Araştırma Makalesi
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Türkiye’deki 11. Sınıf Matematik Ders Kitaplarının Radyan Tanım ve Şekil Temsillerinin İncelenmesi: Nitel ve Nicel Açı Görüşü

Yıl 2022, Cilt: 39-1 Sayı: 2, 71 - 97, 31.12.2022
https://doi.org/10.52597/buje.909571

Öz

Bu çalışmanın amacı Türkiye’deki matematik ders kitaplarında yer alan radyan tanım ve şekil temsillerinin incelenmesidir. Bu nitel araştırmanın verileri 2019-2020 eğitim-öğretim yılında 11. sınıf ortaöğretim matematik derslerinde okutulması kararlaştırılan beş ders kitabından toplanmıştır. Bu belgelerden elde edilen veriler Alyami’nin (2020) radyan açı ölçüsünün tanım ve şekilleri için nitel ve nicel açı görüşü ayrımına dayanan analiz çerçevesi kullanılarak betimleme çözümlemesine tabi tutulmuştur. Araştırmanın sonuçlarına göre ders kitaplarındaki radyan tanımları ve tanımı açıklayan radyan şekil temsilleri bir radyana odaklanmaktadır. Bu tanım ve şekillerde yay uzunluğu ile yarıçapın eşitlik dışındaki orantısal ilişkiye yeterince vurgu yapılmamıştır. Araştırmanın sonuçları doğrultusunda ders kitaplarındaki radyan tanımı ve radyan temsili şekillerde yay uzunluğu ile yarıçap uzunluğunun eşitlik dışındaki nicel ilişkisinin ön plana çıkarılması önerilebilir.

