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İlkokul Öğrencilerinin Sayıların Parça-Bütün İlişkisine Yönelik Toplama İşlemlerindeki Performanslarının ve Stratejilerinin İncelenmesi

Year 2023, Issue: 57, 1887 - 1905, 30.09.2023
https://doi.org/10.53444/deubefd.1300137

Abstract

Bu araştırmanın amacı, ilkokul öğrencilerinin sayıların parça-bütün ilişkisine yönelik toplama işlemlerindeki performanslarını ve stratejilerini incelemektir. Bu amaçla ilkokul 2, 3 ve 4. sınıf öğrencilerinin toplama işlemlerinde sergiledikleri performanslar ve kullandıkları stratejiler sınıf düzeyine göre incelenmiştir. Nicel ve nitel araştırma yöntemlerinin bir arada kullanıldığı karma araştırma yöntemi ile yürütülen bu araştırmanın katılımcılarını 378 ilkokul öğrencisi oluşturmaktadır. Veriler, parça-bütün ilişkisindeki sonuç bilinmeyen, değişim ve telafi yapıları dikkate alınarak araştırmacı tarafından geliştirilen “Toplama İşlemi Testi” aracılığıyla toplanmıştır. Araştırmanın nicel verilerinin analizinde öğrencilerin toplama işlemlerindeki performanslarının sınıf düzeyine göre değişimi tek yönlü varyans analizi ile test edilmiştir. Araştırmanın nitel kısmında ise ilkokul öğrencilerinin toplama işlemlerinde kullandıkları stratejiler içerik analizinden yararlanılarak analiz edilmiştir. Araştırmanın sonucunda ilkokul öğrencilerinin toplama işlemlerindeki performanslarının yüksek düzeyde olduğu tespit edilmiştir. Performanslar soru türleri bazında değerlendirildiğinde öğrencilerin en çok sonuç bilinmeyen problem türündeki sorularda performanslarının yüksek olduğu saptanmıştır. Ayrıca telafi sorularında değişim sorularına nazaran daha düşük bir performans sergiledikleri bulunmuştur. Bununla birlikte, öğrencilerin toplama işlemlerindeki performansları ile sınıf düzeyi arasında istatistiksel olarak anlamlı bir fark bulunmamıştır. Stratejilere ilişkin araştırma bulgularında ise ilkokul öğrencilerinin üç sınıf düzeyinde de toplama işlemlerinde genellikle geleneksel algoritmaları kullandıkları gözlenmiştir. Üçüncü sınıf düzeyinde diğer sınıf düzeylerine göre parça-bütün stratejilerinin daha fazla kullanılması dikkati çekmektedir.

