Learning to calculate surface area: a focus on strategy choice

References

• Australian Curriculum Assessment and Reporting Authority. (2016). National Assessment Program – Literacy and Numeracy 2016: Technical report. Sydney: ACARA.
   Google Scholar
• Battista, M. T. (2012). Cognition-based assessment & teaching of geometric measurement: Building on students’ reasoning. Heinemann.
   Google Scholar
• Cobb, P., Jackson, K., & Dunlap, C. (2016). Design research: An analysis and critique. In L. D. English, & P. A. Kirschner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 481–503). New York, NY: Routledge.
   Google Scholar
• Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3–4), 175–190. doi:10.1080/00461520.1996.9653265
   Web of Science ®Google Scholar
• Cohen, A., Moreh, A. B., & Chayoth, R. (1999). Hands-on method for teaching the concept of the ratio between surface area and volume. The American Biology Teacher, 61(9), 691–695. doi:10.2307/4450805
   Web of Science ®Google Scholar
• Confrey, J., & Lachance, A. (2000). Transformative teaching experiments through conjecture-driven research design. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 231–265). Mahwah, NJ: L. Erlbaum.
   Google Scholar
• Corbin, J. M., & Strauss, A. L. (2015). Basics of qualitative research: Techniques and procedures for developing grounded theory (4th ed.). Thousand Oaks, CA: SAGE Publications.
   Google Scholar
• Dogruer, S. S., & Akyuz, D. (2020). Mathematical practices of eighth graders about 3D shapes in an argumentation, technology, and design-based classroom environment. International Journal of Science and Mathematics Education, 18(8), 1485–1505. doi:10.1007/s10763-019-10028-x
   Web of Science ®Google Scholar
• Ellis, S. (1997). Strategy choice in sociocultural context. Developmental Review, 17(4), 490–524. doi:10.1006/drev.1997.0444
   Web of Science ®Google Scholar
• Heinze, A., Arend, J., Gruessing, M., & Lipowsky, F. (2018). Instructional approaches to foster third graders’ adaptive use of strategies: An experimental study on the effects of two learning environments on multi-digit addition and subtraction. Instructional Science, 46(6), 869–891. doi:10.1007/s11251-018-9457-1
   Web of Science ®Google Scholar
• Heinze, A., Marschick, F., & Lipowsky, F. (2009). Addition and subtraction of three-digit numbers: Adaptive strategy use and the influence of instruction in German third grade. ZDM, 41(5), 591–604. doi:10.1007/s11858-009-0205-5
   Google Scholar
• Hiebert, J., & Wearne, D. (2003). Developing understanding through problem solving. In H. L. Schoen (Ed.), Teaching mathematics through problem solving: Grades 6–12 (pp. 3–13). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Kim, E. M., Haberstroh, J., Peters, S., Howell, H., & Oláh, L. N. (2017). A learning progression for geometrical measurement in one, two, and three dimensions (Research Report No. RR–17–55). Educational Testing Service. doi:10.1002/ets2.12189
   Google Scholar
• Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children's learning of multiplication. Journal of Experimental Psychology: General, 124(1), 83–97. doi:10.1037/0096-3445.124.1.83
   PubMed Web of Science ®Google Scholar
• Lieberman, J. (2009). Using lesson study to develop an appreciation of and competence in task design. In B. Clarke, B. Grevholm, & R. Millman (Eds.), Tasks in primary mathematics teacher education: Purpose, use and exemplars (pp. 11–24). Boston, MA: Springer.
   Google Scholar
• Lim, W., Lee, Y., & Lee, J.-E. (2019). Finding the volume and surface area in the gut. Australian Mathematics Education Journal, 1(2), 11–15.
   Google Scholar
• Lobato, J., & Walters, C. D. (2017). A taxonomy of approaches to learning trajectories. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 74–101). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Moore, K. (2018). Minecraft comes to math class. Mathematics Teaching in the Middle School, 23(6), 334–341. doi:10.5951/mathteacmiddscho.23.6.0334
   Google Scholar
• Pitta-Pantazi, D., & Christou, C. (2010). Spatial versus object visualisation: The case of mathematical understanding in three-dimensional arrays of cubes and nets. International Journal of Educational Research, 49(2–3), 102–114. doi:10.1016/j.ijer.2010.10.001
   Google Scholar
• Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educational Studies in Mathematics, 75(2), 191–212. doi:10.1007/s10649-010-9251-8
   Web of Science ®Google Scholar
• Pólya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.
