# THE CONCEPT OF ANGLE IN TURKISH AND SINGAPOREAN PRIMARY SCHOOL MATHEMATICS TEXTBOOKS: DYNAMIC OR STATIC?

## Abstract

The present study compared Turkish and Singaporean textbooks with respect to their instructional contents on a difficult topic for most students: the concept of angle. The study used the 3^{rd} and 4^{th} grade mathematics textbooks taught in Turkish and Singaporean schools. The analysis showed that Turkish textbooks defined the angle as a static concept, and Singaporean textbooks defined it as both a static and dynamic concept. The definitions of the concept of angle included in the textbooks reflect on the representation of the angle, instructional tools and problems. Turkish students learn angle from textbooks only as a static concept, so they may have difficulties and misconceptions about the subject and related concepts. The findings showed that the contents of Singaporean textbooks offer students more opportunities than Turkish textbooks in learning about the angle as a static and dynamic concept.

**Keywords:** Singapore, Turkey, mathematics, textbook, the concept of angle.

**REFERENCES** (*Textbooks Used in the Study)

Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. *Education Studies in Mathematics*, *79*(2), 239–261.

Argün, Z., Arıkan, A., Bulut, S., & Halıcıoğlu, S. (2014). *Temel matematik kavramların künyesi *[Identification of basic mathematical concepts]. Ankara: Gazi Publishing.

Barmby, P., Bilsborough, L., Harries, T., & Higgins, S. (2009). *Primary mathematics: teaching for understanding*. NY: McGraw Hill.

Baya’a, N., Daher, W., & Mahagna, S. (2017). The effect of collaborative computerized learning using GeoGebra on the development of concept images of the angle among seventh graders (pp.208-215). In G. Aldon & J. Trgalova (Eds.), *Proceedings of the 13th International Conference on Technology in Mathematics Teaching* (ICTMT 13), Lyon, France: Ecole Normale Sup´erieure de Lyon.

Bingölbali, E. (2016). Kavram tanımı ve kavram imajı. (In; *Matematik Eğitiminde Teoriler*, Ed, Bingölbali, E., Arslan, S., and Zembat, İ. Ö.). p. 136-148. Ankara: Pegem Akademi.

Boo, J. Y., & Leong, K. E. (2016). Teaching and learning of Geometry in Primary School using GeoGebra. *Proceedings of the 21st Asian Technology Conference in Mathematics*, p. 289-300.

Bütüner, S. Ö., & Filiz, M. (2017). Exploring high-achieving sixth grade students’ erroneous answers and misconceptions on the angle concept. *International Journal of Mathematical Education in Science and Technology*, *48*(4), 533-554.

Bütüner, S. Ö. (2019). Problem analysis in Turkish and Singapore mathematics textbooks: division of fraction. *Pamukkale University Journal of Education, 47*, 370-394.

Bütüner, S. Ö. (2020). A comparison of the instructional content on division of fractions in Turkish and Singaporean textbooks. *International Journal of Mathematical Education in Science and Technology, 51*(2), 265-293.

Choi, E., Kim, S. Y., & Kwon, O. N. (2019). An International Comparison study in Mathematics Curriculum - Contents for Angle among the Korea, Singapore U.K., Australia and U.S. *Communications of Mathematical Education*, *33*(3), 295–317.

Clausen-May T. (2005). *Teaching maths to pupils with different learning styles*. London: Paul Chapman Publishing.

Clausen-May, T. (2008). Another angle on angles. *Australian Primary Mathematics Classroom, 13*(1), 4-8.

Clements, D. H., & Battista, M. T. (1989). Learning of geometric concepts in a Logo environment. *Journal for Research in Mathematics Education, 20*, 450-467.

Clements, D. H., & Battista, M. T. (1990). The effects of logo on children's conceptualizations of angle and polygons. *Journal for Research in Mathematics Education, 21*, 356-371.

Clements, D. H., & Battista, M. T. (1994). Computer environments for learning geometry. *Journal of Educational Computing Research, 10*(2), 173-197.

Clements, D. H., Battista, M. T., Sarama, J., & Swaminathan, S. (1996). Development of turn and turn measurement concepts in a computer-based instructional unit. *Educational Studies in Mathematics, 30*(4), 313-337.

Clements D. H., & Burns B. A. (2000). Students’ development of strategies for turn and angle measure. *Educational Studies in Mathematics, 41*, 31–45.