References

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  • Björklund, C., Marton, F., & Kullberg, A. (2021). What is to be learnt? Critical aspects of elementary arithmetic skills. Educational Studies in Mathematics, 107, 261-284. doi: https://doi.org/10.1007/s10649-021-10045-0
  • Bütüner, S. Ö. (2020). Türk ve Singapur Matematik Ders Kitaplarının Zihinden Hesaplama Konusunda Kullanılan Stratejiler Açısından Karşılaştırılması. Turkish Journal of Mathematics Education, 1(1), 79-112.
  • Canobi, K. H. (2004). Individual differences in children’s addition and subtraction knowledge. Cognitive Development, 19(1), 81-93. doi:https://doi.org/10.1016/j.cogdev.2003.10.001
  • Canobi, K. H., Reeve, R. A., & Pattison, P. E. (2003). Patterns of knowledge in children's addition. Developmental Psychology, 39(3), 521-534. doi:https://doi.org/10.1037/0012-1649.39.3.5 21
  • Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 3-20. doi: https://doi.o rg/10.2307/749715
  • Cheng, Z-J. (2012). Teaching young children decomposition strategies to solve addition problems: An experimental study. Journal of Mathematical Behavior, 31(1), 29– 47. doi: https://doi.org/10.1016/j.jmathb.2011.09.002
  • Cowan, R., Donlan, C., Shepherd, D. L., Cole-Fletcher, R., Saxton, M., & Hurry, J. (2011). Basic calculation proficiency and mathematics achievement in elementary school children. Journal of Educational Psychology, 103(4), 786-803. doi: https://doi.org/10.1037/a0024 556
  • Creswell, J. W. (2021). Karma Yöntem Araştırmalarına Giriş. (Çev. M. Sözbilir). Pegem Akademi.
  • Fischer, F. E. (1990). A part-part-whole curriculum for teaching number in the kindergarten. Journal for Research in Mathematics Education, 21(3), 207-215. doi: https://doi.org/10.23 07/749374
  • Fuson, K. C., Wearne, D., Hiebert, J. C., Murray, H. G., Human, P. G., Olivier, A. I., Carpenter, T. P., & Fennema, E. (1997). Children's conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, 28(2), 130-162. doi: https://doi.org/10.2307/749759
  • Gaidoschik, M. (2019). Considerations on developmental stage models, learning trajectories and maybe better ways to guide early arithmetic instruction. In Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 419-426). Freudenthal Group & Freudenthal Institute, Utrecht University, Netherlands and ERME.
  • Hopkins, S., Russo, J., & Siegler, R. (2022). Is counting hindering learning? An investigation into children’s proficiency with simple addition and their flexibility with mental computation strategies. Mathematical Thinking and Learning, 24(1), 52-69. doi:10.1080/10986065.20 20.1842968
  • Irwin, K. C. (1996). Children's understanding of the principles of covariation and compensation in part-whole relationships. Journal for Research in Mathematics Education, 27(1), 25-40. doi: https://doi.org/10.2307/749195
  • Langhorst, P., Ehlert, A., & Fritz, A. (2012). Non-numerical and numerical understanding of the part-whole concept of children aged 4 to 8 in word problems. Journal für Mathematik-Didaktik, 2(33), 233–262. doi:10.1007/s13138-012-0039-5
  • Laski, E. V., Ermakova, A., & Vasilyeva, M. (2014). Early use of decomposition for addition and its relation to base-10 knowledge. Journal of Applied Developmental Psychology, 35(5), 444-454. doi: https://doi.org/10.1016/j.appdev.2014.07.002
  • Marcruz, O. Y. L., Carrie, H. K. L., Manabu, K., Mayumi, T., & Kumpei, M. (2022). Understanding of base-10 concept and its application: a cross-cultural comparison between Japan and Singapore. International Journal of Early Years Education, 30(4), 766-780. doi:https://doi.org/10.1080/09669760.2020.1848525
  • Milli Eğitim Bakanlığı (MEB), (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). https://tegm.meb.gov.tr/dosya/okuloncesi/ooproram.pdf
  • Millî Eğitim Bakanlığı (MEB), (2013). 36-72 Aylık Çocuklar için Okul Öncesi Eğitim Programı. http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
  • Putnam, R. T., de Bettencourt, L. U., & Leinhardt, G. (1990). Understanding of derived-fact strategies in addition and subtraction. Cognition and Instruction, 7(3), 245-285. doi:https://doi.org/10.1207/s1532690xci0703_3
  • Resnick, L. B. (1984). A developmental theory of number understanding. In H. Ginsburg (Ed.), The development of mathematical thinking (pp. 109-151). Academic Press.
  • Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children's success, methods and strategies. Educational Studies in Mathematics, 47, 145-173.
  • Steinke, D. (2008). Using part-whole thinking in math. Focus on Basics Connecting Research & Practice. 9(A), 1-7.
  • Sophian, C. & Vong, K. I. (1995). The parts and wholes of arithmetic story problems: Developing knowledge in the preschool years. Cognition and Instruction, 13(3), 469-477. doi: https://doi.org/10.1207/s1532690xci1303_5
  • Sun, X. H., Xin, Y. P., & Huang, R. (2019). A complementary survey on the current state of teaching and learning of Whole Number Arithmetic and connections to later mathematical content. ZDM Mathematics Education, 51, 1-12. doi: https://doi.org/10.1007/s11858-019-01041-z
  • Torbeyns, J., Hickendorff, M., & Verschaffel, L. (2017). The use of number-based versus digit-based strategies on multi-digit subtraction: 9–12-year-olds' strategy use profiles and task performance. Learning and Individual Differences, 58, 64-74.
  • Tsamir, P., Tirosh, D., Levenson, E., Tabach, M., & Barkai, R. (2015). Analyzing number composition and decomposition activities in kindergarten from a numeracy perspective. ZDM Mathematics Education, 47, 639–651. doi: 10.1007/s11858-015-0668-5
  • Wolters, M. A.D. (1983). The part-whole schema and arithmetical problems. Educational Studies in Mathematics, 14(2), 127-138.
  • Verschaffel, L. (2023). Strategy flexibility in mathematics. ZDM Mathematics Education, 1-12. https://doi.org/10.1007/s11858-023-01491-6
  • Young-Loveridge, J. (2001). Helping children move beyond counting to part-whole strategies. Teachers and Curriculum, 5,72-78. doi: https://doi.org/10.15663/tandc.v5i1.229
Year 2023, Issue: 57, 1887 - 1905, 30.09.2023
https://doi.org/10.53444/deubefd.1300137

