The Implications of a Pacing Guide on the Development of Students Ability to Prove in Geometry

Ruthmae Sears

doi:10.12973/iejme/3835

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Ruthmae Sears ¹ ^*

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¹ University of South Florida, USA^* Corresponding Author

Abstract

This study examined the influence of a departmental decision to use the same pacing guide on the planning and enactment of proof tasks of the district-adopted textbook (Prentice Hall Geometry). Quantitative data were collected from a textbook analysis and the tasks students were assigned, and the qualitative data were collected from classroom observations, teachers’ artifacts and interviews. The results indicate that teachers adhere to their departmental pacing guide by assigning the same tasks, however, there existed variation in the enacted lessons. Additionally, the results suggest the proof tasks assigned in the pacing guide generally required little cognitive rigor. This study has implication on the development of students’ proof skills.

Keywords

geometry
proof
textbook
planning guide

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 13, Issue 3, October 2018, 171-183

https://doi.org/10.12973/iejme/3835

Publication date: 25 Aug 2018

Article Views: 3264

Article Downloads: 2901

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References

Alibert, D., & Thomas, M. (1991). Research on mathematical proof Advanced mathematical thinking (pp. 215-230): Springer.
Bass, L. E., Charles, R. I., Johnson, A., & Kennedy, D. (2004). Prentice hall mathematics geometry. Upper Saddle River, NJ: Pearson Education, Inc.
Blanton, M. L., & Stylianou, D. A. (2009). Interpreting a community of practice perspective in discipline-specific professional development in higher education. Innovative Higher Education, 34(2), 79-92. https://doi.org/10.1007/s10755-008-9094-8
Brown, J., & Stillman, G. (2009). Preservice secondary teachers’ competencies in proof. in Mathematics Education, 94.
Brown, T., & McNamara, O. (2011). Theorising teacher identity becoming a mathematics teacher (pp. 87-109): Springer. https://doi.org/10.1007/978-94-007-0554-8
Cobb, P., McClain, K., de Silva Lamberg, T., & Dean, C. (2003). Situating teachers’ instructional practices in the institutional setting of the school and district. Educational Researcher, 32(6), 13-24. https://doi.org/10.3102/0013189X032006013
Davies, B. (1991). The concept of agency. Social Analysis, 30, 42-53
Donoghue, E. F. (2003). Algebra and geometry textbooks in twentieth-century America. A history of school mathematics, 329-398.
Franke, M. L., & Kazemi, E. (2001). Teaching as learning within a community of practice: Characterizing generative growth. Beyond classic pedagogy: Teaching elementary school mathematics, 47-74.
Furinghetti, F., & Morselli, F. (2011). Beliefs and beyond: Hows and whys in the teaching of proof. ZDM, 43(4), 587-599. https://doi.org/10.1007/s11858-011-0316-7
Fussell, K. (2005). The educational purposes of geometric proof in the high school curriculum (Master’s Degree Thesis), North Carolina State University, Raleigh, North Carolina.
Glaser, B. G., & Strauss, A. L. (2009). The discovery of grounded theory: Strategies for qualitative research: Transaction Books.
Grouws, D. A., & Smith, M. S. (2000). NAEP findings on the preparation and practices of mathematics teachers. Results from the seventh mathematics assessment of the National Assessment of Educational Progress, 107-139.
Grouws, D. A., Smith, M. S., & Sztajn, P. (2004). The preparation and teaching practices of United States mathematics teachers: Grades 4 and 8 (pp. 221-269). Reston, VA: National Council of Teachers of Mathematics.
Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428. https://doi.org/10.2307/749651
Heinze, A., & Reiss, K. (2009). Developing argumentation and proof competencies in mathematics classroom In D. A. Stylianou, M. L. Blanton & E. J. Knuth (Eds.), Teaching and learning proof across the grades. New York Routledge.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549. https://doi.org/10.2307/749690
Herbst, P. G. (2002). Establishing a custom of proving in American school geometry: Evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics, 49(3), 283-312. https://doi.org/10.1023/A:1020264906740
Herbst, P. G., Chen, C., Weiss, M., Gonzalez, G., Nachlieli, T., Hamlin, M., & Brach, C. (2009). “Doing proofs” in geometry classrooms. In D. A. Stylianou, M. L. Blanton & E. J. Knuth (Eds.), Teaching and learning proof across the grades (pp. 250-268). New York Routledge.
Jones, K. (2000). Critical issues in the design of the school geometry curriculum. In B. Barton (Ed.), Readings in mathematics education (pp. 75-90). Auckland, New Zealand: University of Auckland.
Jones, K. (2002). Issues in the teaching and learning of geometry. In L. Haggarty (Ed.), Aspects of teaching secondary mathematics: Perspectives on practice. (pp. 121-139). London, UK: Routledge Falmer. https://doi.org/10.1002/tl.62
Knuth, E. J. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405. https://doi.org/10.2307/4149959
Knuth, E. J., Choppin, J., & Bieda, K. (2009). Middle school students’ production of mathematical justifications. In D. A. Stylianou, M. L. Blanton & E. J. Knuth (Eds.), Teaching and learning proof across the grades. New York: Routledge.
Lloyd, G., Remillard, J. T., & Herbel-Eisenmann, B. (2009). Teachers’ use of curriculum materials: An emerging field. In J. T. Remillard, B. A. Herbel-Eisenmann & G. M. Lloyd (Eds.), Mathematics teachers at work (pp. 3-14). New York: Routledge.
Martin, T. S., McCrone, S. M. S., Bower, M. L. W., & Dindyal, J. (2005). The interplay of teacher and student actions in the teaching and learning of geometric proof. Educational Studies in Mathematics, 60(1), 95-124. https://doi.org/10.1007/s10649-005-6698-0
Philipp, R. A. (2007). Mathematics teachers. Beliefs and A ect‚Äô. In: FK Lester, Jr.(ed.): Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Publishing, 257-315.
Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211-211. https://doi.org/10.3102/00346543075002211
Remillard, J. T. (2009). Part ii commentary: Considering what we know about the relationship between teachers and curriculum materials (pp. 85-92). New York: Routledge.
Schwarz, B. R., & Kaiser, G. (2009). Professional competence of future mathematics teachers on argumentation and proof and how to evaluate it. Mathematics Education, 190.
Sears, R., & Chávez, Ó. (2014). Opportunities to engage with proof: The nature of proof tasks in two geometry textbooks and its influence on enacted lessons. ZDM, 46(5), 767-780.
Spillane, J. P. (2000). A fifth-grade teacher’s reconstruction of mathematics and literacy teaching: Exploring interactions among identity, learning, and subject matter. The Elementary School Journal, 307-330. https://doi.org/10.1086/499644
Stein, M. K., Remillard, J. T., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. J. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 319-369). Charlotte, NC: Information Age Publishing
Stylianides, G. J. (2008). Investigating the guidance offered to teachers in curriculum materials: The case of proof in mathematics. International Journal of Science and Mathematics Education, 6(1), 191-215. https://doi.org/10.1007/s10763-007-9074-y
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477. https://doi.org/10.2307/749877

