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İlköğretim Matematik Öğretmen Adaylarının Çokgenlere Dair Geometri Bilgilerinin İncelenmesi

Year 2017, Volume: 18 Issue: 2, 375 - 399, 01.05.2017

Abstract

Öğretmenlerin geometri bilgileri, öğrencilerin geometri perfromanslarını etkileyen önemli bir faktördür. Bu önem göz önüne alınarak bu çalışmada ilköğretim matematik öğretmen adaylarının çokgenlere dair geometri bilgilerinin incelenmesi amaçlanmıştır. Bir durum çalışması olarak tasarlanan çalışmaya amaçlı örnekleme yoluyla seçilen ilköğretim matematik eğitiminde öğrenim görmekte olan 33 üçüncü sınıf öğretmen adayıkatılmıştır. Veri toplama aracı olarak araştırmacılar tarafından geliştirilen ve 19 açık uçlu sorudan oluşan Çokgenler Konu Testi kullanılmıştır. Sorular; i tanım, ii matematiksel ilişki ve bağıntı ve iii matematikel işlem ve süreçleri bilmeyi gerektiren sorular olmak üzere üç alt gruba ayrılmış ve bir rubrik ile analiz edilmiştir. Araştırma sonuçlarına göre, öğretmen adaylarının matematiksel tanım bilmeyi gerektiren sorularda diğer alt gruplarda yer alan sorulara göre daha başarılı olduğu ve öğretmen adaylarının doğru cevabı bulsalar bile cevaplarını açıklamak için yeterli ve matematiksel düşünceye uygun gerekçelerde bulunamadıkları gözlemlenmiştir. Bu çerçevede öğretmen adaylarına geometrik argüman yazma ve geometrik ispat yapma konusunda daha fazla imkan verilmesi önerilmiştir.

