing mathematics. However, surprise does not appear to be on the radar of most mathematics curriculum documents. In this paper, we present an analysis of TCs' online journals and their associated online discussions from a K-6 mathematics teacher education blended course. This online component of an otherwise face-to-face course also included readings and viewings of documentaries from classroombased research, along with mathematician interviews, animations, and other support material (available at researchideas.ca/wmt), which connected to, and extended face-to-face course activities. We address the question: How did this limited online experience affect TCs’ thinking about mathematics teaching and learning? Participants were 168 K-6 TCs, distributed among six sections of a mandatory mathematics methods course. We employed a case study approach and qualitative content analysis of TC discussions of journals and related online resources, and we identified six themes: (1) low floor, high ceiling approach; (2) contrast with personal math learning experience; (3) visual and concrete representations; (4) real world contexts; (5) aesthetic math experience; and (6) sharing math experiences

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Aycock, A., Garnham, C., & Kaleta, R. (March 20, 2002). Lessons learned from the hybrid course project. Teaching with Technology Today, 8(6), 1-6.

Berg, B.L. (2004). Qualitative research methods for the social sciences. New York: Pearson Publishers.

Boorstin, J. (1990). The Hollywood Eye: What Makes Movies Work. NY: Harper Collins Publishers.

Borba, M. C., & Villarreal, M. E. (2005). Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modeling, visualization, and experimentation. New York, NY: Springer. doi:10.1007/b105001

Boyd, B. (2001) The origin of stories: Horton hears a Who. Philosophy and Literature, 25(2), 197-214.

British Columbia Ministry of Education (2007). Mathematics K-7. Victoria, BC: Author.

Burton, L. (1999) Learning Mathematics: From Hierarchies to Networks. New York, NY: Falmer Press

Christensen, M. K. (2012). Biographical Learning. In N. M. Steel (Ed), Encyclopedia of the Sciences of Learning, (pp. 457-460). Boston, MA: Springer US.

Collis, B., & Jung, I. S. (2003). Uses of information and communication technologies in teacher education. In B. Robinson & C. Latchem (Eds.), Teacher education through open and distance learning, London: Routledge Falmer, 171-192.

DeCorte, E. (1996). Learning bad and good things from instruction: A European perspective. Paper presented at the Annual Meeting of the American Psychological Association, Toronto, Ontario, Canada.

Dewey, J. (1899). The school and society. Chicago, IL: University of Chicago Press.

Dewey, J. (1934). Art as experience. New York: Minton, Balch.

Dunst, C. J. (2006). Parent-mediated everyday child learning opportunities: I. Foundations and operationalization. CASEinPoint, 2(2), 1–10

Durmus, S., & Karakirik, E. (2006). Virtual manipulatives in mathematics education: A theoretical framework. TOJET : The Turkish Online Journal of Educational Technology, 5(1)

Eisner, E.W. (2002). The educational imagination: On the design and evaluation of school programs. Upper Saddle River, NJ: Merrill Prentice Hall.

Ferguson, R. F. (2008). Teacher perceptions and expectations and the Black- White test score gap. Urban Education, 38, 460-507.

Futch, L. (2005). A study of blended learning at a metropolitan research university (Doctoral dissertation). Retrieved from etd.fcla.edu/CF/CFE0000843/Futch_Linda_S_200512_EdD.pdf

Gadanidis, G. (2009). I heard this great math story the other day. Education Canada, 49(5), 44.

Gadanidis, G. (2012). Why can't I be a mathematician? For the Learning of Mathematics, 32(2), 20–26.

Gadanidis, G. (2014). Why you hate math and how to feel the love! In search of cool answers to "what did you do in math today?". Gazette - Ontario Association for Mathematics, 52(4), 37-40

Gadanidis, G. & Borba, M. (2008). Our lives as performance mathematicians. For the Learning of Mathematics, 28(1), 42-49.

Gadanidis, G., Borba, M., Hughes, J. and Lacerda, H. (2016). Designing aesthetic experiences for young mathematicians: A model for mathematics education reform. International Journal for Research in Mathematics Education, 6(2), 225-244

Gadanidis, G. & Hughes, J. (2011). Performing big math ideas across the grades. Teaching Children Mathematics, 17(8), 486-496.

Gadanidis, G., Hughes, J., Minniti, L. & White, B. (2016). Computational thinking, grade 1 students and the Binomial Theorem. Digital Experience in Mathematics Education.

Gadanidis, G. & Namukasa, I. (2007). Math-for-teachers (and students). Journal of Teaching and Learning, 5(1), 13-22.

Garrison, D. R., & Vaughan, N. D. (2008). Blended learning in higher education: framework, principles, and guidelines (1st ed.). San Francisco: Jossey-Bass.

Ginsburg, H.G. (2002). Little children, big mathematics: Learning and teaching in the pre-school. Proceedings of the 26th Conference of PME (Vol.1, pp. 3-14), University of East Anglia: PME.

Girod, M. (2012). Science, Art, and Learning Experiences. In N. M. Steel (Ed), Encyclopedia of the Sciences of Learning, (pp. 2972-2974). Boston, MA: Springer US.

Girod, M., Twyman, T., & Wojcikiewicz, S. (2010). Teaching and learning science for transformative, aesthetic experience. Journal of Science Teacher Education, 21, 801–824.

