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A Comparative Analysis of Turkey and Singapore 5th Grade Mathematics Textbooks in Terms of Worked Examples and Questions

Year 2019, , 539 - 566, 10.09.2019
https://doi.org/10.16949/turkbilmat.490210

Abstract

This study aims at
comparing Turkey and Singapore 5th grade mathematics textbooks in terms of
learning opportunities offered to students through worked-examples and
questions posed (potential cognitive demand, reasoning and proof). The study
that adopts document analysis technique reveals that Singapore textbook
includes more visual representations and graphical displays, provides more
multiple solution methods, uses modeling more effectively while the Turkish
textbook includes more real-life related worked-examples. Results show that the
questions in Singapore 5th grade textbook entail relatively higher cognitive
demand but that most questions in both Turkey and Singapore textbooks are at
memorization level. It was also found out that Singapore textbook includes more
reasoning and proof questions and there was more variety of reasoning and proof
questions. However, there were no questions to encourage evaluating
justifications, generic examples, and empirical types of elicited arguments in
both books.

References

  • Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181-214.
  • Bentley, B., & Yates, G. C. (2017). Facilitating proportional reasoning through worked examples: Two classroom-based experiments. Cogent Education, 4(1), 1-14.
  • Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71-80.
  • Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A., & Zaslavsky, O. (2006). Exemplification in mathematics education. Retrieved October, 12, 2018, from http://mcs.open.ac.uk.
  • Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27-40.
  • Cai, J., & Cirillo, M. (2014). What do we know about reasoning and proving? Opportunities and missing opportunities from curriculum analyses. International Journal of Educational Research, 64, 132-140.‏
  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
  • Chavez-Lopez, O. (2003). From the textbook to the enacted curriculum: Textbook use in the middle school mathematics classroom (Unpublished doctoral dissertation). University of Missouri, USA.
  • 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.
  • Cırıtcı, H., Gönen, İ., Kavas, D., Özarslan, M., Pekcan, N. ve Şahin, M. (2017). Ortaokul matematik ders kitabı 5. İstanbul: Milli Eğitim Bakanlığı Yayınları.
  • Davis, J. D., Smith, O., Roy, A. R., Bilgic, Y. K. (2014). Reasoning-and-proving in algebra: The case of two reform-oriented U.S. textbooks. International Journal of Educational Research, 64, 92-106.
  • Dole, S., & Shield, M. (2008). The capacity of two Australian eighth-grade textbooks for promoting proportional reasoning. Research in Mathematics Education, 10(1), 19-35.
  • Ecemiş, U. O. (2017). A comparison of cognitive demand levels of tasks in 5th grade mathematics textbook used in Singapore, the United States, and Turkey. EJMS European Journal of Multidisciplinary Studies Articles, 5(1),469-469.
  • Engin, Ö. (2015). Türkiye 7. sınıf matematik ders kitabındaki etkinliklerin bilişsel istem düzeylerinin program ve farklı ülkelerle karşılaştırılması (Yüksek lisans tezi). Ankara Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Erbaş, A. K., Alacacı, C., & Bulut, M. (2012). A comparison of mathematics textbooks from Turkey, Singapore, and the United States of America. Educational Sciences: Theory and Practice, 12(3), 2324-2329.
  • Fan, L. (2010, March). Principles and processes for publishing textbooks and alignment with standards: A case in Singapore. Paper presented at the APEC Conference on Replicating Exemplary Practices in Mathematics Education, Koh Samui, Thailand.
  • Fong, A. (2015). Educational resource development in Singapore. Retrieved September, 3, 2018, from https://www.internationalpublishers.org.
  • Fujita, T., & Jones, K. (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81-91.
  • Georgius, K. (2014). Planning and enacting mathematical tasks of high cognitive demand in the primary classroom (doctoral dissertation). Retrieved May 14, 2018 from http://digitalcommons.unl.edu.
  • Gracin, D. G., & Matić, L. J. (2016). The role of mathematics textbooks in lower secondary education in Croatia: An empirical study. The Mathematics Educator, 16(2), 31-58.
  • Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French and German classrooms: Who gets an opportunity to learn what? British Educational Research Journal, 28(4), 567-590.
  • Harel, G., & Sowder, L. (2007). Toward a comprehensive perspective on proof. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805-842). Charlotte: National Council of Teachers of Mathematics.
  • Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428.
  • Henningsen, M., & Stein, M. (1997). Mathematical tasks and student’s cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524-549.
  • Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Human, P., Murray, H., & Olivier, A. (1997). Making sense: Teaching and learning mathematics with understanding. Potsmouth, NH: Heinemann.