Clements, D. H., Wilson, D. C., & Sarama, J. (2004). Young children’s composition of geometric figures: A learning trajectory. *Mathematical Thinking and Learning, 6*(2), 163-184.

Crompton, H. (2013). *Coming to understand angle and angle measure: a design-based research curriculum study using context-aware ubiquitous learning*. Unpublished PhD dissertation, University of North Carolina at Chapel Hill.

Erbaş, A. K., Alacacı, C., & Bulut, M. A. (2012). Comparison of Mathematics Textbooks from Turkey, Singapore and the United States of America. *Educational Sciences: Theory and Practice, 12*(3), 2311-2329.

Fan, L., & Zhu, Y. (2000). Problem solving in Singaporean secondary mathematics textbooks. Mathematics Education, *5*(1/2), 117-141.

Fyhn, A. B. (2006). A climbing girl's reflections about angles. *The Journal of Mathematical Behavior, 25*, 91-102.

Fyhn, A. B. (2007). A climbing class' reinvention of angles. *Educational Studies in Mathematics, 67*, 19-35.

*Genç, H., Güleç, H., Şahin, N., & Taşcı, S. (2019). *Primary school mathematics 3 ^{rd} grade textbook*, Ankara: National Education Publications.

Hansen, A. (2017). *Children’s errors in Mathematics*. Sage Publications: California.

Henderson, D. W., & Taimina, D. (2005). *Experiencing geometry: Euclidean and non-Euclidean with history*. New York (NY): Prentice Hall.

Hong, D. S., & Choi, K. M. (2014). A comparison of Korean and American secondary school textbooks: The case of quadratic equations. *Educational Studies in Mathematics, 85*(2), 241-263.

Hirsch, C., Lappan, G., Reys, B., & Reys, R. (2005). Curriculum as a focus for improving school mathematics. *Mathematicians and Education Reform Forum Newsletter, 18*(1), 12-14.

Kaur, H. (2020). Introducing the concept of angle to young children in a dynamic geometry environment. *International Journal of Mathematical Education in Science and Technology, 51*(2), 161-182.

*Kayapınar, A., Şahin, N., Erdem, G., & Leylek, B. Ş. (2019). *Primary school mathematics 4 ^{th} grade textbook*, Ankara: National Education Publications.

Keiser, J. (2004). Struggles with developing the concept of angle: Comparing sixth-grade students’ discourse to the history of angle concept. *Mathematical Thinking and Learning, 6*(3), 285-306.

Kim, S. M. (2018a). Research of the Definitions of Angles in the Past Korean Elementary Mathematics Textbooks. *Journal of Educational Research in Mathematics, 28*(3), 265-282.

Kim, S. M. (2018b). Angle concepts and introduction methods of angles in elementary mathematics textbooks. *Education of Primary School Mathematics, 21*(2), 209-221.

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.

Ministry of Education Singapore [MES] (2012). Mathematics syllabus Primary one to six, Singapore.

Miles, M. B, & Huberman, M. A. (1994). *An expanded sourcebook qualitative data analysis*. London: Sage.

Ministry of National Education [MONE], (2018). Elementary mathematics curriculum: Grades 1-4, Ankara.

*Ming, E. C. C. (2016a). *Targeting mathematics 3B*. Singapore: Star Publishing.

*Ming, E. C. C. (2016b). *Targeting mathematics 4A*. Singapore: Star Publishing.

Mitchelmore, M. C. (1998). Young students' concepts of turning and angle. *Cognition and Instruction, 16*(3), 265-284.

Mitchelmore, M. C., & White, P. (1998). Development of angle concepts: a framework for research. *Mathematics Education Research Journal, 10*, 4-27.

Mitchelmore, M. C., & White, P. (2000). Development of angle concepts by progressive abstraction and generalisation. *Educational Studies in Mathematics, 41*, 209–238.

Moore, K. (2013). Making sense by measuring arcs: A teaching experiment in angle measure. *Educational Studies in Mathematics, 83*, 225-245.

Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). *TIMSS 2015 international results in mathematics.* TIMSS and PIRLS International Study Center, Boston College, Chestnut Hill, MA.

Munier, V., Devichi, C., & Merle, H. A. (2008). Physical situation as a way to teach angle. *Teaching Children Mathematics, 14*, 402-407.

