A CONCEPTUAL FRAMEWORK FOR EXAMİNİNG MATHEMATİCS TEACHERS’ PEDAGOGİCAL CONTENT KNOWLEDGE İN THE CONTEXT OF SUPPORTİNG MATHEMATİCAL THİNKİNG

Berna Tataroğlu Taşdan, Adem Çelik

Abstract


This study has been aimed to propose a conceptual framework that helps researchers examine mathematics teachers’ PCK in the context of supporting students’ mathematical thinking. “Advancing Children’s Thinking Framework” which is a pedagogical model developed by Fraivillig, Murphy and Fuson (1999) that supports the development of students’ conceptual understanding of mathematics has been adopted as the theoretical foundation. Pedagogical content knowledge (knowledge of students’ thinking and knowledge of instructional strategies and representations) has been examined in the context of supporting mathematical thinking and has been interconnected to Advancing Children’s Thinking Framework. Then, a new framework has been obtained. Instructional examples included within the framework suggested as a result of the interconnection have become the indicators regarding PCK of mathematics teachers in the context of supporting mathematical thinking. Some examples from a performed research where this framework has been used as an analytical framework have been presented. As a conclusion, it can be said that the suggested framework may be a useful tool for the researchers and teacher educators who are dealing with teachers’ knowledge focusing on students’ mathematical thinking and a guide for the teachers.

 

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Keywords


conceptual framework, pedagogical content knowledge, mathematics teachers, mathematical thinking

References


Alkan, H. & Bukova Güzel, E. (2005). Öğretmen adaylarında matematiksel düşünmenin gelişimi. Gazi University Journal of Gazi Educational Faculty, 25(3), 221-236.

An, S., Kulm, G. & Wu, Z. (2004) The pedagogical content knowledge of middle school athematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145- 172.

Arslan, S. & Yıldız, C. (2010). 11. sınıf öğrencilerinin matematiksel düşünmenin aşamalarındaki yaşantılarından yansımalar. Education and Science, 35(156), 17-31.

Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, Volume: 59 Number: 5, 389- 407.

Burton, L. (1984). Mathematical thinking: The Struggle for meaning. Journal for Research in Mathematics Education, Vol.15, No.1, 35-49.

Carpenter, T.P., Fenneme, E., Peterson, P. L. Chiang, C. P. & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimantal study. American Educational Research Journal, 26(4): 499-531.

Cengiz, N., Kline, K. & Grant, T. J. (2011). Extending students’ mathematical thinking during whole-group discussions. Journal of Mathematics Teacher Education, 14: 355–374.

Chamberlin, M. (2002). Teacher investigation of students work: The evaluation of teacher’s social process and interpretations of students’ thinking. Unpublished doctoral dissertation, Purdue University, Indiana, U.S.

Even, R. & Tirosh, D. (2008). Teacher knowledge and understanding of students’ mathematical learning and thinking. In L. D. English (Eds.), Handbook of international research in mathematics education (2nd Edition, pp. 202-222). New York: Routledge.

Fennema, E. & Franke, M. (1992). Teachers’ knowledge and its impact. In D. Grouws (Ed.), Handbook of Research on Mathematical Teaching and Learning (pp. 575-596). New York: Macmillan.

Fraivillig, J. L., Murphy, L. A. & Fuson, K. C. (1999). Advancing children’s mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30(2), 148-170.

Fraivillig, J. (2001). Strategies for advancing children's mathematical thinking. Teaching Children Mathematics, 7(8), 454 - 459.

Gearhart, M. & Saxe, G. B. (2004). When teachers know what students know: integrating assessment in elementary mathematics teaching. Theory into Practice, 43, pp: 304-313.

Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.

Harel, G., & Lim, K. (2004). Mathematics teachers' knowledge base: Preliminary results. In M. Hoines & A. Fuglestad (Eds.), Proceeding of the 28th annual meeting of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 25-32). Bergen, Norway: Bergen University College.

