Developing complex analysis textbook to enhance students’ critical thinking

Fariz Setyawan(1*), Puguh Wahyu Prasetyo(2), Burhanudin Arif Nurnugroho(3)

(1) Department of Mathematics Education, Universitas Ahmad Dahlan
(2) Department of Mathematics Education, Universitas Ahmad Dahlan
(3) Department of Mathematics Education, Universitas Ahmad Dahlan
(*) Corresponding Author


Critical thinking skill was needed since problems in daily life required a solution. To solve the problems, the students collect the data as a consideration in making the right decision. Moreover, the students also need good critical thinking skills. To develop a good critical thinking skill, the researcher develops a textbook of Complex Analysis and Application, especially in complex numbers. In this research, a qualitative investigation was carried out in the development of the textbook. This textbook supports the mathematics education students of Universitas Ahmad Dahlan in learning complex analysis course. Researchers did a walkthrough to the expert in assessing the content and construct to validate the textbook. The development model used by researchers is a 4-D model. A 4-D model used in this study is consists of defining, designing, developing, and disseminating. In defining, the researcher adequate materials related to the complex numbers such as the rational number and real number and its properties in addition and multiplication. In designing, some explanation in the textbook is followed by Why and How questions. Open questions are used to stimulate the students’ critical thinking. Based on the walkthrough result, some notation in the textbook, especially mathematics symbols, must be revised using a proper mathematics equation. In addition, some concept should be clearly defined such as  where the value of . As a result of the validity construct, the explanation given in the textbook used a step-by-step exercise. In disseminating, the students can easily access the textbook and answer the questions using their reasoning. The textbook is valid and readable.


Critical thinking, textbook, complex numbers

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Apriliana, L. P., Handayani, I., & Awalludin, S. A. (2019). The Effect of a Problem Centered Learning on Student’s Mathematical Critical Thinking. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 4(2), 124–133.

Cahdriyana, R. A., Richardo, R., Fahmi, S., & Setyawan, F. (2019). Pseudo-thinking process in solving logic problem. Journal of Physics: Conference Series, 1188(No. 1), 012090.

Carey, S. S. (2011). A beginner’s guide to scientific method. Boston, USA: Cengage Learning.

Changwong, K., Sukkamart, & A.Sisan, B. (2018). Critical thinking skill development: Analysis of a new learning management model for Thai high schools. Journal of International Studies, 11(2), 37–48.

Ennis, R. H. (1958). An appraisal of the watson-glaser critical thinking appraisal. Journal of Educational Research.

Helmstadter, G. (1965). Watson-Glaser Critical Thinking Appraisal. Journal of Educational Measurement, 2(2), 254–256. Retrieved from

Himmah, W. I., Nayazik, A., & Setyawan, F. (2019). Revised Bloom’s taxonomy to analyze the final mathematics examination problems in Junior High School. Journal of Physics: Conference Series, 1188(1), 012028.

Khabibah, S., Manuharawati, M., & Agung, L. (2018). Problem Solving Ability: A case study in Postgraduate Mathematics Student. Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018).

Krathwohl, D. R. (2002). A revision of Bloom’s taxonomy: An overview. Theory into Practice. 41(4), 212–218.

Kristanto, Y. D., Amin, S. M., & Khabibah, S. (2016). The Development of Investigative Learning Materials Using Computer Assisted Instruction in the Topic of Reflection for Grade VII. Journal of Research and Advances in Mathematics Education, 1(2), 172–182.

Krulik, S., & Rudnick, J. A. (1995). The New Sourcebook for Teaching Reasoning and Problem Solving in Elementary School. A Longwood Professional Book. Boston, USA: Allyn & Bacon

Lawhon, D. (1976). Instructional development for training teachers of exceptional children: A sourcebook. Journal of School Psychology.

Panasuk, R. M. (2010). Three Phase Ranking Framework for Assessing Conceptual Understanding in Algebra Using Multiple Representations. Education, 131(2), 235–257. Retrieved from 1a2be947be6957d85e1369a4de313c4965fe.pdf

Rahayunigrum, A., Setyawan, F., & Khasanah, U. (2018). Profil Pemecahan Masalah Pada Materi Persamaan Linier Satu Variabel Dengan Menggunakan Pendekatan Model Eliciting Activities (MEAs) Dilihat Dari Kemampuan Matematika. AlphaMath: Journal of Mathematics Education, 4(1), 15–22.

Rezat, S. (2010). The utilization of mathematics textbooks as instruments for learning. Proceedings of CERME, 6, 1260–1269. Retrieved From

Schmidt, H. G., Wagener, S. L., Smeets, G. A. C. M., Keemink, L. M., & van der Molen, H. T. (2015). On the Use and Misuse of Lectures in Higher Education. Health Professions Education, 1(1), 12–18.

Setyawan, F. (2015). Conceptual Understanding Profile of LEOV Junior High School Students Based on Kolb’s Learning Style. International Conference on Mathematics, Science, and Education (ICSME), 61–63. Retrieved from

Smith, D. G. (1977). College classroom interactions and critical thinking. Journal of Educational Psychology, 69(2), 180–190.

Uribe-Enciso, O. L., Enciso, D. S. U., & Daza, M. D. P. V. (2017). Critical thinking and its importance in education: some reflections. Rastros Rostros, 19(34), 78–88.

Zapalska, A. M., Nowduri, S., Imbriale, P., & Wroblewski, B. (2018). A Framework for Critical Thinking Skills Development Across Business Curriculum Using the 21 st Century Bloom ’ s Taxonomy Keywords. Interdisciplinary Education and Psychology, 2(1), 1–14.

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