24 SES 06, Text books Analysis
Mathematics education community has called for the importance of connecting mathematics to the real world (Bonotto & Basso, 2001). In the literature some benefits provided by the connections between mathematics and real-life are mentioned as improving students’ understanding of the mathematical concepts, helping them use mathematics in their daily lives (Bonotto & Basso, 2001), and enhancing their interest and motivation (Stylianides & Stylianides, 2008). One possible way to connect mathematics and the real world is including tasks and problems embedded in real life contexts in mathematics textbooks since textbooks are essential elements in teaching of mathematics in such a way that they function as vehicles through which students interact with mathematics (Weinberg & Wiesner, 2011).
Despite this great emphasis on using real life contexts in mathematical tasks there are also some studies questioning the worthiness of these tasks since they may not in fact serve mathematics well (Stylianides & Stylianides, 2008). Filloy and Sutherland (1996) found that including real life contexts in algebra tasks might move teachers’ and students’ attention from algebraic solutions to an isolated solution methods such as trial and refinement. Besides, Lave (1988) found that using the real life context of shopping in mathematics lessons was not beneficial for using mathematics in everyday activity of shopping. Similarly, in studies conducted by Greer (1993) and Vershcaffel, De Corte, and Lasure (1994) students’ high rate of ignorance of relevant and realistic aspects while dealing with word problems were reported. Students were found to have the belief that school problems are distinct from the real world and only requires certain kinds of operations with the given numbers in the problem. Furthermore, many teachers themselves exclude real life knowledge when solving word problems (Verschaffel, De Corte, & Borghart, 1997) and consider real contexts of word problems irrelevant distractors and barriers for learning (Boaler, 1993).
While there are contradictory arguments related to the use of real life contexts in mathematics problems the tasks including real-life contexts have not received the attention it deserved in the research community despite of reform movements’ emphasis on them (Stylianides & Stylianides, 2008). Therefore this study attempts to investigate the potential role of real life context use in mathematical tasks in a textbook. The focus in this study is on the mathematical tasks embedded in real-life contexts in 9th grade mathematics textbook published by Ministry of National Education in Turkey (MoNE, 2013). In this study, real-life contexts are referred to as everyday activities or mathematical applications in various disciplines including science, business, engineering, and economics (Stylianides, 2005). The problems were analyzed by using a framework developed by Zhu and Fan (2006). Even though there are many categories classified in this framework the category of application and non-application problems were used within the context of this study. Non-application problems were defined as including a situation which is not connected to real life and application problems as problems connected to or arises under the context of real life situations by Zhu and Fan. The category of application problems were further divided into two subcategories as fictitious application problems in which conditions or data are made up by the authors and authentic application problems in which conditions and data are taken from real life situations or gathered by students from their daily lives.
The 9th grade textbook is separated into three parts. The first part of the book included two units as Unit 1 Sets and Unit 2 Equations and Inequalities. At the second unit, there is the Section 2.4 called Applications related to Equations and Inequalities. Below this section, there is the subsection 2.4.2 Problems which is the part analyzed in this study. Thirty exemplary problems with solutions at this subsection were analyzed. Exemplary problems were selected for the unit of analysis since they are the problems through which the concepts are taught. The research method of the study was content analysis. . Therefore, this study was guided by the following research questions: • How many application and non-application problems are there in the selected part of the book? • How many of the application problems are fictitious and authentic application problems in the selected part of the book? • What are the characteristics of the fictitious application problems and authentic application problems in the selected part of the book? In order to answer the first two research questions each page was checked for the presence of mathematical tasks embedded in real-life contexts. The definitions of application and non-application problems, and fictitious and authentic application problems made by Zhu and Fan (2006) were used for the analysis. That is to say, if the problem is embedded in real life contexts it is considered as application problem if it is not it is categorized as non-application problem. In addition, if the data are taken from real life the problem is categorized as authentic application problem and if the author made up the story and the data the problem is categorized as fictitious application problem. In order to investigate the third research problem, results of studies related to effects of real life contexts on students’ thinking and sense-making are taken into consideration. Besides, expected student thinking invoked by the context of the problem are considered.