  • Jones, D. L., & Tarr, J. E. (2007). An examination of the levels of cognitive demand required by probability tasks in middle grades mathematics textbooks. Statistics Education Research Journal, 6(2), 4-27. ‏
  • Kaur, B., Soh, C. K., Wong, K. Y., Tay, E. G., Toh, T. L., Lee, N. H., Ng, F. S., Dindyal, J., Yen, Y. P., Loh, M. Y., Tan, H. C. J., & Tan, L.C. (2015). Mathematics education in Singapore. In Cho, S. J. (Ed.), The proceedings of the 12th international congress on mathematical education: intellectual and attitudinal challenges (pp. 311-316). Cham Heidelberg: Springer.
  • Kheong, F. H., Soon, G. K. & Ramakrishnan, C. (2017). My pals are here: Maths 5 B. Singapore: Marshall Cavendish Education.
  • Knuth, E. J., & Sutherland, J. (2004). Student understanding of generality. In D. E. McDougall, & J. A. Ross (Eds.), Proceedings of the 26th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol.2, pp. 561–567). Toronto: OISE/UT.
  • LeFevre, J. A., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3(1), 1-30.
  • Mayer, R. E., Tajika, H., & Stanley, C. (1991). Mathematical problem solving in Japan and the United States: A controlled comparison. Journal of Educational Psychology, 83(1), 69-72.
  • Mayer, R. E., Sims, V., & Tajika, H. (1995). Brief note: A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32(2), 443-460.
  • Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks: An empirical approach. Educational Studies in Mathematics, 56(2-3), 255-286.
  • Ministry of Education [MOE]. (2017). Compulsory education. Retrieved May 3, 2018 from https://www.moe.gov.sg.
  • Mullis, I. V., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Retrieved May 12, 2018 from https://timssandpirls.bc.edu
  • National Council of Teachers of Mathematics [NCTM]. (1989). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics [NCTM]. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.
  • Oates, T. (2014). Why textbooks count. A policy paper. Retrieved February 6, 2018 from http://www.cambridgeassessment.org.uk.
  • Özer, E., & Sezer, R. (2014). A 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.
  • Özgeldi, M. (2012). Middle school mathematics teachers use of textbooks and integration of textbooks tasks into practise: A mixed methods study (Unpublished doctoral dissertation). Middle East Technical University, Graduate School of Social Sciences, Turkey.
  • Özgeldi, M., & Esen, Y. (2010). Analysis of mathematical tasks in Turkish elementary school mathematics textbooks. Procedia-Social and Behavioral Sciences, 2(2), 2277-2281.
  • Özmantar, M. F., Dapgın, M., Çırak Kurt, S., & İlgün, Ş. (2017). Mathematics teachers’ use of source books other than textbooks: Reasons, results and implications. Gaziantep University Journal of Social Sciences, 16(3), 741-758.
  • Özmantar, M. F., Öztürk, A. ve Bay, E. (2016). Reform ve değişim bağlamında ilkokul matematik öğretim programları. Ankara: Pegem Akademi Yayıncılık.
  • Pepin, B., & Haggarty, L. (2007). Making connections and seeking understanding: Mathematical tasks in English, French and German textbooks. Retrieved October 12, 2018, from www.maths-ed.org.uk.
  • Reçber, H. (2012). Türkiye 8. sınıf matematik ders kitabındaki etkinliklerin bilişsel düzeylerinin programdakilerle ve diğer ülkelerle karşılaştırılması (Yayınlanmamış yüksek lisans tezi). Ankara Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211-246.
  • Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why mathematics textbooks matter. Educational Leadership, 61(5), 61–66.
  • Sağlam, R. (2012). A comparative analysis of quadratics in mathematics textbooks from Turkey, Singapore, and the International Baccalaureate Diploma Programme. (Unpublished master’s thesis). Bilkent University, Graduate School of Education, Ankara.
  • Sarpkaya, G. (2011). İlköğretim ikinci kademe cebir öğrenme alanı ile ilgili matematiksel görevlerin bilişsel istemler açısından incelenmesi: Matematik ders kitapları ve sınıf uygulamaları (Yayınlanmamış doktora tezi). Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Schmidt, W. H., McKnight, C. C., Houang, R. T., Wang, H., Wiley, D. E., Wolfe, R. G. (2001). Why schools matter: A cross-national comparison of curriculum and learning. San Francisco (CA): Jossey-Bass.
  • Schoenfeld, A. H. (2009). Series editor’s foreword: The soul of mathematics. In D. A. Stylianou, M. L. Blanton, & E. J. Knuth (Eds.), Teaching and learning proof across the grades: A K–16 perspective (pp. xii–xvi). New York, NY: Routledge.
  • Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 165-197). New York: MacMillan.
  • Shen, C. Y., & Tsai, H. C. (2009). Design principles of worked examples: A review of the empirical studies. Journal of Instructional Psychology, 36(3), 238-244.
  • Smith, M. P., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics in the Middle School, 3(5), 344-350.
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Türkiye ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler ve Sorular Açısından Karşılaştırmalı Analizi

