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İlköğretim Matematik Öğretmenlerinin Açılar Konusundaki Öğrenci Kavram Yanılgılarının Farkındalıklarının Belirlenmesi

Yıl 2018, Sayı: 35, 123 - 144, 30.06.2018

Suphi Önder Bütüner Mehmet Filiz

Öz

Bu
çalışmanın amacı ortaokul matematik öğretmenlerinin öğrencilerde açı kavramı
ile ilgili var olan kavram yanılgıları ile ilgili farkındalık durumlarını
belirlemektir. Çalışmanın örneklemini, çalışmaya katılmaya gönüllü olan 16
matematik öğretmeni oluşturmaktadır. Veri toplama aracı olarak “demografik
bilgiler” ve “kavram yanılgılarının farkındalıkları” olmak üzere iki ana
kısımdan oluşan bir form kullanılmıştır. Veriler üzerinde içerik analizi
yapılmış, analiz sonuçları karşılaştırıldığında ise iki araştırmacının
kodlamaları arasındaki uyum indeksi 0.88 olarak bulunmuştur. Çalışmaya katılan
öğretmenlerin tamamının, derslerde sadece açının statik tanımı üzerinde
durdukları ve öğrencilerin açılar konusunda yaşadıkları kavram yanılgılarını
tespit etmede zorluklar yaşadıkları tespit edilmiştir. Çalışmaya katılan
öğretmenler, kavram yanılgılarını gidermek için kavramları yeniden anlatma,
açının statik tanımına ek olarak açı konusunda ki bazı yaygın kavram
yanılgılarına vurguda bulunma ve somut materyal kullanma gibi öğretim
yöntemlerine başvurabileceklerini belirtmişlerdir. Çalışmanın
sonucuna dayalı olarak, öğretmenlere, öğrencilerde oluşabilecek kavram yanılgılarını gidermek
için nasıl öğretim faaliyetleri tasarlayabileceklerine yönelik hizmet içi
eğitim kursları düzenlenebilir.

