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İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar

Year 2013, Volume: 12 Issue: 4, 1141 - 1156, 26.06.2013

Abstract

Araştırmanın amacı, ilköğretim matematik öğretmenlerinin 8. sınıf matematik öğretim programında yer alan histogram konusuyla ilgili kavrayışlarını ve öğretim sürecinde yaşadıkları sorunlarla ilgili görüşlerini ortaya çıkarmaktır. Katılımcılar, amaçlı örneklem yöntemine göre belirlenen ve Ankara’daki farklı devlet okullarında veya özel okullarda öğretmenlik yapan altı ilköğretim matematik öğretmeninden oluşmaktadır. Veriler, araştırmacı tarafından hazırlanan yarı yapılandırılmış bir görüşme formu aracılığıyla elde edilmiştir. Görüşmeler bireysel olarak yapılmıştır ve ses kayıt cihazı ile kaydedilmiştir. Sonuçlar, öğretmenlerin birçoğunun histogram, grup genişliği ve grup sayısı gibi kavramların anlamlarına yönelik derinlemesine muhakeme yapamadıklarını ortaya çıkarmıştır. Ek olarak, öğretmenlerin histogramın öğretim sürecinde; sekizinci sınıf matematik öğretmen kılavuz kitaptaki hatalar, öğrencilerin yaşadığı sıkıntılar ve okul dışı etkenler nedeniyle çeşitli problemler yaşadıkları tespit edilmiştir. Öğretmenler, özellikle sekizinci sınıf öğretmen kılavuz kitabında verilen histogramda grup genişliğinin bulunmasıyla ilgili açıklamaları tutarsız bulduklarını belirtmişlerdir

