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Öğretmen Adaylarının Geometrik Düşünme Alışkanlıklarının Değişimi

Year 2020, Volume: 48, 431 - 453, 07.01.2020

Abstract

Karşılaşılan
problemlerin üstesinden gelebilmek için bireylerin ilişkilendirme, özel
durumları düşünme ve genelleme, keşfetme ve yansıtma ile değişmezleri araştırma
gibi geometrik düşünme alışkanlıklarına sahip olması gerekir. Bireylerin
problem çözme süreçlerini incelerken de geometrik düşünme alışkanlıklarındaki
değişim sürecinin incelenmesi gerekmektedir. Dolayısıyla bu çalışmada
üniversite birinci sınıfa başlayan öğretmen adaylarının son sınıfa
geldiklerinde geometrik düşünme alışkanlıklarının nasıl değiştiğinin
belirlenmesi amaçlanmıştır. Boylamsal araştırma yönteminin kullanıldığı bu
çalışmanın katılımcılarını bir devlet üniversitesinde ilköğretim matematik
öğretmenliği lisans programına 2012 yılında kayıt olan ve 2016 yılında mezun
olan 31 öğretmen adayı oluşturmaktadır. Veri toplama aracı olarak her bir
geometrik düşünme alışkanlığını kapsayan dört açık uçlu problem kullanılmıştır.
Hazırlanan problemlere uzman görüşleri doğrultusunda son hali verilmiştir.
Çalışmanın sonucunda öğretmen adaylarının birinci sınıfa kıyasla keşfetme ve
yansıtma ile ilişkilendirme alışkanlıklarını daha çok kullandığı görülmüştür.
Bu durum üniversitelerde yürütülen derslerde öğretmen adaylarının daha çok
keşfetme ve yansıtma ile ilişkilendirme alışkanlıklarına yönlendirdiğini göstermektedir.
Oysa ki, adayların karşılaştığı geometri problemlerinin üstesinden gelebilmesi
için diğer geometrik düşünme alışkanlıklarını da kullanabilmeleri
gerekmektedir. Bu nedenle üniversitelerde yürütülen derslerin öğrencileri
farklı geometrik düşünme alışkanlıklarına yönlendirebilecek nitelikte olması
gerekmektedir. Bunun gerçekleştirebilmesi için de derslerde gösterilen geometri
problemlerinin farklı düşünme alışkanlıklarını kullanmaya yönlendirici olmasına
dikkat edilmelidir.

