Evaluation of Questions in Middle School Mathematics Textbooks in Terms of Problem Solving Strategies

Year 2024, Volume: 32 Issue: 4, 554 - 567, 28.10.2024

Samet Korkmaz , Sedef Çelik Demirci , Ümit Kul

https://doi.org/10.24106/kefdergi.1574325

Abstract

Purpose: This study aims to analyze solved problems in mathematics textbooks, focusing on both general and specific problem-solving strategies. By conducting a detailed analysis of each general strategy, the study seeks to provide a comprehensive evaluation of the problem-solving approaches presented in the textbooks.
Design/Methodology/Approach: The document analysis method was utilized in this study. Solved problems from the mathematics textbooks published by the Ministry of National Education (MoNE) for 5th, 6th, 7th, and 8th grades during the 2023-2024 academic year were examined. Data were collected using the “Solved Problems Checklist” and “Problem-Solving Strategies Determination Form” developed by Hatay (2020). A qualitative descriptive analysis method was employed to analyze the data, with percentage and frequency values calculated to present the findings.
Findings: The analysis revealed that the stages of planning and implementing a solution plan were prominently featured in the middle school mathematics textbooks. Specifically, the initial stage of understanding the problem often included visual aids such as figures, diagrams, tables, and pictures. In the planning phase, the predominant solutions involved discussions of mathematical operations.
Highlights: The study’s findings indicate that while problem-solving strategies are generally emphasized in mathematics education, certain steps, such as solution evaluation, are given greater focus. Additionally, the research highlights a significant gap in the inclusion of the problem-posing stage, the final step of general problem-solving strategies, in the analyzed mathematics textbooks.