How to cite this article

APA

Sears, R. (2018). The Implications of a Pacing Guide on the Development of Students Ability to Prove in Geometry. International Electronic Journal of Mathematics Education, 13(3), 171-183. https://doi.org/10.12973/iejme/3835

Vancouver

Sears R. The Implications of a Pacing Guide on the Development of Students Ability to Prove in Geometry. INT ELECT J MATH ED. 2018;13(3):171-83. https://doi.org/10.12973/iejme/3835

AMA

Sears R. The Implications of a Pacing Guide on the Development of Students Ability to Prove in Geometry. INT ELECT J MATH ED. 2018;13(3), 171-183. https://doi.org/10.12973/iejme/3835

Chicago

Sears, Ruthmae. "The Implications of a Pacing Guide on the Development of Students Ability to Prove in Geometry". International Electronic Journal of Mathematics Education 2018 13 no. 3 (2018): 171-183. https://doi.org/10.12973/iejme/3835

Harvard

Sears, R. (2018). The Implications of a Pacing Guide on the Development of Students Ability to Prove in Geometry. International Electronic Journal of Mathematics Education, 13(3), pp. 171-183. https://doi.org/10.12973/iejme/3835

MLA

Sears, Ruthmae "The Implications of a Pacing Guide on the Development of Students Ability to Prove in Geometry". International Electronic Journal of Mathematics Education, vol. 13, no. 3, 2018, pp. 171-183. https://doi.org/10.12973/iejme/3835