vmt-award-2024_47-1-_blue

most drastic of which was a strictly online context, which is the one we have chosen to address in this article. The transition from face - to - face to online teaching necessitated shifts in some of the thinking class room practices. We have discussed one such prac tice—the types of tasks we use. Our exploration of the adaptations needed for this practice to be effec tive in the online setting indicates a need for con sidering the modes of communication required of students and their technological competence with the tools being used for this communication. In particular, tasks may be designed to emphasize ver bal, gestural, written, object - oriented, or diagram matic modes of communication depending on the technological capacity in the learning environment. We conclude that engendering a culture of collabo rative thinking in an online classroom setting re mains possible even if there are some technological limitations. In the end, the COVID - 19 lockdown has forced upon us a new perspective on which practices continue to work, why they work, and what they offer in the synergy of the overall BTC framework. By creating a breach between the fa miliar face - to - face context and a new online con text, the aspects that make the BTC framework so effective have been illuminated. And, by consider ing these aspects, appropriate modifications have become evident for alternative settings. While there are evidently limitations, the essence of a thinking classroom can live on in novel contexts. Cobb, P., Wood, T., & Yackel, E. (1991). Analo gies from the philosophy and sociology of science for understanding classroom life. Science Education, 75 (1), 23 - 44. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in math ematics Education, 27 (4), 458 - 477. Liljedahl, P. (2020). Building thinking classrooms in mathematics (Grades K - 12): 14 teaching practices for enhancing learning. Thousand Oaks, CA: Corwin Press Inc. References

Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (Eds.), Posing and Solving Mathematical Prob lems: Advances and New Perspectives (pp. 361 - 386). New York, NY: Springer. Liu, M. & Liljedahl, P. (2012). ‘ Not normal ’ class room norms. In T.Y. Tso (Ed.), Proceed ings of the 36th Conference of the Interna tional Group for the Psychology of Mathe matics Education , Vol. 4(pp. 300). Taipei, Taiwan. Lithner, J. (2008). A research framework for crea tive and imitative reasoning. Educational Studies in Mathematics, 67 (3), 255 - 276. Mason, J., Burton, L., & Stacey, K. (2011). Think ing mathematically (2nd ed.). Pearson Higher Ed. National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. NCTM, Reston, Va. Pólya, G. (1945). How to solve It. Princeton, NJ: Princeton University. Roddy et al. (2017, November 21). Applying best

practice online learning, teaching, and sup port to intensive online environments: An integrative review , Frontiers in Educa tion. https://www.frontiersin.org/ articles/10.3389/feduc.2017.00059/full

Van de Walle, J., Karp, K., Bay - Williams, J., McGarvey, L., & Folk, S. (2015). Elemen tary and middle school mathematics: Teaching developmentally (4th ed.). Pear son.

Dr. Peter Liljedahl Professor Simon Fraser University liljedahl@sfu.ca

Dr. Judy Larsen Associate Professor University of the Fraser Valley Judy.Larsen@ufv.ca

Virginia Mathematics Teacher vol. 47, no. 1

14