References

  • Athanasopoulou, A. (2008). An inquiry approach to the study of quadrilaterals using Geometer’s Sketchpad: A study with pre-service and in-service teachers. Unpublished doctoral dissertation, The University of North Carolina, Charlotte.
  • Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The elementary school journal, 90(4), 449-466.
  • Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator (Fall),14-46.
  • 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.
  • Baltacı, S., & Baki, A. (2017). Bağlamsal öğrenme ortamı oluşturmada GeoGebra yazılımının rolü: Elips Örneği, Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi (KEFAD), 18(1), 429-449.
  • Bowles, M. A. ( 2010 ). The think-aloud controversy in second language research. London: Routledge.
  • Bryan, T. J. (1999). The conceptual knowledge of pre-service secondary mathematics teachers: How well do they know the subject matter they will teach? Issues in the Undergraduate Mathematics of School Teachers: The Journal. Volume 1: Content Knowledge.
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2011). Bilimsel araştırma yöntemleri. Pegem-A Yayınları. Ankara.
  • Carreño, E., Ribeiro, C. M., & Climent, N. (2013). Specialized and horizon content knowledge–Discussing prospective teachers knowledge on polygons. Proceedings of the Eight Congress of European Mathematics Education, 2966-2975.
  • Clements, D. H. (1999). Teaching length measurement: Research challenges. School Science and Mathematics, 99(1), 5-11.
  • 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.
  • Dillman, D. A. (2011). Mail and Internet surveys: The tailored design method-2007 Update with new Internet, visual, and mixed-mode guide. John Wiley & Sons.
  • Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the cracks: Complexities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, 24(1), 8-40.
  • Ekawati, R., Lin, F. L., & Yang, K. L. (2015). Developing an instrument for measuring teachers’ Mathematics Content Knowledge on ratio and proportion: a case of Indonesian primary teachers. International Journal of Science and Mathematics Education, 13(1), 1-24.
  • Erbas, A. K., & Yenmez, A. A. (2011). The effect of inquiry-based explorations in a dynamic geometry environment on sixth grade students’ achievements in polygons. Computers & Education, 57, 2462-2475.
  • Erdogan, E. O., & Dur, Z. (2014). Preservice mathematics teachers’ personal figural concepts and classifications about quadrilaterals. Australian Journal of Teacher Education, 39(6), 106-133.
  • Fennema A., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning, (pp. 147-164). New York: Macmillan Publishing Company.
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2011). Validity and reliability, how to design and evaluate research in science education (8th Ed.). Mc Graw-Hill Companies.
  • Fujita, T., & Jones, K. (2006) Primary trainee teachers’ understanding of basic geometrical figures in Scotland. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, 3, 14-21.
  • Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing. Research in Mathematics Education, 9(1), 3-20.
  • Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among Monograph, 3, 1-196. for Research in Mathematics Education.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press, Teachers College, Columbia University.
  • Günhan, B. C. (2014). An Investigation of Pre-Service Elementary School Teachers' Knowledge Concerning Quadrilaterals. Çukurova University. Faculty of Education Journal, 43(2), 137-154.
  • Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1–27). Hillsdale: Erlbaum.
  • İlköğretim Matematik Öğretmenliği Lisans Programı. (2016). İlköğretim matematik öğretmenliği http://www.yok.gov.tr/documents/10279/49665/ilkogretim_matematik/cca48fad- 63d7-4b70-898c-dd2eb7afbaf5 adresinden ulaşılmıştır. 03/01/2016 tarihinde
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • Knight, K. C. (2006). An investigation into the change in the Van Hiele levels of understanding geometry of pre-service elementary and secondary mathematics teachers. Unpublished doctoral dissertation, The University of Maine, Orono.
  • Lehrer, R. (2003). Developing understanding of measurement. In J. Kilpatrick, W. G. Martin, & D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 179–192). Reston, VA: National Council of Teachers of Mathematics.
  • Lin, C. Y., Becker, J., Byun, M. R., Yang, D. C., & Huang, T. W. (2013). Preservice teachers’ conceptual and procedural knowledge of fraction operations: A comparative study of the United States and Taiwan. School Science and Mathematics, 113(1), 41-51.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. NJ: Lawrence Erlbaum Associates.
  • Marchis, I. (2012). Preservice Primary School Teachers’ Elementary Geometry Knowledge, Acta Didactica Napocensia, 5(2), 33-40.
  • Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of teacher education, 41(3), 3-11.
  • Mayberry, J. (1983). The van Hiele levels of geometric thought in undergraduate preservice teachers. Journal for research in mathematics education, 14(1), 58-69.
  • Merriam, S. (1998). Qualitative research and case study applications in education. San Francisco: Jossey-Bass.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation (Revised and expanded from qualitative research and case study application in education). San Francisco: Jossey-Bass.
  • Miles, M., & Huberman, A. M. (1994). Qualitative Data Analysis. Beverly Hills, California: Sage.
  • Milli Eğitim Bakanlığı (MEB). (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıf) öğretim programı. 14/04/2015 tarihinde http://ttkb.meb.gov.tr/www/ogretim- programlari/icerik/72 adresinden erişilmiştir.
  • Morkoyunlu, Z., Kıymaz, Y., & Kartal, B. (2016). İlköğretim Matematik Öğretmen Adaylarının Matematiksel İletişim Becerilerinin İncelenmesine Dair Bir Çalışma. 3rd International Eurasian Educational Research Congress, 1321-1322.
  • Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080- 1110.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14.
  • Steele, M. D. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks. Journal of Mathematics Teacher Education, 16(4), 245-268.
  • Timur, B. (2011). Fen Bilgisi Öğretmen Adaylarının Kuvvet ve Hareket Konusundaki Teknolojik Pedagojik Alan Bilgilerinin Gelişimi. Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, İlköğretim Anabilim Dalı Fen Bilgisi Eğitimi Bilim Dalı, Doktora Tezi.
  • Tsamir, P., Tirosh, D., & Stavy, R. (1998). Do equilateral polygons have equal angels? In Proceeding of the 22nd Conference of the International Group for the Psychology of Mathematics Education 4, 137-144.
  • Türnüklü, E., & Berkün, M. (2013). İlköğretim 5 ve 7. Sınıf Öğrencilerinin Çokgenleri Sınıflandırma Stratejileri. Kastamonu Eğitim Dergisi, 21(1), 337-356.
  • Van de Walle, J. A., Karp, K. S., & Williams, J. M. B. (2010). Elementary and middle school mathematics: Teaching developmentally (7th Ed.). New York: Longman.
  • Wearne, D., & Hiebert, J. (1988). Constructing and using meaning for mathematical symbols: The case of decimal fractions. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 220– 235). Reston, VA: National Council of Teachers of Mathematics.
  • Yanık, A., & Ada, T. (2013). Investigation of the Development of 7th Grade Students’ Skills to Define, Construct and Classify Polygons with Cabri Geometry. Turkish Online Journal of Qualitative Inquiry, 4(3), 48-60.

