Developing Critical Thinking Skills of Students in Mathematics Learning

Firdaus Firdaus, Ismail Kailani, Md. Nor Bin Bakar, Bakry Bakry


Critical thinking skills should be owned by students. Therefore, schools should be responsible to develop and  evaluate critical thinking skills through teaching and learning process in schools. This study aims to identify the effects of mathematical learning modules based on problem-based learning to critical thinking skills at secondary school students in District of Bone. Assessment of critical thinking skills in mathematical problem solving non-routine includes three parts;  the identification and interpretation of information, information analysis, and evaluate of evidence and arguments. This study involved a total of 68 students grade 12 science state secondary school (SMAN) in Bone District of South Sulawesi, Indonesia in academic year 2014-2015. The sample consists of 38 students in the city and 30 rural students. The design of the study was quasi experimental one group pretest-posttest. The data was analysed using the inferential t-test with SPSS 20.0 for windows. The study found that there are effects of the use of mathematical learning module based PBL to enhance the ability of critical thinking skills in mathematics students in all three components, namely, identifying and interpreting information, information analysis, and evaluate of evidence and argument.

Full Text:



Abd. Rahman Abd. Rasyid. (1999). Kemahiran Berfikir Merentasi Kurikulum. Syah Alam: Penerbit Fajar Bakti

Abrami, P. C., Bernard, R. M., Borokhovski, E., Wade, A., Surkes, M. A., Tamim, R. and Zhang, Dai. (2008). Instructional Interventions Affecting Critical Thinking Skills and Dispositions: A Stage 1 Meta-Analysis. Review of Educational Research. 78(4), 1102-1134

Appelbaum, P. (2004). Critical Thinking and Learning. (online). Retrieved April 25, 2012 from

Arends, I. R. (2007). Learning to Teach. (7th ed.). New York: McGraw Hill Companies

Brookhart, S. M. (2010). How to Assess High Order Thinking Skills in Your Classroom. Alexandria, VA: Association for supervision and curriculum Development.

Campbell, D. T. and Stanley, J. C. (1963). Experimental and Quasi-Experimental Designs For Research. Boston: Houghton Mifflin

Cobb, P; Wood, T; Yackel, E. and McNeal, B. (1992). Characteristics of Classroom mathematics Tradition: An interactional analysis. American Educational Research Journal. 29, 573-604

Creswell, J. W. (2012). Educational Research: Planning, Conducting, and Evaluating. Quantitative and Qualitative Research (4nd ed.). Boston: Pearson

Cronbach, L. J. (1984). Essentials of psychological testing. (4th ed.). New York: Harper & Row

Dochy, F., Segers, M., Van den Bossche, P. and Gijbels, D. (2003). Effects of problem-based learning: a meta analysis. Learning and Instruction. 13, 533-568

Duplass, J. A. and Ziedler, D. L. (2002). Critical thinking and logical argument. Social Education. 66(5), 10-14

Ennis, R. H. (1996). Critical Thinking. Upper Saddle River, New Jersey : Prentice Hall, Inc

Facione, P. A. (1994). Holistic Critical Thinking Scoring Rubric. (online). Retrieved Februari 10, 2013 from Scoring%20rubric.v2.pdf

Facione, P. A. (2010). Critical Thinking: What it is and Why it Counts. (online). Retrieved October 8, 2012 from

Gable, R. K. and Wolf, M. B. (1993). Instrument Development in The Effective Domain. (2nd ed.). Boston: Kluwer Academic Publisher

Gallagher, S. A. (1997). Problem-based learning: Where did it come from, what does it do, and where is it going?Journal for the Education of the Gifted. 20(4), 332-362

Glazer, E. (2001). Using Internet Primary Sources to Teach Critical Thinking Skills in Mathematics. Westport, CT: Greenwood Publishing Group

Henningsen, M. and Stein, M. K. (1997). Mathematical tasks and student cognition: classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education. 25(5), 524-549

Herman, T. (2006). Pembelajaran Berbasis Masalah Untuk Meningkatkan Kemampuan Berfikir Matematis Tingkat Tinggi Siswa Sekolah Menengah Pertama (SMP). Disertasi pada Program Pasca Sarjana UPI: Tidak Diterbitkan

Kauchak, D. P. and Eggen, P. D. (2007). Learning and Teaching: Research-Based Methods. Boston: Pearson Education Inc.

Klauer, K. J. (1990). Paradigmatic teaching of inductive thinking. In H. Mandl, E. De Corte, S. N. Bennett, dan H. F. Friedrich (Eds.), Learning and instruction. European Research in an International context. Analysis of complex skills and complex knowledge domains (pp. 23–45). Oxford: Pergamon Press.

Krulik, S. and Rudnick, J. A. (1995). The New Sourcebook for Teaching Reasoning and Problem Solving in Elementary School. Needham Heights: Allyn dan Bacon.

Lewis, A. and Smith, D. (1993). Defining Higher Order Thinking. Teory into Practice. 32(3), 131-137

Lipman, M. (1985). Thinking skills fostered by Philosophy for Children. In J. W. Segal, S. F. Chipman, dan R. Glaser (Eds.), Thinking and learning skills (pp. 83–108). Hillsdale, NJ: Lawrence Erlbaum Associates.

