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Original Articles

Examining aspects of elementary grades pre-service teachers’ mathematical reasoning

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References

  • Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433–456). Washington, DC: American Educational Research Association.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. doi:10.1177/0022487108324554
  • Batanero, C., Navarro-Pelayo, V., & Godino, J. D. (1997). Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils. Educational Studies in Mathematics, 32(2), 181–199. doi:10.1023/A:1002954428327
  • Bergqvist, T., Lithner, J., & Sumpter, L. (2008). Upper secondary students’ task reasoning. International Journal of Mathematical Education in Science and Technology, 39(1), 1–12. doi:10.1080/00207390701464675
  • Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999). How people learn: Brain, mind, experience, and school. Washington, D.C.: National Academy Press.
  • Council of Chief State School Officers. (2010). Common Core State Standards Initiative. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  • Creswell, J. W., Klassen, A. C., Plano Clark, V. L., & Smith, K. C. (2011). Best practices for mixed methods research in the health sciences. Bethesda, MD: National Institutes of Health.
  • Eizenberg, M. M., & Zaslavsky, O. (2004). Students’ verification strategies for combinatorial problems. Mathematical Thinking and Learning, 6(1), 15–36. doi:10.1207/s15327833mtl0601_2
  • English, L. D. (1991). Young children’s combinatorics strategies. Educational Studies in Mathematics, 22(5), 451–474. doi:10.1007/BF00367908
  • English, L. D. (1993). Children’s strategies for solving two- and three-dimensional combinatorial problems. Journal for Research in Mathematics Education, 24(3), 255–273. doi:10.2307/749347
  • Fischbein, E., & Gazit, A. (1988). Combinatorial problem solving capacity of children. ZDM: International Reviews on Mathematics Education, 5, 391–391.
  • Goldin, G. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517–545). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Hadar, N., & Hadass, R. (1981). The road to solve combinatorial problems is strewn with pitfalls. Educational Studies in Mathematics, 12, 435–443. doi:10.1007/BF00308141
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. doi:10.3102/00028312042002371
  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up. Mathematics Learning Study Committee, Center for Education, Washington, DC: National Academy Press.
  • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 29–63. doi:10.3102/00028312027001029
  • Lannin, J. K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231–258. doi:10.1207/s15327833mtl0703_3
  • Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 763–804). Charlotte, NC: Information Age Publishing.
  • Lithner, J. (2000). Mathematical reasoning in school tasks. Educational Studies in Mathematics, 41(2), 165–190. doi:10.1023/A:1003956417456
  • Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52(1), 29–55. doi:10.1023/A:1023683716659
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Maher, C. A., & Martino, A. M. (1996). The development of the idea of mathematical proof: A 5-year case study. Journal for Research in Mathematics Education, 27, 194–214. doi:10.2307/749600
  • Maher, C. A., Powell, A. B., & Uptegrove, E. B. (Eds.). (2010). Combinatorics and reasoning: Representing, justifying and building isomorphisms (Vol. 47). New York, NY: Springer Science & Business Media.
  • Maher, C. A., Sran, M. K., & Yankelewitz, D. (2010). Towers: Schemes, strategies, and arguments. In C. A. Maher, A. B. Powell, & E. B. Uptegrove (Eds.), Combinatorics and Reasoning (pp. 27–43). New York, NY: Springer Science & Business Media.
  • Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. The Journal of Mathematical Behavior, 18(1), 53–78. doi:10.1016/S0732-3123(99)00017-6
  • Mason, J. (1996). Expressing generality and roots of algebra. In L. Lee (Ed.), Approaches to algebra: Perspectives for research and teaching (pp. 65–86). Dordrecht, The Netherlands: Kluwer Academic.
  • National Council of Teachers of Mathematics. (2014). Principles to action. Reston, VA: NCTM.
  • Palm, T., Boesen, J., & Lithner, J. (2006). The requirements of mathematical reasoning in upper secondary level assessments. Research Reports in Mathematics Education, 5, 1–24.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York, NY: Macmillan.
  • Seaman, C. E., & Szydlik, J. E. (2007). Mathematical sophistication among pre-service elementary teachers. Journal of Mathematics Teacher Education, 10(3), 167–182. doi:10.1007/s10857-007-9033-0
  • Stylianides, A. J., & Ball, D. L. (2008). Understanding and describing mathematical knowledge for teaching: Knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11(4), 307–332. doi:10.1007/s10857-008-9077-9
  • Teddlie, C., & Tashakkori, A. (2009). Foundations of mixed methods research: Integrating quantitative and qualitative approaches in the social and behavioral sciences. Los Angeles, CA: Sage Publications.
  • Verschaffel, L., Greer, B., & de Corte, E. (2000). Making sense of word problems. Educational Studies in Mathematics, 42(2), 211–213. doi:10.1023/A:1004190927303

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