Improving Problem Solving Skills Using Critical Thinking Learning Strategy in Integral Calculus


  • Nurul Shida Department of Mathematics, Science and Computer, Polytechnic Ibrahim Sultan, Johor, MALAYSIA
  • Naksa Ahmad Department of Mathematics, Science and Computer, Polytechnic Ibrahim Sultan, Johor, MALAYSIA
  • Julaila Sapari Department of Mathematics, Science and Computer, Polytechnic Ibrahim Sultan, Johor, MALAYSIA



Critical Thinking, Problem Solving, Polytechnic, Integral Calculus


This research tries to develop a Critical thinking learning strategy called CThink and to test its effectiveness in enhancing students’ problem-solving ability when solving Integral Calculus topics as compared to the traditional teaching method (TRad). This study applied the Analyse, Design, Develop, Implement and Evaluate or ADDIE model to develop the CThink strategy. A mixed method approach encompassing quasi-experimental techniques and interviews was adopted. Two groups of students from a polytechnic participated in the research to create the experimental (CThink) (n=34) and control (TRad) (n=33) groups. Enhancement in students' problem-solving ability was analysed using the mean score in the pre-test and post-test. The major studies revealed that the mean scores of students who were introduced to CThink are significantly higher than those who were introduced to TRAD in the post-test t (55.16) =7.11, p<.05. Findings showed the benefits of using the CThink strategy to enhance problem-solving skills in Integral Calculus. In addition, parametric tests revealed that CThink students demonstrated significantly better mean scores in the post-test in comparison to the TRad group. This suggests that students' problem skills ability in the CThink group showed greater improvement.


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Aizikovitsh-Udi, E., & Cheng, D. (2015). Developing critical thinking skills from dispositions to abilities: mathematics education from early childhood to high school. Creative education, 6(04), 455.

Alsaleh, N. J. (2020). Teaching Critical Thinking Skills: Literature Review. Turkish Online Journal of Educational Technology-TOJET, 19(1), 21-39.

Amineh, R. J., & Asl, H. D. (2015). Review of constructivism and social constructivism. Journal of Social Sciences, Literature and Languages, 1(1), 9-16.

Arcana, I. N. (2012). Inplementasi Polya’s Model pada Problem Solving tentang Aplikasi Integral dalam Fisika. Magister Scientiae, (32), 95-106.

Ayllón, M. F., Gómez, I. A., & Ballesta-Claver, J. (2016). Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving. Journal of Educational Psychology-Propósitos y Representaciones, 4(1), 195-218.

Bajracharya, R. R., Wemyss, T. M., & Thompson, J. R. (2012, February). Student interpretation of the signs of definite integrals using graphical representations. In AIP Conference Proceedings (Vol. 1413, No. 1, pp. 111-114). American Institute of Physics.

Bajracharya, R. R. (2014). Student application of the fundamental theorem of calculus with graphical representations in mathematics and physics. The University of Maine.

Benacka, J. (2016). Introduction to integral calculus at high school through calculating area and volume with spreadsheets. International Journal of Mathematical Education in Science and Technology, 47(1), 149-155.

Bressoud, D., Ghedamsi, I., Martinez-Luaces, V., & Törner, G. (2016). Teaching and learning of calculus. Springer Nature.

Bikić, N., Maričić, S. M., & Pikula, M. (2016). The effects of differentiation of content in problem-solving in learning geometry in secondary school. Eurasia Journal of Mathematics, Science and Technology Education, 12(11), 2783-2795.

Butterworth, J., & Thwaites, G. (2013). Thinking skills: Critical thinking and problem solving. Cambridge University Press.

Caligaris, M. G., Schivo, M. E., & Romiti, M. R. (2015). Calculus & GeoGebra, an interesting partnership. Procedia-Social and Behavioral Sciences, 174, 1183-1188.

Conole, G., Klobučar, T., Rensing, C., Konert, J., & Lavoué, E. (Eds.). (2015). Design for Teaching and Learning in a Networked World: 10th European Conference on Technology Enhanced Learning, EC-TEL 2015, Toledo, Spain, September 15-18, 2015, Proceedings (Vol. 9307). Springer.

