# Investigation of Libyan and Turkish students' thinking levels in solving quadratic word problems based on SOLO Taxonomy

## DOI:

https://doi.org/10.14527/pegegog.2020.010## Abstract

This article presents a study of the skills of Libyan and Turkish students in their quadratic word problems based on SOLO Taxonomy. The research model used in this study is a case study. The participants were 27 students at a high school in Kastamonu, Turkey and were 27 students at a high school in the city of Tripoli, Libya. The data were obtained by thinking test consisting of three problems. The test was applied to the students in the spring semester of 2017-2018 academic year. Overall, the results showed that Turkish students had multiple structural levels of 48.15% and relational structural levels of 10.37%, which is considered a good ratio, and were better than Libyan students with multiple structural levels of 21.50% and relational-structural levels of 9.00%. This shows that the majority of Turkish students participating in the study may be successful in moving advanced thinking levels in these problems. On the other hand, there are students who cannot answer the problems as well as pre-structural and uni-structural students. Some of the reasons why these students’ levels are low may be misinterpretation of the problem, difficulty in understanding word problems and turning them into mathematical symbols, and negligence.

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## References

Aniano, L. C. (2010). Difficulties in solving word problem on fractions among grade VI pupils of balara elementary school. Unpublished master thesis, University of Rizal, Morong.

Bardillion, R. U. (2004). Students’ filipino verbal and symbolic tranlations, problem solving ability and attitude towards mathematics word problems. Unpublished master thesis, University of the Philippines, Quezon.

Barwell, R. (2011). Word problems connecting language, Mathematics and life. What Works? Research into Practice, 3-4. Retrieved from

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/WW_Word_Problems.pdf

Bernadette, E. (2009). Third grade students' challenges and strategies to solving mathematical word problems. M.A. dissertation, The University of Texas at El Paso, United States.

Bernardo, A. B. (1999). Overcoming obstacles to understanding and solving word problems in mathematics. Educational Psychology, 19(2), 149-163.

Bernardo, A. B. (2002). Language and mathematical problem solving among bilinguals. The Journal of Psychology, 136(3), 283-297.

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.

Boonen, A. J., van der Schoot, M., van Wesel, F., de Vries, M. H., & Jolles, J. (2013). What underlies successful word problem solving?. A path analysis in sixth grade students. Contemporary Educational Psychology, 38(3), 271-279.

Chassapis, D. (2010). A framing of the world by mathematics: A Study of word problems in greek primary school mathematics textbooks. In. U. Gellert, E. Jablonka & C. Morgan. In Proceedings of the Sixth International Mathematics Education and Society Conference (pp. 209-218). Freie Universität Berlin Publishing.

Chaudhary, M. P. (2013).Utility of mathematics. International Journal of Mathematical Archive, 4 (2), 76-77.

Dela Cruz, J.K.B., & Lapinid, M.R.C. (2014). Students’ difficulties in translating worded problems into mathematical symbols. Paper Presented at the DLSU Research Congress 2014 De La Salle University, Manila, Philippines.

Gooding, S. (2009). Children's difficulties with mathematical word problems. Proceedings of the British Society for Research into Learning Mathematics, 29(3), 31-36.

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.

İncikabı, L., & Sancar-Tokmak, H. (2012). Uzman bakışıyla öğretmen adaylarının eğitimsel yazılım değerlendirme süreci üzerine bir araştırma. Kastamonu Eğitim Dergisi, 20(3), 939-954.

Jimoyiannis, A. (2013). Using Solo taxonomy to explore students’ mental models of the programming variable and the assignment statement. Themes in Science and Technology Education, 4(2), 53-74.

K.N.E.C., (2007). Examination report. Nairobi. KNEC.

Krulik, S., & Rudnick, J. (1996). The new sourcebook for teaching reasoning and problem solving in junior and senior high school. Needham Height, Massachusetts: Allyn&Bacon.

Lam, P. & Foong, Y. (1996). Rasch analysis of math Solo taxonomy levels using hierarchical items in testlets, ERIC-ED 398271.

Lee, K., Ng, E. L., & Ng, S. F. (2009). The contributions of working memory and executive functioning to problem representation and solution generation in algebraic word problems. Journal of Educational Psychology, 101(2), 373-387.

