An Investıgatıon of Pre-Servıce Elementary School Teachers’ Knowledge Concernıng Quadrilaterals

Yıl 2014, Cilt: 43 Sayı: 2, 137 - 154, 02.09.2014

Berna Cantürk Günhan

https://doi.org/10.14812/cufej.2014.017

Cited By: 2

Öz

The purpose of this study was to examine pre-service teachers’ subject matter knowledge (SMK) and pedagogical content knowledge (PCK) about quadrilaterals. The research was a case study. Within the scope of the research, five open-ended questions concerning quadrilaterals were asked to pre-service teachers, who are at five different geometrical thinking levels. According to the research, it was determined that of the pre-service teachers, the SMK of those whose geometrical thinking levels were low was poor and they confused the relationships among quadrilaterals. In the light of the research, it was suggested that emphasis be placed on making the pre-service teachers acquire the SMK and PCK while they were being trained and the atmosphere where they can share these knowledge be created.

Anahtar Kelimeler

Pedagogical content knowledge, Subject matter knowledge, Pre-service teachers, Quadrilateral

Kaynakça

• Altunışık, R., Coşkun, R., Bayraktaroğlu, S. & Yıldırım, E. (2004). Sosyal bilimlerde arastırma yöntemleri. Sakarya: Sakarya Kitapevi.
• An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7 (2), 145–172.
• Aslan-Tutak, F. (2011). Öğretmen adaylarının geometrik kavram yanılgıları: simetri ve eslik. Matematik Öğretimine Çağdaş Yaklaşımlar Sempozyumu, Çalıştaylar ve Bildiri Özetleri Kitabı, 27. Denizli.
• Babbington, S. & Lomas, G. (2004). Enhancing mathematical content knowledge in new zealand early childhood education. The International Congress of Mathematics Education. Copenhagen, Denmark.
• Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi. Ankara: Harf Egitim Yayıncılık.
• Ball D., L, Lubienski S.,T. & Mewborn D., S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In Richardson V (Ed.), Handbook of research on teaching (pp. 433–456) 4th edn. New York: Macmillian.
• Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90 (4), 449-466.
• Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 83–104). Westport, CT: Ablex.
• Ball, D. L., & McDiarmid, G. W. (1988). Research on teacher learning: Studying how teachers’ knowledge changes. Action in Teacher Education, 10 (2), 17-24.
• Ball, D. L., & McDiarmid, G. W. (1990). The subject matter preparation of teachers. In W. R. Houston (Ed.), Handbook of research on teacher education: A project of the Association of Teachers (pp. 437-449). New York: MacMillan.
• Ball, D.L. (1988a). Unlearning to teach mathematics. For the Learning of Mathematics, 8 (1), 40–48.
• Ball, D.L. (1988b). The subject matter preparation of prospective mathematics teachers: Challenging the myths. (Research Report 88-3. East Lansing, MI: National Center for Research on Teacher Education). Retrieved January 3, 2013,from http://ncrtl.msu.edu/http/rreports/html/pdf/rr883.pdf
• 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.
• Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31, 235-268.
• Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van hiele levels of development in geometry. Journal For Research in Mathematics Education, 17 (1), 31-48.
• Bütün, M. (2005). A study on primary mathematics teachers’ pedagogical content knowledge. Unpublished master’s thesis, Karadeniz Teknik University, Trabzon.
• Carpenter, T., Fennema, E., Peterson, P., Chiang, C., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26 (4), 499-531.
• Chinnappan, M., Nason, R., & Lawson, M. (1996). Pre-service 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.
• Clements, D. H. (1998). Geometric and spatial thinking in young children. Arlington, VA: National Science Foundation.
• Clements, D. H. (1999). Geometric and spatial thinking in young children. In J. V. Copley (Ed.), Mathematics in the early years (pp. 66–79). Reston, VA: National Council of Teachers of Mathematics.
• Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: an integrative model for teacher preparation. Journal of Teacher Education 44(4), 263–272.
• Cunningham, F. & Roberts, A. (2010). Reducing the mismatch of geometry concept definitions and concept images held by pre-service teachers. IUMPS The Journal, 1, 1-17.
• Currie, P., & Pegg, J. (1998). Investigating students' understanding of the relationships among quadrilaterals. In C. Kanes, M. Goos, & E. Warren. (Eds.), Teaching Mathematics in New Times: Conference Proceedings. Melbourne: Mathematics Education Research Group of Australasia Incorporated.
• De Villiers, M., (1996). The future of secondary school geometry. Slightly adapted version of Plenary presented at the SOSI Geometry Imperfect Conference, October 2-4, 1996, UNISA, Pretoria.
