A Comparative Analysis of Ratio and Proportion Problems in Libyan and Turkish Mathematics Textbooks

Abstract

This study investigates the similarities and differences between ratio and proportion problems in Libyan mathematics textbooks (8th and 9th grades) and Turkish mathematics textbooks (6th and 7th grades). A content analysis methodology, based on a three-dimensional framework developed by Li, involving mathematical features, contextual features, and performance requirements is used and the use of technology is also considered. The results can be summarized as follows. In general, there were only small differences in the results for all three dimensions. Most of the problems analyzed required using multiple computation procedures to produce numerical answers, and focused more on the cognitive domain of knowing but less on applying and reasoning. In addition, none of the problems in the Libyan textbooks required the use of technology, while 1% of the problems in the Turkish ones did.

Keywords

• Mathematics textbook,Ratio and proportion problems,Content analysis

References

1. Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183-198.
2. Alajmi, H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait, Educational Studies in Mathematics, 79(2), 239-261.
3. Beaton, A. E., Mullis, I. V., Martin, M. O., Gonzalez, E. J., Kelly, D. L., & Smith, T. A. (1996). Mathematics achievement in the middle school years: IEA’s third international mathematics and science study (TIMSS). Boston, MA: Center for the Study of Testing, Evaluation and Educational Policy, Boston College.
4. Beckmann, S. (2004). Solving algebra and other story problems with simple diagrams: A method demonstrated in grade 4–6 texts used in Singapore. The Mathematics Educator, 14(1), 42-46.
5. Carter, J., Li, Y., & Ferrucci, B. (1997) A comparison of how textbooks present integer addition and subtraction in China and the United States. Mathematics Educator, 2, 197-209.
6. Charalambous, C. Y., Delaney, S., Hsu, H. Y., & Mesa, V. (2010) A comparison analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12, 117-151.
7. Conklin, M. (2004) found in translation: A comparison of American, German, and Japanese mathematics texts and exercises (Doctoral dissertation, University of Maryland). Retrieved from http://drum.lib.umd.edu//handle/1903/1847
8. Erbas, A. K., Alacaci, C., & Bulut, M. (2012). A Comparison of Mathematics Textbooks from Turkey, Singapore, and the United States of America. Educational Sciences: Theory and Practice, 12(3), 2324-2329.

9. 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(1), 61-75.
10. Gelfman, E., Podstrigich, A., & Losinskaya, R. (2004) On the problem of typology and functions of school texts, Discussion Group 14, Focus on the Development and Research of Mathematics Textbooks, ICME X, Copenhagen, Denmark, July
11. Hu, Q. (2011). How textbooks influence students’ algebra learning: A comparative study on the initial treatment of the concept of function (Master’s thesis). Retrieved from https:// trace.tennessee.edu/utk_gradthes/884/
12. İncikabi, L., & Tjoe, H. (2013) A Comparative analysis of ratio and proportion problems in Turkish and the US middle school mathematics textbooks. Journal of Kirsehir Education Faculty, 14(1)
13. Li, Y. (2000). A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. Journal for Research in Mathematics Education, 31(2), 234-241.
14. Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks: An empirical approach. Educational Studies in Mathematics, 56, 255-286.
15. Mullis, I. V., Martin, M. O., Ruddock, G. J., O’Sullivan, C. Y., & Preuschoff, C. (2009). TIMSS 2011 Assessment Frameworks. International Association for the Evaluation of Educational Achievement, Herengracht 487, Amsterdam, 1017 BT, the Netherlands.‏
16. Nicol, C. C., & Crespo, S. M. (2006). learning to teach with mathematics textbooks: How preservice teachers interpret and use curriculum materials. Educational Studies in Mathematics, 62(3), 331-355.
17. Ravitch, D. (2003). The language police: How pressure groups restrict what students learn. New York: Alfred A. Knopf.
18. Schmidt, W. H., McKnight, C. C., Valverde, G. A., Houang, R. T., & Wiley, D.E. (1997). Many visions, many aims: A cross-national investigation of curricular intentions in school mathematics (Vol. 1). Dordrecht: Kluwer Academic.
19. Son, J. W., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74(2), 117-142.
20. Stevenson, H. W., & Bartsch, K. (1992). An analysis of Japanese and American textbooks in mathematics. In R. Lestma, & H. J. Walberg (Eds.), Japanese educational productivity (pp. 103-283), University of Michigan, Ann Arbor, Michigan: Center for Japanese Studies.
21. Stigler, J. W., Fuson, K. C., Ham, M., & Kim, M. S. (1986). an analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cognition and Instruction, 3, 153-171.
22. Valverde, G., Bianchi, L., Wolfe, R., Schmidt, W., & Houang, R. (2002). According to the book: using timss to investigate the translation of policy into practice through the world of textbooks, London: Kluwer Academic Publishers.
23. Yeap, B. H. (2005). Building foundations and developing creativity: An analysis of Singapore mathematics textbooks. Paper presented at the Third East Asia Regional Conference on Mathematics Education in Shanghai, China.