Eliciting Students� Critical Thinking to Connect Phenomena and Representations on Context-Based Writing-to-Learn Assignments in Mathematics

Cerys Rogers University of Michigan–Ann Arbor ; Field M. Watts University of Michigan–Ann Arbor ; Nicole Brown University of Michigan–Ann Arbor ; Solaire A. Finkenstaedt-Quinn University of Michigan–Ann Arbor

Abstract

This tenth-anniversary volume is an occasion to read A Journal of Critical Thinking and Writing reflexively, by turning its focus on critical thinking and writing back on itself as an academic genre that organizes knowledge according to time.A journal assumes time to be a linear, unidirectional movement segmented into a past, which has already happened; a present, which is happening; and a future, which has yet to happen.This sequence is inscribed in a journal's paratextuality, such as a chronological division into annual volumes, which conforms reading to knowledge configured temporally: a reference to a text locates that text in the past; an argument against locates a text in the present; and questions for further research locate a text in the future.This commonplace notion of time informs a process of inquiry understandable across the disciplines, but it is also at odds with disciplinary theories of temporality.Consider, for a moment, how the visual arts can realign perception with uncommon patterns of time.When this volume's cover image is viewed according to its title, Counter-Curve (see Figure 1), it creates a curvilinear motion that either quickens along contracting concentric circles or slows along expanding concentric circles.Each motion, as a counter-curve, implies the other, inverse motion, but the either/or structure of perception limits our awareness of time's bidirectionality, described by the image's artist, Dana Karwas (n.d.), as "a single moment curving infinitely around on itself" (para.10).As a moment, time is undivided into past, present, and future.It is instead composed of recurrences that simultaneously spiral inwardly toward an infinitesimal center of nonrecurrence, a point of origin, and outwardly toward an infinite circumference that is the end of time.Because our perception can align with time's contraction or expansion, but not both at once, Counter-Curve can perhaps explain an otherwise paradoxical experience of the moment as ephemeral and durable.If the last ten years of Double Helix is telescoped to this swirl of time, then the practice of reading the journal changes.It locates one in the moment, a condition of "mindfulness" that Ellen Carillo (2016) has advocated for reading, in which one sustains attention to the text, undistracted by the past or the future, because, in this case, neither the past nor the future exists.A sequence of texts is thereby converted into an intertext, and a reference to, an argument against, and questions for further research become recurring features of intertextuality that advance an area of knowledge toward pure originality and the completion of knowledge as ideal and inverse limits of inquiry (see Figure 2).

Journal
Double Helix
Published
2022-01-01
DOI
10.37514/dbh-j.2022.10.1.03
CompPile
Open Access
OA PDF Gold
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References (66) · 5 in this index