Examining Pre-service Mathematics Teachers’ Geometry Knowledge of Polygons

Year 2017, Volume: 18 Issue: 2, 375 - 399, 01.05.2017

Abstract

Teachers’ geometry knowledge is an important factor that affects students’ achievement in geometry. Taking this importance into consideration, this study aimed to examine preservice mathematics teachers’ geometry knowledge of polygons. The study was designed as a case study. 33 junior pre-service mathematics teachers were participated in study via purposeful sampling. Polygon Questionnaire was developed by reseaerchers and used as data collection tool. There are 19 open-ended questions that were divided into three groups; i definition-based, ii mathematical relationship-based, and iii mathmematical process-based questions. Data was analyzed via rubric. According to findings, pre-service teachers were more successful in definition-based questions than in other groups. Even though they found the correct answer, they failed to make adequate and mathematically valid justifications in order to explain their answers. It was suggested to give pre-service teachers more opportunities to write geometric arguments and prove geometrically

References

  • Athanasopoulou, A. (2008). An inquiry approach to the study of quadrilaterals using Geometer’s Sketchpad: A study with pre-service and in-service teachers. Unpublished doctoral dissertation, The University of North Carolina, Charlotte.
  • Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The elementary school journal, 90(4), 449-466.
  • Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator (Fall),14-46.
  • 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.
  • Baltacı, S., & Baki, A. (2017). Bağlamsal öğrenme ortamı oluşturmada GeoGebra yazılımının rolü: Elips Örneği, Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi (KEFAD), 18(1), 429-449.
  • Bowles, M. A. ( 2010 ). The think-aloud controversy in second language research. London: Routledge.
  • Bryan, T. J. (1999). The conceptual knowledge of pre-service secondary mathematics teachers: How well do they know the subject matter they will teach? Issues in the Undergraduate Mathematics of School Teachers: The Journal. Volume 1: Content Knowledge.
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2011). Bilimsel araştırma yöntemleri. Pegem-A Yayınları. Ankara.
  • Carreño, E., Ribeiro, C. M., & Climent, N. (2013). Specialized and horizon content knowledge–Discussing prospective teachers knowledge on polygons. Proceedings of the Eight Congress of European Mathematics Education, 2966-2975.
  • Clements, D. H. (1999). Teaching length measurement: Research challenges. School Science and Mathematics, 99(1), 5-11.
  • 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.
  • Dillman, D. A. (2011). Mail and Internet surveys: The tailored design method-2007 Update with new Internet, visual, and mixed-mode guide. John Wiley & Sons.
  • Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the cracks: Complexities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, 24(1), 8-40.
  • Ekawati, R., Lin, F. L., & Yang, K. L. (2015). Developing an instrument for measuring teachers’ Mathematics Content Knowledge on ratio and proportion: a case of Indonesian primary teachers. International Journal of Science and Mathematics Education, 13(1), 1-24.
  • Erbas, A. K., & Yenmez, A. A. (2011). The effect of inquiry-based explorations in a dynamic geometry environment on sixth grade students’ achievements in polygons. Computers & Education, 57, 2462-2475.
  • Erdogan, E. O., & Dur, Z. (2014). Preservice mathematics teachers’ personal figural concepts and classifications about quadrilaterals. Australian Journal of Teacher Education, 39(6), 106-133.
  • Fennema A., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning, (pp. 147-164). New York: Macmillan Publishing Company.
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2011). Validity and reliability, how to design and evaluate research in science education (8th Ed.). Mc Graw-Hill Companies.
  • Fujita, T., & Jones, K. (2006) Primary trainee teachers’ understanding of basic geometrical figures in Scotland. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, 3, 14-21.
  • Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing. Research in Mathematics Education, 9(1), 3-20.
  • Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among Monograph, 3, 1-196. for Research in Mathematics Education.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press, Teachers College, Columbia University.
