“Is It Valid or Not?”: Pre-Service Teachers Judge the Validity of Mathematical Statements and Student Arguments

Zulfiye Zeybek Simsek 1 *
More Detail
1 Department of Mathematics and Science Education, Tokat Gaziosmanpasa University, Tokat, TURKEY
* Corresponding Author
EUR J SCI MATH ED, Volume 9, Issue 2, pp. 26-42. https://doi.org/10.30935/scimath/10772
OPEN ACCESS   1605 Views   830 Downloads
Download Full Text (PDF)

ABSTRACT

There is a wide recognition that reasoning abstractly, constructing arguments, or critiquing arguments should be an important educational goal in the mathematical experiences of all students in the standards for school mathematics. Seeing these standards as an essential element for developing deep mathematical understanding; however, call for a strong knowledge of proof for teachers. Thus, the purpose of this study is to investigate how pre-service middle school teachers (PSMTs) decide whether a presented mathematical statement is true or false and how they verify student arguments presented for these statements. 50 PSMTs participated in the study. Individual interviews were conducted with 7 PSMTs to further delve into the verification processes of the PSMTs. The results of the study demonstrated that meeting the expectations of the current standards is not an easy feat by documenting that most of the PSMTs struggled with evaluating mathematical tasks and constructing arguments.
Keywords: counterexamples, empirical arguments, geometry, verifications

CITATION

Zeybek Simsek, Z. (2021). “Is It Valid or Not?”: Pre-Service Teachers Judge the Validity of Mathematical Statements and Student Arguments. European Journal of Science and Mathematics Education, 9(2), 26-42. https://doi.org/10.30935/scimath/10772

