# A study of geometry content knowledge of elementary preservice teachers

## Main Article Content

## Abstract

The purpose of this research is to examine preservice elementary school teachers’ geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as a beginning teacher. The thematic analysis findings yield to three themes: history of learning geometry, perceptions about geometry, effective geometry instructional practices. The findings informed the quantitative investigation on geometry content knowledge for the case of quadrilaterals. During the second phase of the study, 102 participants who enrolled in the methods course completed pre and post test of teachers’ geometry content knowledge. Treatment group participants (n=54) received series of activities (geometry activities and student work analysis) focusing on quadrilaterals, and control group participants (n=48) received traditional instruction. Repeated measures ANOVA results showed a significant change in treatment group participants’ geometry content knowledge. The mixed ANOVA results indicated a significant main effect of knowledge but no significant interaction between geometry content knowledge and grouping. Even though treatment group participants’ geometry content knowledge growth was significant, the difference between treatment group and control group participants’ growth in geometry content knowledge was not significant. This study informs mathematics teacher education in three important areas; limited knowledge of preservice teachers’ geometry content knowledge, integrating mathematics content and the context of teaching into methods course, and use of student work with preservice teachers.

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## Article Details

**International Electronic Journal of Elementary Education**, [S.l.], v. 7, n. 3, p. 301-318, aug. 2017. ISSN 1307-9298. Available at: <https://www.iejee.com/index.php/IEJEE/article/view/82>. Date accessed: 21 july 2019.

## References

Ball, D. L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40-48.

Ball, D. L. (1990a). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466.

Ball, D. L. (1990b). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.

Ball, D. L. (2000). Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51(3), 241.

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.

Barrantes, M., Blanco, L. J. (2006). A study of prospective primary teachers’ conceptions of teaching and learning school geometry. Journal of Mathematics Teacher Education, 9, 411-436.

Brown, C. A., & Borko, H. (1992). Becoming a mathematics teacher. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 209–239). New York: Macmillan.

Browing, C., Edson, A.J., Kimani, P., Aslan-Tutak, F. (2014) Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Geometry and Measurement. The Mathematics Enthusiast, 11(2), 333–384

Bruner, J. (1990). Acts of Meaning. Cambridge, MA: Harvard University Press.

Carpenter, T. P., Fennema,E., Peterson, P. L. & Carey, D. A. (1988). Teachers’ Pedagogical Content Knowledge of Students’ Problem Solving in Elementary Arithmetic. Journal for Research in Mathematics Education, 19(5), 385-401.

Carrillo, J., Climent, N, Contreras, L.C. & Muñoz-Catalán, M.C. (2013). Determining specialised knowledge for Mathematics teaching. Proceedings of Eighth Congress of European Research in Mathematics Education (CERME 8), Retrieved from http://cerme8.metu.edu.tr/wgpapers/WG17/Wg17_Climent.pdf

Carter, K. (1993). The place of story in the study of teaching and teacher education. Educational Researcher, 22(1), 5-12.

Chinnappan, M., Nason, R., Lawson, M. (1996). Perservice teachers’ pedagogical and content knowledge about trigonometry and geometry: An initial investigation. In P.C. Clarkson (Ed.), Proceedings of the 19th Annual Conference of the Mathematics Education Research Group of Australasia. Melbourne MERGA.

Clandinin, D.J. and Connelly, F.M. (1996). Teachers’ professional knowledge landscapes: Teacher stories – stories of teachers – school stories – stories of schools, Educational Researcher, 25(3), 24–30.

Coffey, A., & Atkinson, P. (1996). Making sense of qualitative data: Complementary

strategies. Thousand Oaks, CA: Sage.

Cortazzi, M. (1993). Narrative Analysis. London: Falmer.

Doyle W. & Carter K. (2003). Narrative and learning to teach: Implications for teacher education curriculum, Journal of Curriculum Studies, 35(2), 129-137.

Driscoll, M., Egan, M., Dimatteo, R. W. & Nikula, J. (2009). Fostering geometric thinking in the middle grades: Professional development for teachers in grades 5-10. In T. V. Craine & R. Rubenstein (Eds) Understanding geometry for a changing world: Seventy-first yearbook (pp. 155-171). Reston, VA: National Council of Teachers of Mathematics.

Elbaz, F. (1991), Research on teachers’ knowledge: The evolution of a discourse, Journal of Curriculum Studies, 23(1), 1–19.

Franke, M.L., & Kazemi, E. (2001). Learning to teach mathematics: Developing a focus on students’ mathematical thinking. Theory into Practice, 40, 102-109.

