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Knowledge Quartet’s Unit of Contingency in the Light of Mathematics Content Knowledge

Year 2014, Volume: 5 Issue: 1, 89 - 107, 18.04.2014

Semiha Kula , Esra Bukova Güzel

https://doi.org/10.16949/turcomat.87246
Cited By: 1

Abstract

The purpose of this study is to introduce the Contingency unit of Knowledge Quartet, which is a framework used in assessing mathematics student teachers’ subject matter knowledge and pedagogical knowledge, address its significance and demonstrate examples from its reflections on classroom setting. The study initially covers the type of knowledge that teachers should possess and Knowledge Quartet, which enables examining and assessing subject matter knowledge and pedagogical knowledge together. Next, general information was given regarding knowledge units of this model and it was explained including contingency components. Finally, the importance of Contingency was mentioned and some examples in classroom setting were discussed. It is thought that through this study, awareness of mathematics student teachers can be made ensured with regards to situations that teachers may encounter and that are almost impossible to plan in advance.

Key Words:    Contingency, knowledge quartet, mathematics student teacher, subject matter knowledge, pedagogical content knowledge

Keywords

Contingency knowledge quartet mathematics student teacher subject matter knowledge pedagogical content knowledge

References

  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education. 7, 145–172.
  • Ball, D. (2003). What mathematical knowledge is needed for teaching mathematics? http://www.erusd.k12.ca.us/ProjectALPHAweb/index_files/MP/BallMathSummitFeb03. pdf adresinden 26.11.2010 tarihinde erişilmiştir.
  • Ball, D. L., & McDiarmid, G. W. (1990). The subject matter preparation of teachers. In R. Houston (Ed.), Handbook of Research on Teacher Education. New York: Macmillan. Ball, D. L., & Sleep (2007, January). What is knowledge for teaching, and what are features of tasks that can be used to develop MKT? Presentation Made at the Center for Proficiency in Teaching Mathematics (CPTM) Pre-session of The Annual Meeting of The Association of Mathematics Teacher Educators (AMTE), Irvine, CA.
  • Ball, D., & 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, Westport, CT: Ablex.
  • Ball, D.L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education. 21(2), 132- 144.
  • Borko, H., & Putnam, R. T. (1996). Learning to Teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 673–708). New York: Macmillan.
  • Bukova Güzel, E. (2010). An investigation of pre-service mathematics teachers’ pedagogical content knowledge, using solid objects. Scientific Research and Essays. 5(14), pp. 1872-1880.
  • Bütün, M. (2005). İlköğretim matematik öğretmenlerinin alan eğitimi bilgilerinin nitelikleri üzerine bir çalışma (Yüksek lisans tezi). Karadeniz Teknik Üniversitesi, Trabzon.
  • Chick, H., Baker, M., Pham, T. & Cheng, H. (2006). Aspects of teachers’ pedagogical content knowledge for decimals. In J. Novotna, H. Moraova, M. Kratka & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 297-304). Prague: PME.
  • Cox, S. (2008). A conceptual analysis of technological pedagogical content knowledge (Unpublished dissertation). Brigham Young University, Provo, UT.
  • Doyle. W. (1986). Classroom organization and management. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed.). New York: Macmillan.
  • Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children's mathematics. In D. Tirosh & T. Wood (Eds.), Tools and Processes in Mathematics Teacher Education (pp. 257-281). Rotterdam: Sense Publishers.
  • Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29, 1–20.
  • Graeber, A. O. (1999). Forms of knowing mathematics: what preservice teachers should learn. Educational Studies in Mathematics, 38(1-3),189-208.
  • Grossman, P. L. (1990). The Making of a Teacher: Teacher Knowledge and Teacher Education. New York: Teachers College Press.
  • Gülden, D. (2009). Matematik öğretmen adaylarının limit ve süreklilik kavramlarına ilişkin pedagojik alan bilgilerinin değerlendirilmesi (Yüksek lisans tezi). Marmara Üniversitesi Eğitim Bilimleri Enstitüsü, İstanbul.
  • Hill, H., Ball, D. L., & Schilling, S. (2008). Unpacking 'pedagogical content knowledge': conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372-400.
  • Huckstep, P., Rowland, T., & Thwaites, A. (2006). The knowledge quartet: considering Chloe. In M. Bosch (Ed.) Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 1568-1578). Barcelona, Spain: FUNDEMI IQS, Universitat Ramon Llull.
  • Kovarik, K. (2008). Mathematics educators’ and teachers’ perceptions of pedagogical content knowledge (Doctoral dissertation). Columbia University.
  • Kula, S. (2011). Matematik öğretmen adaylarının dörtlü bilgi modeli ile alan ve alan öğretimi bilgilerinin incelenmesi: Limit örneği (Yüksek lisans tezi). Dokuz Eylül Üniversitesi, İzmir, Türkiye.
  • Kula, S. ve Bukova Güzel, E. (2010). Matematik Öğretmen Adaylarının Kavram Yanılgıları Bilgisinin İncelenmesi: Limit Örneği. 9.Matematik Sempozyumu. Karadeniz Teknik Üniversitesi.
  • Leavit, (2008). German mathematics teachers’ subject content and pedagogical content knowledge (Doctoral dissertation). University of Nevada, Las Vegas.
  • Lloyd, G. M., ve Wilson, M. (1998). Supporting innovation: The impact of a teacher’s conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education, 29(3), 248-274.