Kaynakça

  • Abramson, J. P. (2018). Precalculus [eKitap]. OpenStax. https://shareok.org/handle/11244/301394
  • Akbaş, M. (Haz.). (2019). Ortaöğretim matematik 11 ders kitabı (2. Baskı). Millî Eğitim Bakanlığı Yayınları.
  • Akkoç, H. (2008). Pre-service mathematics teachers’ concept images of radian. International Journal of Mathematical Education in Science and Technology, 39(7), 857-878. https://dx.doi.org/10.1080/0020739080 2054458
  • Akkoç, H., ve Akbaş-Gül, N. (2010). Analysis of a teaching approach aiming at eliminating student difficulties with radian. Ankara University Journal of Faculty of Educational Sciences (JFES), 43(1), 97-129. https://dx.doi.org/10.1501/Egifak_0000001192
  • Akkoç, H., ve Katmer, V. (2011). Pre-service mathematics teachers' concept images of π. B. Ubuz (Haz.), Proceedings of the 35th International Conference on the Psychology of Mathematics Education, 1, s. 243. Ankara, Türkiye. PME.
  • Alyami, H. (2020). Textbook representations of radian angle measure: The need to build on the quantitative view of angle. School Science and Mathematics, 120(1), 15-28. https://dx.doi.org/10.1111/ssm.12380
  • Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2017). Australian curriculum: Mathematics. https://www.australiancurriculum.edu.au/
  • Barrera, A. (2014). Unit circles and inverse trigonometric functions. Mathematics Teacher, 108(2), 114-119. https://dx.doi.org/10.5951/mathteacher.108.2.0114
  • Bowen, G. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27-40. https://dx.doi.org/10.3316/QRJ0902027
  • Bressoud, D. M. (2010). Historical reflections on teaching trigonometry. Mathematics Teacher, 104(2), 106-112. https://dx.doi.org/10.2307/20876798
  • Creswell, J. W. (2014). Araştırma deseni: Nitel, nicel ve karma yöntem yaklaşımları. (S. B. Demir, Çev.). (4.baskıdan çeviri). Eğiten Kitap.
  • Demir, Ö. (2012). Students’ concept development and understanding of sine and cosine functions: A new theoretical and educational approach. [Yayımlanmamış doktora tezi]. Amsterdam University.
  • Eğitim Bilişim Ağı [EBA]. (t.y.). Ders kitapları. https://www.eba.gov.tr/ adresinden 14.01.2020 tarihinde erişildi.
  • Erdem, E. ve Man, S. (2018). Ortaokul matematik öğretmenlerinin radyan’a ve özelde π sayısına ilişkin kavramsal bilgileri. Ege Eğitim Dergisi / Ege Journal of Education, 19(2), 488-504. https://dx.doi.org/10.12984/egeefd.401997
  • Erduran, A. ve Özdemir, M. F. (2019). Ortaöğretim matematik 11. sınıf ders kitabı. Top Yayıncılık.
  • Euclid. (2013). Öklid’in öğelerinin 13 kitabından birinci kitap. (Ö. Öztürk ve D. Pierce, Çev.). California, USA. (Orijinal çalışma: Euclidis elementa, volume I of Euclidis Opera Omnia. Teubner. Edidit et Latine interpretatvs est I. L. Heiberg, 1883). Mimar Sinan Güzel Sanatlar Üniversitesi Matematik Bölümü.
  • Fan, L., Zhu, Y., ve Miao, Z. (2013). Textbook research in mathematics education: Development status and directions. ZDM Mathematics Education, 45(5), 633-646. https://dx.doi.org/10.1007/s11858-013-0539-x
  • Fi, C. D. (2003). Preservice secondary school mathematics teachers’ knowledge of trigonometry: Subject matter content knowledge, pedagogical content knowledge and envisioned pedagogy. [Yayımlanmamış doktora tezi]. University of Iowa. https://dx.doi.org/10.17077/etd.hgi8dv0k
  • Forster, N. (1995). The analysis of company documentation. C. Cassell ve G. Symon içinde, Qualitative methods in organizational research: A practical guide. Sage.
  • Guba, E. G., ve Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. Educational Communication and Technology Journal, 30(4), 233-252.
  • Gökçek, T. ve Hacısalihoğlu-Karadeniz, M. (2013). Ortaöğretimde matematik ders kitabı yerine alternatif kaynakların tercih edilme nedenleri. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 4(1), 20-31.
  • Gümüşel, İ. S. ve Deviren, M. E. (2019). Ortaöğretim matematik temel düzey ders kitabı 11. MHG Kitap Basım Yayın Ticaret A. Ş.
  • Güntekin, H. ve Akgün, L. (2011). Trigonometrik kavramlarla ilgili öğrencilerin sahip olduğu hatalar ve öğrenme güçlükleri. Çukurova Üniversitesi Eğitim Fakültesi Dergisi, 40(1), 98-113.
  • Heath, T. (1956). The thirteen books of Euclid’s Elements. Translated from the text of Heiberg with introduction and commentary (Sayı I). (2. baskı). Dover.
  • Hertel, J., ve Cullen, C. (2011). Teaching trigonometry: A directed length approach. L. R., Wiest, ve T. Lamberg (Haz.), Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (s. 1400-1407). University of Nevada, Reno.
  • Kamber, D., ve Takaci, D. (2018). On problematic aspects in learning trigonometry. International Journal of Mathematical Education in Science and Technology, 49(2), 161-175. https://dx.doi.org/10.1080/0020739X.2017.1357846
  • Keiser, J. M. (2004). Struggles with developing the concept of angle: Comparing sixth-grade students' discourse to the history of the angle concept. Mathematical Thinking and Learning, 6(3), 285-306. https://dx.doi.org/10.1207/s1532 7833m tl0603_2
  • Kells, L. M. (2014). Radian measure. AccessScience. https://doi.org/10.1036/1097-8542.565900
  • Kupková, E. (2008). Developing the radian concept understanding and the historical point of view. Itália: Scienze Matematiche.
  • Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. K. Lester Jr. (Haz.), Second handbook of research on mathematics teaching and learning (s. 629-667). Information Age.
  • Lindkvist, J. (2019). The circle constant remastered for less misconceptions: A textual analysis of the introduction of radians in mathematics education textbooks for the Swedish upper secondary school. Stockholm Universitet, Sweden.
  • Lobato, J., ve Ellis, A. (2010). Developing essential understanding of ratios, proportions & proportional reasoning for teaching mathematics in grades 6–8. National Council of Teachers of Mathematics.
  • Maknun, C. L., Rosjanuardi, R., ve Jupri, A. (2018). Lesson design on the relationship between radian and degree. AIP Conference Proceeding. AIP Publishing. https://dx.doi.org/10.1063/1.5054435
  • Martinez-Sierra, G. (2008, Temmuz). On the transit from trigonometry to calculus:The case of the conceptual breaks in the construction of the trigonometric functions in school. [Sözlü sunum] 11th International Congress on Mathematical Education. Monterrey, Meksika.
  • Masal, E. (Haz.). (2019). Ortaöğretim temel düzey matematik 11 ders kitabı. Millî Eğitim Bakanlığı Yayınları.
  • Matos, J. (1990). The historical development of the concept of angle. The Mathematics Educator, 1(1), 4-11.
  • Mesa, V., ve Goldstein, B. (2017). Conceptions of angles, trigonometric functions, and inverse trigonometric functions in college textbooks. International Journal of Research in Undergraduate Mathematics Education, 3(2), 338-354. https://dx.doi.org/10.1007/s40753-016-0042-1
  • Miles, M. B., ve Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2.baskı.). Sage Publications, Inc.
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Investigation of the Radian Definitions and Figure Representations in 11th Grade Mathematics Textbooks in Turkey: Qualitative and Quantitative Views of Angle

