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The Effects of an Early Algebra Intervention on Third-Grade Students’ Algebraic Thinking Skills

Yıl 2023, Cilt: 52 Sayı: 3, 758 - 799, 31.12.2023

Işıl İşler Baykal Nejla Öztürk Tavşan Gizem Güzeller İlkay Saygılı

https://doi.org/10.14812/cuefd.1126186

Öz

The importance of early algebra has been emphasized in international literature, and it has been discussed in many studies that students who are involved in a comprehensive intervention improve their algebraic thinking skills. The aim of this study was to test the effects of an early algebra intervention on the algebraic thinking skills of 3rd-grade students. The 3rd-grade intervention and control groups were included in the study, and both groups were given pre-test and post-test. In the findings, although there was no statistical difference between the 3rd-grade intervention and control group performances in the pre-test, a statistically significant difference was found in the post-test. Analysis of the students' strategies revealed that the students in the intervention group used algebraic thinking strategies more in the post-test than the control group in three big ideas, which are equality, expressions, equations and inequalities, generalized arithmetic, and functional thinking.

Anahtar Kelimeler

Early Algebra Quasi-experimental Design Third-grade Students

Destekleyen Kurum

Orta Doğu Teknik Üniversitesi BAP Koordinatörlüğü

Proje Numarası

Proje No: YÖP-501-2018- 2678

Teşekkür

Project LEAP members

Kaynakça

  • Baran Bulut, D., Aygün, B., & İpek, A. S. (2018). Meaning of the primary and secondary school students towards equal sign. Turkish Journal of Teacher Education, 7(1), 1–16.
  • Blanton, M. L., & Kaput, J. J. (2003). Developing elementary teachers' algebra eyes and ears. Teaching Children Mathematics, 10(2), 70–77. https://doi.org/10.5951/TCM.10.2.0070
  • Blanton, M. L., & Kaput, J. J. (2004). Elementary grade students’ capacity for functional thinking. Proceedings of The International Group for The Psychology of Mathematics Education, 28(2), 135–142.
  • Blanton, M., Schifter, D., Inge, V., Lofgren, P., Willis, C., Davis, F., & Confrey, J. (2007). Early algebra. In V. J. Katz (Ed.), Algebra: gateway to a technological future (pp. 7–14). Mathematical Association of America.
  • Blanton, M., Stephens, A., Knuth, E., Murphy Gardiner, A., Isler, I., & Kim, J. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39–87. https://doi.org/10.5951/jresematheduc.46.1.0039
  • Blanton, M., Brizuela, B. M., Stephens, A., Knuth, E., Isler, I., Gardiner, A. M., Stroud, R., Fonger, N. L., & Stylianou, D. (2018). Implementing a framework for early algebra. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5-to 12-year-olds (pp. 27–49). Springer. https://doi.org/10.1007/978-3-319-68351-5_2
  • Blanton, M., Isler-Baykal, I., Stroud, R., Stephens, A., Knuth, E., & Murphy Gardiner, A. (2019). Growth in children’s understanding of generalizing and representing mathematical structure and relationships. Educational Studies in Mathematics, 102, 193–219. https://doi.org/10.1007/s10649-019-09894-7
  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann.
  • Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669–705). Information Age Publishing.
  • Carraher, D. W., Schliemann, A. D., & Schwartz, J. (2008). Early algebra is not the same as algebra early. In J. Kaput, D. W. Carraher, & M. Blanton (Eds.), Algebra in the early grades. Erlbaum.
  • Common Core State Standards Initiative. (2010). Common Core State Standards for mathematics. http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2011). How to design and evaluate research in education. McGraw-Hill Humanities/Social Sciences/Languages.
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139–151.
  • Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312. https://doi.org/10.2307/30034852
  • Matthews, P., Rittle-Johnson, B., McEldoon, K., & Taylor, R. (2012). Measure for measure: What combining diverse measures reveals about children's understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education, 43(3), 316–350. https://doi.org/10.5951/jresematheduc.43.3.0316
  • Ministry of National Education (MoNE) (2018). Mathematics curriculum (Grades 1-8) [Matematik dersi (1, 2, 3 ,4, 5, 6, 7 ve 8. sınıflar) öğretim programı] Retrieved from http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
  • O’Connor, C., & Joffe, H. (2020). Intercoder reliability in qualitative research: Debates and practical guidelines. International Journal of Qualitative Methods, 19, 1–13. https://doi.org/10.1177/16094069198992
  • Ramirez Uclés, R., Brizuela, B. M., & Blanton, M. (2022). Kindergarten and first-grade students’ understandings and representations of arithmetic properties. Early Childhood Education Journal, 50(2), 345–356. https://doi.org/10.1007/s10643-020-01123-8
  • Stephens, A. C., Ellis, A. B., Blanton, M., & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 386–420). National Council of Teachers of Mathematics.
  • Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M., Knuth, E., & Murphy Gardiner, A. (2017). A learning progression for elementary students’ functional thinking. Mathematical Thinking and Learning, 19(3), 143–166. https://doi.org/10.1080/10986065.2017.1328636
  • Stephens, A. C., Knuth, E. J., Blanton, M. L., Isler, I., Gardiner, A., & Marum, T. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings. Journal of Mathematical Behavior, 32(2), 173–182. https://doi.org/10.1016/j.jmathb.2013.02.001
  • Stephens, A., Stroud, R., Strachota, S., Stylianou, D., Blanton, M., Knuth, E., & Gardiner, A. (2021). What early algebra knowledge persists 1 year after an elementary grades intervention? Journal for Research in Mathematics Education, 52(3), 332–348. https://doi.org/10.5951/jresematheduc-2020-0304
  • Stephens, A., Veltri Torres, R. V., Sung, Y., Strachota, S., Gardiner, A. M., Blanton, M., Stroud, R. & Knuth, E. (2021). From “You have to have three numbers and a plus sign” to “It’s the exact same thing”: K–1 students learn to think relationally about equations. The Journal of Mathematical Behavior, 62, 100871. https://doi.org/10.1016/j.jmathb.2021.100871
  • Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 421–456). National Council of Teachers of Mathematics.
  • Turgut, S., & Doğan Temur, Ö. (2017). Erken cebir öğretim etkinliklerinin ilkokul dördüncü sınıf öğrencilerinin akademik başarılarına etkisi. Amasya Üniversitesi Eğitim Fakültesi Dergisi, 6(1), 1-31.
  • Türkmen, H. & Tanışlı, D. (2019). Cebir öncesi: 3. 4. ve 5. sınıf öğrencilerinin fonksiyonel ilişkileri genelleme düzeyleri. Journal of Qualitative Research Education, 7(1), 344–372. https://doi.org/10.14689/issn.2148-2624.1.7c1s.16m
  • Yaman, H., Toluk, Z., & Olkun, S. (2003). İlköğretim öğrencileri eşit işaretini nasıl algılamaktadırlar? Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 142–151.