Anahtar Kelimeler

Açı kavram yanılgısı matematik öğretmeni

Kaynakça

  • 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.
  • Asquith, P., Stephens, A., Knuth, E., & Alibali, M. (2007). Middle school teachers‟ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
  • Bağcı, O. (2014). Ortaokul matematik 6 ders kitabı. Ankara: Dikey Yayıncılık.
  • Bütüner, S. Ö., & Filiz, M. (2017). Exploring high-achieving sixth grade students’ erroneous answers and misconceptions on the angle concept. International Journal of Mathematical Education in Science and Technology, 48(4), 533-554.
  • Chick, H. L., & Baker, M. K. (2005). Investigating teachers’responses to student misconceptions. In H. L. Chick, &, M. K. Baker (eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 249-256). Melbourne: PME
  • Clausen-May, T. (2008). Another angle on angles. Australian Primary Mathematics Classroom, 13(1), 4–8.
  • Clements, D. H. & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed), Handbook on mathematics teaching and learning. (pp. 420-464). New York: Macmillan.
  • Clements, D., & Burns, B. (2000). Students’ development of strategies for turn and angle measure. Educational Studies in Mathematics, 41, 31–45.
  • Clements, D. H. (2004). Major themes and recommendations. In Clements, D. H., Sarama, J., & DiBiase, A. M. (Eds.). Engaging young children in mathematics: Standards for early childhood mathematics education. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Cohen L, Manion L., & Morrison K. (2007). Research methods in education. 6th edn. London: Routledge
  • Çakıroğlu, Ü., Güven, B. ve Akkan, Y. (2008). Matematik öğretmenlerinin matematik eğitiminde bilgisayar kullanımına yönelik inançlarının incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 35, 38-52.
  • Dale, L. (2013). Importance of angles in mathematics.15 ocak 2017 tarihinde http://www.ehow.com/info8466997importance-angles maths.html#ixzz2nypd6hqW adresinden alınmıştır.
  • Feza, N., & Webb, P. (2005). Assessment standards, van Hiele levels, and grade seven learners‟ understanding of geometry. Pythagoras, 62, 36-47.
  • Gökkurt, B., Şahin, Ö., Soylu, Y., & Doğan, Y. (2015). Öğretmen adaylarının geometrik cisimler konusuna ilişkin öğrenci hatalarına yönelik pedagojik alan bilgileri. İlköğretim Online, 14(1), 55-71.
  • Graeber, A. O. (1999). Forms of knowing mathematics: What preservice teachers should learn. Educational Studies in Mathematics, 38, 189-208.
  • Griffiths, A. K., & Preston, K. R. (1989). An ınvestigation of grade 12 students' misconceptions relating to fundamental characteristics of molecules and atoms. Journal of Research in Science Teaching, 29, 611-628
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
  • Gürbüz, R., & Erdem, Z. Ç. (2015). Öğrenci hata ve yanılgılarına ilişkin öğretmen görüşleri: Denklem örneği. Kuramsal Eğitim Bilim Dergisi, 8(3), 360-379.
  • Henderson, D., & Taimina, D. (2005). Experiencing geometry: Euclidean and non euclidean with history, New York: Cornell University
  • Karaağaç, M. K., & Köse, L. (2015). Öğretmen ve öğretmen adaylarının öğrencilerin kesirler konusundaki kavram yanılgıları ile ilgili bilgilerinin incelenmesi. Sakarya Üniversitesi Eğitim Fakültesi Dergisi,30, 72-92.
  • Keiser, J. (2004). Struggles with developing the concept of angle: Comparing sixth-grade students’ discourse to the history of angle concept. Mathematical Thinking and Learning, 6(3), 285–306.
  • Kim, O. K., & Lee, J. H. (2014). Representations of Angle and Lesson Organization in Korean and American Elementary Mathematics Curriculum Programs. KAERA Research Forum, 1(3), 28–37.
  • Marchis, I. (2008). Geometry in primary school mathematics. Educatia, 21(6), 131-139.
  • Mewborn, D. S. (2003). Teaching, teachers’ knowledge, and their Professional development. In J. Kilpatrick, W. G. Martin, and D. Schifter (Eds.), A research companion to principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.
  • Mitchelmore, M.C. (1998). Young students' concepts of turning and angle. Cognition and Instruction, 16(3), 265-284.
  • Moore, K. (2013). Making sense by measuring arcs:A teaching experiement in angle measure. Educational Studies in Mathematics, 83, 225-245.
  • Munier, V., Devichi, C., & Merle, H. (2008). A physical situation as a way to teach angle. Teaching Children Mathematics, March, 402-407.
  • Munier, V., & Merle, H. (2009). Interdisciplinary Mathematics–Physics Approaches to Teaching the Concept of Angle in Elementary School. International Journal of Science Education, 31(14), 1857–1895.
  • Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. Chestnut Hill, MA, USA: Boston College, TIMSS & PIRLS International Study Center. http://timssandpirls.bc.edu/timss2015/international-results/ adresinden 12 ocak 2017 tarihinde alınmıştır.
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Özdemir, B. G., Bayraktar, R., & Yılmaz, M. (2017). Sınıf ve matematik öğretmenlerinin kavram yanılgılarına ilişkin öğretimsel açıklamaları. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 7(2), 284-305.
  • Park, S., & Oliver, J. S. (2007). Revisiting the conceptualization of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Science Education, 38 (3), 261-184.
  • Ryan, J., & Williams, J. (2007). Children’s mathematics 4-15: learning from errors and misconceptions, McGraw Hill:Open University Press.
  • 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.
  • Smith, C. P., King, B. , & Hoyte, J. (2014). Learning angles through movement: Critical actions for developing understanding in an embodied activity. The Journal of Mathematical Behavior, 36, 95–108.
  • Stavy, R., & Tirosh, D. (2000). How students (mis-)understand science and mathematics: Intuitive Rules. New York: Teachers College Press.
  • T.C. Millî Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı. (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. http://ttkb.meb.gov.tr/dosyalar/programlar/ilkogretim/matematik_5-8.rar adresinden erişildi.
  • Tanisli, D., & Kose, N. Y. (2013). Pre-service mathematics teachers’ knowledge of students about the algebraic concepts. Australian Journal of Teacher Education, 38 (2), 1-18.
  • Ural, A. (2014). Geometri öğretiminde MS Paint kullanımı. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 29, 92-107.
  • Ural, A . (2015). Ortaokul matematik öğretmenlerinin bilgi iletişim teknolojisi ve psikomotor beceri kullanimlarinin incelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 6 (1), 93-116.
  • Wilson, P., & Adams, V. (1992). A dynamic way to teach angle and angle measure. The Arithmetic Teacher, 39(5), 6-13.
  • Zuya, H. E. (2014). Investigating elementary school mathematics teachers’ knowledge of students about some numbers. International Journal for Innovation Education and Research, 2(12), 150-160.