References

  • Abramovich, S., & Connell, M. L. (2014). Using technology in elementary mathematics teacher education: a sociocultural perspective. Hindawi Publishing Corporation ISRN Education, 1-9.
  • Bonn, T. V. (2015). Discovering and applying geometric transformations: Transformations to Show congruence and similarity. Unpublished master thesis, California State University, San Bernardino:CA.
  • Chan Y. (2003). GeoGebra as a tool to explore, conjecture, verify, justify and prove: The case of a circle. North American GeoGebra Journal, 2 (1), 2162-3856.
  • Costa, A. L. & Kallick, B. (2000). Discovering ang exploring habits of mind. Alexandria, VA: Association for Supervision & Curriculum Development.
  • Coxford, A. F., Fey, J. T., Hirsch, C. R., Schoen, H. L., Burrill, G., Hart, E. W. & Watkins, A.E. (1998). Contemporary mathematics in context: A unified approach. Implementing the core-plus mathematics curriculum. Chicago: Everyday Learning Corporation.
  • Cuoco, A., Goldenberg, E. & Mark, J. (1996). Habits of mind: an organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15(4), 375-402.
  • Cuoco, A., Goldenberg, E.P. & Mark, J. (2010). Organizing a curriculum around mathematical habits of mind. Mathematics teacher, 103(9), 682-688.
  • Driscoll, M. J., DiMatteo, R. W., Nikula, J. & Egan, M. (2007). Fostering geometric thinking: A guide for teachers grades 5-10. Portsmouth, NH: Heinemann.
  • Driscoll, M. J., DiMatteo, R. W., Nikula, J., Egan, M., Mark, J. & Kelemanik, G. (2008). The Fostering Geometric Thinking Toolkit: A Guide for Staff Development. Portsmouth, NH: Heinemann.
  • Friel, S. N. & Markworth, A. (2009). A framework for analyzing geometric pattern tasks. Mathematics Teaching in Middle School, 15(1), 24-33.
  • Goldenberg, E. P. (1996). “Habits of Mind” as an organizer for the curriculum. Journal of Education, 178(1), 13-34.
  • Goldenberg, E. P., Mark, J. & Cuoco, A. (2010). An algebraic habits of mind perspective on elementary school. Teaching Children Mathematics, 16(9), 548-556.
  • Harel, G. & Sowder, L. (2005). Advanced mathematical-thinking at any age: its nature and its development. Mathematical Thinking & Learning, 7(1), 27–50
  • Hu, H-W. (2005). Developing siblings and peer tutors to assist native Taiwanese children in learning habits of mind for math success. Dissertation Abstracts International, 256B (UMI No. 3179886).
  • Jacobbe, T. & Millman, R. S. (2009). Mathematical habits of mind for preservice teachers. School Science and Mathematics, 109(5), 298-302.
  • Lim, K. H. & Selden, A. (2009). Mathematical habits of mind. In S. L. Swars, D. W. Stinson and S. Lemons-Smith (Eds.). Proceedings of the 31th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University.
  • Marshall, A. R (2004). High school mathematics habits of mind instruction: Student growth and development. Dissertation Abstract International, 115B, (UMI No. 1421654).Marzano, R. J., Pickering, D. & McTighe, J. (1993). Assessing student outcomes: Performance assessment using the dimension of learning model. Alexandria, VA: Association for Supervision and Curriculum Development.
  • Matsuura, R., Sword, S., Piecham, M. B., Stevens, G. & Cuoco, A. (2013). Mathematical habits of mind for teaching: Using language in algebra classrooms. The Mathematics Enthusiast, 10(3), 735-776.
  • Rolle, Y. A. (2008). Habits of practice: A qualitative case study of a middle-school mathematics teacher. Dissertation Abstract International, 309B, (UMI No. 3325854).
  • Samson, D. (2014). Visualising and generalising with square arrays. Australian Mathematics Teacher, 70(2), 4-12.
  • Seago, N., Jacobs, K. J., Driscoll, M., Nikula, J., Matassa, M. & Callahan, P. (2013). Developing teacher’s knowledge of a transformation-based approach to geometric similarity. Mathematics Teacher Educator, 2(1), 74-85.
  • Seago, N. M., Jacobs, J. K., Heck, D. J., Nelson, C. L. & Malzahn, K. A. (2014). Impacting teachers’ understanding of geometric similarity: Results from field testing of the learning and teaching geometry Professional development materials. Professional Development in Education, 40(4), 627-653.
  • Yazar1. (2016). Yayımlanmamış Doktora Tezi. Karadeniz Teknik Üniversitesi, Trabzon.

The Change of Geometric Thinking Habit of Prospective Teachers

Year 2020, Volume: 48, 431 - 453, 07.01.2020

Abstract

Individuals
need to have some geometric habits of minds such as reasoning with the
relationship, considering the specific cases and generalizing geometric ideas,
exploration, and reflection, and investigating invariants as well as content
knowledge. In this study, it was aimed to investigate the changes in preservice
mathematics teachers' habits of mind through the freshmen year to senior year
in a teacher education program. In this direction, the main purpose of this
study was to discuss teacher training programs in universities. The
participants of this study, which is conducted by longitudinal research method,
were 31 preservice teachers who enrolled in a mathematics teacher education
undergraduate program in a state university in 2012 - 2016. Data collection
tools were four open-ended questions addressing to geometric habits of mind.
The data were analyzed via geometric habits of mind’s indicators. The results
showed that preservice teachers used exploration and reflection, and reasoning
with relationship habits more in their senior year in comparison with their
freshman year. This result means that the context of the courses directed
preservice teachers to the habits of exploration and reflection and reasoning
with a relationship. Yet, preservice teachers need to use other geometric habits
of mind to overcome geometry problems.