  • Magnusson, S., Borko, H., ve Krajcik, J. (1999). Nature, sources, and development of pedagogical content knowledge for science teaching. In Gess-Newsome, J., & Lederman, N.G. (eds.), Examining Pedagogical Content Knowledge (pp. 95-132). Dordrecht: Kluwer Academic Publishers.
  • Marks, R. (1990). Pedagogical content knowledge: from a mathematical case to a modified conception. Journal of Teacher Education, 41(3), 3-11.
  • Noss, R. ve Baki, A. (1996). Liberating school mathematics from procedural view. Journal of Education Hacettepe University, 12, 179-182.
  • Petrou, M. (2009). Adapting the knowledge quartet in the cypriot mathematics classroom. CERME 6: Conference Of The European Society For Research In Mathematics Education (p. 385-394). N. 6, 2009. Proceedings. Lyon, França. Université de Lyon.
  • Roth, K.J., Givvin, K.B., Chen, C., Lemmens, M. & Garnier, H. (2010). Pre-service teacher learning from online, videocase-based modules: Results from the Videocases for Science Teaching Analysis (ViSTA) study. Paper presented at the annual meeting of the National Association for Research in Science Teaching (NARST), Philadelphia, PA.
  • Rowland, T. (2005). The Knowledge Quartet: A Tool for Developing Mathematics Teaching. In A. Gagatsis (Ed) Proceedings of the Fourth Mediterranean Conference on Mathematics Education (pp. 69-81) Nicosia, Cyprus: Cyprus Mathematical Society.
  • Rowland, T. (2007). Developing Knowledge for Mathematics Teaching: A Theoretical Loop. In S. Close, D Corcoran and T. Dooley (Eds.) Proceedings of the Second National Conference on Research in Mathematics Education, 13-26. Dublin: St Patrick’s College. Rowland, T. (2013). Responding to students’ ideas. http://www.knowledgequartet.org/category/contingency/responding-to-students-ideas adresinden 20 Mayıs 2013 tarihinde erişilmiştir.
  • Rowland, T., & Turner, F. (2007). Developing and using the ‘knowledge quartet’: a framework for the observation of mathematics teaching. The Mathematics Educator, 10(1), 107-124.
  • Rowland, T., Huckstep, P., & Thwaites, A. (2003). The Knowledge Quartet. Proceedings of the British Society for Research into Learning Mathematics, 23(3), 97-102.
  • Rowland, T., Huckstep, P., & Thwaites, A. (2004). Reflecting on Prospective Elementary Teachers’ Mathematics Content Knowledge: The Case of Laura. In M. J. Hİines and A. B. Fugelstad, (Eds.) Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 121-128). Bergen, Norway: Bergen University College.
  • Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281.
  • Rowland, T., Thwaites, A. and Jared, L. (2011) Triggers of contingency in mathematics teaching. In B. Ubuz (Ed.). Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 73-80). Ankara, Turkey: PME.
  • Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009). Developing Primary Mathematics Teaching: Reflecting on Practice with the Knowledge Quartet. London: Sage.
  • Şahin, S., Atasoy, B. ve Somyürek, S. (2010). Öğretmen eğitiminde örnek olay yöntemi. Sosyal Bilimler Dergisi. 9(2). 253-277.
  • Schoenfeld, A. H. (1998). Toward a theory of teaching-in-context. Issues in Education, 4(1), 1–94.
  • Schoenfeld, A. H. (2005, July). Problem solving from cradle to grave. Paper Presented at the Symposium ‘Mathematical Learning From Early Childhood To Adulthood’, Mons, Belgium.
  • Shulman, L. (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., & Ball, D. L. (2009). What mathematical demands will tomorrow’s teachers face? http://www.pearsonschool.com/index.cfm?locator=PSZkWo adresinden 26 Kasım 2010 tarihinde erişilmiştir.
  • Thwaites, A., Huckstep, P., & Rowland, T. (2005) The Knowledge Quartet: Sonia’s Reflections. In D. Hewitt and A. Noyes (Eds) Proceedings of the Sixth British Congress of Mathematics Education (pp.168-175). London: British Society for Research into Learning Mathematics.
  • Thwaites, A., Jared, L. and Rowland, T. (2011) Analysing secondary mathematics teaching with the Knowledge Quartet. Research in Mathematics Education, 13(2), 227-8
  • Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51–64, 19
  • Toluk Uçar, Z. (2010, Mayıs). Sınıf öğretmeni adaylarının matematiksel bilgileri ve öğretimsel açıklamaları. 9. Ulusal Sınıf Öğretmenliği Eğitimi Sempozyumu, 261-264.
  • Turner, F. & Rowland, T. (2011). The Knowledge Quartet as an organising framework for developing and deepening teachers’ mathematics knowledge. In T. Rowland & K. Ruthven (Eds) Mathematical Knowledge in Teaching (pp.195-212). New York: Springer.
  • Turner, F. (2007). Development in the mathematics teaching of beginning elementary school teachers: An approach based on focused reflections. Proceedings of the Second National Conference on Research in Mathematics Education, Mathematics in Ireland (Vol. 2, pp. 377-386) , Dublin: St Patrick's College
  • Turner, F. (2009, March). Developing The Ability to Respond to The Unexpected. Informal Proceedings of the British Society for Research into Learning Mathematics. Paper presented in Cambridge.
  • Van Der Valk, T. A. E., & Broekman, H. H. G. B. (1999). The lesson preparation method: a way of investigating pre-service teachers' pedagogical content knowledge. European Journal of Teacher Education, 22(1), 11-22.
  • Weston, T. (2013). Responding to the (Un)Availability of Tools and Resources www.knowledgequartet.org/433/rat-scenario-1-2/ adresinden 20 Mayıs 2013 tarihinde erişilmiştir.
  • Weston, T. L., Cleve, B. & Rowland, T. (2012). Developing an online coding manual for The Knowledge Quartet: An international project. In C. Smith (Ed.) Proceedings of the British Society for Research into Learning Mathematics, 32(3).

