A Comparative Analysis of Measures of Central Tendency in Mathematics Textbooks from Turkey, Singapore and The United States

Author(s):

Mehtap Ozen(presenting / submitting)Erdinc Cakiroglu

Conference:

ECER 2012

Network:

21. Emerging Researchers' Group (for presentation at Emerging Researchers' Conference)

Format:

Paper

Session Information

ERG SES H 06, Mathematics education

Parallel Paper Session

Time:

2012-09-18

13:15-14:45

Room:

FCEE - Aula 2.6

Chair:

Contribution

For the last two decades, there has been a considerable attention to the cross-national comparison of countries among the educational research domain. Specially, in mathematics education, international comparative studies such as Trends in International Mathematics and Science Study (TIMSS) and Program for International Students Assessment (PISA) lead to acceleration of comparative studies in countries around the world. Such studies draw attention to textbooks that are regarded as a reflection of national curricula and written sources that teachers and students frequently use (Valverde, Bianchi, Wolfe, Schmidt, & Houang, 2002).

Measures of central tendency have been included in school textbooks for many years (Jacobbe & Carvalho, 2011). The reason behind this phenomenon is that they are essential concepts regarded as a summary and representative value of the data set in statistics (Shaughnessy, 2007). However, recent researches indicated that both students and teachers have difficulty in conceptualizing mean, median, and mode concepts and it is possible to improve comprehensively conceptual and procedural understanding of the measures of central tendency in teaching and learning of mathematics (Groth & Bergner, 2009). Cross-cultural studies in the learning domain of data analysis and probability will enlighten our understanding of such issues in different contexts. In order to explain cross-national differences in educational opportunities and in achievement with regard to the results of the international comparative studies such as TIMSS, many studies were conducted. Cai, Lo & Watanabe (2004), for example, conducted a comparative analysis of the measures of central tendency in U.S.A. and some Asian textbooks so that it could contribute to interpretation of cross-national differences. In Turkey, there are cross-national studies comparing textbooks involving the U.S.A., Singapore. There is still a need for further research on comparing the coverage of specific concept such as measures of central tendency (Erbas & Alacaci, 2009).

The purpose of this study was to investigate the presentation of measures of central tendency concepts in mathematics textbooks in Turkey, Singapore and U.S.A. It is hoped that this study would help educational research community to understand the cross-national differences among these countries and contribute to cross-national studies with regard to the learning domain of data analysis.

Method

Textbook Selection Turkey and Singapore’s educational systems are centralized and textbooks are approved by Minister of Education. In Turkey, selected textbooks are used in almost all schools. In Singapore, My Pals Are Here! Textbook series for sixth grades was selected since it is the most widely used textbooks in Singapore (Yang, Reys, & Wu, 2010). For seventh and eighth grades, New Syllabus Mathematics series were selected since they are widely used. However, there is not a national curriculum and centralized education system in the U.S. A. Textbook series improved by the University of Chicago School Mathematics Project was used because of widely usage in the U.S.A. (Fan & Kaeley, 2000). Data Analysis The analysis included (1) examining the sequence of topics across grades among the textbooks (2) approaches to the content presentation in each textbook (3) the way of the content presentation in written concept explanations and worked-out examples. It was guided by determining focus of each textbook on the presentation of the concepts as procedurally direct application or as representative value of data set (What they mean, how they work and differ). Since the authors of this study are from Turkey, the comparisons are based on Turkish perspective.

Expected Outcomes

The analysis was resulted in three main findings. The first finding is that Turkish textbooks present the mean at sixth grade and the median and mode at seventh grade. The U.S.A. textbooks describe the measures of central tendency at both sixth and eighth grades. In contrast, Singaporean textbook presents these concepts together at eighth grade. Another finding is that Turkish and Singaporean textbooks have similar approaches to presentation of the content. Singaporean and Turkish textbooks start with real life problems and descriptions are made through worked-out examples. On the other hand, in the U.S.A. textbooks, after written explanations of the concepts, the content is developed through worked-out examples involving mostly real life situations. The last finding is that concepts are implicitly described in Turkish and Singaporean textbooks through worked-out examples. Contrary, in U.S.A. textbooks, concepts are explicitly described, then developed through worked-out examples. In Turkish and U.S.A. textbooks, written concept explanations and related worked-out examples focus more on computational procedures than representativeness of data set. Conversely, Singaporean textbooks focus on both computational procedures and conceptually understanding of what they represent, how they differ.

References

Cai, J., Lo, J. J., & Watanabe, T. (2002). Intended treatments of arithmetic average in U.S. and Asian school mathematics. School Science and Mathematics, 102(8), 391–404. Erbas, A. K., Alacaci, C. (2009). Comparative analysis of sixth and seventh grade Turkish, American, and Singaporean textbooks. TUBITAK Project, Number 107K547. Fan, L., & Kaeley, G. S. (2000). The influence of textbook on teaching strategies: An empirical study. Mid-Western Educational Researcher, 13(4), 2–9. Groth, R. E., & Bergner, J. A. (2006). Preservice elementary teachers’ conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8(1), 37–64. Jacobbe, T. & Carvalho, C. (2011). Teachers’ understanding of averages. In C. Batanero G. Burrill & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education: A joint ICMI/IASE study: The 18th ICMI study (pp. 199-209). International Commission on Mathematical Instruction: Springer. Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In The Second Handbook of Research on Mathematics, Ed. F.K. Lester, pp. 957–1010. Reston, VA: National Council of Teachers of Mathematics (NCTM). Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbook. Dordrecht; Boston: Kluwer Academic Publishers. Yang, D-C., Reys, R. E., & Wu, L-L. (2010). Comparing the development of fractions in the fifth- and sixth- graders’ textbooks of Singapore, Taiwan, and the USA. School Science and Mathematics, 110(3), 118-127.

Author Information

Mehtap Ozen (presenting / submitting)

Middle East Technical University

Elementary Science and Mathematics Education

Ankara

Erdinc Cakiroglu

Middle East Technical University, Turkey

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