Yıl: 2020 Cilt: 20 Sayı: 85 Sayfa Aralığı: 135 - 168 Metin Dili: İngilizce DOI: 10.14689/ejer.2020.85.7 İndeks Tarihi: 18-10-2020

Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment

Öz:
Purpose: Since there are a limited number of studies on how to develop relational thinking in secondary school students in mathematics education literature,this study will contribute to the field both in theoretical terms and concerning the implications for in-class applications. In this respect, this study aims to examine how to develop the relational thinking skills of 5th-grade students.Research Methods: The participants of this study, which was adopted as a research design of the teaching experiment, were six students attending 5thgrade in secondary school. The teaching process was eight sessions per week with one session. The main data source of this study was in-class teaching videos. The data were analyzed descriptively Findings: The questions, the in-class dialogues directing relational thinking and activities in each session of the teaching experiment conducted with the fifth-grade students were presented under related themes.Implications for Research and Practice: The most general result was that at the end of the teaching process based on numbers, relationships between numbers, operations and properties, the students made use of equality axioms to evaluate the true/false and open number sentences without any calculation. It was also seen that the students made connections between addition-subtraction, addition-multiplication and multiplication-division and that they made effective use of commutative, associative and distributive properties.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students' understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9(3), 221-247.
  • Baek, J.-M. (2008). Developing algebraic thinking through explorations in multiplication. In C. E. Greenes & R. Rubenstein (Eds.), Algebra and Algebraic Thinking in School Mathematics: Seventieth yearbook of the National Council of Teachers of Mathematics (NCTM; pp. 141–154). Reston, VA: NCTM.
  • Bastable, V., & Schifter, D. (2008). Classroom stories: Examples of elementary students engaged in early algebra. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades (pp. 165–184). Mahwah, NJ: Lawrence Erlbaum/Taylor & Francis Group; Reston, VA: NCTM.
  • Blanton, M.L. (2008). Algebra and the elementary classroom: Transforming thinking, transforming practice. Portsmouth: Heinemann.
  • Boulton G. M., Lewis G., Cooper T. J., Atweh B., Pillay H. & Wills L. (2000). Readiness of algebra. In T. Nakahara & M. Koyama (Eds.), Proceeding of the 24th Conference of the International Group for the Psychology of Mathematics Educationvol. 2, pp. 89-105). Hiroshima, Japan: International Group for the Psychology of Mathematics Education.
  • Blanton, M., Stephens, A., Knuth, E., 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.
  • Byrd, C. E., McNeil, N. M., Chesney, D. L., & Matthews, P. G. (2015). A specific misconception of the equal sign acts as a barrier to children's learning of early algebra. Learning and Individual Differences, 38, 61-67.
  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in the elementary school. Portsmouth, NH: Heinemann.
  • Carpenter, T. P., Levi, L., Berman, P., & Pligge, M. (2005). Developing algebraic reasoning in the elementary school. In T. A. Romberg, T. P. Carpenter, & F. Dremock (Eds.), Understanding Mathematics and Science Matters (pp. 81–98). Mahwah, NJ: Lawrence Erlbaum.
  • Chapman, O. (2011). Elementary school teachers’ growth in inquiry-based teaching of mathematics. ZDM Mathematics Education, 43(6), 951-963.
  • Eichhorn, M.S., Perry, L.E., & Brombacher, A. (2018). Students’ early grade understanding of the equal sign and non-standard equations in Jordan and India. International Journal of Research in Education and Science, 4(2), 655-669. doi:10.21890/ijres.432520
  • Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children's understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 232-236.
  • Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children's algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258-288.
  • Kızıltoprak, A. & Yavuzsoy Köse, N. (2017). Relational thinking: The bridge between arithmetic and algebra. International Electronic Journal of Elementary Education, 10 (1), 131-145.
  • 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.
  • Koehler, J.L. (2004). Learning to think relationally: Thinking relationally to learn (University of Wisconsin-Madison) Retrieved from ProQuest Dissertations and Theses. (AAT 3143187).
  • Köse, N., & Tanışlı, D. (2011). Equal sign and relational thinking in elementary mathematics textbooks. Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education, 2(5), 251-277.
  • Malara, N., & Navarra, G. (2006). Approaching the distributive law with young pupils. In M. Bosch (Ed.), Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 363-373). Sant Feliu de Guíxols: FUNDEMI IQS –Universitat Ramon Llull.
  • Matthews, P., & Rittle-Johnson, B. (2009). In pursuit of knowledge: Comparing selfexplanations, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology, 104, 1–21. doi:10.1016/j.jecp.2008.08.004
  • 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
  • McNeil, N., & Alibali, M. (2005). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development, 6(2), 285-306. doi:10.1207/s15327647jcd0602_6
  • Molina, M., & Ambrose, R. C. (2006). Fostering relational thinking while negotiating the meaning of the equals sign. Teaching Children Mathematics, 13(2), 111-117.
  • Molina, M., & Ambrose, R. (2008). From an operational to a relational conception of the equal sign. Thirds graders’ developing algebraic thinking. Focus on Learning Problems in Mathematics, 30(1), 61-80.
  • Molina, M., Castro, E., & Mason, J. (2008). Elementary school students approaches to solving true/false number sentences. PNA. Revista de Investigación en Didáctica de la Matemática, 2(2), 75-86.