Erken Cebir Uygulamasının Üçüncü Sınıf Öğrencilerinin Cebirsel Düşünme Becerileri Üzerindeki Etkileri

Yıl 2023, Cilt: 52 Sayı: 3, 758 - 799, 31.12.2023

Işıl İşler Baykal Nejla Öztürk Tavşan Gizem Güzeller İlkay Saygılı

https://doi.org/10.14812/cuefd.1126186

Öz

Uluslararası alan yazında erken cebirin önemi vurgulanmış ve kapsamlı bir uygulamaya dâhil olan öğrencilerin cebirsel düşünme becerilerini geliştirdikleri birçok çalışmada ele alınmıştır. Bu çalışmanın amacı, bir erken cebir uygulamasının, 3. sınıf öğrencilerin cebirsel düşünme becerilerine etkilerini test etmektir. 3. sınıf uygulama ve kontrol grupları çalışmaya dâhil edilmiştir ve her iki gruba ön ve son test uygulanmıştır. Bulgularda, 3. sınıf uygulama ve kontrol grupları performansları arasında ön testte istatiksel bir fark olmamasına rağmen son testte istatiksel olarak anlamlı bir farklılık bulunmuştur. Öğrencilerin stratejilerine yönelik yapılan analizler, uygulama grubu öğrencilerinin son testte eşitlik, cebirsel ifadeler, denklemler ve eşitsizlikler; genelleştirilmiş aritmetik ve fonksiyonel düşünme üç ana alanında cebirsel düşünmeye dayalı stratejileri kontrol grubuna kıyasla daha çok kullandıklarını ortaya çıkarmıştır.