Keywords

Problem solving, Middle school mathematics textbooks, Matematik eğitimi

References

• Arslan, Ç., & Altun, M. (2007). Learning to solve non-routine mathematical problems. Elementary Education Online, 6(1), 50-61.
• Arslan, G. (2023). Investigation of 10th grade mathematics textbook in terms of problem solving strategies [Master’s thesis]. Afyon Kocatepe University.
• Arslan, S., & Özpınar, İ. (2009). Evaluation of 6th grade mathematics textbooks along with the teacher opinions. Dicle University Ziya Gökalp Education Faculty Journal, (12), 97-113.
• Bayrak, M. T. (2022). The effect of problem solving and posing ınstruction on non-routine problem solving and posing skills of 8th grade students [Master’s thesis]. Bursa Uludag University.
• Böge, H. & Akıllı, R. (2021). Ortaokul ve imam hatip ortaokulu matematik 8 ders kitabı. Ankara: MEB Yayınları.
• Brehmer, D., Ryve, A., & VanSteenbrugge, H. (2016). Problem solving in Swedish mathemat-ics textbooks for upper secondary school. Scandinavian Journal of Educational Research, 60(6), 577–593.
• Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem solving: From research to effective practice (pp. 3-34). Springer
• Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37-46. https://doi.org/10.1177/001316446002000104
• Creswell, J. W. (2016). Research design qualitative, quantitative, and mixed methods approaches. Eğiten kitap.
• Çağlayan, N., Dağıstan, A. & Korkmaz, B. (2021). Ortaokul ve imam hatip ortaokulu matematik 6 ders kitabı. Ankara: MEB Yayınları.
• Çelik, M. A. (2019). Investigation of 10th grade mathematics textbook in terms of problem solving strategies [Master's thesis]. Necmettin Erbakan University.
• Çelik, S., & Kul, Ü. (2021). The analysis of problem posing activities in Turkish and Canadian mathematics textbooks: A comparative study. Studies in Educational Research and Development, 5(2), 148-179.
• Çepni, S. (2014). Araştırma ve proje çalışmalarına giriş (Geliştirilmiş 7. Baskı). Trabzon: Celepler Matbaacılık.
• Çolpan Kuru, B. (2021). Evaluation of the problem-solving approach in terms of various theories. CRES Journal, 2(1), 50-58.
• Dayak, E. (1998). İlköğretim 5. sınıf matematik ders kitaplarının eğitim-öğretime uygunluğunun değerlendirilmesi [Master’s thesis]. Marmara University.
• Deringöl, Y. (2020). Problem posing activities in primary school mathematics textbooks. Elementary Education Online, 19(3), 1619-1646.
• El Sayed, R. A-E. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of science and mathematics education in Southeast Asia, 25(1), 56-69.
• Fan, L., & Zhu, Y. (2007). Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks. Educational studies in Mathematics, 66, 61-75.
• Galiç, S., Urhan, S., & Dost, Ş. (2024). Textbook use in mathematics learning environments in Turkey. Trakya Journal of Education, 14(3), 1945-1964.
• Garderen, D.V. (2006). Spatial visualization, visual ımaginary and mathematical problem solving of students with varying abilities. Journal of Learning Disabilities 39(6): 496– 506
• Gelbal, S. (1991). Problem çözme. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 6, 167-173.
• Glasnovic Gracin, D. (2018). Requirements in mathematics textbooks: A five-dimensional analysis of textbook exercises and examples. International journal of mathematical education in science and technology, 49(7), 1003-1024.
• Gonzales, N. A. (1994). Problem posing: A neglected component in mathematics courses for prospective elementary and middle school teachers. School Science and Mathematics, 94(2), 78-84. https://doi.org/10.1111/j.1949- 8594.1994.tb12295.x
• Hatay, A., & Cihangir, A. (2021). Investigation of 7th grade mathematics course books in point of the development of problem solving skills and problem solving strategies. Journal of Ahmet Keleşoğlu Education Faculty, 3(1), 117-146.
• Hatay, G. A. (2020). Investigation of 7th grade mathematics course books in point of the development of problem solving skills and problem solving strategies [Master’s thesis]. Necmettin Erbakan University.
• Intaros, P., Inprasitha, M., & Srisawadi, N. (2014). Students’ problem solving strategies in problem solving-mathematics classroom. Procedia-Social and Behavioral Sciences, 116, 4119-4123.
• Jäder, J., Lithner, J., & Sidenvall, J. (2020). Mathematical problem solving in textbooks from twelve countries. International Journal of Mathematical Education in Science and Technology, 51(7), 1120-1136.
• Karakelleoğlu, S. (2007). Primary school 4th class mathematics opinions of theachers, students and specialist on textbooks [Master's thesis]. Balıkesir University.
• Kazanci Dede, S. Ç. (2020). Examination of the content of secondary school 11th grade mathematics textbook and determination of teachers' opinions [Master's thesis]. Trabzon University.
• Kıral-Demir, B., & Katrancı, Y. (2023). Examining the problems in the middle school mathematics textbooks according to the problem-solving stages. Educational Academic Research, 50, 90-103.
• Koç Koca, A., & Gürbüz, R. (2021). Problem solving strategies used by gifted secondary school students to solve math problems. Bolu Abant İzzet Baysal University Journal of Faculty of Education, 21(1), 348-359. https://dx.doi.org/10.17240/aibuefd.2021.21.60703-862916
