360
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Teachers’ abilities to make sense of variable parts reasoning

ORCID Icon &
Pages 254-270 | Received 08 Feb 2019, Accepted 11 Jul 2020, Published online: 17 Jul 2020

References

  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., … Tsai, Y. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Education Research Journal, 4(1), 133–180. https://doi.org/10.3102/0002831209345157
  • Beckmann, S., & Izsák, A. (2014). Variable parts: A new perspective on proportional relationships and linear functions. In C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of thirty-eighth conference of the international meeting of the Psychology of mathematics education and the thirty-sixth meeting of the north American chapter of the international group for the Psychology of mathematics education (Vol. 2, pp. 113–120). PME.
  • Beckmann, S., & Kulow, T. K. (2018). How future teachers reasoned with variable parts and strip diagrams to develop equations for proportional relationships and lines. In L. Yeping, J. W. Lewis, & J. Madden (Eds.), Mathematics matters in education: Essays in honor of Roger E. Howe (pp. 117–148). Springer.
  • Beckmann, S., & Izsák, A. (2015). Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. Journal for Research in Mathematics Education, 46(1), 17–38. https://doi.org/10.5951/jresematheduc.46.1.0017
  • Beckmann, S., Izsák, A., & Ölmez, I. B. (2015). From multiplication to proportional relationships. In X. Sun, B. Kaur, & J. Novotna (Eds.), Proceedings of the twenty-third ICMI study: Primary mathematics study on whole numbers (pp. 518–525). Macau, China: University of Macao.
  • Bédard, J., & Chi, M. T. H. (1992). Expertise. Current Directions in Psychological Science, 1(4), 135–139. https://doi.org/10.1111/1467-8721.ep10769799
  • Berk, D., Taber, S. B., Gorowara, C. C., & Poerzl, C. (2009). Developing prospective elementary teachers’ flexibility in the domain of proportional reasoning. Mathematical Thinking and Learning, 11(3), 113–135. https://doi.org/10.1080/10986060903022714
  • Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999). How people learn. National Academy Press.
  • Corbin, J., & Strauss, A. (2014). Basics of qualitative research: Techniques and procedures for developing grounded theory (4th ed.). Sage.
  • Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage.
  • diSessa, A. A. (1988). Knowledge in pieces. In G. Forman & P. Pufall (Eds.), Constructivism in the computer age (pp. 49–70). Lawrence Erlbaum Associates, Inc.
  • diSessa, A. A. (2006). A history of conceptual change research: Threads nad fault lines. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 265–282). Cambridge University Press.
  • diSessa, A. A., Sherin, B. L., & Levin, M. (2016). Knowledge analysis: An introduction. In A. A. diSessa, M. Levin, & N. J. S. Brown (Eds.), Knowledge and interaction: A synthetic agenda for the learning sciences (pp. 30–71). Routledge.
  • Franke, M. L., & Kazemi, E. (2001). Learning to teach mathematics: Focus on student thinking. Theory into Practice, 40(2), 102–109. https://doi.org/10.1207/s15430421tip4002_4
  • Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics, Physics Education Research Supplement, 68(S1), S52–S59. https://doi.org/10.1119/1.19520
  • Harel, G., & Behr, M. (1995). Teachers’ solutions for multiplicative problems. Hiroshima Journal of Mathematics Education, 3, 31–51.
  • Hill, H. C., Ball, D. L., & Schilling, S. C. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400. https://www.jstor.org/stable/i40023255
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’; mathematics knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. https://doi.org/10.3102/00028312042002371
  • Jacobson, E., Lobato, J., & Orrill, C. H. (2018). Middle school teachers’ use of mathematics to make sense of student solutions to proportional reasoning problems. International Journal of Science and Mathematics Education, 16(8), 1541–1559. https://doi.org/10.1007/s10763-017-9845-z
  • Karplus, R., Pulos, S., & Stage, E. (1983). Adolescents’ proportional reasoning on ‘rate’ problems. Educational Studies in Mathematics, 14(3), 219–233. https://doi.org/10.1007/BF00410539
  • Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 629–667). Information Age Publishing.
  • Lobato, J., & Ellis, A. B. (2010). Developing essential understanding of ratios, proportions, and proportional reasoning for teaching mathematics: Grades 6–8. National Council of Teachers of Mathematics.
  • Maxwell, J. A. (2012). Qualitative research design: An interactive approach (3rd ed.). Sage.
  • Mitchelmore, M., White, P., & McMaster, H. (2007). Teaching ratio and rates for abstraction. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Proceedings of the 30th annual conference of the Mathematics education research group of Australasia (pp. 503–512). MERGA.
  • Ölmez, İ. B. (2016). Two distinct perspectives on ratios: Additive and multiplicative relationships between quantities. Elementary Education Online, 15(1), 186–203. http://ilkogretim-online.org.tr/index.php/io/article/view/1223
  • Noelting, G. (1980a). The development of proportional reasoning and the ratio concept Part I - Differentiation of stages. Educational Studies in Mathematics, 11(2), 217–253.
  • Noelting, G. (1980b). The development of proportional reasoning and the ratio concept Part II- Problem-structure at successive stages: Problem-solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11(3), 331–363.
  • Orrill, C. H., & Brown, R. E. (2012). Making sense of double number lines in professional development: Exploring teachers’ understandings of proportional relationships. Journal of Mathematics Teacher Education, 15(5), 381–403. https://doi.org/10.1007/s10857-012-9218-z
  • Orrill, C. H., Izsák, A., Cohen, A., Templin, J., & Lobato, J. (2010). Preliminary observations of teachers’ multiplicative reasoning: Insights from does it work and diagnosing teachers’ multiplicative reasoning projects (Technical Report #6). Kaput Center for Research and Innovation in STEM Education, University of Massachusetts Dartmouth.
  • Pitta-Pantazi, D., & Constantino, C. (2011). The structure of prospective kindergarten teachers’ proportional reasoning. Journal of Mathematics Teacher Education, 14(2), 149–169. https://doi.org/10.1007/s10857-011-9175-y
  • Riley, K. J. (2010). Teachers’ understanding of proportional reasoning. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd annual meeting of the North American chapter of the international group for the Psychology of Mathematics education (pp. 1055–1061). The Ohio State University.
  • Son, J.-W., Kim, H.-J., & Jo, S. (2018, April). Exploring learning opportunities in Korean textbooks for developing proportional reasoning. Roundtable presented at the Annual Meeting of the American Educational Research Association, New York.
  • Thompson, P. W., & Thompson, A. G. (1994). Talking about rates conceptually, Part I: A teacher’s struggle. Journal for Research in Mathematics Education, 25(3), 279–303. https://doi.org/10.2307/749339
  • Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16(2), 181–204.
  • Van Dooren, W., De Bock, D., Janssens, D., & Verschaffel, L. (2008). The linear imperative: An inventory and conceptual analysis of students’ overuse of linearity. Journal for Research in Mathematics Education, 39(3), 311–342. https://doi.org/10.2307/30034972
  • Weiland, T., Orrill, C. H., Nagar, G. G., Brown, R. E., & Burke, J. (2020). Framing a robust understanding of proportional reasoning for teachers. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-019-09453-0

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.