Anahtar Kelimeler

Erken Cebir Yarı-deneysel Desen Üçüncü Sınıf Öğrencileri

Proje Numarası

Proje No: YÖP-501-2018- 2678

Kaynakça

  • Baran Bulut, D., Aygün, B., & İpek, A. S. (2018). Meaning of the primary and secondary school students towards equal sign. Turkish Journal of Teacher Education, 7(1), 1–16.
  • Blanton, M. L., & Kaput, J. J. (2003). Developing elementary teachers' algebra eyes and ears. Teaching Children Mathematics, 10(2), 70–77. https://doi.org/10.5951/TCM.10.2.0070
  • Blanton, M. L., & Kaput, J. J. (2004). Elementary grade students’ capacity for functional thinking. Proceedings of The International Group for The Psychology of Mathematics Education, 28(2), 135–142.
  • Blanton, M., Schifter, D., Inge, V., Lofgren, P., Willis, C., Davis, F., & Confrey, J. (2007). Early algebra. In V. J. Katz (Ed.), Algebra: gateway to a technological future (pp. 7–14). Mathematical Association of America.
  • Blanton, M., Stephens, A., Knuth, E., Murphy Gardiner, A., Isler, I., & Kim, J. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39–87. https://doi.org/10.5951/jresematheduc.46.1.0039
  • Blanton, M., Brizuela, B. M., Stephens, A., Knuth, E., Isler, I., Gardiner, A. M., Stroud, R., Fonger, N. L., & Stylianou, D. (2018). Implementing a framework for early algebra. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5-to 12-year-olds (pp. 27–49). Springer. https://doi.org/10.1007/978-3-319-68351-5_2
  • Blanton, M., Isler-Baykal, I., Stroud, R., Stephens, A., Knuth, E., & Murphy Gardiner, A. (2019). Growth in children’s understanding of generalizing and representing mathematical structure and relationships. Educational Studies in Mathematics, 102, 193–219. https://doi.org/10.1007/s10649-019-09894-7
  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann.
  • Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669–705). Information Age Publishing.
  • Carraher, D. W., Schliemann, A. D., & Schwartz, J. (2008). Early algebra is not the same as algebra early. In J. Kaput, D. W. Carraher, & M. Blanton (Eds.), Algebra in the early grades. Erlbaum.
  • Common Core State Standards Initiative. (2010). Common Core State Standards for mathematics. http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2011). How to design and evaluate research in education. McGraw-Hill Humanities/Social Sciences/Languages.
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139–151.
  • Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312. https://doi.org/10.2307/30034852
  • Matthews, P., Rittle-Johnson, B., McEldoon, K., & Taylor, R. (2012). Measure for measure: What combining diverse measures reveals about children's understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education, 43(3), 316–350. https://doi.org/10.5951/jresematheduc.43.3.0316
  • Ministry of National Education (MoNE) (2018). Mathematics curriculum (Grades 1-8) [Matematik dersi (1, 2, 3 ,4, 5, 6, 7 ve 8. sınıflar) öğretim programı] Retrieved from http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
  • O’Connor, C., & Joffe, H. (2020). Intercoder reliability in qualitative research: Debates and practical guidelines. International Journal of Qualitative Methods, 19, 1–13. https://doi.org/10.1177/16094069198992
  • Ramirez Uclés, R., Brizuela, B. M., & Blanton, M. (2022). Kindergarten and first-grade students’ understandings and representations of arithmetic properties. Early Childhood Education Journal, 50(2), 345–356. https://doi.org/10.1007/s10643-020-01123-8
  • Stephens, A. C., Ellis, A. B., Blanton, M., & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 386–420). National Council of Teachers of Mathematics.
  • Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M., Knuth, E., & Murphy Gardiner, A. (2017). A learning progression for elementary students’ functional thinking. Mathematical Thinking and Learning, 19(3), 143–166. https://doi.org/10.1080/10986065.2017.1328636
  • Stephens, A. C., Knuth, E. J., Blanton, M. L., Isler, I., Gardiner, A., & Marum, T. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings. Journal of Mathematical Behavior, 32(2), 173–182. https://doi.org/10.1016/j.jmathb.2013.02.001
  • Stephens, A., Stroud, R., Strachota, S., Stylianou, D., Blanton, M., Knuth, E., & Gardiner, A. (2021). What early algebra knowledge persists 1 year after an elementary grades intervention? Journal for Research in Mathematics Education, 52(3), 332–348. https://doi.org/10.5951/jresematheduc-2020-0304
  • Stephens, A., Veltri Torres, R. V., Sung, Y., Strachota, S., Gardiner, A. M., Blanton, M., Stroud, R. & Knuth, E. (2021). From “You have to have three numbers and a plus sign” to “It’s the exact same thing”: K–1 students learn to think relationally about equations. The Journal of Mathematical Behavior, 62, 100871. https://doi.org/10.1016/j.jmathb.2021.100871
  • Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 421–456). National Council of Teachers of Mathematics.
  • Turgut, S., & Doğan Temur, Ö. (2017). Erken cebir öğretim etkinliklerinin ilkokul dördüncü sınıf öğrencilerinin akademik başarılarına etkisi. Amasya Üniversitesi Eğitim Fakültesi Dergisi, 6(1), 1-31.
  • Türkmen, H. & Tanışlı, D. (2019). Cebir öncesi: 3. 4. ve 5. sınıf öğrencilerinin fonksiyonel ilişkileri genelleme düzeyleri. Journal of Qualitative Research Education, 7(1), 344–372. https://doi.org/10.14689/issn.2148-2624.1.7c1s.16m
  • Yaman, H., Toluk, Z., & Olkun, S. (2003). İlköğretim öğrencileri eşit işaretini nasıl algılamaktadırlar? Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 142–151.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Eğitim Üzerine Çalışmalar
Bölüm Makaleler
Yazarlar

Işıl İşler Baykal 0000-0002-2779-9241

Nejla Öztürk Tavşan 0000-0002-4803-2023

Gizem Güzeller 0000-0003-0832-9516

İlkay Saygılı 0000-0002-4757-3530

Proje Numarası Proje No: YÖP-501-2018- 2678
Yayımlanma Tarihi 31 Aralık 2023
Gönderilme Tarihi 6 Haziran 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 52 Sayı: 3

Kaynak Göster

APA İşler Baykal, I., Öztürk Tavşan, N., Güzeller, G., Saygılı, İ. (2023). The Effects of an Early Algebra Intervention on Third-Grade Students’ Algebraic Thinking Skills. Cukurova University Faculty of Education Journal, 52(3), 758-799. https://doi.org/10.14812/cuefd.1126186
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