References

  • Abramovich, S., & Connell, M. L. (2014). Using technology in elementary mathematics teacher education: a sociocultural perspective. Hindawi Publishing Corporation ISRN Education, 1-9.
  • Bonn, T. V. (2015). Discovering and applying geometric transformations: Transformations to Show congruence and similarity. Unpublished master thesis, California State University, San Bernardino:CA.
  • Chan Y. (2003). GeoGebra as a tool to explore, conjecture, verify, justify and prove: The case of a circle. North American GeoGebra Journal, 2 (1), 2162-3856.
  • Costa, A. L. & Kallick, B. (2000). Discovering ang exploring habits of mind. Alexandria, VA: Association for Supervision & Curriculum Development.
  • Coxford, A. F., Fey, J. T., Hirsch, C. R., Schoen, H. L., Burrill, G., Hart, E. W. & Watkins, A.E. (1998). Contemporary mathematics in context: A unified approach. Implementing the core-plus mathematics curriculum. Chicago: Everyday Learning Corporation.
  • Cuoco, A., Goldenberg, E. & Mark, J. (1996). Habits of mind: an organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15(4), 375-402.
  • Cuoco, A., Goldenberg, E.P. & Mark, J. (2010). Organizing a curriculum around mathematical habits of mind. Mathematics teacher, 103(9), 682-688.
  • Driscoll, M. J., DiMatteo, R. W., Nikula, J. & Egan, M. (2007). Fostering geometric thinking: A guide for teachers grades 5-10. Portsmouth, NH: Heinemann.
  • Driscoll, M. J., DiMatteo, R. W., Nikula, J., Egan, M., Mark, J. & Kelemanik, G. (2008). The Fostering Geometric Thinking Toolkit: A Guide for Staff Development. Portsmouth, NH: Heinemann.
  • Friel, S. N. & Markworth, A. (2009). A framework for analyzing geometric pattern tasks. Mathematics Teaching in Middle School, 15(1), 24-33.
  • Goldenberg, E. P. (1996). “Habits of Mind” as an organizer for the curriculum. Journal of Education, 178(1), 13-34.
  • Goldenberg, E. P., Mark, J. & Cuoco, A. (2010). An algebraic habits of mind perspective on elementary school. Teaching Children Mathematics, 16(9), 548-556.
  • Harel, G. & Sowder, L. (2005). Advanced mathematical-thinking at any age: its nature and its development. Mathematical Thinking & Learning, 7(1), 27–50
  • Hu, H-W. (2005). Developing siblings and peer tutors to assist native Taiwanese children in learning habits of mind for math success. Dissertation Abstracts International, 256B (UMI No. 3179886).
  • Jacobbe, T. & Millman, R. S. (2009). Mathematical habits of mind for preservice teachers. School Science and Mathematics, 109(5), 298-302.
  • Lim, K. H. & Selden, A. (2009). Mathematical habits of mind. In S. L. Swars, D. W. Stinson and S. Lemons-Smith (Eds.). Proceedings of the 31th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University.
  • Marshall, A. R (2004). High school mathematics habits of mind instruction: Student growth and development. Dissertation Abstract International, 115B, (UMI No. 1421654).Marzano, R. J., Pickering, D. & McTighe, J. (1993). Assessing student outcomes: Performance assessment using the dimension of learning model. Alexandria, VA: Association for Supervision and Curriculum Development.
  • Matsuura, R., Sword, S., Piecham, M. B., Stevens, G. & Cuoco, A. (2013). Mathematical habits of mind for teaching: Using language in algebra classrooms. The Mathematics Enthusiast, 10(3), 735-776.
  • Rolle, Y. A. (2008). Habits of practice: A qualitative case study of a middle-school mathematics teacher. Dissertation Abstract International, 309B, (UMI No. 3325854).
  • Samson, D. (2014). Visualising and generalising with square arrays. Australian Mathematics Teacher, 70(2), 4-12.
  • Seago, N., Jacobs, K. J., Driscoll, M., Nikula, J., Matassa, M. & Callahan, P. (2013). Developing teacher’s knowledge of a transformation-based approach to geometric similarity. Mathematics Teacher Educator, 2(1), 74-85.
  • Seago, N. M., Jacobs, J. K., Heck, D. J., Nelson, C. L. & Malzahn, K. A. (2014). Impacting teachers’ understanding of geometric similarity: Results from field testing of the learning and teaching geometry Professional development materials. Professional Development in Education, 40(4), 627-653.
  • Yazar1. (2016). Yayımlanmamış Doktora Tezi. Karadeniz Teknik Üniversitesi, Trabzon.
There are 23 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Buket Özüm Bülbül 0000-0001-9610-7053

Bülent Güven 0000-0001-8767-6051

Publication Date January 7, 2020
Submission Date January 15, 2019
Acceptance Date August 19, 2019
Published in Issue Year 2020 Volume: 48

Cite

APA Bülbül, B. Ö., & Güven, B. (2020). Öğretmen Adaylarının Geometrik Düşünme Alışkanlıklarının Değişimi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 48, 431-453.