Reconstructing the unit on the number line: Tasks to extend fourth graders’ fraction understandings

References

• Barnett-Clarke, C., Fisher, W., Marks, R., & Ross, S. (2010). Developing essential understanding of rational number: Grades 3-5. Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Behr, M., Lesh, R., Post, T., & Silver, E. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91–125). New York, NY: Academic Press.
   Google Scholar
• Behr, M., & Post, T. (1992). Teaching rational number and decimal concepts. In T. Post (Ed.), Teaching mathematics in grades K-8: Research-based methods (2nd ed., pp. 201–248). Boston, MA: Allyn & Bacon.
   Google Scholar
• Bright, G., Behr, M., Post, T., & Wachsmuth, I. (1988). Identifying fractions on number lines. Journal for Research in Mathematics Education, 19, 215–232. doi:10.2307/749066
   Google Scholar
• Confrey, J., & Lachance, A. (2000). Transformative teaching experiments through conjecture-driven research design. In A. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 231–265). Mahwah, NJ: Lawrence Erlbaum Associates.
   Google Scholar
• Cramer, K., Ahrendt, S., Monson, D., Wyberg, T., & Miller, C. (2016). Making sense of third grade students’ misunderstandings of the number line. Investigations in Mathematics Learning. Retrieved from (www.tandfonline.com/doi/full/10.1080/19477503.2016.1245035?scroll=top&needAccess=true)
   Google Scholar
• Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., Jordan, N. C., Siegler, R., Gersten, R., & Changas, P. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology, 105(3), 683–700. doi:10.1037/a0032446
   Google Scholar
• Gearhart, M., & Saxe, G. (2014). Differentiated instruction in shared mathematical contexts. Teaching Children Mathematics, 20(7), 426–435. doi:10.5951/teacchilmath.20.7.0426
   Google Scholar
• Hamdan, N., & Gunderson, E. A. (2017). The number line is a critical spatial-numerical representation: Evidence from a fraction intervention. Developmental Psychology, 53(3), 587–596. doi:10.1037/dev0000252
   Google Scholar
• National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
   Google Scholar
• National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%Standards.pdf
   Google Scholar
• National Mathematics Advisory Panel (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
   Google Scholar
• Ni, Y. (2000). How valid is it to use number lines to measure children’s conceptual knowledge about rational number? Educational Psychology, 20(2), 139–152. doi:10.1080/713663716
   Google Scholar
• Norton, A. H., & McCloskey, A. V. (2008). Modeling students’ mathematics using Steffe’s fraction schemes. Teaching Children Mathematics, 15(1), 48–54.
   Google Scholar
• Pearn, C., & Stephens, M. (2007). Whole number knowledge and number lines to develop fraction concepts. In J. Watson & K. Beswick (Eds.), Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Austrailia (pp. 601–610). MERGA Inc.
   Google Scholar
• Saxe, G., Shaughnessy, M., Gearhart, M., & Haldar, L. C. (2013). Coordinating numeric and linear units: Elementary students’ strategies for locating whole numbers on the number line. Mathematical Thinking and Learning, 15(4), 235–268. doi:10.1080/10986065.2013.812510
   Google Scholar
• Saxe, G., Shaughnessy, M. M., Shannon, A., Garcia De Osuna, J., Chinn, R., & Gearhart, M. (2007). Learning about fractions as points on a number line. In W. G. Martin, M. E. Strutchens, & P. C. Elliott (Eds.), The learning of mathematics: 69th yearbook (pp. 221–238). Reston, VA: NCTM.
   Google Scholar
• Saxe, G. B., Diakow, R., & Gearhart, M. (2013). Towards curricular coherence in integers and fractions: A study of the efficacy of a lesson sequence that uses the number line as the principal representational context. ZDM, 45(3), 343–364. doi:10.1007/s11858-012-0466-2
   Google Scholar
• Shaughnessy, M. M. (2011). Identify fractions and decimals on a number line. Teaching Children Mathematics, 17(7), 428–434.
   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
   Google Scholar
• Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267–306). Mahwah, NJ: Erlbaum.
   Google Scholar
• Tunç-Pekkan, Z. (2015). An analysis of elementary school children’s fractional knowledge depicted with circle, rectangle, and number line representations. Educational Studies in Mathematics, 89, 419–441. doi:10.1007/s10649-015-9606-2
   Google Scholar