  1. Abassian, A., Safi, F., Bush, S., & Bostic, J. (2020). Five different perspectives on mathematical modeling i…
     ↗
  2. Research in the Teaching of English
  3. Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in …
     ↗
  4. Ärlebäck, J. B., Doerr, H. M., & O'Neil, A. H. (2013). A modeling perspective on interpreting rates of change…
     ↗
  5. Asempapa, R. S. (2015). Mathematical modeling: Essential for elementary and middle school students. Journal o…
Show all 66 →
  1. Balgopal, M., & Wallace, A. (2013). Writing-to-learn, writing-to-communicate, & scientific Literacy. The Amer…
     ↗
  2. Bangert-Drowns, R. L., Hurley, M. M., & Wilkinson, B. (2004). The effects of school-based writing-to-learn in…
     ↗
  3. Bazerman, C. (2009). Genre and cognitive development: Beyond writing to learn. In C.
     ↗
  4. Bazerman, A. Bonin, & D. Figueiredo (Eds.), Genre in a changing world (pp. 279-294). The WAC Clearninghouse a…
     ↗
  5. Bicer, A., Perihan, C., & Lee, Y. (2018). The impact of writing practices on students' mathematical attainmen…
     ↗
  6. Brandfonbrener, P. B., Watts, F. M., & Shultz, G. (2021). Organic chemistry students' written descriptions an…
     ↗
  7. Brannan, J. R., & Boyce, W. E. (2015). Differential equations: An introduction to modern methods and applicat…
  8. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(…
     ↗
  9. Campbell, J. L., Quincy, C., Osserman, J., & Pedersen, O. K. (2013). Coding in-depth semistructured interview…
     ↗
  10. Carlson, M., Jacobs, S. Coe, E., Sean, L., & Hsu, E. (2002). Applying covariational reasoning while modeling …
     ↗
  11. Cox, C. T., Poehlmann, J. S., Ortega, C., & Lopez, J. C. (2018). Using writing assignments as an intervention…
     ↗
  12. Crouch, R. & Haines, C. (2007). 3.1 -Exemplar Models: Expert-Novice Student Behaviours. In C. Haines, P. Galb…
     ↗
  13. Czocher, J. A. (2017). How can emphasizing mathematical modeling principles benefit students in a traditional…
     ↗
  14. Czocher, J. A., Melhuish, K., & Kandasamy, S. S. (2020). Building mathematics self-efficacy of STEM undergrad…
     ↗
  15. David, E. J. (2018, February 22-24). Peter's evoked concept images for absolute value inequalities in calculu…
  16. David, E. J., Roh, K. H., & Sellers, M. E. (2019). Value-thinking and location-thinking: Two ways students vi…
     ↗
  17. Across the Disciplines
  18. Finkenstaedt-Quinn, S. A., Halim, A. S., Chambers, T. G., Moon, A., Goldman, R. S., Gere, A. R., & Shultz, G.…
     ↗
  19. Finkenstaedt-Quinn, S. A., Halim, A. S., Kasner, G., Wilhelm, C. A., Moon, A., Gere, A. R., & Shultz, G. V. (…
     ↗
  20. Finkenstaedt-Quinn, S. A., Petterson, M., Gere, A. R., Shultz, G. V. (2021). Praxis of writing-to- learn: A m…
     ↗
  21. Written Communication
  22. Finkenstaedt-Quinn, S. A., Snyder-White, E. P., Connor, M. C., Gere, A. R., & Shultz, G. V. (2019). Character…
     ↗
  23. Finkenstaedt-Quinn, S. A., Watts, F. M., Gere, A. R., & Shultz, G. V. (in press). A portrait of MWrite as a r…
  24. Written Communication
  25. Gilbert, J. K. (2005). Visualization: A metacognitive skill in science and science education. In J. K. Gilber…
     ↗
  26. Gouvea, J., & Passmore, C. (2017). 'Models of' versus 'models for.' Science & Education, 26(1), 49-63. https:…
     ↗
  27. Gupte, T., Watts, F. M., Schmidt-McCormack, J. A., Zaimi, I., Gere, A. R., & Shultz, G. V. (2021). Students' …
     ↗
  28. Halim, A. S., Finkenstaedt-Quinn, S. A., Olsen, L. J., Gere, A. R., & Shultz, G. V. (2018). Identifying and r…
     ↗
  29. Herbert, S., & Pierce, R. (2011). What is rate? Does context or representation matter? Mathematics Education …
     ↗
  30. Janvier, C. (1987). Translation processes in mathematics education. Problems of representation in the teachin…
  31. KarimiFardinpour, Y., & Gooya, Zahra. (2018). Comparing three methods of geometrical approach in visualizing …
     ↗
  32. Kozma, R., & Russell, J. (2005). Students becoming chemists: Developing representational competence. In J. K.…
     ↗
  33. Krippendorff, K. (2004). Unitizing. In Content analysis : An introduction to its methodology (2 nd ed.). Sage.
  34. Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of…
  35. Miles, B. M., Huberman, A.M., & Saldana, J. (2014). Qualitative data analysis (3 rd ed.). Sage.
  36. Moon, A., Moeller, R., Gere, A. R., & Shultz, G. V. (2019). Application and testing of a framework for charac…
     ↗
  37. Moon, A., Zotos, E., Finkenstaedt-Quinn, S., Gere, A. R., & Shultz, G. (2018). Investigation of the role of w…
     ↗
  38. Moore, K. (2016, August 3-7). Graphing as figurative and operative thought [Conference presentation]. 40th co…
  39. Moore, K., & Thompson, P. (2015). Shape thinking and students' graphing activity. In T. Fukawa-Connelly, N. I…
  40. National Research Council. (2012). Discipline-based education research: Understanding and improving learning …
  41. NGSS Lead States. (2013). Next generation science standards: For states, by States. The National Academies Pr…
     ↗
  42. Double Helix
  43. Parr, E. K. (2021). Undergraduate students' interpretations of expressions from calculus statements within th…
     ↗
  44. Passmore, C., Schwartz, C. V., & Mankowski, J. (2016). Developing and using models. In C. Schwarz, C. Passmor…
  45. Passmore, C., Gouvea, J. S., & Giere, R. (2014). Models in science and in learning science: Focusing scientif…
     ↗
  46. Petterson, M. N., Finkenstaedt-Quinn, S. A., Gere, A. R., & Shultz, G. V. (2022). The role of authentic conte…
     ↗
  47. Presmeg, N. (2006). Research on visualization in learning and teaching mathematics: Emergence from psychology…
     ↗
  48. Prior, P. (2006). A sociocultural theory of writing. In C. A. MacArthur, S. Graham, & J. Fitzgerald (Eds.), H…
  49. Rasmussen, C. L. (2001). New directions in differential equations: A framework for interpreting students' und…
     ↗
  50. Rowland, D. R., & Jovanoski, Z. (2004). Student interpretations of the terms in first-order ordinary differen…
     ↗
  51. Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research revie…
     ↗
  52. Schmidt-McCormack, J. A., Judge, J. A., Spahr, K., Yang, E., Pugh, R., Karlin, A., Sattar, A., Thompson, B. C…
     ↗
  53. Schukajlow, S., Kaiser, G., & Stillman, G. (2021). Modeling from a cognitive perspective: theoretical conside…
     ↗
  54. Shultz, G. V., & Gere, A. R. (2015). Writing-to-Learn the nature of science in the context of the Lewis dot s…
     ↗
  55. Stillman, G. A., & Brown, J. P. (2021). Modeling the phenomenon versus modeling the data set. Mathematical Th…
  56. Stillman, G., Brown, J., & Czocher, J. (2020). Yes, mathematicians do X so students should do X, but it's not…
     ↗
  57. Van Dyke, F., Malloy, E. J., & Stallings, V. (2015). Conceptual writing in college-level mathematics courses …
     ↗
  58. Watts, F. M., Park, G. Y, Petterson, M. N., & Shultz, G. (2022). Considering alternative reaction mechanisms:…
     ↗
  59. Watts, F. M., & Finkenstaedt-Quinn, S. A. (2021). The current state of methods for establishing reliability i…
     ↗
  60. Watts, F. M., Schmidt-McCormack, J. A., Wilhelm, C. A., Karlin, A., Sattar, A., Thompson, B. C., Gere, A. R.,…
     ↗
  61. Zbiek, R. M., & Conner, A. (2006). Beyond motivation: Exploring mathematical modeling as a context for deepen…
     ↗