• Duatepe, A. (2000). An investigation of the relationship between van Hiele geometric level of thinking and demographic variables for pre-service elementary school teachers. Unpublished master’s thesis, Middle East Technical University, Ankara.
• Durmuş, S., Toluk, Z., & Olkun, S. (2002). Sınıf öğretmenliği ve matematik öğretmenliği öğrencilerinin geometrik düşünme düzeyleri. 5. Ulusal Fen Bilimleri ve Matematik Egitimi Kongresi, 16-18 Eylul: ODTU, Ankara.
• Fennema, E. & Franke, M. (1992). Teachers’ knowledge and its impact. In D. Grouws (Ed.) Handbook of research on mathematics teaching and learning (pp.147-164). New York: Macmillan.
• Foss, D. H., & Kleinsasser, R. C. (1996). Pre-service elementary teachers’ view of pedagogical and mathematical content knowledge. Teaching and Teacher Education, 12(4), 429-442.
• Fujita, T. (2008). Learners’ understanding of the hierarchical classification of quadrilaterals. Joubert , M. (Ed.). Proceedings of the British Society for Research into Learning Mathematics 28 (2), pp. 31-36.
• Fujita, T. & Jones, K. (2006a). Primary trainee teachers’ understanding of basic geometrical figures in Scotland. In Novotná, J., Moraová, H., Krátká, M. & Stehlíková, N. (Eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education (pp. 129-136). Prague: PME.
• Fujita, T. & Jones, K. (2006b). Primary trainee teachers’ knowledge of parallelograms. Hewitt, D. (Ed.). Proceedings of the British Society for Research into Learning Mathematics 26 (2) , pp. 25-30.
• Fuller, R. A. (1997). Elementary teachers’ pedagogical content knowledge of mathematics. Mid-Western Educational Researcher, 10(2), 9-16.
• Fuys, D., Geddes, D., & Tischler, R. (1988). The Van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education. Monograph, 3. Reston, VA: National Council of Teachers of Mathematics.
• Gal, H. (1998). What do they really think? What students think about the median and bisector of an angle in the triangle, what they say and what their teachers know about it. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd PME International Conference, 2, 321-328.
• Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. London: Teachers College Press.
• Heaton, R. M. (1992). Who is minding the mathematics content? A case study of a fifth grade teacher. The Elementary School Journal, 93(2), 153-162.
• Hershkowitz, R., & Vinner, S. (1984). Children’s concepts in elementary geometry. A reflection of teacher’s concepts?. In B. Southwell R. Eyland, M. Cooper, J. Conroy, & K. Collis (Eds.), Proceedings of the 8th PME International Conference (pp. 63-69). Darlinghurst, Australia: Mathematical Association of New South Wales.
• Hill, H., Blunk, M., Charambous, C., Lewis, J., Phelps, G., Sleep, L., & Ball, D. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26, 430-511.
• 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.
• Işıksal, M. (2006). A Study on Pre-Service Elementary Mathematics Teachers’ Subject Matter Knowledge and Pedagogical Content Knowledge Regarding the Multiplication and Division of Fractions. Unpublished doctorate dissertation. Middle East Technical University, Ankara.
• 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: Routledge Falmer.
• Knight, K. C. (2006). An investigation into the change in the van Hiele level of understanding geometry of pre-service elementary and secondary mathematics teachers. Unpublished master’s thesis. University of Maine.
• Kow, K. & Yeo, J. (2008). Teaching area and perimeter: mathematics pedagogical content knowledge in action. M. Goos, R. Brown, & K. Makar (Eds.), Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, MERGA Inc.
• Kulm, G., Capraro, R. M., Capraro, M. M., Burghardt, R. & Ford, K. (2001). Teaching and learning mathematics with understanding in an era of accountability and highstakes testing. The 79th annual meeting of the National Council of Teachers of Mathematics. Orlando, FL.
• Laborde, C., Kynigos, C., Hollebrands, K., & Strasser, R. (2006). Teaching and learning geometry with technoloy. In A. Gutiérrez & P. Boero (Eds.), Handbook of Research on The Psychology of Mathematics Education: Past, Present and Future. (pp. 275-304). Rotterdam: Sense Publishers.
• Lee, W. (1999). The relationship between students’ proof-writing ability and van hiele levels of geometric thought in a college geometry course. Unpublished Doctoral Dissertation. University of Northern Colorado, UMI.
• Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children’s reasoning about space and geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137-167). Mahwah, NJ: Lawrence Erlbaum.
• Lenhart, S., T. (2010). The effect of teacher pedagogical content knowledge and the instruction of middle school geometry. Unpublished Doctoral Dissertation, The Liberty University.
• Ma, L. (1999). Knowing and teaching mathematics: teachers’ understanding of fundamental mathematics in China and United States. LEA: Mahwah, NJ. Lawrence Erlbaum Associates