Matematik ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi

Year 2014, Volume: 5 Issue: 1, 89 - 107, 18.04.2014

Semiha Kula , Esra Bukova Güzel

https://doi.org/10.16949/turcomat.87246
Cited By: 1

Abstract

Bu çalışmanın amacı, matematik öğretmeni adaylarının alan ve alan öğretimi bilgilerinin değerlendirilmesinde kullanılan bir çerçeve olan Dörtlü Bilgi Modeli’nin Beklenmeyen Olaylar Bilgisi birimini tanıtmak, önemini belirtmek ve sınıf ortamına yansımalarından örnekler sunmaktır. Çalışmada, matematik öğretmenlerinin öğretimleri için gerekli olan alan ve alan öğretimi bilgilerini ayrıntılı olarak incelemeyi ve değerlendirmeyi mümkün kılan Dörtlü Bilgi Modeli’nin tanıtımına yer verilmiştir. Ardından söz konusu modele ait birimlere ilişkin genel bilgilendirme yapılmış ve bu birimlerden biri olan “Beklenmeyen Olaylar Bilgisi” detaylandırılmıştır. Son olarak “Beklenmeyen Olaylar Bilgisi”nin öneminden bahsedilmiş ve gerçek sınıf ortamlarından alınan kesitlerle bazı örnekler sunulmuştur. Sunulan çalışma ile matematik öğretmeni adaylarının önceden planlanması neredeyse imkansız olan ve öğretimlerinde karşılaşabilecekleri durumlara ilişkin farkındalıklarının sağlanacağı düşünülmektedir.