   Google Scholar
• Rasmussen, C., & Stephan, M. (2008). A methodology for documenting collective activity. In A. E. Kelley, R. Lesh, & J. Y. Baek (Eds.), Handbook of design research methods in education: Innovations in science, technology, engineering, and mathematics learning and teaching (pp. 195–215). New York, NY: Routledge.
   Google Scholar
• Rasmussen, C., Yackel, E., & King, K. (2003). Social and sociomathematical norms in the mathematics classroom. In H. L. Schoen (Ed.), Teaching mathematics through problem solving: Grades 6–12 (pp. 143–154). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Saxe, G. B., de Kirby, K., Le, M., & Sitabkhan, Y. (2015). Understanding learning across lessons in classroom communities: A multi-leveled analytic approach. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 253–318). Dordrecht: Springer. doi:10.1007/978-94-017-9181-6
   Google Scholar
• Sáiz, M., & Figueras, O. (2009). A research-based workshop design for volume tasks. In B. Clarke, B. Grevholm, & R. Millman (Eds.), Tasks in primary mathematics teacher education: Purpose, use and exemplars (pp. 147–160). Boston, MA: Springer.
   Google Scholar
• Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
   Google Scholar
• Seah, R., & Horne, M. (2018). Middle school students’ reasoning about volume and surface area. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 131–138). Umeå: PME.
   Google Scholar
• Seah, R. T. K., & Horne, M. (2020). The influence of spatial reasoning on analysing about measurement situations. Mathematics Education Research Journal, 32(2), 365–386. doi:10.1007/s13394-020-00327-w
   Web of Science ®Google Scholar
• Siegler, R. S. (1991). Strategy choice and strategy discovery. Learning and Instruction, 1(1), 89–102. doi:10.1016/0959-4752(91)90020-9
   Google Scholar
• Siegler, R. S., & Lemaire, P. (1997). Older and younger adults’ strategy choices in multiplication: Testing predictions of ASCM using the choice/no-choice method. Journal of Experimental Psychology: General, 126(1), 71–92. doi:10.1037/0096-3445.126.1.71
   PubMed Web of Science ®Google Scholar
• Siegler, R. S., & Shipley, C. (1995). Variation, selection, and cognitive change. In T. Simon, & G. Halford (Eds.), Developing cognitive competence (pp. 31–76). New York, NY: Psychology Press.
   Google Scholar
• Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. doi:10.2307/749205
   Web of Science ®Google Scholar
• Star, J. R., Newton, K., Pollack, C., Kokka, K., Rittle-Johnson, B., & Durkin, K. (2015). Student, teacher, and instructional characteristics related to students’ gains in flexibility. Contemporary Educational Psychology, 41, 198–208. doi:10.1016/j.cedpsych.2015.03.001
   Web of Science ®Google Scholar
• Strutchens, M. E., Martin, W. G., & Kenney, P. A. (2003). What students know about measurement: Perspectives from the national assessments of educational progress. In D. H. Clements, & G. W. Bright (Eds.), Learning and teaching measurement: 2003 yearbook (pp. 195–207). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Tan Sisman, G., & Aksu, M. (2016). A study on sixth grade students’ misconceptions and errors in spatial measurement: Length, area, and volume. International Journal of Science and Mathematics Education, 14(7), 1293–1319. doi:10.1007/s10763-015-9642-5
   Web of Science ®Google Scholar
• Toulmin, S. (1969). The uses of arguments. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Vasilyeva, M., Ganley, C. M., Casey, B. M., Dulaney, A., Tillinger, M., & Anderson, K. (2013). How children determine the size of 3D structures: Investigating factors influencing strategy choice. Cognition and Instruction, 31(1), 29–61. doi:10.1080/07370008.2012.742086
   Web of Science ®Google Scholar
• Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24(3), 335–359. doi:10.1007/BF03174765
   Web of Science ®Google Scholar
• Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477. doi:10.2307/749877
   Web of Science ®Google Scholar