Jenkins, O. F. (2010). Developing teachers’ knowledge of students as learners of mathematics through structured interviews. Journal of Mathematics Teacher Education, 13: 141–154.

Kılıç, H. (2010). The nature of preservice mathematics teachers’ knowledge of students. Procedia Social and Behavioral Sciences, 9 (2010) 1096–1100.

Kılıç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2).

Kovarik, K. (2008). Mathematics educators' and teachers' perceptions of pedagogical content knowledge. Doctoral Dissertation. Columbia University, Graduate School of Arts and Sciences.

Lee, K. (2006). Teacher’s knowledge of middle school students’ mathematical thinking in algebra word problem solving. Doctor of Philosophy Dissertation. Oregon State University.

Magnusson, S., Krajcik, J. & Borko, H. (1999). Nature, sources and development of pedagogical content knowledge for science teaching. In J. GessNewsome and N.G. Lederman (Eds.), Examining pedagogical content knowledge. (95–132). Dordrecht, The Netherlands: Kluwer Academic Publishers.

Ministry of National Education [MNE], (2005).Ortaöğretim Matematik (9, 10, 11 ve 12. Sınıflar) Dersi Öğretim Programı, Ankara: Milli Eğitim Press.

Ministry of National Education [MNE], (2011). Ortaöğretim Matematik (9, 10, 11 ve 12. sınıflar) Dersi Öğretim Programı & Ortaöğretim Seçmeli Matematik (9, 10, 11 ve 12. sınıflar) Dersi Öğretim Programı, Ankara. http://ttkb.meb.gov.tr/program.aspx. Accessed 10 February 2011.

National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

Norton, A., McCloskey, A., & Hudson, R. (2011). Prediction assessments: using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking. Journal of Mathematics Teacher Education, DOI 10.1007/s10857-011-9181-0.

Park, S. & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge (Pck): Pck as a conceptual tool to understand teachers as professionals. Research in Science Education, 38: 261- 284.

Romberg (1994). Classroom instruction that fosters mathematical thinking and problem solving: connections between theory and practice (pp. 287-304). In Ed. Alan H. Schoenfeld, Mathematical Thinking and Problem Solving. Hillsdale, NJ: Lawrence Erlbaum.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334-370). New York: Macmillan.

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.

Sleep, L., & Boerst, T. (2012). Preparing beginning teachers to elicit and interpret students' mathematical thinking. Teaching and Teacher Education, 28(7), 1038-1048.

Stacey, K. (2010). What is mathematical thinking and why is it important? http://marsigitpsiko.blogspot.com /2008/12/what-is-mathematical-thinking-and-whay.html, Accessed 11 November 2010.

Swan, M. & Ridgway, J. (2002). Mathematical thinking CATs. Fiels-tested learning assessment.http: // www . wcer. wisc. edu /archieve /cl1 /fla g/extra/download/cat/math/math/mathpdf. Accessed 23 January 2009.

Tataroğlu Taşdan, B. (2014). Matematik öğretmenlerinin pedagojik alan bilgilerini matematiksel düşünmeyi destekleme bağlamında geliştirmeyi amaçlayan bir öğretim tasarımı. Doctoral Dissertation. Dokuz Eylul University, Turkey.

Umay, A. (2003). Matematiksel muhakeme yeteneği. Hacettepe University Journal of Education, 24, 234-243.

Umay, A. (2007). Eski arkadaşımız okul matematiğinin yeni yüzü. Ankara: Aydan Publishing.

Yeşildere-İmre, S. & Akkoç, H. (2012). Investigating the development of prospective mathematics teachers’ pedagogical content knowledge of generalising number patterns through school practicum. Journal of Mathematics Teacher Education, 3(15), 207–226.

Yıldırım, C. (2004). Matematiksel düşünme. Istanbul: Remzi Bookstore.


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