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Türk ve Singapur Matematik Ders Kitaplarında Problem Analizi: Kesirlerde Bölme İşlemi

Year 2019, Volume: 47, 370 - 394, 12.09.2019
https://doi.org/10.9779/pauefd.522909

Abstract

Bu
çalışmada Türk ve Singapur matematik ders kitapları kesirlerde bölme işlemi
konusunda yer verilen problemler açısından karşılaştırılmıştır. Kitaplarda yer
alan problemler; adım sayısı, cevap tipi, bağlam ve bilişsel beklenti
özellikleri açısından sınıflandırılmışlardır. Analizler iki farklı araştırmacı
tarafından yapılmış, araştırmacılar arasındaki Cohen Kappa uyum indeksi her bir
kategori için 0.98-1.00 arasında bulunmuştur. Elde edilen bulgulara göre, Singapur
kitabında, Türk kitaplarına kıyasla çok adımlı, açıklama-çözüm gerektiren
problem sayısı daha fazladır. Her iki ülke kitabındaki kesir bölmesiyle ilgili
tüm problemler yeterli veri içermektedir. Ders kitaplarındaki günlük hayat
problemi sayısı azdır. Ayrıca Singapur ders kitabının çoklu formda ifade
edilmiş problemler bakımından Türk kitaplarından zengin olduğu tespit
edilmiştir. Türk kitaplarında, Singapur kitabına nazaran matematiksel muhakeme
ve temsil kategorisine giren problem sayısı oldukça az olup, Türk kitaplarında
kavramsal bilgi kategorisine giren hiçbir problem yoktur. Bu durum Singapur’un
uluslararası sınavlarda Türkiye’den daha iyi bir performans göstermesinin
nedenlerinden biri olarak düşünülebilir. 