Lian, L.H., & Idris, N. (2006). Assessing algebraic solving ability of form four students. International Electronic Journal of Mathematics Education (IEJME), 1(1), 55-76.

MOEST. (2001). Teaching and learning mathematics in primary classroom: School based teacher development. Nairobi: MOEST.

Ng, S. F., & Lee, K. (2009). The model method: Singapore children's tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282-313.

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.

Pfannenstiel, K. H., Bryant, D. P., Bryant, B. R., & Porterfield, J. A. (2015). Cognitive strategy instruction for teaching word problems to primary-level struggling students. Intervention in School and Clinic, 50(5), 291-296.

Polya, G. (1957). How to solve it: A new aspects of mathematical methods. Prentice University Press.

Potter, M. K., & Kustra, E. (2012). A primer on learning outcomes and the Solo taxonomy. Course Design for Constructive Alignment,(Winter 2012), 1-22.

Putri, U. H., Mardiyana, M., & Saputro, D. R. S. (2017, September). How to analyze the students’ thinking levels based on Solo Taxonomy? . In Journal of Physics: Conference Series (Vol. 895, No. 1, p. 012031). IOP Publishing.

Rasmussen, C. L., & King, K. D. (2000). Locating starting points in differential equations: A realistic mathematics education approach. International Journal of Mathematical Education in Science and Technology, 31(2), 161-172.

Roslina, R. (1997). Keupayaan algebra asas pelajar tingkatan empat sekolah menengah kerajaan Daerah Hulu Langat.[The ability of Form Four students in basic algebra]. Master of Education Research Project. Universiti Kebangsaan Malaysia.

Schumacher, S., & Mcmillan, J. (2006). Research in Education Evidence–Based Inquiry. Boston: Pearson Education.

Silver, E. A. (1992). Referential mappings and the solution of division story problems involving remainders. Focus on Learning Problems in Mathematics, 14(3), 29-39.

Swanson, H. L., Orosco, M. J., & Lussier, C. M. (2014). The effects of mathematics strategy instruction for children with serious problem-solving difficulties. Exceptional Children, 80(2), 149-168.

Thevenot, C. (2010). Arithmetic word problem solving: Evidence for the construction of a mental model. Acta psychologica, 133(1), 90-95.

Timmermans, R. E., Van Lieshout, E. C., & Verhoeven, L. (2007). Gender-related effects of contemporary math instruction for low performers on problem-solving behavior. Learning and Instruction, 17(1), 42-54.

Tindowen, D. J. C., Ramirez, N. K., & Sales, J. G. (2019). Students’ difficulties in translating mathematics word statements. Journal of Humanities and Education Development (JHED), 1(1), 11-18.

Verschaffel, L., Greer, B., & De Corte, E. (2002). Everyday knowledge and mathematical modeling of school word problems. In Symbolizing, modeling and tool use in mathematics education (pp. 257-276). Springer, Dordrecht.

Verschaffel, L., Greer, B., & De Corte, E.(2000). Making Sense of Word Problems. Netherlands: Swets & Zeitlinger.

Vista, E. M. (2010). Developing comprehension of word problems in mathematics through grammar integration. Unpublished master thesis, University of the Philippines, Quezon.

Yeo, K. K. J. (2009). Secondary 2 students' difficulties in solving non-routine problems. International Journal for Mathematics Teaching and Learning, 211. Retrieved from http://www.cimt.org.uk/journal/yeo.pdf

Zawaiza, T. R. W., & Gerber, M. M. (1993). Effects of explicit instruction on math word-problem solving by community college students with learning disabilities. Learning Disability Quarterly, 16(1), 64-79.

Zentall, S. S., & Ferkis, M. A. (1993). Mathematical problem solving for youth with ADHD, with and without learning disabilities. Learning Disability Quarterly, 16(1), 6-18.

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*Pegem Eğitim Ve Öğretim Dergisi*,

*10*(1), 283-316. https://doi.org/10.14527/pegegog.2020.010

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Copyright (c) 2020 Awatef ELAZZABİ, Ahmet KAÇAR (Author)

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