Yıl 2022, Cilt: 39-1 Sayı: 2, 71 - 97, 31.12.2022
https://doi.org/10.52597/buje.909571

Öz

This study aims to examine the radian definition and figure representations in mathematics textbooks in Turkey. The data of this qualitative research consist of five 11th grade upper secondary mathematics textbooks used during the 2019-2020 academic year. Definitions and figures of radian angle measurement were analyzed descriptively using Alyami’s (2020) framework based on qualitative and quantitative views of angle. According to the findings, the definitions and representations of radian focus on one radian rather than the proportional relationships except the case of equality of arc length and radius. Considering the findings, we propose that the textbooks definitions and figures should highlight the quantitative relationships in addition to the case of equality of arc length and radius.

Kaynakça

  • Abramson, J. P. (2018). Precalculus [eKitap]. OpenStax. https://shareok.org/handle/11244/301394
  • Akbaş, M. (Haz.). (2019). Ortaöğretim matematik 11 ders kitabı (2. Baskı). Millî Eğitim Bakanlığı Yayınları.
  • Akkoç, H. (2008). Pre-service mathematics teachers’ concept images of radian. International Journal of Mathematical Education in Science and Technology, 39(7), 857-878. https://dx.doi.org/10.1080/0020739080 2054458
  • Akkoç, H., ve Akbaş-Gül, N. (2010). Analysis of a teaching approach aiming at eliminating student difficulties with radian. Ankara University Journal of Faculty of Educational Sciences (JFES), 43(1), 97-129. https://dx.doi.org/10.1501/Egifak_0000001192
  • Akkoç, H., ve Katmer, V. (2011). Pre-service mathematics teachers' concept images of π. B. Ubuz (Haz.), Proceedings of the 35th International Conference on the Psychology of Mathematics Education, 1, s. 243. Ankara, Türkiye. PME.
  • Alyami, H. (2020). Textbook representations of radian angle measure: The need to build on the quantitative view of angle. School Science and Mathematics, 120(1), 15-28. https://dx.doi.org/10.1111/ssm.12380
  • Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2017). Australian curriculum: Mathematics. https://www.australiancurriculum.edu.au/
  • Barrera, A. (2014). Unit circles and inverse trigonometric functions. Mathematics Teacher, 108(2), 114-119. https://dx.doi.org/10.5951/mathteacher.108.2.0114
  • Bowen, G. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27-40. https://dx.doi.org/10.3316/QRJ0902027
  • Bressoud, D. M. (2010). Historical reflections on teaching trigonometry. Mathematics Teacher, 104(2), 106-112. https://dx.doi.org/10.2307/20876798
  • Creswell, J. W. (2014). Araştırma deseni: Nitel, nicel ve karma yöntem yaklaşımları. (S. B. Demir, Çev.). (4.baskıdan çeviri). Eğiten Kitap.
  • Demir, Ö. (2012). Students’ concept development and understanding of sine and cosine functions: A new theoretical and educational approach. [Yayımlanmamış doktora tezi]. Amsterdam University.
  • Eğitim Bilişim Ağı [EBA]. (t.y.). Ders kitapları. https://www.eba.gov.tr/ adresinden 14.01.2020 tarihinde erişildi.
  • Erdem, E. ve Man, S. (2018). Ortaokul matematik öğretmenlerinin radyan’a ve özelde π sayısına ilişkin kavramsal bilgileri. Ege Eğitim Dergisi / Ege Journal of Education, 19(2), 488-504. https://dx.doi.org/10.12984/egeefd.401997
  • Erduran, A. ve Özdemir, M. F. (2019). Ortaöğretim matematik 11. sınıf ders kitabı. Top Yayıncılık.
  • Euclid. (2013). Öklid’in öğelerinin 13 kitabından birinci kitap. (Ö. Öztürk ve D. Pierce, Çev.). California, USA. (Orijinal çalışma: Euclidis elementa, volume I of Euclidis Opera Omnia. Teubner. Edidit et Latine interpretatvs est I. L. Heiberg, 1883). Mimar Sinan Güzel Sanatlar Üniversitesi Matematik Bölümü.
  • Fan, L., Zhu, Y., ve Miao, Z. (2013). Textbook research in mathematics education: Development status and directions. ZDM Mathematics Education, 45(5), 633-646. https://dx.doi.org/10.1007/s11858-013-0539-x
  • Fi, C. D. (2003). Preservice secondary school mathematics teachers’ knowledge of trigonometry: Subject matter content knowledge, pedagogical content knowledge and envisioned pedagogy. [Yayımlanmamış doktora tezi]. University of Iowa. https://dx.doi.org/10.17077/etd.hgi8dv0k