Anahtar Kelimeler:    Dörtlü bilgi modeli, beklenmeyen olaylar bilgisi, matematik öğretmen adayı, alan bilgisi, alan öğretimi bilgisi

Keywords

Dörtlü bilgi modeli beklenmeyen olaylar bilgisi matematik öğretmen adayı alan bilgisi alan öğretimi bilgisi

References

  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education. 7, 145–172.
  • Ball, D. (2003). What mathematical knowledge is needed for teaching mathematics? http://www.erusd.k12.ca.us/ProjectALPHAweb/index_files/MP/BallMathSummitFeb03. pdf adresinden 26.11.2010 tarihinde erişilmiştir.
  • Ball, D. L., & McDiarmid, G. W. (1990). The subject matter preparation of teachers. In R. Houston (Ed.), Handbook of Research on Teacher Education. New York: Macmillan. Ball, D. L., & Sleep (2007, January). What is knowledge for teaching, and what are features of tasks that can be used to develop MKT? Presentation Made at the Center for Proficiency in Teaching Mathematics (CPTM) Pre-session of The Annual Meeting of The Association of Mathematics Teacher Educators (AMTE), Irvine, CA.
  • Ball, D., & 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, Westport, CT: Ablex.
  • Ball, D.L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education. 21(2), 132- 144.
  • Borko, H., & Putnam, R. T. (1996). Learning to Teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 673–708). New York: Macmillan.
  • Bukova Güzel, E. (2010). An investigation of pre-service mathematics teachers’ pedagogical content knowledge, using solid objects. Scientific Research and Essays. 5(14), pp. 1872-1880.
  • Bütün, M. (2005). İlköğretim matematik öğretmenlerinin alan eğitimi bilgilerinin nitelikleri üzerine bir çalışma (Yüksek lisans tezi). Karadeniz Teknik Üniversitesi, Trabzon.
  • Chick, H., Baker, M., Pham, T. & Cheng, H. (2006). Aspects of teachers’ pedagogical content knowledge for decimals. In J. Novotna, H. Moraova, M. Kratka & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 297-304). Prague: PME.
  • Cox, S. (2008). A conceptual analysis of technological pedagogical content knowledge (Unpublished dissertation). Brigham Young University, Provo, UT.
  • Doyle. W. (1986). Classroom organization and management. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed.). New York: Macmillan.
  • Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children's mathematics. In D. Tirosh & T. Wood (Eds.), Tools and Processes in Mathematics Teacher Education (pp. 257-281). Rotterdam: Sense Publishers.
  • Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29, 1–20.
  • Graeber, A. O. (1999). Forms of knowing mathematics: what preservice teachers should learn. Educational Studies in Mathematics, 38(1-3),189-208.
  • Grossman, P. L. (1990). The Making of a Teacher: Teacher Knowledge and Teacher Education. New York: Teachers College Press.
  • Gülden, D. (2009). Matematik öğretmen adaylarının limit ve süreklilik kavramlarına ilişkin pedagojik alan bilgilerinin değerlendirilmesi (Yüksek lisans tezi). Marmara Üniversitesi Eğitim Bilimleri Enstitüsü, İstanbul.
  • Hill, H., Ball, D. L., & Schilling, S. (2008). Unpacking 'pedagogical content knowledge': conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372-400.
  • Huckstep, P., Rowland, T., & Thwaites, A. (2006). The knowledge quartet: considering Chloe. In M. Bosch (Ed.) Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 1568-1578). Barcelona, Spain: FUNDEMI IQS, Universitat Ramon Llull.
  • Kovarik, K. (2008). Mathematics educators’ and teachers’ perceptions of pedagogical content knowledge (Doctoral dissertation). Columbia University.
  • Kula, S. (2011). Matematik öğretmen adaylarının dörtlü bilgi modeli ile alan ve alan öğretimi bilgilerinin incelenmesi: Limit örneği (Yüksek lisans tezi). Dokuz Eylül Üniversitesi, İzmir, Türkiye.
  • Kula, S. ve Bukova Güzel, E. (2010). Matematik Öğretmen Adaylarının Kavram Yanılgıları Bilgisinin İncelenmesi: Limit Örneği. 9.Matematik Sempozyumu. Karadeniz Teknik Üniversitesi.
  • Leavit, (2008). German mathematics teachers’ subject content and pedagogical content knowledge (Doctoral dissertation). University of Nevada, Las Vegas.
  • Lloyd, G. M., ve Wilson, M. (1998). Supporting innovation: The impact of a teacher’s conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education, 29(3), 248-274.
  • Magnusson, S., Borko, H., ve Krajcik, J. (1999). Nature, sources, and development of pedagogical content knowledge for science teaching. In Gess-Newsome, J., & Lederman, N.G. (eds.), Examining Pedagogical Content Knowledge (pp. 95-132). Dordrecht: Kluwer Academic Publishers.
  • Marks, R. (1990). Pedagogical content knowledge: from a mathematical case to a modified conception. Journal of Teacher Education, 41(3), 3-11.
  • Noss, R. ve Baki, A. (1996). Liberating school mathematics from procedural view. Journal of Education Hacettepe University, 12, 179-182.
  • Petrou, M. (2009). Adapting the knowledge quartet in the cypriot mathematics classroom. CERME 6: Conference Of The European Society For Research In Mathematics Education (p. 385-394). N. 6, 2009. Proceedings. Lyon, França. Université de Lyon.