Determining Elementary School Mathematics Teachers’ Awareness of Students’ Misconceptions on the Angle Concept

Yıl 2018, Sayı: 35, 123 - 144, 30.06.2018

Suphi Önder Bütüner Mehmet Filiz

Öz

This study aims to detect elementary school
mathematics teachers’ awareness of students’ misconceptions of the angle
concept. Sixteen mathematics teachers working at eight different elementary
schools in Yozgat, Turkey, voluntarily participated in this study. Teachers
completed a questionnaire consisting of two main components; namely,
“demographic information” and “awareness of misconceptions”, and the gathered
data were analysed with content analysis. This analysis was performed by two
researchers, and their inter-rater agreement was calculated as 0.88. We found
that all of the teachers in our sample were only able to provide a static definition
of the angle concept in their classes and they encountered challenges in
determining students’ misconceptions on the angle concept. To assist students
to overcome their misconceptions on the angle concept, the teachers in our
sample indicated that they could employ several teaching methods including
re-explaining, mentioning several misconceptions in addition to the static
definition of the angle concept, and using concrete materials for teaching the
angle concept. Based on these findings, we recommend further investigation of
teaching practices in this regard and if found valid, an in-service teacher
training program should be implemented. In this way mathematics teachers in
Turkey will be enabled to create teaching activities that address students’
misconceptions of the angle concept.