References

  • Alajmi, A. M. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan and Kuwait. Educational Studies in Mathematics, 79, 239-261.
  • Black, P., & Wiliam, D. (1998). Inside the black box: raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139–148.
  • Brenner, M.E., Herman, S., Ho, H. & Zimmer, J.M. (1999). Cross-national comparison of representational competence. Journal for Research in Mathematics Education, 30(5), 541–557.
  • Brown G., & Quinn R. J. (2007). Fraction proficiency and success in algebra: What does research say?. Australian Mathematics Teacher, 63(3): 23-30.
  • Cai, J. (1995). A cognitive analysis of U.S. and Chinese students’ mathematical performance on tasking involving computation, simple problem solving, and complex problem solving. Journal for Research in Mathematics Education (Monograph series 7). Reston, VA: National Council of Teachers of Mathematics.
  • Cai J., & Hwang S. (2002). Generalized and generative thinking in US andChinese students’mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21, 401–421.
  • Carpenter, T.P., Corbitt, M.K., Kepner, H.S. Jr., Lindquist, M.M. & Reys, R.E. (1980). Solving verbal problems: Results and implications from national assessment. Arithmetic Teacher, 28(1), 8–12.
  • Carpenter T. C., Lindquist M. M., Brown C. A., Kouba V. L., Silver E. A., & Swafford J. O. (1988). Results of the fourth NAEP assessment of mathematics: Trends and conclusions. Arithmetic Teacher, 36(4), 38–41.
  • Charalambous, C. Y., Delaney S., Hsu. H. Y., & Mesa V. (2010). A Comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12 (2), 117–151.
  • Chinnapan, M., & Forrester, T. (2014). Generating procedural and conceptual knowledge of fractions by pre-service teachers. Mathematics Education Research Journal, 26(4), 871-896.
  • Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37–46.
  • Duval, R. (2006). A cognitive analysis of problems of comprehesion in a learning of Mathematics. Educational Studies in Mathematics, 61, 103-131.
  • Erbaş A. K., Alacacı C., & Bulut M. A. (2012). Comparison of mathematics textbooks from Turkey, Singapore and the United States of America. Educational Sciences: Theory and Practice, 12(3), 2311 – 2329.
  • Gravemeijer, K., Cobb, P., Bowers, J., & Whitenack, J. (2000). Symbolizing, modeling, and instructional design. In P. Cobb, E. Yackel, & K. McClain (Eds.), Communicating and symbolizing in mathematics: Perspectives on discourse, tools, and instructional design (pp. 225–274). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Isıksal M., ve Çakıroğlu E. (2008). Preservice teachers knowledge of students cognitive processes about the division of fractions. Hacettepe University Journal of Education, 35, 175-185.
  • Kar, T., Güler, G., Şen, C., ve Özdemir, E. (2018). Comparing the development of the multiplication of fractions in Turkish and American Textbooks. International Journal of Mathematical Education in Science and Technology, 49(2), 200-226.
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: helping children learn mathematics. Washington, DC: National Academy Press.
  • Leung I. K. C., & Carbone R. E. (2013). Pre-service teachers knowledge about fraction division reflected through problem posing. The Mathematics Educator, 14(1-2): 80-92.
  • Li, Y., Chen, X., & An, S. (2009). Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: The case of fraction division. ZDM Mathematics Education, 41, 809 –826.
  • 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.
  • MEB (2013). İlköğretim matematik dersi 5-8. sınıflar öğretim programı. T.C. Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı, Ankara.
  • Mullis I.V.S., Martin M. O., Foy P., & Hooper M. (2015). TIMSS 2015 International results in Mathematics, [Internet]. [cited 2017 Oct 18]. Available from http://timssandpirls.bc.edu/timss2015/internationalresults/
  • Özer E., ve Sezer R. A. (2014). Comparative analysis of questions in American, Singaporean, and Turkish mathematics textbooks based on the topics covered in 8th grade in Turkey. Educational Sciences: Theory and Practice, 14(1), 411-421.
  • Scouller, K. (1998). The influence of assessment method on students’ learning approaches: Multiple choice question examination versus assignment essay. Higher Education, 35, 453–472.
  • Siegler R. P., Carpenter T., Fennell F., Geary D., Lewis J., Okamoto Y., Thompson L., & Wray J. (2010). Developing effective fractions instruction for kindergarten through 8th grade (NCEE 2010-4039). Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance.
  • Silver E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
  • Simon M. A. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24, 233–254.
  • Son, J. W., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74 (2), 117–142.
  • Son, J. W. (2012). A Cross-National comparison of reform curricula in Korea and the US in terms of cognitive complexity: the case of fraction addition and subtraction. ZDM Mathematics Education, 44 (2), 161–174.
  • Son J. W. (2011). A global look at math instruction. Teaching Children Mathematics, 17(6), 360-368.
  • Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences learning. İçinde F. Lester (Ed.), Second handbook of research on Mathematics teaching and learning (pp. 319-370). Charlotte, NC: Information Age.
  • Tall, D. (1988). Concept image and concept definition. In J de Lange & M. Doorman (Eds.), Senior secondary Mathematics education (pp. 37-41). Utrecht:OW&OC.
  • Tang, K.C.C. (1992). Perceptions of task demand, strategy attributions and student learning. Research and Development in Higher Education, 15, 474–481.
  • Tirosh D. (2000). Enhancing prospective teacher’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.
  • Van de Walle J. A., Karp K. S., & Bay-Williams J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.). Boston: Allyn & Bacon.
  • Vula, E., Kingji-Kastrati, J., & Podvorica, F. (2015). A comparative analysis of mathematics textbooks from Kosovo and Albania based on the topic of fractions. In K. Krainer & N. Vondrová (Eds). Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, CERME 9 (pp. 1759–1765). Czech Republic: Prague.
  • Yang, D. C. (2018). Study of fractions in elementary mathematics textbooks from Finland and Taiwan. Educational Studies, 44(2), 190-211.
  • Yang, D. C., Reys, R. E., & Wu, L. L. (2010). Comparing how fractions were developed in textbooks used by the 5th- and 6th-graders in Singapore, Taiwan, and the U.S.A. School Science and Mathematics, 110(3), 118–127.
  • Yang, D. C., & Wu, W. R. (2010). The study of number sense realistic activities integrated into third grade math classes in Taiwan. The Journal of Educational Research. 103(6), 379-392.
  • Viera & Garrett (2005). Understanding interobserver agreement: The Kappa statistic. Family Medicine, 360-363.
  • Zhu Y., & Fan L. (2006). Focus on the representation of problem types in intended curriculum: A comparison of selected mathematics textbooks from Mainland China and the United States. International Journal of Science and Mathematics Education, 4(4), 609–626.

