An examination of Libyan and Turkish Students' Thinking Skill Levels Through their Generalization in Quadratic Patterns according to SOLO Taxonomy
Keywords:
Libyan and Turkish Students, Thinking Skills, Generalization in Quadratic Patterns, SOLO TaxonomyAbstract
This study aimed to an examination of Libyan and Turkish students' thinking skill levels through generalization in quadratic patterns according to SOLO taxonomy. The study model was a hybrid design with predominantly qualitative design. In this study, the working group was consisted of 112 from Libyan students at three high school in the city of Tripoli in Libya and 129 Turkish students at three high school in the city of Kastamonu in Turkey. The study was undertaken in the 2018-2019 academic year. Overall, the results showed that most Turkish and Libyan students who participated in the study mostly their level on the Uni-structural level, the Multi structural level and the Relational structure level, However, some of them were able to reach successful in moving Advanced thinking levels. Despite of this, there Libyan and Turkish students left the problems blank and there were students at the pre-structural level. Obtaining ideas about students' thinking and knowledge levels about the patterns is rather important. So, recommend supporting students to develop their thinking skills by solving problems and getting them involved in different activities that are aimed at promoting their skills and improving their ability in thinking. This means, mathematics teachers should create opportunities for students to relate their mathematical ideas and concepts to enable the students to promote their ability in thinking especially algebraic thinking, as well support students' thinking skills in moving from a design-based learning environment that encourages "recalling facts" to one that encourages "analysis and synthesis". Thus, students will attain a higher level of thinking in understanding Generalization in Quadratic Patterns.
References
Akkan, Y. (2013). Comparison of 6th-8th graders‟ efficiencies, strategies and representations regarding generalization patterns. Bolema, 27 (47), 703-732.
Amit, M &Neria, D. (2008). Rising to the challenge: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM Mathematics Education, 40, 111–129
Andini, W., & Suryadi, D. (2017). Student obstacles in solving algebraic thinking problems. In Journal of Physics: Conference Series, 895(1).
Bağdat, O. (2013). Ilköğretim 8. Sınıf Öğrencilerinin Cebirsel Düşünme Becerilerinin SOLO Taksonomisi Ile Incelenmesi. Yüksek Lisans Tezi, Eskişehir Osmangazi Üniversitesi Eğitim Bilimleri Enstitüsü. Eskişehir.
Berg, D. M. (2012). Algebraic thinking in the elementary classroom. Doctoral Dissertation, Simon Fraser University, Faculty of Education. Canada.
Biggs, J., & Collis, K. (1991). Multimodal learning and the quality of intelligent behaviour. In H.Rowe( Ed.), Intelligence: Reconceptualization and measurement (pp.57-76). New Jersey: Laurence Erlbaum Assoc.
Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2003). Learning mathematics in elementary and middle schools. (3rd ed.). Englewood Cliffs, N.J.: Merrill/Prentice Hall.
Çayır, M. Y., & Akyüz, G. (2015). 9. Sınıf öğrencilerinin örüntü genelleme problemlerini çözme stratejilerinin belirlenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 9(2), 205-229.
Çelik, D. (2007). Öğretmen Adaylarının Cebirsel Düşünme Becerilerinin Analitik Incelenmesi. Yayınlanmamış Doktora Tezi, Karadeniz Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Trabzon.
Dindyal, J. (2003). Algebraic thinking in geometry at high level school. Doctoral Dissertation, Illinois Universitesi, Matematik Bölümü.
Elazzabi, A., & Kaçar, A. (2020). Investigation of Libyan and Turkish students' thinking levels in solving quadratic word problems based on SOLO Taxonomy. Pegem Eğitim ve Öğretim Dergisi, 10(1), 283-316.
Fraenkel, J. R., & Wallen, N., E. (2006). How to design and evaluate research in Education (6 th Ed.). McGraw-Hill International Edition.