Goodson, I. F. (2003). Professional knowledge, professional lives: Studies in education and change. Buckingham: Open University Press.

Gravemeijer, K., Lehrer, R., van Oers, B., & Verschaffel, L. (2002). Symbolization, modeling and tool use in mathematics education. Dorchedt: Kluwer.

Guillaume, A. M., & Kirtman, L. (2010). Mathematics stories: Preservice teachers' images and experiences as learners of mathematics. Issues in Teacher Education, 19(1), 121-143.

Hardy, I. & Koerber, S. (2012). Scaffolding Learning by the Use of Visual Representations. In N. M. Steel (Ed), Encyclopedia of the Sciences of Learning, (pp. 2926-2929). Boston, MA: Springer US.

Holtzman, C. & Susholtz, L. (2011). Object Lessons: Teaching Math through the Visual Arts, K-5. Portland: Stenhouse Publishers.

Jung, I. (2005). ICT-pedagogy integration in teacher training: Application cases worldwide. Journal of Educational Technology & Society, 8(2), 94-100.

Kleiner, I., & Movshovitz-Hadar, N. (1994). The role of paradoxes in the evolution of mathematics. The American Mathematical Monthly, 101(10), 963-974.

Lake, J. (2009). Math memories you can count on: A literature-based approach to teaching mathematics in the primary classrooms. Markham, Ont: Pembroke Publishers.

Lefrancois, G. (1995). Theories of Human Learning (3rd Ed.). U.S.A.: Brookes /Cole.

Levy, P. (1997). Collective intelligence: Mankind's emerging world in cyberspace. New York: Basic Books.

Macedo, L, Reisenzein, R., & Cardoso, A. (2012). Surprise and anticipation in learning. In N. M. Steel (Ed), Encyclopedia of the Sciences of Learning, (pp. 3250-3253). Boston, MA: Springer US.

Marley, S. C., & Carbonneau, K. J. (2014). Theoretical perspectives and empirical evidence relevant to classroom instruction with manipulatives. Educational Psychology Review, 26(1), 1-7. doi:10.1007/s10648-014-9257-3

McVarish, J. (2008). Where's the wonder in elementary math?: Encouraging mathematical reasoning in the classroom. New York: Routledge.

Means, B., Bakia, M., & Murphy, R. (2014). Learning online: What research tells us about whether, when and how. New York: Routledge.Meyer, W. U., Reisenzein, R., & Schützwohl, A. (1997). Towards a process analysis of emotions: The case of surprise. Motivation and Emotion, 21, 251–274.

Movshovitz-Hadar, N. (1994). Mathematics Theorems: An Endless Source of Surprise. For the Learning of Mathematics, 8(3), 34-40

Norman, D.A. (2004). Emotional Design: Why we Love (or Hate) Everyday Things. NY: Basic Books.

Papert, S. (1993). The children's machine: Rethinking school in the age of the computer. New York: BasicBooks.

Pekrun, R. (2012). Emotions: Functions and Effects on Learning. In N. M. Steel (Ed), Encyclopedia of the Sciences of Learning, (pp. 1141-1146). Boston, MA: Springer US.

Podolski, A. (2012). Functional Context Theory of Learning. In N. M. Steel (Ed), Encyclopedia of the Sciences of Learning, (pp. 1328-1330). Boston, MA: Springer US.

Pugh, K. J., Linnenbrink-Garcia, L., Koskey, K. L. K., Stewart, V. C., & Manzey, C. (2010). Motivation, learning, and transformative experience: A study of deep engagement in science. Science Education, 94, 1–28.

Sands, P. (2002.) Inside outside, upside downside: Strategies for connecting online and face-to-face instruction in hybrid courses. Teaching with Technology Today, 8(6).

Sinclair, N. & Watson, A. (2001). Wonder, the rainbow, and the aesthetics of rare experiences. The aesthetic is relevant. For the Learning of Mathematics, 21(1): 25-32.

Stake, R. (2000a). Case Studies. In N. Denzin & Y. Lincoln (Eds.). Handbook of Qualitative Research, 2nd Ed. (pp. 435-454). Thousand Oaks, CA: Sage Publications.

Stake, R.E. (1995). The art of case study research. Thousand Oaks, CA: Sage.

Stake, R.E. (2000b). The case study method in social inquiry. In R. Gomm, M. Hammersley & P. Foster (Eds). Case study method: Key issues, key texts. London: Sage Publications.

Vygotsky, L.S. (1978). Mind in society. Cambridge, MA: Harvard University Press.

Watson, A. & Mason, J. (2007). Surprise and inspiration. Mathematics Teaching, 200, 4-7.

Willis, J. (2010). Learning to love math: Teaching strategies that change student attitudes and get results. Alexandria, Va: ASCD.

Yin, R. (1994). Case study research: Design and methods (2nd ed.). Beverly Hills, CA: Sage Publishing.

Zaslavsky, O. (2005). Seizing the opportunity to create uncertainty in learning mathematics. Educational Studies in Mathematics, 60, 297-321.

Publicado

2017-08-01

Cómo citar

GADANIDIS, G.; ARAUJO, R. C. Teacher candidates’ online math journals: a search for pedagogical surprise. Revista Internacional de Pesquisa en Educación Matemática, v. 7, n. 1, p. 19-42, 1 ago. 2017.

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