Year 2019, , 539 - 566, 10.09.2019
https://doi.org/10.16949/turkbilmat.490210

Abstract

Bu çalışma,
Türkiye ve Singapur 5. sınıf matematik ders kitaplarının öğrencilerine sunduğu
öğrenme fırsatlarını çözümlü örnekler ve öğrencilerin çözmesi beklenen sorular
(potansiyel bilişsel istem, muhakeme ve ispat) yoluyla karşılaştırmayı
amaçlamıştır. Doküman analizi tekniği kullanılan araştırma, çözümlü örnekler
açısından Singapur 5. sınıf matematik kitabının daha fazla görsel temsil ve
grafiksel resim içerdiğini, bu kitabın farklı çözüm yollarına daha fazla yer
verdiğini, modellemeyi daha etkin kullandığını, Türk kitabında ise günlük
hayatla ilişkili çözümlü örneklerin daha fazla olduğunu ortaya koymuştur.
Singapur 5. sınıf matematik ders 
kitabındaki soruların göreceli olarak daha yüksek seviyede bilişsel
istem gerektirdiği fakat her iki ülke kitabında soruların çoğunun hatırlama
düzeyinde olduğu bulunmuştur. Ayrıca, Singapur ders kitabında daha fazla
muhakeme ve ispat gerektiren soru olduğu ve bu soruların çeşitliliğinin fazla
olduğu bulunmuştur. Bununla beraber, her iki ülke kitabında da gerekçeleri değerlendirmeye,
kapsamlı örneğe  ve denemeye dayalı
argümana teşvik eden sorulara rastlanmamıştır.  