  • Roth, K.J., Givvin, K.B., Chen, C., Lemmens, M. & Garnier, H. (2010). Pre-service teacher learning from online, videocase-based modules: Results from the Videocases for Science Teaching Analysis (ViSTA) study. Paper presented at the annual meeting of the National Association for Research in Science Teaching (NARST), Philadelphia, PA.
  • Rowland, T. (2005). The Knowledge Quartet: A Tool for Developing Mathematics Teaching. In A. Gagatsis (Ed) Proceedings of the Fourth Mediterranean Conference on Mathematics Education (pp. 69-81) Nicosia, Cyprus: Cyprus Mathematical Society.
  • Rowland, T. (2007). Developing Knowledge for Mathematics Teaching: A Theoretical Loop. In S. Close, D Corcoran and T. Dooley (Eds.) Proceedings of the Second National Conference on Research in Mathematics Education, 13-26. Dublin: St Patrick’s College. Rowland, T. (2013). Responding to students’ ideas. http://www.knowledgequartet.org/category/contingency/responding-to-students-ideas adresinden 20 Mayıs 2013 tarihinde erişilmiştir.
  • Rowland, T., & Turner, F. (2007). Developing and using the ‘knowledge quartet’: a framework for the observation of mathematics teaching. The Mathematics Educator, 10(1), 107-124.
  • Rowland, T., Huckstep, P., & Thwaites, A. (2003). The Knowledge Quartet. Proceedings of the British Society for Research into Learning Mathematics, 23(3), 97-102.
  • Rowland, T., Huckstep, P., & Thwaites, A. (2004). Reflecting on Prospective Elementary Teachers’ Mathematics Content Knowledge: The Case of Laura. In M. J. Hİines and A. B. Fugelstad, (Eds.) Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 121-128). Bergen, Norway: Bergen University College.
  • Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281.
  • Rowland, T., Thwaites, A. and Jared, L. (2011) Triggers of contingency in mathematics teaching. In B. Ubuz (Ed.). Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 73-80). Ankara, Turkey: PME.
  • Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009). Developing Primary Mathematics Teaching: Reflecting on Practice with the Knowledge Quartet. London: Sage.
  • Şahin, S., Atasoy, B. ve Somyürek, S. (2010). Öğretmen eğitiminde örnek olay yöntemi. Sosyal Bilimler Dergisi. 9(2). 253-277.
  • Schoenfeld, A. H. (1998). Toward a theory of teaching-in-context. Issues in Education, 4(1), 1–94.
  • Schoenfeld, A. H. (2005, July). Problem solving from cradle to grave. Paper Presented at the Symposium ‘Mathematical Learning From Early Childhood To Adulthood’, Mons, Belgium.
  • Shulman, L. (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., & Ball, D. L. (2009). What mathematical demands will tomorrow’s teachers face? http://www.pearsonschool.com/index.cfm?locator=PSZkWo adresinden 26 Kasım 2010 tarihinde erişilmiştir.
  • Thwaites, A., Huckstep, P., & Rowland, T. (2005) The Knowledge Quartet: Sonia’s Reflections. In D. Hewitt and A. Noyes (Eds) Proceedings of the Sixth British Congress of Mathematics Education (pp.168-175). London: British Society for Research into Learning Mathematics.
  • Thwaites, A., Jared, L. and Rowland, T. (2011) Analysing secondary mathematics teaching with the Knowledge Quartet. Research in Mathematics Education, 13(2), 227-8
  • Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51–64, 19
  • Toluk Uçar, Z. (2010, Mayıs). Sınıf öğretmeni adaylarının matematiksel bilgileri ve öğretimsel açıklamaları. 9. Ulusal Sınıf Öğretmenliği Eğitimi Sempozyumu, 261-264.
  • Turner, F. & Rowland, T. (2011). The Knowledge Quartet as an organising framework for developing and deepening teachers’ mathematics knowledge. In T. Rowland & K. Ruthven (Eds) Mathematical Knowledge in Teaching (pp.195-212). New York: Springer.
  • Turner, F. (2007). Development in the mathematics teaching of beginning elementary school teachers: An approach based on focused reflections. Proceedings of the Second National Conference on Research in Mathematics Education, Mathematics in Ireland (Vol. 2, pp. 377-386) , Dublin: St Patrick's College
  • Turner, F. (2009, March). Developing The Ability to Respond to The Unexpected. Informal Proceedings of the British Society for Research into Learning Mathematics. Paper presented in Cambridge.
  • Van Der Valk, T. A. E., & Broekman, H. H. G. B. (1999). The lesson preparation method: a way of investigating pre-service teachers' pedagogical content knowledge. European Journal of Teacher Education, 22(1), 11-22.
  • Weston, T. (2013). Responding to the (Un)Availability of Tools and Resources www.knowledgequartet.org/433/rat-scenario-1-2/ adresinden 20 Mayıs 2013 tarihinde erişilmiştir.
  • Weston, T. L., Cleve, B. & Rowland, T. (2012). Developing an online coding manual for The Knowledge Quartet: An international project. In C. Smith (Ed.) Proceedings of the British Society for Research into Learning Mathematics, 32(3).
There are 52 citations in total.