REFERENCES

  • Alcock, L. (2004). Uses of example objects in proving. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol.2, pp. 17-24). Bergen, Norway.
  • Ball, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2002). The teaching of proof. In L. I. Tatsien (Ed.), Proceedings of the International Congress of Mathematicians (Vol. III, pp. 907-920). Beijing: Higher Education Press.
  • Brown, S. A. (2014). On skepticism and its role in the development of proof in the classroom. Educational Studies in Mathematics, 86(3), 311-335. https://doi-org.proxyiub.uits.iu.edu/10.1007/s10649-014-9544-4
  • Buchbinder, O., & McCrone, S. (2020), Preservice teachers learning to teach proof through classroom implementation: Successes and challenges. The Journal of Mathematical Behavior, 58,100779. https://doi.org/10.1016/j.jmathb.2020.100779
  • Buchbinder, O., & Zaslavsky, O. (2019). Students’ understanding of the role of examples in proving: strengths and inconsistencies. Journal of Mathematical Behavior, 53, 129-147. https://doi.org/10.1016/j.jmathb.2018.06.010
  • Cañadas, M. C., Deulofeu, J., Figueiras, L., Reid, D., & Yevdokimov, O. (2007). The conjecturing process: perspectives in theory and implications in practice. Journal of Teaching and Learning, 5(1), 55-72. https://doi.org/10.22329/jtl.v5i1.82
  • Cirillo, M., Kosko, K. W., Newton, J., Staples, M., & Weber, K. (2015). Conceptions and consequences of what we call argumentation, justification, and proof. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the thirty-seventh annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Critical responses to enduring challenges in mathematics education (pp. 1343-1351). East Lansing: Michigan State University.
  • Czocher, J. A., & Weber, K. (2020). Proof as a cluster category. Journal for Research in Mathematics Education, 51(1), 50-74. https://doi.org/10.5951/jresematheduc.2019.0007
  • Dawkins, P. C., & Weber, K. (2017). Values and norms of proof for mathematicians and students. Educational Studies in Mathematics, 95(2), 123-142. https://doi.org/10.1007/s10649-016-9740-5
  • Ellis, A. B., Bieda, K., & Knuth, E. (2012). Developing essential understanding of proof and proving for teaching mathematics in grades 9-12. Reston, VA: National Council of Teachers of Mathematics.
  • Glaser, B. G., & Strauss, A. L. (1967). Discovery of grounded theory. Mill Valley, Ca.: Sociology Press.
  • Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics (pp. 805-842). Reston, VA: National Council of Teachers of Mathematics.
  • Kinzel, M. T., & Cavey, L. O. (2017). The role of examples in teaching. The Mathematics Teacher, 111(2), 140-143. https://doi.org/10.5951/mathteacher.111.2.0140
  • Lannin, J. K., Ellis, A. B., & Elliott, R. (2011). Developing essential understanding of mathematical reasoning for teaching mathematics in prekindergarten-grade 8. National Council of Teachers of Mathematics.
  • Lesseig, K. (2016). Investigating mathematical knowledge for teaching proof in professional development. International Journal of Research in Education and Science, 2(2), 253-270. https://doi.org/10.21890/ijres.13913
  • Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169-186. https://doi.org/10.1007/s10649-017-9773-4
  • MEB (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics lesson curriculum (primary and secondary school 1st, 2nd, 3rd, 4th, 5th, 6th, 7th and 8th grades)]. https://ttkb.meb.gov.tr/
  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics.
  • National Governors Association Center for Best Practices, & Council of Chief State School Officers (NGA & CCSSO) (2010). Common core state standards mathematics.
  • Riley, K. J. (2003). An investigation of prospective secondary mathematics teachers’ conceptions of proof and refutations (Unpublished doctoral dissertation), Montana State University, Bozeman.
  • Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading and Writing Quarterly, 23(2), 139-159. https://doi.org/10.1080/10573560601158461
  • Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38, 289-321. https://doi.org/10.2307/30034869
  • Stylianides, A. J., & Stlyianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72, 237-253. https://doi.org/10.1007/s10649-009-9191-3
  • Stylianides, A., Bieda, K., & Morselli, F. (2016). Proof and argumentation in mathematics education research. In A. Gutierez, G. Leder, & P. Boero (Eds.), 2nd handbook on the psychology of mathematics education (pp. 315-351). Sense Publishers. https://doi.org/10.1007/978-94-6300-561-6_9
  • Stylianides, G. (2008). An analytic framework of reasoning-and-proving. For the Learning of Mathematics, 28(1), 9-16. http://www.jstor.org/stable/40248592
  • Stylianides, G. J., & Stylianides, A. J. (2017). Research-based interventions in the area of proof: The past, the present, and the future. Educational Studies in Mathematics, 96(2), 119-127. https://doi.org/10.1007/s10649-017-9782-3
  • Stylianides, G. J., Stylianides, A. J., & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. In J. Cai (Ed.). Compendium for research in mathematics education (pp. 237-266). National Council of Teachers of Mathematics.
  • Weiss, M., & Herbst, P. (2015). The role of theory building in the teaching of secondary geometry. Educational Studies in Mathematics, 89(2), 205-229. https://doi.org/10.1007/s10649-015-9599-x
  • Zaslavsky, O., & Peled, I. (1996). Inhibiting factors in generating examples by mathematics teachers and student teachers: The case of binary operation. Journal for Research in Mathematics Education, 27(1), 67-78. https://doi.org/10.2307/749198
  • Zazkis, R., Liljedahl, P., & Chernoff, E. J. (2008). The role of examples in forming and refuting generalizations. ZDM - The International Journal on Mathematics Education, 40, 131-141. https://doi.org/10.1007/s11858-007-0065-9
  • Zeybek Simsek, Z. (2020). Constructing-evaluating-refining mathematical conjectures and proofs. International Journal for Mathematics Teaching and Learning, 21(2), 197-215.
  • Zeybek, Z. (2017). Pre-service elementary teachers’ conceptions of counterexamples. International Journal of Education in Mathematics, Science and Technology, 5(4), 295-316. https://doi.org/10.18404/ijemst.70986