Anahtar Kelimeler

The angle concept misconceptions mathematics teachers teachers’ awareness

Kaynakça

  • 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.
  • Asquith, P., Stephens, A., Knuth, E., & Alibali, M. (2007). Middle school teachers‟ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
  • Bağcı, O. (2014). Ortaokul matematik 6 ders kitabı. Ankara: Dikey Yayıncılık.
  • Bütüner, S. Ö., & Filiz, M. (2017). Exploring high-achieving sixth grade students’ erroneous answers and misconceptions on the angle concept. International Journal of Mathematical Education in Science and Technology, 48(4), 533-554.
  • Chick, H. L., & Baker, M. K. (2005). Investigating teachers’responses to student misconceptions. In H. L. Chick, &, M. K. Baker (eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 249-256). Melbourne: PME
  • Clausen-May, T. (2008). Another angle on angles. Australian Primary Mathematics Classroom, 13(1), 4–8.
  • Clements, D. H. & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed), Handbook on mathematics teaching and learning. (pp. 420-464). New York: Macmillan.
  • Clements, D., & Burns, B. (2000). Students’ development of strategies for turn and angle measure. Educational Studies in Mathematics, 41, 31–45.
  • Clements, D. H. (2004). Major themes and recommendations. In Clements, D. H., Sarama, J., & DiBiase, A. M. (Eds.). Engaging young children in mathematics: Standards for early childhood mathematics education. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Cohen L, Manion L., & Morrison K. (2007). Research methods in education. 6th edn. London: Routledge
  • Çakıroğlu, Ü., Güven, B. ve Akkan, Y. (2008). Matematik öğretmenlerinin matematik eğitiminde bilgisayar kullanımına yönelik inançlarının incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 35, 38-52.
  • Dale, L. (2013). Importance of angles in mathematics.15 ocak 2017 tarihinde http://www.ehow.com/info8466997importance-angles maths.html#ixzz2nypd6hqW adresinden alınmıştır.
  • Feza, N., & Webb, P. (2005). Assessment standards, van Hiele levels, and grade seven learners‟ understanding of geometry. Pythagoras, 62, 36-47.
  • Gökkurt, B., Şahin, Ö., Soylu, Y., & Doğan, Y. (2015). Öğretmen adaylarının geometrik cisimler konusuna ilişkin öğrenci hatalarına yönelik pedagojik alan bilgileri. İlköğretim Online, 14(1), 55-71.
  • Graeber, A. O. (1999). Forms of knowing mathematics: What preservice teachers should learn. Educational Studies in Mathematics, 38, 189-208.
  • Griffiths, A. K., & Preston, K. R. (1989). An ınvestigation of grade 12 students' misconceptions relating to fundamental characteristics of molecules and atoms. Journal of Research in Science Teaching, 29, 611-628
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
  • Gürbüz, R., & Erdem, Z. Ç. (2015). Öğrenci hata ve yanılgılarına ilişkin öğretmen görüşleri: Denklem örneği. Kuramsal Eğitim Bilim Dergisi, 8(3), 360-379.
  • Henderson, D., & Taimina, D. (2005). Experiencing geometry: Euclidean and non euclidean with history, New York: Cornell University
  • Karaağaç, M. K., & Köse, L. (2015). Öğretmen ve öğretmen adaylarının öğrencilerin kesirler konusundaki kavram yanılgıları ile ilgili bilgilerinin incelenmesi. Sakarya Üniversitesi Eğitim Fakültesi Dergisi,30, 72-92.
  • Keiser, J. (2004). Struggles with developing the concept of angle: Comparing sixth-grade students’ discourse to the history of angle concept. Mathematical Thinking and Learning, 6(3), 285–306.
  • Kim, O. K., & Lee, J. H. (2014). Representations of Angle and Lesson Organization in Korean and American Elementary Mathematics Curriculum Programs. KAERA Research Forum, 1(3), 28–37.
  • Marchis, I. (2008). Geometry in primary school mathematics. Educatia, 21(6), 131-139.
  • Mewborn, D. S. (2003). Teaching, teachers’ knowledge, and their Professional development. In J. Kilpatrick, W. G. Martin, and D. Schifter (Eds.), A research companion to principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.
  • Mitchelmore, M.C. (1998). Young students' concepts of turning and angle. Cognition and Instruction, 16(3), 265-284.
  • Moore, K. (2013). Making sense by measuring arcs:A teaching experiement in angle measure. Educational Studies in Mathematics, 83, 225-245.
  • Munier, V., Devichi, C., & Merle, H. (2008). A physical situation as a way to teach angle. Teaching Children Mathematics, March, 402-407.
  • Munier, V., & Merle, H. (2009). Interdisciplinary Mathematics–Physics Approaches to Teaching the Concept of Angle in Elementary School. International Journal of Science Education, 31(14), 1857–1895.
  • Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. Chestnut Hill, MA, USA: Boston College, TIMSS & PIRLS International Study Center. http://timssandpirls.bc.edu/timss2015/international-results/ adresinden 12 ocak 2017 tarihinde alınmıştır.
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Özdemir, B. G., Bayraktar, R., & Yılmaz, M. (2017). Sınıf ve matematik öğretmenlerinin kavram yanılgılarına ilişkin öğretimsel açıklamaları. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 7(2), 284-305.
  • Park, S., & Oliver, J. S. (2007). Revisiting the conceptualization of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Science Education, 38 (3), 261-184.
  • Ryan, J., & Williams, J. (2007). Children’s mathematics 4-15: learning from errors and misconceptions, McGraw Hill:Open University Press.
  • 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.
  • Smith, C. P., King, B. , & Hoyte, J. (2014). Learning angles through movement: Critical actions for developing understanding in an embodied activity. The Journal of Mathematical Behavior, 36, 95–108.
  • Stavy, R., & Tirosh, D. (2000). How students (mis-)understand science and mathematics: Intuitive Rules. New York: Teachers College Press.
  • T.C. Millî Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı. (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. http://ttkb.meb.gov.tr/dosyalar/programlar/ilkogretim/matematik_5-8.rar adresinden erişildi.
  • Tanisli, D., & Kose, N. Y. (2013). Pre-service mathematics teachers’ knowledge of students about the algebraic concepts. Australian Journal of Teacher Education, 38 (2), 1-18.
  • Ural, A. (2014). Geometri öğretiminde MS Paint kullanımı. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 29, 92-107.
  • Ural, A . (2015). Ortaokul matematik öğretmenlerinin bilgi iletişim teknolojisi ve psikomotor beceri kullanimlarinin incelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 6 (1), 93-116.
  • Wilson, P., & Adams, V. (1992). A dynamic way to teach angle and angle measure. The Arithmetic Teacher, 39(5), 6-13.
  • Zuya, H. E. (2014). Investigating elementary school mathematics teachers’ knowledge of students about some numbers. International Journal for Innovation Education and Research, 2(12), 150-160.
Toplam 42 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Suphi Önder Bütüner

Mehmet Filiz

Yayımlanma Tarihi 30 Haziran 2018
Gönderilme Tarihi 21 Ekim 2017
Yayımlandığı Sayı Yıl 2018 Sayı: 35

Kaynak Göster

APA Bütüner, S. Ö., & Filiz, M. (2018). İlköğretim Matematik Öğretmenlerinin Açılar Konusundaki Öğrenci Kavram Yanılgılarının Farkındalıklarının Belirlenmesi. Sakarya Üniversitesi Eğitim Fakültesi Dergisi(35), 123-144.
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Bu eser Creative Commons Atıf-GayriTicari 4.0 Uluslararası Lisansı ile lisanslanmıştır.