The Development of 7th Grade Students’ Algebraic Thinking Through Task-assisted Instruction

Yıl 2024, Sayı: 60, 1045 - 1068, 28.06.2024

Nil Arabacı , Yeşim İmamoğlu , Hulya Kılıc

https://doi.org/10.53444/deubefd.1384576

Öz

This study aims to investigate how the algebraic thinking skills of seventh-grade students develop with the task-assisted teaching approach. The study was conducted in a seventh-grade class at a public school in Istanbul. The tasks were designed to support the basic components of students’ algebraic thinking processes - pattern recognition, writing algebraic expressions, constructing and solving equations. During the implementation, the students in the class were divided into groups of three and four, and a teacher candidate in each group was responsible for implementing the tasks. Teacher candidates were informed about the instructions provided by the researcher, the implementation principles, and possible student errors before each task. The entire implementation process was recorded with the consent of the students. This paper focused on the pattern recognition component of algebraic thinking. Video analysis and students' responses showed that their algebraic thinking processes improved in the pattern recognition component, and furthermore, the pattern recognition component evaluation through qualitative analysis showed that there was an improvement in the students' algebraic thinking skills compared to their previous performance. The results indicate that task-assisted instruction could be an effective method for improving students' algebraic thinking skills and supporting their algebra learning.

Anahtar Kelimeler

algebraic thinking, pattern tasks, task-assisted instruction, task design

Destekleyen Kurum

TUBITAK

Proje Numarası

215K049

Teşekkür

A part of this study was supported by The Scientific and Technological Research Council of Turkey (TUBITAK, Grant no: 215K049).

7. Sınıf Öğrencilerinin Cebirsel Düşünmelerinin Görev Destekli Öğretim Yoluyla Geliştirilmesi

Öz

Bu çalışmanın amacı, yedinci sınıf öğrencilerinin cebirsel düşünme becerilerinin görev destekli öğretim yaklaşım ile nasıl geliştiğini araştırmaktır. Çalışma İstanbul'daki bir devlet okulunun yedinci sınıfındaki öğrenciler ile gerçekleştirilmiştir. Görevler, öğrencilerin cebirsel düşünme süreçlerinin temel bileşenlerini -örüntü tanıma, cebirsel ifadeleri yazma, denklem kurma ve çözme- desteklemek amacıyla tasarlanmıştır. Uygulama sırasında sınıftaki öğrenciler üçerli ve dörderli gruplara ayrılmış ve her grupta bir öğretmen adayı görevlerin uygulanmasından sorumlu olmuştur. Öğretmen adayları, her bir görev öncesinde araştırmacı tarafından sağlanan yönergeler, uygulama prensipleri ve olası öğrenci hataları hakkında bilgilendirilmişlerdir. Tüm uygulama süreci, öğrencilerin onayı alınarak kaydedilmiştir. Bu makalede cebirsel düşünmenin örüntü tanıma bileşenine odaklanılmıştır. Video analizi ve öğrencilerin yanıtları, onların cebirsel düşünme süreçlerinin örüntü tanıma bileşeninde gelişme gösterdiğini ve ayrıca, nitel analiz yoluyla yapılan örüntü tanıma bileşeni değerlendirmesi de, öğrencilerin cebirsel düşünme becerilerinde önceki performanslarına göre bir gelişim olduğunu göstermiştir. Sonuçlar, öğrencilerin cebirsel düşünme becerilerini geliştirmek ve cebir öğrenimlerini desteklemek için görev temelli öğretimin etkili bir yöntem olabileceğini göstermektedir.