As Bonotto and Basso (2001) argued that the relationship between mathematics and real-life has always been and will always be complex, intricate, though, interesting and it will never be possible to analyze it completely. However, as an initial attempt to investigate this relationship the findings of this study revealed that all of the 30 exemplary problems were application problems whereas no non-application problem was encountered. Nevertheless, of these 30 application problems, only 6 (20%) were authentic application problems while 24 (80%) of them were fictitious application problems in which the story is made up. Even though this study included problems from a Turkish textbook, this result might be applicable to the textbooks in some other countries too. Examples of application, non-application, fictitious and authentic problems are provided, and their potential on student understanding and learning are further discussed. Since authentic problems use real data from the daily life of students they have more potential for improving students’ sense making and learning of mathematics. Therefore increasing the number of authentic application problems is suggested rather than including a variety of fictitious application problems including procedures that are not encountered in students’ everyday life such as adding or multiplying the ages of persons. No single task can provide a wide application that is familiar and sense-making for all students (Boaler, 1993). However it is of great importance that contexts are familiar to the students (Gravemeijer, 1997). It is also important to note that learning of students from real life contexts depends on how students engage with them (Hiebert et al., 1996). That is to say, every person constructs his or her meaning from the context. Therefore, including real world texts is not enough; in addition students’ own cultural values should be recognized for the aim of enhancing their individual meanings (Maier, 1991).
Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics more "real"? For the Learning of Mathematics, 13(2), 12-17. Bonotto, C., & Basso, M. (2001). Is it possible to change the classroom activities in which we delegate the process of connecting mathematics with reality?. International Journal of Mathematical Education in Science and Technology, 32 (3), 385-399. De Corte, E., Verschaffel, L., & Greer, B. (2000, November). Connecting mathematics problem solving to the real world. In Proceedings of the International Conference on Mathematics Education into the 21st Century: Mathematics for living (pp. 66-73). Filloy, E., & Sutherland, R. (1996). Designing curricula for teaching and learning algebra. In International handbook of mathematics education (pp. 139-160). Springer: Netherlands. Gravemeijer, K. (1997). Mediating between concrete and abstract. In T. Nunes and P. Bryant (Eds.), Learning and Teaching Mathematics. An International Perspective (pp.315-345), Psychology Press. Greer, B. (1993). The mathematical modeling perspective on wor(l)d problems. The Journal of Mathematical Behavior, 12(3), 239-250. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., et al. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12–21. Maier, E. (1991). Folk Mathematics, in Harris, M. (Ed.) School mathematics and work. The Farmer Press: Basingstoke. Ministry of National Education (2013). Ortaöğretim Matematik 9. Sınıf 1. Kitap. [Secondary School Grade 9 Mathematics Textbook, Part I]. Ankara: MEB. Stylianides, A. J., & Stylianides, G. J. (2008). Studying the classroom implementation of tasks: High-level mathematical tasks embedded in ‘real-life’ contexts. Teaching and Teacher Education, 24(4), 859-875. Stylianides, G. J. (2005). Investigating students’ opportunities to develop proﬁciency in reasoning and proving: A curricular perspective. Unpublished doctoral dissertation, University of Michigan, Ann Arbor. Weinberg, A., & Wiesner, E. (2011). Understanding mathematics textbooks through reader-oriented theory. Educational Studies in Mathematics, 76(1), 49-63. Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers' conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction, 7(4), 339-359. Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4(4), 273-294. Zhu, Y., & Fan, L. (2006). Focus on the representation of problem types in intended curriculum: A comparison of selected mathematics textbooks from Mainland China and the United States. International Journal of Science and Mathematics Education, 4(4), 609-626.
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