  • Molina, M., & Mason, J. (2009). Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic. Canadian Journal of Science, Mathematics and Technology Education, 9(4), 224-242.
  • Napaphun, V. (2012). Relational thinking: Learning arithmetic in order to promote algebraic thinking. Journal of Science and Mathematics Education in Southeast Asia, 35 (2), 84-101.
  • Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91, 175–189. doi:10.1037/0022-0663.91.1.175
  • Rittle-Johnson, B. , Matthews, P. G., Taylor, R. S. & McEldoon, K. L. (2011). Assessing knowledge of mathematical equivalence: A construct modeling approach. Journal of Educational Psychology, 103 (1), 85-104. doi: 10.1037/a0021334
  • Sáenz-Ludlow, A. & Walgamuth, C. (1998). Third graders’ interpretations of equality and the equal symbol. Educational Studies in Mathematics, 35(2), 153-87. doi:10.1023/A:1003086304201
  • Seo, K.-H., & Ginsburg, H. P. (2003). ‘‘You’ve got to carefully read the math sentence...”: Classroom context and children’s interpretations of the equals sign. In A. J. Baroody & A. Dowker (Eds.), The Development of Arithmetic Concepts and Skills. Mahwah, NJ: Lawrence Erlbaum.
  • Steinweg, A. S., Akinwunmi, K. & Lenz, D. (2018). Making implicit algebraic thinking explicit: Exploiting national characteristics of German approaches. In C. Kieran (Ed.), Teaching and Learning Algebraic Thinking with 5-to 12-Year-Olds (pp.283-307). ICME-13 Monographs. Cham: Springer.
  • Steffe, L. P. & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 267-307). Hillsdale: Erlbaum.
  • Steffe, L. P. & Ulrich, C. (2014). The constructivist teaching experiment. In S. Lerman (Ed.) Encyclopedia of Mathematics Education (pp. 102-109). Springer, Berlin
  • Stephens, M. (2006). Describing and exploring the power of relational thinking. Retrieved from http://www.merga.net.au/documents/RP552006.pdf
  • Stephens, M. & Ribeiro, A. (2012). Working towards algebra: The importance of relational thinking, Revista Latinoamericana de Investigación en Mathemática Educativa, 15 (3), 373-402.
  • Stephens, A.C., Ellis, A. B., Blanton, M. & Brizuel, B. M. (2017). Algebraic thinking in the elementary and middle grades. In J. Cai (Ed.), Compendium for Research in Mathematics Education (386-420). Reston, VA: NCTM.
  • Strachota, S., Knuth, E. & Blanton, M. (2018). Cycles of generalizing activities in the classroom. In C. Kieran (Ed.), Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds (pp.351-378). ICME-13 Monographs. Cham: Springer.
  • Yaman H., Toluk Z., & Olkun S. (2003). How the elementary school students would perceive equal sign? Hacettepe University Journal of Education, 24, 142-151.
APA Köse N, Kızıltoprak A (2020). Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. , 135 - 168. 10.14689/ejer.2020.85.7
Chicago Köse Nilüfer,Kızıltoprak Ayhan Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. (2020): 135 - 168. 10.14689/ejer.2020.85.7
MLA Köse Nilüfer,Kızıltoprak Ayhan Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. , 2020, ss.135 - 168. 10.14689/ejer.2020.85.7
AMA Köse N,Kızıltoprak A Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. . 2020; 135 - 168. 10.14689/ejer.2020.85.7
Vancouver Köse N,Kızıltoprak A Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. . 2020; 135 - 168. 10.14689/ejer.2020.85.7
IEEE Köse N,Kızıltoprak A "Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment." , ss.135 - 168, 2020. 10.14689/ejer.2020.85.7
ISNAD Köse, Nilüfer - Kızıltoprak, Ayhan. "Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment". (2020), 135-168. https://doi.org/10.14689/ejer.2020.85.7
APA Köse N, Kızıltoprak A (2020). Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. Eurasian Journal of Educational Research, 20(85), 135 - 168. 10.14689/ejer.2020.85.7
Chicago Köse Nilüfer,Kızıltoprak Ayhan Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. Eurasian Journal of Educational Research 20, no.85 (2020): 135 - 168. 10.14689/ejer.2020.85.7
MLA Köse Nilüfer,Kızıltoprak Ayhan Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. Eurasian Journal of Educational Research, vol.20, no.85, 2020, ss.135 - 168. 10.14689/ejer.2020.85.7
AMA Köse N,Kızıltoprak A Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. Eurasian Journal of Educational Research. 2020; 20(85): 135 - 168. 10.14689/ejer.2020.85.7
Vancouver Köse N,Kızıltoprak A Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment. Eurasian Journal of Educational Research. 2020; 20(85): 135 - 168. 10.14689/ejer.2020.85.7
IEEE Köse N,Kızıltoprak A "Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment." Eurasian Journal of Educational Research, 20, ss.135 - 168, 2020. 10.14689/ejer.2020.85.7
ISNAD Köse, Nilüfer - Kızıltoprak, Ayhan. "Development of Secondary School Students’ Relational Thinking Skills with a Teaching Experiment". Eurasian Journal of Educational Research 20/85 (2020), 135-168. https://doi.org/10.14689/ejer.2020.85.7