• Kolovou, A., Van Den Heuvel-Panhuizen, M., & Bakker, A. (2011). Non-routine problem solving tasks in primary school mathematics textbooks–a needle in a haystack. Mathematical Problem Solving Primary School, 8, 45.
• Korkmaz, B., Yiğit Meşe, D. & Arslan, H. T. (2023). Ortaokul ve imam hatip ortaokulu 5. sınıf matematik ders kitabı. Ankara: MEB Yayınları.
• Kul, Ü., Sevimli, E., & Aksu, Z. (2018). A comparison of mathematics questions in Turkish and Canadian school textbooks in terms of synthesized taxonomy. Turkish Journal of Education, 7(3), 136-155. https://doi.org/10.19128/turje.395162
• Külköylüoğlu, A., Güneş, M., Selçuk, M. & Tuğrul, Y. (2023). Ortaokul ve imam hatip ortaokulu matematik 7 ders kitabı. Ankara: MEB Yayınları.
• Kusumadewi, C. A., & Retnawati, H. (2020). Identification of elementaryschool students’ difficulties in mathematical problem solving. Journal of Physics: Conference series, 1511, 1-10. http://dx.doi.org/10.1088/1742-6596/1511/1/012031
• Marchis, I. (2012). Non-routine problems in primary mathematics workbooks from Romania. Acta Didactica Napocensia, 5(3), 49-56.
• Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks, CA: SAGE Publications.
• Ministry of National Education [MoNE]. (2013). Secondary school (5-8th grade) mathematics course curriculum. Ankara: MoNE Publishing.
• Ministry of National Education [MoNE]. (2018). Mathematics course curriculum (Primary and secondary school). Ankara: MoNE Publishing.
• Mullis, I. V., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Amsterdam: International Association for the Evaluation of Educational Achievement.
• O’Keeffe, L. (2014). Mathematics textbook analysis; supporting the implementation of a new mathematics curriculum. In Proceedings of the International Conference on Mathematics Textbook Research and Development (Southampton: ICMT-2014) (p. 365).
• Ontario Ministry of Education (OME). (2005). Mathematics curriculum grades 1–8. Ottawa, ON: Queen’s Printer for Ontario.
• Özdişci, S., & Katrancı, Y. (2020). Investigation of middle school students’ problem solving and problem posing skills. Journal Of National Education, 49(226), 149-184.
• Özsoy, G. (2014). The relationship between problem solving skills and mathematical achievement. Gazi University Journal of Gazi Educational Faculty, 25(3), 179-190.
• Phonapichat, P., Wongwanich, S., & Sujiva, S. (2014). An analysis of elementary school students’ difficulties in mathematical problem solving. Procedia-Social and Behavioral Sciences, 116, 3169-3174.
• Polya, G. (1973). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton
• Polya, G. (1997). Nasıl çözmeli? (Çeviren: Halatçı F.). İstanbul: Sistem Yayıncılık.
• Posamentier, A. S. & Krulik, S. (1998). Problem-solving strategies for efficient and elegant solutions. A Research for the Mathematics Teacher. California: Corwin Press
• Rahimah, D., & Visnovska, J. (2021). Analysis of mathematics textbook use: An argument for combining horizontal, vertical, and contextual analyses. In Journal of Physics: Conference Series (Vol. 1731, No. 1, p. 012048). IOP Publishing.
• Reys, B. J., Reys, R. E. ve Chavez., O. (2004). Why mathematics textbooks matter. Educational Leadership, 61(5),61-66.
• Sevimli, E., Çelik, S., & Kul, Ü. (2022). Comparison of the frequency of mathematics teachers’ use of mathematics textbooks in face-to face and distance education. Turkish Journal of Education, 11(1), 16-35. https://doi.org/10.19128/turje.896355
• Soylu, C., & Pala, F. C. (2018). Age related differences in problem solving performance. Current Approaches in Psychiatry, 10(3), 290-301.
• Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Mathematics Education Research Group of Australasia.
• Sulistyani, D., Subekti, E. E., & Wardana, M. Y. S. (2021). Students' learning difficulties review from mathematics problem-solving ability in third-grade elementary school. Indonesian Journal Of Educational Research and Review, 4(2), 345-351.
• Şişçi, T. (2023). Secondary grade 11 and 12 basic mathematics textbooks investigation according to problem solving strategies [Master’s thesis]. Zonguldak Bülent Ecevit University.
• Toh, T. L., Chan, C. M. E., Tay, E. G., Leong, Y. H., Quek, K. S., Toh, P. C., Ho, W. K., Dindyal, J., Ho, F. H., & Dong, F. M. (2019). Problem solving in the Singapore school mathematics curriculum. In T. L. Toh, B. Kaur, & E. G. Tay (Eds.), Mathematics Education in Singapore (pp. 141–164). Springer.
• Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation. 31(4), 315-327.
• Türkmen, S. (2022) Mi̇ddle school examining mathematics textbooks in terms of problem solving strategies: Numbers and operations learning domain [Master’s thesis]. Gazi University.
• UK Department for Education (2013). The National curriculum in England: Key stages 3 and 4 framework document. London, UK: Department for Education. Retrived 12 July, 2019, from www.gov.uk/dfe/nationalcurriculum
• Xin, Y. P. (2007). Word problem solving tasks in textbooks and their relation to student performance. The Journal of Educational Research, 100(6), 347-360.
• Yıldız, Ş., & Ev Çimen, E. (2017). A review of problem posing activities in secondary school mathematics textbooks. Turkish Journal of Computer and Mathematics Education, 8(3), 378-407.