Abstract

References

  • Baki, A. & Gökçek, T. (2012). Karma yöntem araştırmalarına genel bir bakış. Electronic Journal of Social Sciences, 11(42), 1-21.
  • Björklund, C., Marton, F., & Kullberg, A. (2021). What is to be learnt? Critical aspects of elementary arithmetic skills. Educational Studies in Mathematics, 107, 261-284. doi: https://doi.org/10.1007/s10649-021-10045-0
  • Bütüner, S. Ö. (2020). Türk ve Singapur Matematik Ders Kitaplarının Zihinden Hesaplama Konusunda Kullanılan Stratejiler Açısından Karşılaştırılması. Turkish Journal of Mathematics Education, 1(1), 79-112.
  • Canobi, K. H. (2004). Individual differences in children’s addition and subtraction knowledge. Cognitive Development, 19(1), 81-93. doi:https://doi.org/10.1016/j.cogdev.2003.10.001
  • Canobi, K. H., Reeve, R. A., & Pattison, P. E. (2003). Patterns of knowledge in children's addition. Developmental Psychology, 39(3), 521-534. doi:https://doi.org/10.1037/0012-1649.39.3.5 21
  • Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 3-20. doi: https://doi.o rg/10.2307/749715
  • Cheng, Z-J. (2012). Teaching young children decomposition strategies to solve addition problems: An experimental study. Journal of Mathematical Behavior, 31(1), 29– 47. doi: https://doi.org/10.1016/j.jmathb.2011.09.002
  • Cowan, R., Donlan, C., Shepherd, D. L., Cole-Fletcher, R., Saxton, M., & Hurry, J. (2011). Basic calculation proficiency and mathematics achievement in elementary school children. Journal of Educational Psychology, 103(4), 786-803. doi: https://doi.org/10.1037/a0024 556
  • Creswell, J. W. (2021). Karma Yöntem Araştırmalarına Giriş. (Çev. M. Sözbilir). Pegem Akademi.
  • Fischer, F. E. (1990). A part-part-whole curriculum for teaching number in the kindergarten. Journal for Research in Mathematics Education, 21(3), 207-215. doi: https://doi.org/10.23 07/749374
  • Fuson, K. C., Wearne, D., Hiebert, J. C., Murray, H. G., Human, P. G., Olivier, A. I., Carpenter, T. P., & Fennema, E. (1997). Children's conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, 28(2), 130-162. doi: https://doi.org/10.2307/749759
  • Gaidoschik, M. (2019). Considerations on developmental stage models, learning trajectories and maybe better ways to guide early arithmetic instruction. In Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 419-426). Freudenthal Group & Freudenthal Institute, Utrecht University, Netherlands and ERME.
  • Hopkins, S., Russo, J., & Siegler, R. (2022). Is counting hindering learning? An investigation into children’s proficiency with simple addition and their flexibility with mental computation strategies. Mathematical Thinking and Learning, 24(1), 52-69. doi:10.1080/10986065.20 20.1842968
  • Irwin, K. C. (1996). Children's understanding of the principles of covariation and compensation in part-whole relationships. Journal for Research in Mathematics Education, 27(1), 25-40. doi: https://doi.org/10.2307/749195
  • Langhorst, P., Ehlert, A., & Fritz, A. (2012). Non-numerical and numerical understanding of the part-whole concept of children aged 4 to 8 in word problems. Journal für Mathematik-Didaktik, 2(33), 233–262. doi:10.1007/s13138-012-0039-5
  • Laski, E. V., Ermakova, A., & Vasilyeva, M. (2014). Early use of decomposition for addition and its relation to base-10 knowledge. Journal of Applied Developmental Psychology, 35(5), 444-454. doi: https://doi.org/10.1016/j.appdev.2014.07.002