Özer, E., & Sezer, R. A. (2014). Comparative analysis of questions in American, Singaporean, and Turkish mathematics textbooks based on the topics covered in 8th grade in Turkey. *Educational Sciences: Theory and Practice, 14*(1), 411-421.

Park, K. S. (2015). A comparative study on teaching contents for angle and measure of an angle in elementary mathematics textbook between Korea and Japan. *School Mathematics*, *17*(1), 35-46.

Sağlam, R., & Alacacı, C. (2012). A Comparative Analysis of Quadratics Unit in Singaporean, Turkish and IBDP Mathematics Textbooks. *Turkish Journal of Computer and Mathematics Education, 3*(3), 131-147.

Simmons, M., & Cope, P. (1990). Fragile knowledge of angle in turtle geometry. *Educational Studies in Mathematics, 21*, 375-382.

Smith, C. P., King, B., & Hoyte, J. (2014). Learning angles through movement: critical actions for developing understanding in an embodied activity. *The Journal of Mathematical Behavior, 36*, 95-108.

Son, J. W. & Hu, Q. (2016). The initial treatment of the concept of function in the selected secondary school mathematics textbooks in the US and China. *International Journal of Mathematical Education in Science and Technology*, *47*(4), 505-530.

Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why mathematics textbooks matter. *Education Leadership, 61*(5), 61–66.

Rezat, S. (2006). A model of textbook use. In J. Novotna, H. Kratka,& N. Stehlikova (Eds.), *Proceedings of the 30th annual*

*conference of the International Group for the Psychology of Mathematics Education* (Vol. 4, pp. 409–416). Prague: PME.

Rezat S. (2009). The utilization of mathematics textbooks as instruments of learning. In: Durand Guerrier V, Soury‑Lavergne S, Arzarello F, editors. *Proceedings of Congress of European Research in Mathematics Education 6*; Lyon; p. 1260-1269.

Tieng, P. G., & Eu, L. K. (2014). Improving students’ van hiele level of geometric thinking using geometer’s sketchpad. *The Malaysian Online Journal of Educational Technology, 2*(3), 20-31.

Toprak, Z., & Özmantar, M. (2019). A comparative analysis of Turkey and Singapore 5th grade mathematics textbooks in terms of worked examples and questions. *Turkish Journal of Computer and Mathematics Education (TURCOMAT)*, *10*(2), 539-566.

Wilson, P. S., & Adams, V. M. (1992). A dynamic way to teach angle and angle measure. *Arithmetic Teacher, 39*, 6-13.

Wijaya, A., Van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context based tasks provided by mathematics textbooks. *Educational Studies in Mathematics, 89*, 41-65.

Yang, D. C. (2018). Study of fractions in elementary mathematics textbooks from Finland and Taiwan. *Educational Studies,* *44*(2), 190-211.

Yang, D., & Lin, Y. C. (2015). Examining the differences of linear systems between Finnish and Taiwanese textbooks, *Eurasia Journal of Mathematics, Science & Technology Education*, *11*(6), 1265-1281.

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*, 609-626.

## Downloads

## Published

## Issue

## Section

## License

Copyright (c) 2021 International Online Journal of Primary Education (IOJPE)

This work is licensed under a Creative Commons Attribution 4.0 International License.

**Copyright and permissions**

The manuscripts submitted to International Online Journal of Primary Education (IOJPE) for publication should be original studies that were not published before or not submitted to anywhere else for publication.

Authors who submit their manuscript to International Online Journal of Primary Education (IOJPE) should acknowledge that they agree to transfer the copyright of their studies to IOJPE. All Open Access articles are distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.

All articles published in International Online Journal of Primary Education (IOJPE) are licensed under a __Creative Commons Attribution-NonCommercial 4.0 International License (CC BY 4.0).__

Any further distribution or use of content published under CC BY 4.0 must contain the author(s) and the published article’s title, and journal citation. All articles published in IOJPE under a CC BY License may be used for Text and Data Mining purposes, subject to the conditions of the CC BY License terms. The license allows for commercial use. IOJPE allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator.

The journal’s objective is to disseminate articles published are free. Under the Creative Commons license (CC BY 4.00), the journal allows the user to permits unrestricted use, distribution, and reproduction in any medium, and even use the publication for commercial activities, provided that the original work is properly cited.

Open access is an approach that eases the interdisciplinary communication and encourages cooperation among different disciplines. IOJPE, therefore, contributes to its own field by providing more access to its articles and a more transparent review process.