References

  • Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181-214.
  • Bentley, B., & Yates, G. C. (2017). Facilitating proportional reasoning through worked examples: Two classroom-based experiments. Cogent Education, 4(1), 1-14.
  • Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71-80.
  • Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A., & Zaslavsky, O. (2006). Exemplification in mathematics education. Retrieved October, 12, 2018, from http://mcs.open.ac.uk.
  • Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27-40.
  • Cai, J., & Cirillo, M. (2014). What do we know about reasoning and proving? Opportunities and missing opportunities from curriculum analyses. International Journal of Educational Research, 64, 132-140.‏
  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
  • Chavez-Lopez, O. (2003). From the textbook to the enacted curriculum: Textbook use in the middle school mathematics classroom (Unpublished doctoral dissertation). University of Missouri, USA.
  • 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.
  • Cırıtcı, H., Gönen, İ., Kavas, D., Özarslan, M., Pekcan, N. ve Şahin, M. (2017). Ortaokul matematik ders kitabı 5. İstanbul: Milli Eğitim Bakanlığı Yayınları.
  • Davis, J. D., Smith, O., Roy, A. R., Bilgic, Y. K. (2014). Reasoning-and-proving in algebra: The case of two reform-oriented U.S. textbooks. International Journal of Educational Research, 64, 92-106.
  • Dole, S., & Shield, M. (2008). The capacity of two Australian eighth-grade textbooks for promoting proportional reasoning. Research in Mathematics Education, 10(1), 19-35.
  • Ecemiş, U. O. (2017). A comparison of cognitive demand levels of tasks in 5th grade mathematics textbook used in Singapore, the United States, and Turkey. EJMS European Journal of Multidisciplinary Studies Articles, 5(1),469-469.
  • Engin, Ö. (2015). Türkiye 7. sınıf matematik ders kitabındaki etkinliklerin bilişsel istem düzeylerinin program ve farklı ülkelerle karşılaştırılması (Yüksek lisans tezi). Ankara Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Erbaş, A. K., Alacacı, C., & Bulut, M. (2012). A comparison of mathematics textbooks from Turkey, Singapore, and the United States of America. Educational Sciences: Theory and Practice, 12(3), 2324-2329.
  • Fan, L. (2010, March). Principles and processes for publishing textbooks and alignment with standards: A case in Singapore. Paper presented at the APEC Conference on Replicating Exemplary Practices in Mathematics Education, Koh Samui, Thailand.
  • Fong, A. (2015). Educational resource development in Singapore. Retrieved September, 3, 2018, from https://www.internationalpublishers.org.
  • Fujita, T., & Jones, K. (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81-91.
  • Georgius, K. (2014). Planning and enacting mathematical tasks of high cognitive demand in the primary classroom (doctoral dissertation). Retrieved May 14, 2018 from http://digitalcommons.unl.edu.
  • Gracin, D. G., & Matić, L. J. (2016). The role of mathematics textbooks in lower secondary education in Croatia: An empirical study. The Mathematics Educator, 16(2), 31-58.
  • Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French and German classrooms: Who gets an opportunity to learn what? British Educational Research Journal, 28(4), 567-590.
  • Harel, G., & Sowder, L. (2007). Toward a comprehensive perspective on proof. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805-842). Charlotte: National Council of Teachers of Mathematics.
  • Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428.
  • Henningsen, M., & Stein, M. (1997). Mathematical tasks and student’s cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524-549.
  • Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Human, P., Murray, H., & Olivier, A. (1997). Making sense: Teaching and learning mathematics with understanding. Potsmouth, NH: Heinemann.
  • Jones, D. L., & Tarr, J. E. (2007). An examination of the levels of cognitive demand required by probability tasks in middle grades mathematics textbooks. Statistics Education Research Journal, 6(2), 4-27. ‏
  • Kaur, B., Soh, C. K., Wong, K. Y., Tay, E. G., Toh, T. L., Lee, N. H., Ng, F. S., Dindyal, J., Yen, Y. P., Loh, M. Y., Tan, H. C. J., & Tan, L.C. (2015). Mathematics education in Singapore. In Cho, S. J. (Ed.), The proceedings of the 12th international congress on mathematical education: intellectual and attitudinal challenges (pp. 311-316). Cham Heidelberg: Springer.
  • Kheong, F. H., Soon, G. K. & Ramakrishnan, C. (2017). My pals are here: Maths 5 B. Singapore: Marshall Cavendish Education.
  • Knuth, E. J., & Sutherland, J. (2004). Student understanding of generality. In D. E. McDougall, & J. A. Ross (Eds.), Proceedings of the 26th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol.2, pp. 561–567). Toronto: OISE/UT.
  • LeFevre, J. A., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3(1), 1-30.
  • Mayer, R. E., Tajika, H., & Stanley, C. (1991). Mathematical problem solving in Japan and the United States: A controlled comparison. Journal of Educational Psychology, 83(1), 69-72.
  • Mayer, R. E., Sims, V., & Tajika, H. (1995). Brief note: A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32(2), 443-460.
  • Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks: An empirical approach. Educational Studies in Mathematics, 56(2-3), 255-286.
  • Ministry of Education [MOE]. (2017). Compulsory education. Retrieved May 3, 2018 from https://www.moe.gov.sg.
  • Mullis, I. V., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Retrieved May 12, 2018 from https://timssandpirls.bc.edu
  • National Council of Teachers of Mathematics [NCTM]. (1989). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics [NCTM]. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.
  • Oates, T. (2014). Why textbooks count. A policy paper. Retrieved February 6, 2018 from http://www.cambridgeassessment.org.uk.
  • Özer, E., & Sezer, R. (2014). A 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.
  • Özgeldi, M. (2012). Middle school mathematics teachers use of textbooks and integration of textbooks tasks into practise: A mixed methods study (Unpublished doctoral dissertation). Middle East Technical University, Graduate School of Social Sciences, Turkey.
  • Özgeldi, M., & Esen, Y. (2010). Analysis of mathematical tasks in Turkish elementary school mathematics textbooks. Procedia-Social and Behavioral Sciences, 2(2), 2277-2281.
  • Özmantar, M. F., Dapgın, M., Çırak Kurt, S., & İlgün, Ş. (2017). Mathematics teachers’ use of source books other than textbooks: Reasons, results and implications. Gaziantep University Journal of Social Sciences, 16(3), 741-758.
  • Özmantar, M. F., Öztürk, A. ve Bay, E. (2016). Reform ve değişim bağlamında ilkokul matematik öğretim programları. Ankara: Pegem Akademi Yayıncılık.
  • Pepin, B., & Haggarty, L. (2007). Making connections and seeking understanding: Mathematical tasks in English, French and German textbooks. Retrieved October 12, 2018, from www.maths-ed.org.uk.
  • Reçber, H. (2012). Türkiye 8. sınıf matematik ders kitabındaki etkinliklerin bilişsel düzeylerinin programdakilerle ve diğer ülkelerle karşılaştırılması (Yayınlanmamış yüksek lisans tezi). Ankara Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211-246.
  • Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why mathematics textbooks matter. Educational Leadership, 61(5), 61–66.
  • Sağlam, R. (2012). A comparative analysis of quadratics in mathematics textbooks from Turkey, Singapore, and the International Baccalaureate Diploma Programme. (Unpublished master’s thesis). Bilkent University, Graduate School of Education, Ankara.
  • Sarpkaya, G. (2011). İlköğretim ikinci kademe cebir öğrenme alanı ile ilgili matematiksel görevlerin bilişsel istemler açısından incelenmesi: Matematik ders kitapları ve sınıf uygulamaları (Yayınlanmamış doktora tezi). Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Schmidt, W. H., McKnight, C. C., Houang, R. T., Wang, H., Wiley, D. E., Wolfe, R. G. (2001). Why schools matter: A cross-national comparison of curriculum and learning. San Francisco (CA): Jossey-Bass.
  • Schoenfeld, A. H. (2009). Series editor’s foreword: The soul of mathematics. In D. A. Stylianou, M. L. Blanton, & E. J. Knuth (Eds.), Teaching and learning proof across the grades: A K–16 perspective (pp. xii–xvi). New York, NY: Routledge.
  • Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 165-197). New York: MacMillan.
  • Shen, C. Y., & Tsai, H. C. (2009). Design principles of worked examples: A review of the empirical studies. Journal of Instructional Psychology, 36(3), 238-244.
  • Smith, M. P., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics in the Middle School, 3(5), 344-350.
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There are 70 citations in total.