Anahtar Kelimeler

Cebirsel düşünme, örüntü görevleri, görev destekli öğretim, görev tasarımı

Proje Numarası

215K049

Kaynakça

• Adelman, C. (2006). The toolbox revisited: Paths to degree completion from high school through college. US Department of Education.
• Akkaya, R., & Durmus. S. (2006). Misconceptions of elementary school students grades 6-8 on learning algebra. Hacettepe University Education Faculty Journal, 31, 1-12.
• Amit, M., & Neria, D. (2007). Assessing a modeling process of a linear pattern task. Paper presented at the 13th conference of the International Community of Teachers of Mathematical Modeling and Applications, IN, USA.
• Baxter, J. A., & Williams, S. (2010). Social and analytic scaffolding in middle school mathematics: Managing the dilemma of telling. Journal of Mathematics Teacher Education, 13(1), 7-26.
• Billings, E. M. H., Tiedt, T. L., & Slater, L. H. (2007). Algebraic thinking and pictorial growth patterns. Teaching Children Mathematics, 14(5), 302-308.
• Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann.
• Carpenter, T. P., & Lehrer, R. (1999). Teaching and Learning Mathematics With Understanding1. In Mathematics classrooms that promote understanding (pp. 19-32). Routledge.
• Creswell, J. W., Klassen, A. C., Plano Clark, V. L., & Smith, K. C. (2011). Best practices for mixed methods research in the health sciences. Bethesda (Maryland): National Institutes of Health, 2013, 541-545.
• Dede. Y., & Peker. M. (2007). Students’ errors and misunderstanding towards algebra: Pre-Service mathematics teachers’ prediction skills of error and misunderstanding and solution suggestions. Elementary Education Online, 6(1), 35-49.
• Dogan, O., & Donmez, P. (2016). The Effect of Realistic Mathematics Education on Seventh Grade Students’ Algebra Achievement on Algebraic Expressions. 12th National Science and Mathematics Symposium, Trabzon.
• Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide for Teachers Grades 6-10. Heinemann: Portsmouth.
• Jupri. A., Drijvers. P., & Huevel-Panhuizen. M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Group of Australasia, 26, 683-710.
• Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Erlbaum.
• Kılıç, H., & Doğan O. (2022). Preservice mathematics teachers’ noticing in action and in reflection. International Journal of Science and Mathematics Education, 20 (2), 345-366. Kılıç, H., Doğan, O., Arabacı, N., & Tün, S. S. (2019). Preservice teachers’ noticing of mathematical opportunities. The 11th Congress of the European Society for Research in Mathematics Education (CERME 11), Utrecht, Netherlands.
• Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297-312.
• Kriegler, S. (2008). Just what is algebraic thinking? Retrieved September 2, 2022.
• Lannin, J. K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231-258.
• Leatham, K. R., Peterson, B. E., Stokero, S. L., & Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking. Journal for Research in Mathematics Education, 46(1), 88-124.
• Lew, H. C. (2004). Developing algebraic thinking in early grades: Case study of Korean elementary school mathematics. The Mathematics Educator, 8(1), 88-106.
• Liljedahl, P., Chernoff, E., & Zazkis, R. (2007). Interweaving mathematics and pedagogy in task design: a tale of one task. Journal of Mathematics Teacher Education, 10(4), 239-249.
• Lin, P. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students’ mathematical learning. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 3, 257-264.
• Lucariello, J., Tine, M. T., & Ganley, M. C. (2014). A formative assessment of students’ algebraic misconceptions. Journal of Mathematical Behavior, 33(1), 30-41.
• Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco, CA: Jossey-Bass.
• Ministry of National Education, (2018). High School Mathematics Course 9th, 10th, 11th and 12th grade curriculum.
• Moyer-Packenham, P. (2005). Using virtual manipulatives to investigate patterns and generate rules in algebra. Teaching children mathematics, 11(8), 437-444.Ozen, A., & Ergenekon, Y. (2011). Activity based intervention practices in special education. Educational Sciences: Theory&Practice, 11(1), 359-362.
• Palabıyık, U., & Ispir, O. A. (2011). The effects of pattern-based algebra instruction on students’ algebraic thinking and attitudes towards mathematics. Pamukkale University Education Faculty Journal, 30, 111-123.
• Saraswati, S., & Putri, I. R., (2016). Supporting students’ understanding of linear equations with one variable using algebraic tiles. Journal on Mathematics Education, 7(1), 19-30.
• Sibgatullin, I. R., Korzhuev, A. V., Khairullina, E. R., Sadykova, A. R., Baturina, R. V., & Chauzova, V. (2022). A Systematic Review on Algebraic Thinking in Education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), em2065
• Smith, E. (2003). Stasis and Change: Integrating Patterns, Functions, and Algebra throughout the K-12 Curriculum. In J. Kilpatrick, Martin W. G., & Schifter, D. (Eds.), In A Research Companion to Principles and Standards for School Mathematics, pp. 136-50. Reston, VA: National Council of Teachers of Mathematics.
• Steele, D. F. (2005). Using schemas to develop algebraic thinking. Mathematics Teaching in Middle School, 11(1), 40-46.
• Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in Middle School, 3(1), 9-17.
• Stephens, M., & Ribeiro, A. (2012). Working towards algebra: The importance of relational thinking. Revista latinoamericana de investigación en matemática educativa, 15(3), 373-402.
• Store, J. C., Berenson, S. B., & Carter, T. C. (2010). Creating a context to promote algebraic reasoning. Proceedings of the 37th annual meeting of the research council on mathematics learning (pp. 52-58). Conway: Arkansas.
• Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic mathematics education. Encyclopedia of mathematics education, 713-717.
• Walkington, C., Petrosino, A., & Sherman, M. (2013). Supporting algebraic reasoning through personalized story scenarios: How situational understanding mediates performance, Mathematical Thinking and Learning, 15(2), 89-120.
• Warren, E. (2005). Young Children's Ability to Generalise the Pattern Rule for Growing Patterns. International Group for the Psychology of Mathematics Education, 4, 305-312.
• Warren, E., & Cooper T. (2005). Young children’s ability to use the balance strategy to solve for unknowns. Mathematics Education Research Journal, 17(1), 58– 72.
• Welder, R. M. (2012). Improving algebra preparation: Implications from research on student misconceptions and difficulties. School Science and Mathematics, 112(4), 255-26.