Problem Analysis in Turkish and Singapore Mathematics Textbooks: Division of Fraction

Year 2019, Volume: 47, 370 - 394, 12.09.2019
https://doi.org/10.9779/pauefd.522909

Abstract



In this study, Turkish and Singapore mathematics textbooks were compared in terms of the problems included in the subject of the division of fractions. The problems in textbooks were categorized in terms of the number of steps, type of answer, context and cognitive expectation characteristics. The analyses were conducted by two different researchers, and the Cohen Kappa agreement index between the researchers was found between 0.98-1.00 for each category. According to the findings, the Singapore book has more steps and more problems requiring explanation-solution compared to Turkish books. All problems related to dividing fractions in both countries' books contain sufficient data. The number of daily life problems in textbooks is small. In addition, it was determined that the Singapore textbook was richer than the Turkish books in terms of problems expressed in a combined form. In Turkish books, there are few problems in the category of mathematical reasoning and representation compared to the Singapore book, and there is no problem in the Turkish books in the category of conceptual knowledge. The findings can be considered as one of the reasons why Singaporean students perform better than Turkish students in terms of number content domain in international exams. In future studies, it can be investigated what kind of problems mathematics teachers use in their lessons.




References

  • Alajmi, A. M. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan and Kuwait. Educational Studies in Mathematics, 79, 239-261.
  • Black, P., & Wiliam, D. (1998). Inside the black box: raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139–148.
  • Brenner, M.E., Herman, S., Ho, H. & Zimmer, J.M. (1999). Cross-national comparison of representational competence. Journal for Research in Mathematics Education, 30(5), 541–557.
  • Brown G., & Quinn R. J. (2007). Fraction proficiency and success in algebra: What does research say?. Australian Mathematics Teacher, 63(3): 23-30.
  • Cai, J. (1995). A cognitive analysis of U.S. and Chinese students’ mathematical performance on tasking involving computation, simple problem solving, and complex problem solving. Journal for Research in Mathematics Education (Monograph series 7). Reston, VA: National Council of Teachers of Mathematics.
  • Cai J., & Hwang S. (2002). Generalized and generative thinking in US andChinese students’mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21, 401–421.
  • Carpenter, T.P., Corbitt, M.K., Kepner, H.S. Jr., Lindquist, M.M. & Reys, R.E. (1980). Solving verbal problems: Results and implications from national assessment. Arithmetic Teacher, 28(1), 8–12.
  • Carpenter T. C., Lindquist M. M., Brown C. A., Kouba V. L., Silver E. A., & Swafford J. O. (1988). Results of the fourth NAEP assessment of mathematics: Trends and conclusions. Arithmetic Teacher, 36(4), 38–41.
  • Charalambous, C. Y., Delaney S., Hsu. H. Y., & Mesa V. (2010). A Comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12 (2), 117–151.
  • Chinnapan, M., & Forrester, T. (2014). Generating procedural and conceptual knowledge of fractions by pre-service teachers. Mathematics Education Research Journal, 26(4), 871-896.
  • Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37–46.
  • Duval, R. (2006). A cognitive analysis of problems of comprehesion in a learning of Mathematics. Educational Studies in Mathematics, 61, 103-131.
  • Erbaş A. K., Alacacı C., & Bulut M. A. (2012). Comparison of mathematics textbooks from Turkey, Singapore and the United States of America. Educational Sciences: Theory and Practice, 12(3), 2311 – 2329.
  • Gravemeijer, K., Cobb, P., Bowers, J., & Whitenack, J. (2000). Symbolizing, modeling, and instructional design. In P. Cobb, E. Yackel, & K. McClain (Eds.), Communicating and symbolizing in mathematics: Perspectives on discourse, tools, and instructional design (pp. 225–274). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Isıksal M., ve Çakıroğlu E. (2008). Preservice teachers knowledge of students cognitive processes about the division of fractions. Hacettepe University Journal of Education, 35, 175-185.
  • Kar, T., Güler, G., Şen, C., ve Özdemir, E. (2018). Comparing the development of the multiplication of fractions in Turkish and American Textbooks. International Journal of Mathematical Education in Science and Technology, 49(2), 200-226.