Details

Primary Language Turkish
Journal Section Research Articles
Authors

Zehra Toprak

Mehmet Fatih Özmantar

Publication Date September 10, 2019
Published in Issue Year 2019

Cite

APA Toprak, Z., & Özmantar, M. F. (2019). Türkiye ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler ve Sorular Açısından Karşılaştırmalı Analizi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 10(2), 539-566. https://doi.org/10.16949/turkbilmat.490210
AMA Toprak Z, Özmantar MF. Türkiye ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler ve Sorular Açısından Karşılaştırmalı Analizi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). September 2019;10(2):539-566. doi:10.16949/turkbilmat.490210
Chicago Toprak, Zehra, and Mehmet Fatih Özmantar. “Türkiye Ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler Ve Sorular Açısından Karşılaştırmalı Analizi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10, no. 2 (September 2019): 539-66. https://doi.org/10.16949/turkbilmat.490210.
EndNote Toprak Z, Özmantar MF (September 1, 2019) Türkiye ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler ve Sorular Açısından Karşılaştırmalı Analizi. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10 2 539–566.
IEEE Z. Toprak and M. F. Özmantar, “Türkiye ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler ve Sorular Açısından Karşılaştırmalı Analizi”, Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 10, no. 2, pp. 539–566, 2019, doi: 10.16949/turkbilmat.490210.
ISNAD Toprak, Zehra - Özmantar, Mehmet Fatih. “Türkiye Ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler Ve Sorular Açısından Karşılaştırmalı Analizi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10/2 (September 2019), 539-566. https://doi.org/10.16949/turkbilmat.490210.
JAMA Toprak Z, Özmantar MF. Türkiye ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler ve Sorular Açısından Karşılaştırmalı Analizi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2019;10:539–566.
MLA Toprak, Zehra and Mehmet Fatih Özmantar. “Türkiye Ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler Ve Sorular Açısından Karşılaştırmalı Analizi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 10, no. 2, 2019, pp. 539-66, doi:10.16949/turkbilmat.490210.
Vancouver Toprak Z, Özmantar MF. Türkiye ve Singapur 5. Sınıf Matematik Ders Kitaplarının Çözümlü Örnekler ve Sorular Açısından Karşılaştırmalı Analizi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2019;10(2):539-66.