• Manizade, A. G. & Mason, M. M. (2011). Using Delphi methodology to design assessments of teachers’ pedagogical content knowledge. Educational Studies in Mathematics, 76, (2), 183-207.
• Mapolelo, D. C. (1999). Do pre-service teachers who excel in mathematics become good mathematics teachers?. Teaching and Teacher Education, 15,715-725
• Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of Teacher Education, 41(3), 3-11.
• Martin, W. G., & Strutchens, M. E. (2000). Geometry and Measurement. In E. A.Silver & P. A. Kenney (Eds.), Results from the Seventh Mathematics Assessment of the National Assessment of Educational Progress (193–234). Reston, VA: National Council of Teachers of Mathematics.
• Mayberry, J. (1983). The van Hiele level of geometric thought in undergraduate pre-service teachers. Journal for Research in Mathematics Education, 14, 58-69.
• Menon, R. (1998). Pre-service teachers’ understanding of perimeter and area. School Science and Mathematics, 98, (7), 361–367.
• Miles, M.B. & Huberman, A.M. (1994). Qualitative data analysis: an expanded sourcebook. (2nd ed.). Newbury Park, CA: Sage.
• Ministry of National Education [MNE] (2005). İlköğretim matematik dersi (1-5 sınıflar) öğretim programı. Ankara, Turkey: MNE.
• Ministry of National Education [MNE] (2006). 36–72 aylık çocuklar için okul öncesi eğitim programı. Ankara, Turkey: MNE.
• Monaghan, E (2000). What difference does it make? Children's views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42 (2), 179-196.
• National Council of Teachers of Mathematics [NCTM], (2000). Principles and standards for School Mathematics. Reston, VA: NCTM.
• National Research Council [NRC], (2000). How people learn: brain, mind, experience, and school. National Academy Pres, Washington, D. C.
• Okazaki, M. & Fujita, T. (2007). Prototype phenomen and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in japan and scotland. In Woo, J. H., Lew, H. C., Park, K. S. & Seo, D. Y. (Eds.). Proceedings 31st Conference of the International Group for the Psychology of Mathematics Education, 4 (pp 41-48). Seoul: PME.
• Rovegno, I. C. (1992) Learning to teach in a field-based methods course: the development of pedagogical content knowledge. Teaching and Teacher Education, 8, 69-82.
• Rowland, T., Martin, S., Barber, P., & Heal, C. (2001). Investigating the mathematics subject matter knowledge of pre-service elementary school teachers. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th conference of the international group for the psychology of mathematics education 4 (pp. 121–128). Utrecht: Freudenthal Institute.
• Schoenfeld, A.H. (1998) Toward a theory of teaching in context. Issues in Education, 4(1), 1-94.
• 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.
• 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.
• Swenson, K. A., (1998). Middle school mathematics teachers’ subject matter knowledge and pedagogical content knowledge of probability: Its relationship to probability instruction. Unpublished Doctoral Dissertation, Oregon State University.
• Tirosh,D., Fischbein, E., Graeber, A. & Wilson, J., W. (1998). Prospective elementary teachers’ conceptions of rational numbers. Retrieved June 12, 2011, from http://jwilson.coe.uga.edu/texts.folder/tirosh/pros.el.tchrs.html .
• Van De Walle, J. A. (2004). Elementary and middle school mathematics. (5th Ed.) Boston: Allyn and Bacon
• Van der Sandt, S. & Nieuwoudt, H., D. (2003). Grade 7 teachers’ and prospective teachers’ content knowledge of geometry. South African Journal of Education, 23(3) 199–205.
• Van Hiele, P. M. (1986). Structure and insight: a theory of mathematics education. Academic Pres, Inc: Orlando, Florida.
• Wilson, S., M. & Winwberg, S., S. (1989). Peering at history through different lenses: The role of disciplinary perspectives in teaching history. Teaching College Record, 89, 525-539.
• Winsor, M. S. (2003). Pre-service mathematics teachers’ knowledge of functions and its effect on lesson planning at the secondary level. Unpublished doctoral dissertation, University of Iowa, Iowa City.
• Wu, D. & Ma, H. (2005). A study of the geometric concepts of elementary school students at van hiele level one. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 4 (pp. 329-336). Melbourne: PME.
• Yee Han, P. (2003). Primary mathematics teachers’ pedagogical content knowledge of the teaching of quadrilaterals. Unpublished master’s thesis. The University of Hong Kong.
• Yıldırım, A. & Şimşek H. (2004). Sosyal bilimlerde nitel araştirma yöntemleri. Ankara: Seckin Yayincilik.
• Zhou, Z., Peverly, S. T., & Xin, T. (2006). Knowing and teaching fractions: A cross-cultural study of American and Chinese mathematics teachers. Contemporary Educational Psychology, 31(4), 438–457.