Details

Primary Language Turkish
Journal Section Research Articles
Authors

Semiha Kula

Esra Bukova Güzel

Publication Date April 18, 2014
Published in Issue Year 2014 Volume: 5 Issue: 1

Cite

APA Kula, S., & Bukova Güzel, E. (2014). Matematik ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 5(1), 89-107. https://doi.org/10.16949/turcomat.87246
AMA Kula S, Bukova Güzel E. Matematik ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). April 2014;5(1):89-107. doi:10.16949/turcomat.87246
Chicago Kula, Semiha, and Esra Bukova Güzel. “Matematik Ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 5, no. 1 (April 2014): 89-107. https://doi.org/10.16949/turcomat.87246.
EndNote Kula S, Bukova Güzel E (April 1, 2014) Matematik ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 5 1 89–107.
IEEE S. Kula and E. Bukova Güzel, “Matematik ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi”, Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 5, no. 1, pp. 89–107, 2014, doi: 10.16949/turcomat.87246.
ISNAD Kula, Semiha - Bukova Güzel, Esra. “Matematik Ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 5/1 (April 2014), 89-107. https://doi.org/10.16949/turcomat.87246.
JAMA Kula S, Bukova Güzel E. Matematik ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2014;5:89–107.
MLA Kula, Semiha and Esra Bukova Güzel. “Matematik Ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 5, no. 1, 2014, pp. 89-107, doi:10.16949/turcomat.87246.
Vancouver Kula S, Bukova Güzel E. Matematik ve Matematik Öğretimi Bilgisi Işığında Dörtlü Bilgi Modelindeki Beklenmeyen Olaylar Bilgisi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2014;5(1):89-107.

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