  • Marcruz, O. Y. L., Carrie, H. K. L., Manabu, K., Mayumi, T., & Kumpei, M. (2022). Understanding of base-10 concept and its application: a cross-cultural comparison between Japan and Singapore. International Journal of Early Years Education, 30(4), 766-780. doi:https://doi.org/10.1080/09669760.2020.1848525
  • Milli Eğitim Bakanlığı (MEB), (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). https://tegm.meb.gov.tr/dosya/okuloncesi/ooproram.pdf
  • Millî Eğitim Bakanlığı (MEB), (2013). 36-72 Aylık Çocuklar için Okul Öncesi Eğitim Programı. http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
  • Putnam, R. T., de Bettencourt, L. U., & Leinhardt, G. (1990). Understanding of derived-fact strategies in addition and subtraction. Cognition and Instruction, 7(3), 245-285. doi:https://doi.org/10.1207/s1532690xci0703_3
  • Resnick, L. B. (1984). A developmental theory of number understanding. In H. Ginsburg (Ed.), The development of mathematical thinking (pp. 109-151). Academic Press.
  • Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children's success, methods and strategies. Educational Studies in Mathematics, 47, 145-173.
  • Steinke, D. (2008). Using part-whole thinking in math. Focus on Basics Connecting Research & Practice. 9(A), 1-7.
  • Sophian, C. & Vong, K. I. (1995). The parts and wholes of arithmetic story problems: Developing knowledge in the preschool years. Cognition and Instruction, 13(3), 469-477. doi: https://doi.org/10.1207/s1532690xci1303_5
  • Sun, X. H., Xin, Y. P., & Huang, R. (2019). A complementary survey on the current state of teaching and learning of Whole Number Arithmetic and connections to later mathematical content. ZDM Mathematics Education, 51, 1-12. doi: https://doi.org/10.1007/s11858-019-01041-z
  • Torbeyns, J., Hickendorff, M., & Verschaffel, L. (2017). The use of number-based versus digit-based strategies on multi-digit subtraction: 9–12-year-olds' strategy use profiles and task performance. Learning and Individual Differences, 58, 64-74.
  • Tsamir, P., Tirosh, D., Levenson, E., Tabach, M., & Barkai, R. (2015). Analyzing number composition and decomposition activities in kindergarten from a numeracy perspective. ZDM Mathematics Education, 47, 639–651. doi: 10.1007/s11858-015-0668-5
  • Wolters, M. A.D. (1983). The part-whole schema and arithmetical problems. Educational Studies in Mathematics, 14(2), 127-138.
  • Verschaffel, L. (2023). Strategy flexibility in mathematics. ZDM Mathematics Education, 1-12. https://doi.org/10.1007/s11858-023-01491-6
  • Young-Loveridge, J. (2001). Helping children move beyond counting to part-whole strategies. Teachers and Curriculum, 5,72-78. doi: https://doi.org/10.15663/tandc.v5i1.229
There are 30 citations in total.

Details

Primary Language Turkish
Subjects Mathematics Education, Studies on Education
Journal Section Articles
Authors

Mesture Kayhan Altay 0000-0002-1917-2430

Publication Date September 30, 2023
Published in Issue Year 2023 Issue: 57

Cite

APA Kayhan Altay, M. (2023). İlkokul Öğrencilerinin Sayıların Parça-Bütün İlişkisine Yönelik Toplama İşlemlerindeki Performanslarının ve Stratejilerinin İncelenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi(57), 1887-1905. https://doi.org/10.53444/deubefd.1300137