References

  • Alpaslan1907. (2009, Kasım 7). Re: Histogram oluşturma [Online forum comment]. Retrieved from http://www.egitimhane.com/histogram-olusturma-k17391-0.html.
  • Aygün, S. Ç., Aynur, N., Coşkuntürk, N., Çuha, S. S., Karaman, U., Özçelik, U., Ulubay, M. & Ünsal, N. (2011). Matematik Öğretmen Kılavuz Kitabı (4. baskı). Ankara: Özkan Matbaacılık.
  • Ball, D. L. (1990a). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90, 449-466.
  • Ball, D. L. (1990b). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21, 132-134.
  • Bruno, A. & Espinel, M. C. (2009). Construction and evaluation of histograms in teacher training. International Journal of Mathematical Education in Science and Technology, 40(4), 473-493.
  • Carpenter, T., Fennema, E., & Franke, M. (1996). Cognitively guided instruction: a knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3-20.
  • Chase, W., & Bown, F. (1992). General Statistics (Second edition). New York: Wiley.
  • Çakıroğlu, E. (2011, Ekim 10). Histogram [Description of form]. Retrieved from http://blog.metu.edu.tr/erdinc/2011/10/10/histogram/
  • Delmas, R. C., Garfield, J., Ooms, A. & Chance, B. (2007). Assessing students’ conceptual understanding after a first course in statistics. Statistics Education Research Journal, 6(2), 28-58.
  • Dematte, A. & Furinghetti, F. (1999). An exploratory study on students’ beliefs about mathematics as a socio-cultural process. In G. Philippou (Ed.), Mavi-8 Proceedings: Research on Mathematics
  • Dunham, P. H. & A. Osborne. (1991). Learning how to see: Students’ graphing difficulties. Focus on Learning Problems in Mathematics, 13, 35–49.
  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24, 94-116.
  • Friel, S. N., & Bright, G. W. (1996, April). Building a theory of graphicacy: How do students read graphs? Paper presented at the Annual Meeting of the American Educational Research Association, New York. Friel, S. N., Curcio, F., & Bright, G. W., (2001). Making sense of graphs: critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2): 124-1
  • Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524–549.
  • Iman, R. L. (1994). A Data-based Approach to Statistics. Belmont, California: Duxbury Press.
  • Işıksal, M., & Çakıroğlu, E. (2011). The nature of prospective teachers’ pedagogical content knowledge: the case of multiplication of fraction. Journal of Mathematics Teacher Education, 14, 213-230.
  • Kelly, A. E., Sloane, F., & Whittaker, A. (1997). Simple approaches to assessing underlying understanding of statistical concepts. In I. Gal and J. B. Garfield (Ed.), The Assessment Challenge in Statistics Education, (pp. 85-90). Amsterdam: IOS Press and the International Statistical Institute.
  • Kılcan, S. (2006). İlköğretim matematik öğretmenlerinin kavramsal bilgileri: Kesirlerle bölme. Yayınlanmamış Yüksek Lisans Tezi. Abant Izzet Baysal Üniversitesi, Bolu.
  • Kinach, B. M. (2002). A cognitive strategy for developing prospective teachers’ pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18(1), 51–71.
  • Kosslyn, S. (2006). Graph Design for the Eye and Mind. New York, NY: Oxford.
  • Landwehr, J. M., & Watkins, A. E. (1986). Exploring data the quantitative literacy series. California: Dale Seymour Publications.
  • Lee, C., & Meletiou-Mavrotheris, M. (2003). Some difficulties of learning histograms in introductory statistics. Paper presented at the Joint Statistical Meeting Section on Statistical Education. Retrieved from http://www.statlit.org/PDF/2003LeeASA.pdf.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Mattek. (2010, Ekim 17). Re: Histogram konusundaki grup genişliği [Online forum comment]. Retrieved from http://www.ilkmat.net/forum/ilkogretimde-matematik-ogretmenlerinin-sorunlari/histogramkonusundaki-grup-genisligi/?imode.
  • McLeod, D. (1992). Research on affect in mathematics education: a reconceptualization, in Grows, D. A. (Ed.), Handbook of Research on Mathematics Teaching and Learning , New York: Macmillan, 5755
  • M.E.B (2009). İlköğretim matematik dersi 6-8.sınıflar öğretim programı ve kılavuzu. Ankara: Milli Eğitim Basımevi.
  • Meletiou-Mavrotheris, M., & Lee, C. (2005). Exploring Introductory Statistics Students’ Understanding of Variation in Histograms. Proceedings publication in the 4 th Congress of the European Society for Research in Mathematics Education, Sant Feliu de Guíxols, Spain.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd edition). Thousand Oaks, CA: Sage Publications.
  • Moore, D. S. (1991). Statistics: Concepts und controversies (3rd. edition). New York: Freeman.
  • Osman (2008, Ekim 11). Re: Histogram oluşturma [Online forum comment]. Retrieved from http://www.egitimhane.com/histogram-olusturma-k17391-0.html.
  • Paradoks12. (2009, Ekim 11). Re: Kılavuz kitapta histogram grup genişliği ile ilgili çelişkili ifadeler [Online forum comment]. Retrieved from http://www.egitim-forum.com/ilkogretim-matematikdersipaylasimlari/klavuz-kitapta-histogram-grup-genisliginde-celiskili-ifadeler/10/?wap2.
  • Patton, M. Q. (1987). Creative evaluation (2nd ed.). Thousand Oaks, California: Sage Publications.
  • Shaughnessy, J. M. (2007). Research on statistical learning and reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957- 1009). Charlotte, NC: Information Age Publishing.
  • Shaughnessy, J. M. & Pfannkuch, M. (2002). How faithful is Old Faithful? Statistical thinking: A story of variation and prediction. Mathematics Teacher, 95(4), 252-259.
  • Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching, Educational Research 15(3), 4–
  • Thompson, A. (1992). Teachers’ beliefs and conceptions: a synthesis of the research, In Grows, D. A. (Ed.), Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan, 127-146. Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105-127.
  • Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25.
  • Toluk-Uçar, Z. (2011). Öğretmen adaylarının pedagojik içerik bilgisi: öğretimsel açıklamalar. Turkish Journal of Computer and Mathematics Education, 2(2), 87-102.
  • Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.
  • Yıldırım, A. & Simsek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri (6.basım). Ankara: Seçkin Yayıncılık.
  • Zawojewski, J. S. & Shaughnessy, J. M. (2000). Data and chance. In E. A. Silver & P. A. Kenney (Ed.), Results from Seventh Mathematics Assessment of the National Assessment of Educational Progress (235-268). Reston, VA: NCTM.

In-Service Elementary Mathematics Teachers\' Conceptions of Histogram and Difficulties about Its Teaching Process

Year 2013, Volume: 12 Issue: 4, 1141 - 1156, 26.06.2013

Abstract

The aim of this study was to examine in-service elementary mathematics teachers’ conceptions of histogram and their difficulties about its teaching process. By using purposeful sampling method, participants were selected as six in-service elementary mathematics teachers teaching at different private or government schools in Ankara. Data was obtained via a semi-structured interview form which was prepared by the researchers. The interviews were conducted individually and recorded with a voice recorder. The results of the study indicated that some teachers did not make reasonable interpretations about the meaning of histogram, the width of the interval, and the number of the groups. In addition, they had problems in their teaching processes because of the mistakes in the eighth grade mathematics teachers’ book, problems encountering students, and out-of-school education factors. Especially, teachers stated that they found inconsistent the explanations about the width of the interval of a histogram in the teachers’ book for eighth grade level.