Mason, J., Burton, L. and Stacey, K. (2010). Thinking Mathematically. (2nd ed.). London: Pearson Education Limited.

McGregor, Debra. (2007). Developing Thinking Developing Learning. A Guide to Thinking Skill in Education. New York: Open University Press Mohd Majid Konting. (1990). Kaedah Penyelidikan Pendidikan. Kuala Lumpur: Dewan Bahasa dan Pustaka

McGuinnes, C., Sheey, N., Curry, C. and Eakin, A. (2003). ACTs II Sustainable Thinking in Classrooms: A Methodology for Enhancing Thinking across The Curriculum. Materials available from Professor C. McGuinness, School of Psychology, Queen’s University, Belfast, Northern Ireland

Mok Soon Sang. (1994). Penilaian, Pemulihan dan Pengayaan dalam Pendidikan. Selangor: Kumpulan Budiman

Mullis, I., Martin, M. O. and Foy, P. (2012). TIMSS 2011 International Results in Mathematics. Chestnut Hill: TIMSS & PIRLS International Study Center

NCTM. (2000). Principles and Standards For School Mathematics. Reston, VA: NCTM.

OECD. (2013). PISA 2012 Assessment and Analytical Framework Mathematics, Reading, Science, Problem Solving and Financial Literacy. Retrieved October 27, 2014 from

Onosko, J. J. and Newmann, F. M. (1994). Creating more Thoughtful Learning environments. In Dim J. N. Mangieri and C. Block (Eds.). Creating powerful thinking in teachers and students: Diverse perspectives. Fort Worth, TX: Harcourt

Ormrod, J. E. (2008). Education Psychology: Developing Learners. (6th ed.). New York: Merrill Prentice Hall, Inc

Phillips, J.A. (1995). Enhancing the thinking and learning skills of students: The P.A.D.I Programme. In Prosiding Konvensyen Antara Bangsa. Kecemerlangan Berfikir. Selangor Darul Ehsan: Fakulti Pendidikan, UKM. 163-171

Phillips, J.A. (1997). Pengajaran Kemahiran Berfikir: Teori dan Amalan. Cheras, Kuala Lumpur: Utusan Publication & Distributors Sdn. Bhd.

Rajendran, N. S. (2010). Teaching and Acquiring Higher Order Thinking Skills: Theory and Practice. Tanjong Malim, Perak: Penerbit Universiti Pendidikan Sultan Idris

Richard, W. Paul and Linda Elder. (2002). Critical Thinking. New Jersey: Financial Times Prentice Hall

Rohaeti, E. E. (2010). Critical and Creative Mathematical Thinking of Junior High School Student. Educationist Journal. 4(2) Juli 2010.

Sanz de Acedo Lizarraga, M. L., Sans de Acedo Baquedano M. T. and Mangado, T. G., Cardelle-Elawar, M. (2009). Enhancement of thinking skills: Effects of two intervention methods. Thinking Skills and Creativity. 4(2009), 30–43

Savery, J.R and Duffy, T.M. (2001). Problem Based Learning: An Instructional Model and Its Constructivist Framework. Retrieved July 20, 2014 from

Sekaran, U. (1992). Research Methods For Business: A Skill Building Approach. Singapore: John Wiley & Sons, Inc

Silver, E. A. and Kenney, P. A. (1995). Sources of Assessment Information for Instructional Guidance in Mathematics. In T. A. Romberg (Ed.). Reform in School Mathematics and Authentic Assessment (pp. 38-68). Albany: State University of New York Press

Soedjadi, R. (2000). Kiat Pendidikan Matematika di Indonesia: Konstatasi Keadaan Masa Kini Menuju Harapan Masa Depan. Jakarta: Dirjen Dikti Depdiknas

Swartz, R. and Parks, S. (1994). Infusing The Teaching of Critical and Creative Thinking Into Content Instruction: A Lesson Design Handbook for the elementary grades. New York: Critical Thinking Press and Software.

Swartz, R. (2001). Infusing Critical and Creative Thinking Into Content Instruction, In A. L. Costa (Ed.). Developing Minds: A Resource Book For Teaching Thinking, (3rd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.

Tiro, M. A. (2001. Dasar- Dasar Statistika (edisi revisi). Makassar: State University of Makassar Press

Tobin, K. & Gallagher, J. J. (1987). Target students in the science classroom. Journal of Research in Science Teaching. 24(1), 1-75.

Van de Walle, J., Karp, K., & Bay-Williams, J. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.). Massachusetts: Allyn & Bacon

Vygotsky, L. (1978). Mind in Society: The development of higher psychological processes. Cambridge, MA: Harvard University Press



  • There are currently no refbacks.

Copyright (c) 2015 Universitas Ahmad Dahlan

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

Journal of Education and Learning (EduLearn)
ISSN: 2089-9823, e-ISSN 2302-9277
Published by: Universitas Ahmad Dahlan (UAD) in collaboration with Institute of Advanced Engineering and Science (IAES)

View EduLearn Stats