  • Günhan, B. C. (2014). An Investigation of Pre-Service Elementary School Teachers' Knowledge Concerning Quadrilaterals. Çukurova University. Faculty of Education Journal, 43(2), 137-154.
  • Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1–27). Hillsdale: Erlbaum.
  • İlköğretim Matematik Öğretmenliği Lisans Programı. (2016). İlköğretim matematik öğretmenliği http://www.yok.gov.tr/documents/10279/49665/ilkogretim_matematik/cca48fad- 63d7-4b70-898c-dd2eb7afbaf5 adresinden ulaşılmıştır. 03/01/2016 tarihinde
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • Knight, K. C. (2006). An investigation into the change in the Van Hiele levels of understanding geometry of pre-service elementary and secondary mathematics teachers. Unpublished doctoral dissertation, The University of Maine, Orono.
  • Lehrer, R. (2003). Developing understanding of measurement. In J. Kilpatrick, W. G. Martin, & D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 179–192). Reston, VA: National Council of Teachers of Mathematics.
  • Lin, C. Y., Becker, J., Byun, M. R., Yang, D. C., & Huang, T. W. (2013). Preservice teachers’ conceptual and procedural knowledge of fraction operations: A comparative study of the United States and Taiwan. School Science and Mathematics, 113(1), 41-51.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. NJ: Lawrence Erlbaum Associates.
  • Marchis, I. (2012). Preservice Primary School Teachers’ Elementary Geometry Knowledge, Acta Didactica Napocensia, 5(2), 33-40.
  • Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of teacher education, 41(3), 3-11.
  • Mayberry, J. (1983). The van Hiele levels of geometric thought in undergraduate preservice teachers. Journal for research in mathematics education, 14(1), 58-69.
  • Merriam, S. (1998). Qualitative research and case study applications in education. San Francisco: Jossey-Bass.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation (Revised and expanded from qualitative research and case study application in education). San Francisco: Jossey-Bass.
  • Miles, M., & Huberman, A. M. (1994). Qualitative Data Analysis. Beverly Hills, California: Sage.
  • Milli Eğitim Bakanlığı (MEB). (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıf) öğretim programı. 14/04/2015 tarihinde http://ttkb.meb.gov.tr/www/ogretim- programlari/icerik/72 adresinden erişilmiştir.
  • Morkoyunlu, Z., Kıymaz, Y., & Kartal, B. (2016). İlköğretim Matematik Öğretmen Adaylarının Matematiksel İletişim Becerilerinin İncelenmesine Dair Bir Çalışma. 3rd International Eurasian Educational Research Congress, 1321-1322.
  • Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080- 1110.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14.
  • Steele, M. D. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks. Journal of Mathematics Teacher Education, 16(4), 245-268.
  • Timur, B. (2011). Fen Bilgisi Öğretmen Adaylarının Kuvvet ve Hareket Konusundaki Teknolojik Pedagojik Alan Bilgilerinin Gelişimi. Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, İlköğretim Anabilim Dalı Fen Bilgisi Eğitimi Bilim Dalı, Doktora Tezi.
  • Tsamir, P., Tirosh, D., & Stavy, R. (1998). Do equilateral polygons have equal angels? In Proceeding of the 22nd Conference of the International Group for the Psychology of Mathematics Education 4, 137-144.
  • Türnüklü, E., & Berkün, M. (2013). İlköğretim 5 ve 7. Sınıf Öğrencilerinin Çokgenleri Sınıflandırma Stratejileri. Kastamonu Eğitim Dergisi, 21(1), 337-356.
  • Van de Walle, J. A., Karp, K. S., & Williams, J. M. B. (2010). Elementary and middle school mathematics: Teaching developmentally (7th Ed.). New York: Longman.
  • Wearne, D., & Hiebert, J. (1988). Constructing and using meaning for mathematical symbols: The case of decimal fractions. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 220– 235). Reston, VA: National Council of Teachers of Mathematics.
  • Yanık, A., & Ada, T. (2013). Investigation of the Development of 7th Grade Students’ Skills to Define, Construct and Classify Polygons with Cabri Geometry. Turkish Online Journal of Qualitative Inquiry, 4(3), 48-60.
There are 47 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Büşra Kartal This is me

Cengiz Çınar This is me

Publication Date May 1, 2017
Published in Issue Year 2017 Volume: 18 Issue: 2

Cite

APA Kartal, B., & Çınar, C. (2017). İlköğretim Matematik Öğretmen Adaylarının Çokgenlere Dair Geometri Bilgilerinin İncelenmesi. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(2), 375-399.

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