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: helping children learn mathematics. Washington, DC: National Academy Press.
  • Leung I. K. C., & Carbone R. E. (2013). Pre-service teachers knowledge about fraction division reflected through problem posing. The Mathematics Educator, 14(1-2): 80-92.
  • Li, Y., Chen, X., & An, S. (2009). Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: The case of fraction division. ZDM Mathematics Education, 41, 809 –826.
  • 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.
  • MEB (2013). İlköğretim matematik dersi 5-8. sınıflar öğretim programı. T.C. Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı, Ankara.
  • Mullis I.V.S., Martin M. O., Foy P., & Hooper M. (2015). TIMSS 2015 International results in Mathematics, [Internet]. [cited 2017 Oct 18]. Available from http://timssandpirls.bc.edu/timss2015/internationalresults/
  • Özer E., ve Sezer R. A. (2014). Comparative analysis of questions in American, Singaporean, and Turkish mathematics textbooks based on the topics covered in 8th grade in Turkey. Educational Sciences: Theory and Practice, 14(1), 411-421.
  • Scouller, K. (1998). The influence of assessment method on students’ learning approaches: Multiple choice question examination versus assignment essay. Higher Education, 35, 453–472.
  • Siegler R. P., Carpenter T., Fennell F., Geary D., Lewis J., Okamoto Y., Thompson L., & Wray J. (2010). Developing effective fractions instruction for kindergarten through 8th grade (NCEE 2010-4039). Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance.
  • Silver E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
  • Simon M. A. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24, 233–254.
  • Son, J. W., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74 (2), 117–142.
  • Son, J. W. (2012). A Cross-National comparison of reform curricula in Korea and the US in terms of cognitive complexity: the case of fraction addition and subtraction. ZDM Mathematics Education, 44 (2), 161–174.
  • Son J. W. (2011). A global look at math instruction. Teaching Children Mathematics, 17(6), 360-368.
  • Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences learning. İçinde F. Lester (Ed.), Second handbook of research on Mathematics teaching and learning (pp. 319-370). Charlotte, NC: Information Age.
  • Tall, D. (1988). Concept image and concept definition. In J de Lange & M. Doorman (Eds.), Senior secondary Mathematics education (pp. 37-41). Utrecht:OW&OC.
  • Tang, K.C.C. (1992). Perceptions of task demand, strategy attributions and student learning. Research and Development in Higher Education, 15, 474–481.
  • Tirosh D. (2000). Enhancing prospective teacher’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.
  • Van de Walle J. A., Karp K. S., & Bay-Williams J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.). Boston: Allyn & Bacon.
  • Vula, E., Kingji-Kastrati, J., & Podvorica, F. (2015). A comparative analysis of mathematics textbooks from Kosovo and Albania based on the topic of fractions. In K. Krainer & N. Vondrová (Eds). Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, CERME 9 (pp. 1759–1765). Czech Republic: Prague.
  • Yang, D. C. (2018). Study of fractions in elementary mathematics textbooks from Finland and Taiwan. Educational Studies, 44(2), 190-211.
  • Yang, D. C., Reys, R. E., & Wu, L. L. (2010). Comparing how fractions were developed in textbooks used by the 5th- and 6th-graders in Singapore, Taiwan, and the U.S.A. School Science and Mathematics, 110(3), 118–127.
  • Yang, D. C., & Wu, W. R. (2010). The study of number sense realistic activities integrated into third grade math classes in Taiwan. The Journal of Educational Research. 103(6), 379-392.
  • Viera & Garrett (2005). Understanding interobserver agreement: The Kappa statistic. Family Medicine, 360-363.
  • Zhu Y., & Fan L. (2006). Focus on the representation of problem types in intended curriculum: A comparison of selected mathematics textbooks from Mainland China and the United States. International Journal of Science and Mathematics Education, 4(4), 609–626.
There are 41 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Suphi Önder Bütüner 0000-0001-7083-6549

Publication Date September 12, 2019
Submission Date February 5, 2019
Acceptance Date April 9, 2019
Published in Issue Year 2019 Volume: 47

Cite

APA Bütüner, S. Ö. (2019). Türk ve Singapur Matematik Ders Kitaplarında Problem Analizi: Kesirlerde Bölme İşlemi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 47, 370-394. https://doi.org/10.9779/pauefd.522909