References

  • Alpaslan1907. (2009, Kasım 7). Re: Histogram oluşturma [Online forum comment]. Retrieved from http://www.egitimhane.com/histogram-olusturma-k17391-0.html.
  • Aygün, S. Ç., Aynur, N., Coşkuntürk, N., Çuha, S. S., Karaman, U., Özçelik, U., Ulubay, M. & Ünsal, N. (2011). Matematik Öğretmen Kılavuz Kitabı (4. baskı). Ankara: Özkan Matbaacılık.
  • Ball, D. L. (1990a). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90, 449-466.
  • Ball, D. L. (1990b). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21, 132-134.
  • Bruno, A. & Espinel, M. C. (2009). Construction and evaluation of histograms in teacher training. International Journal of Mathematical Education in Science and Technology, 40(4), 473-493.
  • Carpenter, T., Fennema, E., & Franke, M. (1996). Cognitively guided instruction: a knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3-20.
  • Chase, W., & Bown, F. (1992). General Statistics (Second edition). New York: Wiley.
  • Çakıroğlu, E. (2011, Ekim 10). Histogram [Description of form]. Retrieved from http://blog.metu.edu.tr/erdinc/2011/10/10/histogram/
  • Delmas, R. C., Garfield, J., Ooms, A. & Chance, B. (2007). Assessing students’ conceptual understanding after a first course in statistics. Statistics Education Research Journal, 6(2), 28-58.
  • Dematte, A. & Furinghetti, F. (1999). An exploratory study on students’ beliefs about mathematics as a socio-cultural process. In G. Philippou (Ed.), Mavi-8 Proceedings: Research on Mathematics
  • Dunham, P. H. & A. Osborne. (1991). Learning how to see: Students’ graphing difficulties. Focus on Learning Problems in Mathematics, 13, 35–49.
  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24, 94-116.
  • Friel, S. N., & Bright, G. W. (1996, April). Building a theory of graphicacy: How do students read graphs? Paper presented at the Annual Meeting of the American Educational Research Association, New York. Friel, S. N., Curcio, F., & Bright, G. W., (2001). Making sense of graphs: critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2): 124-1
  • Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524–549.
  • Iman, R. L. (1994). A Data-based Approach to Statistics. Belmont, California: Duxbury Press.
  • Işıksal, M., & Çakıroğlu, E. (2011). The nature of prospective teachers’ pedagogical content knowledge: the case of multiplication of fraction. Journal of Mathematics Teacher Education, 14, 213-230.
  • Kelly, A. E., Sloane, F., & Whittaker, A. (1997). Simple approaches to assessing underlying understanding of statistical concepts. In I. Gal and J. B. Garfield (Ed.), The Assessment Challenge in Statistics Education, (pp. 85-90). Amsterdam: IOS Press and the International Statistical Institute.
  • Kılcan, S. (2006). İlköğretim matematik öğretmenlerinin kavramsal bilgileri: Kesirlerle bölme. Yayınlanmamış Yüksek Lisans Tezi. Abant Izzet Baysal Üniversitesi, Bolu.
  • Kinach, B. M. (2002). A cognitive strategy for developing prospective teachers’ pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18(1), 51–71.
  • Kosslyn, S. (2006). Graph Design for the Eye and Mind. New York, NY: Oxford.
  • Landwehr, J. M., & Watkins, A. E. (1986). Exploring data the quantitative literacy series. California: Dale Seymour Publications.
  • Lee, C., & Meletiou-Mavrotheris, M. (2003). Some difficulties of learning histograms in introductory statistics. Paper presented at the Joint Statistical Meeting Section on Statistical Education. Retrieved from http://www.statlit.org/PDF/2003LeeASA.pdf.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Mattek. (2010, Ekim 17). Re: Histogram konusundaki grup genişliği [Online forum comment]. Retrieved from http://www.ilkmat.net/forum/ilkogretimde-matematik-ogretmenlerinin-sorunlari/histogramkonusundaki-grup-genisligi/?imode.
  • McLeod, D. (1992). Research on affect in mathematics education: a reconceptualization, in Grows, D. A. (Ed.), Handbook of Research on Mathematics Teaching and Learning , New York: Macmillan, 5755
  • M.E.B (2009). İlköğretim matematik dersi 6-8.sınıflar öğretim programı ve kılavuzu. Ankara: Milli Eğitim Basımevi.
  • Meletiou-Mavrotheris, M., & Lee, C. (2005). Exploring Introductory Statistics Students’ Understanding of Variation in Histograms. Proceedings publication in the 4 th Congress of the European Society for Research in Mathematics Education, Sant Feliu de Guíxols, Spain.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd edition). Thousand Oaks, CA: Sage Publications.
  • Moore, D. S. (1991). Statistics: Concepts und controversies (3rd. edition). New York: Freeman.
  • Osman (2008, Ekim 11). Re: Histogram oluşturma [Online forum comment]. Retrieved from http://www.egitimhane.com/histogram-olusturma-k17391-0.html.
  • Paradoks12. (2009, Ekim 11). Re: Kılavuz kitapta histogram grup genişliği ile ilgili çelişkili ifadeler [Online forum comment]. Retrieved from http://www.egitim-forum.com/ilkogretim-matematikdersipaylasimlari/klavuz-kitapta-histogram-grup-genisliginde-celiskili-ifadeler/10/?wap2.
  • Patton, M. Q. (1987). Creative evaluation (2nd ed.). Thousand Oaks, California: Sage Publications.
  • Shaughnessy, J. M. (2007). Research on statistical learning and reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957- 1009). Charlotte, NC: Information Age Publishing.
  • Shaughnessy, J. M. & Pfannkuch, M. (2002). How faithful is Old Faithful? Statistical thinking: A story of variation and prediction. Mathematics Teacher, 95(4), 252-259.
  • Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching, Educational Research 15(3), 4–
  • Thompson, A. (1992). Teachers’ beliefs and conceptions: a synthesis of the research, In Grows, D. A. (Ed.), Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan, 127-146. Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105-127.
  • Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25.
  • Toluk-Uçar, Z. (2011). Öğretmen adaylarının pedagojik içerik bilgisi: öğretimsel açıklamalar. Turkish Journal of Computer and Mathematics Education, 2(2), 87-102.
  • Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.
  • Yıldırım, A. & Simsek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri (6.basım). Ankara: Seçkin Yayıncılık.
  • Zawojewski, J. S. & Shaughnessy, J. M. (2000). Data and chance. In E. A. Silver & P. A. Kenney (Ed.), Results from Seventh Mathematics Assessment of the National Assessment of Educational Progress (235-268). Reston, VA: NCTM.
There are 41 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Fadime Ulusoy