  • Forster, N. (1995). The analysis of company documentation. C. Cassell ve G. Symon içinde, Qualitative methods in organizational research: A practical guide. Sage.
  • Guba, E. G., ve Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. Educational Communication and Technology Journal, 30(4), 233-252.
  • Gökçek, T. ve Hacısalihoğlu-Karadeniz, M. (2013). Ortaöğretimde matematik ders kitabı yerine alternatif kaynakların tercih edilme nedenleri. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 4(1), 20-31.
  • Gümüşel, İ. S. ve Deviren, M. E. (2019). Ortaöğretim matematik temel düzey ders kitabı 11. MHG Kitap Basım Yayın Ticaret A. Ş.
  • Güntekin, H. ve Akgün, L. (2011). Trigonometrik kavramlarla ilgili öğrencilerin sahip olduğu hatalar ve öğrenme güçlükleri. Çukurova Üniversitesi Eğitim Fakültesi Dergisi, 40(1), 98-113.
  • Heath, T. (1956). The thirteen books of Euclid’s Elements. Translated from the text of Heiberg with introduction and commentary (Sayı I). (2. baskı). Dover.
  • Hertel, J., ve Cullen, C. (2011). Teaching trigonometry: A directed length approach. L. R., Wiest, ve T. Lamberg (Haz.), Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (s. 1400-1407). University of Nevada, Reno.
  • Kamber, D., ve Takaci, D. (2018). On problematic aspects in learning trigonometry. International Journal of Mathematical Education in Science and Technology, 49(2), 161-175. https://dx.doi.org/10.1080/0020739X.2017.1357846
  • Keiser, J. M. (2004). Struggles with developing the concept of angle: Comparing sixth-grade students' discourse to the history of the angle concept. Mathematical Thinking and Learning, 6(3), 285-306. https://dx.doi.org/10.1207/s1532 7833m tl0603_2
  • Kells, L. M. (2014). Radian measure. AccessScience. https://doi.org/10.1036/1097-8542.565900
  • Kupková, E. (2008). Developing the radian concept understanding and the historical point of view. Itália: Scienze Matematiche.
  • Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. K. Lester Jr. (Haz.), Second handbook of research on mathematics teaching and learning (s. 629-667). Information Age.
  • Lindkvist, J. (2019). The circle constant remastered for less misconceptions: A textual analysis of the introduction of radians in mathematics education textbooks for the Swedish upper secondary school. Stockholm Universitet, Sweden.
  • Lobato, J., ve Ellis, A. (2010). Developing essential understanding of ratios, proportions & proportional reasoning for teaching mathematics in grades 6–8. National Council of Teachers of Mathematics.
  • Maknun, C. L., Rosjanuardi, R., ve Jupri, A. (2018). Lesson design on the relationship between radian and degree. AIP Conference Proceeding. AIP Publishing. https://dx.doi.org/10.1063/1.5054435
  • Martinez-Sierra, G. (2008, Temmuz). On the transit from trigonometry to calculus:The case of the conceptual breaks in the construction of the trigonometric functions in school. [Sözlü sunum] 11th International Congress on Mathematical Education. Monterrey, Meksika.
  • Masal, E. (Haz.). (2019). Ortaöğretim temel düzey matematik 11 ders kitabı. Millî Eğitim Bakanlığı Yayınları.
  • Matos, J. (1990). The historical development of the concept of angle. The Mathematics Educator, 1(1), 4-11.
  • Mesa, V., ve Goldstein, B. (2017). Conceptions of angles, trigonometric functions, and inverse trigonometric functions in college textbooks. International Journal of Research in Undergraduate Mathematics Education, 3(2), 338-354. https://dx.doi.org/10.1007/s40753-016-0042-1
  • Miles, M. B., ve Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2.baskı.). Sage Publications, Inc.
  • Millî Eğitim Bakanlığı [MEB]. (2018). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı. Ankara: MEB Talim Terbiye Başkanlığı Yayınları. http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=343 adresinden 27.01.2019 tarihinde erişildi.
  • Ministry of Education, Singapore [MOE]. (2019). Additional mathematics syllabuses: Secondary three to four express course normal (academic) course. Singapore: Curriculum Planning and Development Division. https://www.moe.gov.sg/secondary/courses adresinden 28.10.2021 tarihinde erişildi.