Hargreaves, M., Shorrocks-Taylor, D. & Threlfall, J. (1999). Children’s strategies with number patterns. Pattern in the teaching and learning of mathematics, 67-83.
Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics, 65-97.
Isik, D., & Tarim, K. (2009). The effects of the cooperative learning method supported by multiple intelligence theory on Turkish elementary students` mathematics achievement. Education Research Institute, Seoul National University, 10, 465– 474. doi: 10.1007/s12564-009-9049-5.
Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 235–272). New York, NY: Lawrence Erlbaum Associates.
Lam, P. ve Foong, Y. (1996). Rasch analysis of math Solo taxonomy levels using hierarchical items in testlets, ERIC-ED 398271.
Lannin, J. K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231-258.
Lee, L. (1996). An initiation into algebraic culture through generalization activities. In Approaches to Algebra (pp. 87-106). Springer, Dordrecht.
Lee, L., & Freiman, V. (2006). Developing algebraic thinking through pattern exploration. Mathematics Teaching in The Middle School, 11(9), 428-433.
Lian, L. H., & Idris, N. (2006). Assessing algebraic solving ability of form four students. International Electronic Journal of Mathematics Education, 1(1), 55-76.
MacGregor, M., & Stacey, K. (1996). Origins of students' interpretations of algebraic notation. In PME Conference (Vol. 3, pp. 3-297). The Program Committee of the 18th PME Conference.
Miles, M. B., Huberman, A. M., Huberman, M. A., & Huberman, M. (1994). Qualitative Data Analysis: An Expanded Sourcebook. Sage.
Mooney, E. S. (2002). A framework for characterizing middle school students' statistical thinking. Mathematical Thinking and Learning, 4(1), 23-63.
Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33-49.
NCTM. (1992). Algebra for the twenty-first century. Proceedings of the August 1992 Conference. Reston, VA: Author.
Olkun, S., Şahin, Ö., Akkurt, Z., Dikkartin, F. T., & Gülbağcı, H. (2009). Modelleme yoluyla problem çözme ve genelleme: İlköğretim öğrencileriyle bir çalışma. Eğitim ve Bilim, 34(151).
Patton, M.Q. (1987). How to use qualitative methods in evaluation. Newbury Park, Sage, pp.169-183.
Palabıyık, U. & Akkuş-İşpir, O. (2011). The effects of pattern-based Algebra instruction on students' Algebraic thinking attitude towards Mathematics. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30, 111-123.
Pegg, J., & Coady, C. (1993). Identifying Solo levels in the formal mode. In Proceedings of the 17th International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 212-219).
Pegg, J., & Tall, D. (2005). The fundamental cycles of concept construction underlying various theoretical frameworks. International Reviews on Mathematical Education, 37(6), 468- 475.
Polat, S. (2010). İlköğretim 6–7. sınıf öğrencilerinin matematik kavramına ilişkin kullandıkları metaforlar. Unpublished master's thesis, Gaziosmanpaşa Üniversitesi Sosyal Bilimler Enstitüsü, Tokat.
Rider, R. L. (2004). The effects of multi-representational methods on students' knowledge of function concepts in developmental college mathematics.
Smith, S. S. (1997). Early childhood mathematics. Needham Heights, MA: Allyn & Bacon.
Stacey,K. (1989). Finding and using patterns in linear generalizing problems. Educational Studies in Mathematics, 20, 147–164.
Yeşildere, S. ve Akkoç, H. (2011). Matematik öğretmen adaylarının şekil örüntülerini genelleme süreçleri. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30, 141-153.
Yildirim, K. (2006). Coklu zeka kurami destekli kubasik ogrenme yonteminin ilkogretim 4. sinif ogrencilerinin matematik dersindeki erisilerine etkisi [The effects of cooperative learning method supported by multiple intelligence theory on elementary school 4th grade students` academic achievement]. Ahi Evran Universitesi Kirsehir Egitim Fakultesi Dergisi, 7(2), 301–315.
Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49(3), 379-402.
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