Erdinç Çakıroğlu

Publication Date June 26, 2013
Published in Issue Year 2013 Volume: 12 Issue: 4

Cite

APA Ulusoy, F., & Çakıroğlu, E. (2013). İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar. İlköğretim Online, 12(4), 1141-1156.
AMA Ulusoy F, Çakıroğlu E. İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar. İOO. December 2013;12(4):1141-1156.
Chicago Ulusoy, Fadime, and Erdinç Çakıroğlu. “İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları Ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar”. İlköğretim Online 12, no. 4 (December 2013): 1141-56.
EndNote Ulusoy F, Çakıroğlu E (December 1, 2013) İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar. İlköğretim Online 12 4 1141–1156.
IEEE F. Ulusoy and E. Çakıroğlu, “İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar”, İOO, vol. 12, no. 4, pp. 1141–1156, 2013.
ISNAD Ulusoy, Fadime - Çakıroğlu, Erdinç. “İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları Ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar”. İlköğretim Online 12/4 (December 2013), 1141-1156.
JAMA Ulusoy F, Çakıroğlu E. İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar. İOO. 2013;12:1141–1156.
MLA Ulusoy, Fadime and Erdinç Çakıroğlu. “İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları Ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar”. İlköğretim Online, vol. 12, no. 4, 2013, pp. 1141-56.
Vancouver Ulusoy F, Çakıroğlu E. İlköğretim Matematik Öğretmenlerinin Histogram Kavramına İlişkin Kavrayışları ve Bu Kavramın Öğretim Sürecinde Karşılaştıkları Sorunlar. İOO. 2013;12(4):1141-56.