Grbich, C. (2007). Qualitative data analysis: An introduction. Thousand Oaks: SAGE.

Hatch, J., A. (2002). Doing qualitative research in education settings. Albany : State University of New York Press.

Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers' mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30.

Hill, H.C., Sleep, L., Lewis, J. M., Ball, D. L. (2008). Assessing teachers' mathematical knowledge: What knowledge matters and what evidence counts? In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 111-155). Charlotte, NC: Information Age Publishing.

Jacobson, C. & Lehrer, R. (2000). Teacher appropriation and student learning of geometry through design. Journal for Research in Mathematics Education, 31(1), 71-88.

Jones, K. (2000). Teacher Knowledge and professional development in geometry. Proceedings of the British Society for Research into Learning Mathematics, 20(3), 109-114.

Kazemi, E., & Franke, M.L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7, 203-235.

Lampert, M. (1988). Teachers’ Thinking about Students' Thinking about Geometry: The Effects of New Teaching Tools. Technical Report, Washington, DC: Office of Educational Research and Improvement.

Labov, W. (1972). Language in the inner city. Philadelphia: University of Pennsylvania Press.

Labov, W. (1982). Speech actions and reactions in personal narratives. In D. Tannen (Ed.), Analyzing discourse: Text and talk (pp. 219-247). Washington, DC: Georgetown University Press.

Lampert, M. & Ball, D. L. (1998). Teaching, multimedia, and mathematics. New York: Teachers College Press.

Leikin, R., Berman, A., Zaslavsky, O. (2000). Learning through teaching: The case of symmetry. Mathematics Education Research Journal, 12(1), 18-36.

Leinhardt, G., & Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge. Journal of Educational Psychology, 77(3), 247-271.

Little, J. W. (2004). “Looking at student work” in the United States: Countervailing impulses in professional development. In C. Day & J. Sachs (Eds.), International handbook on the continuing professional development of teachers. Buckingham, UK: Open University.

Lloyd, G. M. (2005). Beliefs about the teacher’s role in the mathematics classroom: One student teacher’s explorations in fiction and in practice. Journal of Mathematics Teacher Education, 8(6), 441-467.

Lloyd, G. M. (2006). Preservice teachers' stories of mathematics classrooms: Explorations of practice through fictional accounts. Educational Studies in Mathematics, 63(1), 57-87.

McAdams, D.P. (1993). The stories we live by: Personal myths and making of the self. New York: Morrow. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States: Lawrence Erlbaum Associates.

McGuire, P. (2013). Using online error analysis items to support preservice teachers’ pedagogical content knowledge in mathematics. Contemporary Issues in Technology and Teacher Education, 13(3), 207-218.

National Council of Teachers of Mathematics. (2006). Learning from NAEP: Professional Development Materials for Teachers of Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Owens, J. E. (1987). A study of four preservice secondary mathematics teachers' constructs of mathematics and mathematics teaching. Unpublished doctoral dissertation, University of Georgia, Athens, GA.

Post, T., Harel, G., Behr, M. & Lesh, R. (1988). Intermediate teachers' knowledge of rational number concepts. In E. Fennema, T. Carpenter & S. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 194-219). Madison, WI: Wisconsin Center for Education Research, University of Wisconsin.

Riessman, C. K. (1993). Narrative analysis. Newburk Park, CA: Sage.

Riessman, C. (2000). Analysis of personal narratives. In J. Gubrium & J. Holstein (Eds.), Handbook of interviewing (pp. 1-27). Newbury Park, CA: Sage

Robichaux, C. M. (2002). The practice of expert critical care nurse in situations of prognostic conflict at the end of life. Unpublished dissertation: University of Texas at Austin.

Sarac, A. (2012). The relation of teacher efficacy to students’ trigonometry self efficacy

and trigonometry achievement. Unpublished master thesis, Bogazici University, Turkey

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.

Smith, M.S. (2003). Practiced-based professional development for teachers of mathematics. Reston: NCTM.

Steinberg, R., Haymore, J., & Marks, R. (1985, April). Teachers' knowledge and content structuring in mathematics. Paper presented at the annual meeting of the American Educational Research Association, Chicago.

Swafford, J. O., Jones, G. A., Thornton, C. A. (1997). Increased knowledge in geometry and instructional practice. Journal for Research in Mathematics Education, 28(4), 467-483.

Tatto, M., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher education and development study in mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. Amsterdam: IEA.

Van de Walle, J. A. (2007). Elementary and middle school mathematics (6th ed.). Longman: New York.