  • Moore, K. C. (2013). Making sense by measuring arcs: A teaching experiment in angle measure. Educational Studies in Mathematics, 83(2), 225-245. https://dx.doi.org/10.1007/s10649-012-9450-6
  • Moore, K. C. (2014). Quantitative reasoning and the sine function: The case of Zac. Journal for Research in Mathematics Education, 45(1), 102-138. https://dx.doi.org/10.5951/jresematheduc.45.1.0102
  • Moore, K. C., ve LaForest, K. R. (2014). The circle approach to trigonometry. Mathematics Teacher, 107(8), 616-623. https://dx.doi.org/10.5951/mathteacher.107.8.0616
  • Moyer, R. E., ve Ayers, F. (2018). Schaum's outline of trigonometry (6. baskı). McGraw-Hill Education.
  • Norum, K. E. (2008). Artifact analysis. L. M. Given (Haz.), The Sage Encyclopedia of Qualitative Research Methods, 1, s. 23-25. Sage Publications.
  • Orhun, N. (2004). Students’ mistakes and misconceptions on teaching of trigonometry. Journal of Curriculum Studies, 32(6), 797-820.
  • Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri (3. Baskıdan çeviri) (M. Bütün ve S. B. Demir, Çev. Haz.) Pegem Akademi.
  • Sampaio, H. R., ve Batista, I. L. (2018). Mathematics history and cognitive values on a didactic sequence: Teaching trigonometry. REDIMAT – Journal of Research in Mathematics Education, 7(3), 311-332. http://dx.doi.org/10.4471/redimat.2018.2727
  • Spangenberg, E. D. (2021). Manifesting of pedagogical content knowledge on trigonometry in teachers’ practice. Journal of Pedagogical Research, 5(3), 135-163. https:/dx./doi.org/10.33902/JPR.2021371325
  • Steckroth, J. J. (2007). Technology-enhanced mathematics instruction: Effects of visualization on student understanding of trigonometry. [Yayımlanmamış doktora tezi]. University of Virginia.
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  • Sundstrom, T., ve Schlicker, S. (2020). Trigonometry. ScholarWorks@GVSU https://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1012&context=books
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  • Thomas, G. B., Weir, M. D., Hass, J., ve Giordano, F. R. (2009). Thomas' Calculus. (11. Baskıdan çeviri). (R. Korkmaz, Çev.). Beta Basım.
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  • Vinner, S., ve Hershkowitz, R. (1980). Concept images and common cognitive paths in the development of some simple geometrical concepts. Proceedings the Fourth International Conference for the Psychology of Mathematics Education, (s. 177–184). Berkeley, California.
  • Weber, K. (2005). Students’ understanding of trigonometric functions. Mathematics Education Research Journal, 17(3), 91-112. https://dx.doi.org/10.1007/BF03217423
  • Wolbert, R. S., ve Moss, E. R. (2018). Developing the concept of a radian. The Mathematics Teacher, 111(4), 272-278. https://dx.doi.org/10.5951/mathteacher.111.4.0272
  • Yavuz-Mumcu, H., ve Aktürk, T. (2020). Mathematics teachers’ understanding of the concept of radian. Hacettepe University Journal of Education, 35(2), 320-337. https://dx.doi.org/10.16986/HUJE.2019053683
  • Yıldırım, A. ve Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri (10. Baskı). Seçkin Yayınevi.
  • Yıldırım, İ., ve Demir, S. (2014). Use of technology assisted mathematics education and alternative measurement together. Cukurova University Faculty of Education Journal, 42(1), 65-73. https://dergipark.org.tr/tr/pub/cuefd/issue/4135/54281
  • Yılmaz, G., Ertem, E. ve Güven, B . (2010). Dinamik geometri yazılımı Cabri’nin 11. sınıf öğrencilerinin trigonometri konusundaki öğrenmelerine etkisi. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 1(2), 200-216. https://dergipark.org.tr/tr/pub/turkbilmat/issue/21561/231427 adresinden 24.03.2021 tarihinde erişildi.
Toplam 71 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Özgün Çalışma
Yazarlar

Fikret Cihan 0000-0001-8783-4136

Hatice Akkoç 0000-0002-0223-1158

Yayımlanma Tarihi 31 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 39-1 Sayı: 2

Kaynak Göster

APA Cihan, F., & Akkoç, H. (2022). Türkiye’deki 11. Sınıf Matematik Ders Kitaplarının Radyan Tanım ve Şekil Temsillerinin İncelenmesi: Nitel ve Nicel Açı Görüşü. Bogazici University Journal of Education, 39-1(2), 71-97. https://doi.org/10.52597/buje.909571