Dewolf, T., Van Dooren, W., Ev Cimen, E., & Verschaffel, L. (2014). The impact of illustrations and warnings on solving mathematical word problems realistically. The Journal of Experimental Education, 82(1), 103-120.

Deuchar, A. (2010). Opportunities for the development of critical thinking skills in the mathematics classroom (Doctoral dissertation, North-West University).

DiFrancesca, D. (2015). The Impact of Writing Prompts on Learning During Ill-Structured Problem Solving. North Carolina State University.

Driver, M. K., & Powell, S. R. (2017). Culturally and linguistically responsive schema intervention: Improving word problem solving for English language learners with mathematics difficulty. Learning Disability Quarterly, 40(1), 41-53.

Arikan, E. E., & Ünal, H. (2015). Investigation of Problem-Solving and Problem-Posing Abilities of Seventh-Grade Students. Educational Sciences: Theory and Practice, 15(5), 1403-1416.

Ersoy, E., & Guner, P. (2015). The place of problem solving and mathematical thinking in the mathematical teaching. The Online Journal of New Horizons in Education-January, 5(1), 120-130.

Firdaus, F., Kailani, I., Bakar, M. N. B., & Bakry, B. (2015). Developing critical thinking skills of students in mathematics learning. Journal of Education and Learning, 9(3), 226-236.

Hafiyusholeh, M., Budayasa, K., & Siswono, T. Y. E. (2018). Statistical literacy: High school students in reading, interpreting and presenting data. In Journal of Physics: Conference Series (Vol. 947, No. 1, p. 012036). IOP Publishing.

Hamdu, G., Fuadi, F. N., Yulianto, A., & Akhirani, Y. S. (2020). Items quality analysis using rasch model to measure elementary school students’ critical thinking skill on stem learning. JPI (Jurnal Pendidikan Indonesia), 9(1), 61-74.

Hashemi, N., Abu, M. S., & Kashefi, H. (2019). Undergraduate Students’ Difficulties in Solving Derivative and Integral Mathematical Problems. Sains Humanika, 11(2).

Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing learning strategy to improve undergraduate students’ problem solving in derivatives and integrals: A conceptual framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238.

Hashemi, N., Kashefi, H., Mohdsalleh, A., & Rahimi, K. (2013). What are difficulties of learning derivation and integral among undergraduate students. In Proceeding of 4th International Graduate Conference on Engineering Science & Humanity (pp. 1056-1063).

Heller, K. (2013). Helping Your Students Develop Expertise in Problem Solving–While Learning Physics. In USA: University of Minnesota, AAPT New Faculty Workshop.

Hu, D., & Rebello, N. S. (2013). Understanding student use of differentials in physics integration problems. Physical Review Special Topics-Physics Education Research, 9(2), 020108.

Hunter, J. S. (2011). The effects of graphing calculator use on high-school students' reasoning in Integral Calculus (Doctoral dissertation, University of New Orleans).

Hussain, M., Zhu, W., Zhang, W., Abidi, S. M. R., & Ali, S. (2019). Using machine learning to predict student difficulties from learning session data. Artificial Intelligence Review, 52(1), 381-407.

Isa, F. M., Said, S. H., & Hassan, A. (2017). Analisis Kesilapan Dalam Soalan Asas Dan Aplikasi Pengamiran Kursus Matematik Kejuruteraan 2. Politeknik & Kolej Komuniti Journal of Social Sciences and Humanities, 2(1), 198-208.

Jukić Matić, L., & Dahl, B. (2014). Retention of differential and integral calculus: a case study of a university student in physical chemistry. International Journal of Mathematical Education in Science and Technology, 45(8), 1167-1187.

Jusoh, W. I. W., Alwi, W. S. W., Bustamam, M. I. S., & Daud, A. (2020). Hubungan Tahap Pencapaian Matematik Spm Terhadap Keputusan Matematik Kejuruteraan Dan Pencapaian Pelajar Got Di Politeknik Kota Bharu. In Conference Of Future Education And Advances (ICOFEA) 2020 (p. 633).

Khalid, S., Alias, M., Razzaly, W., & Suradi, Z. (2007). The influence of multimedia supported courseware with collaborative learning in algebraic fractions and problem solving skills among Pre-University students. International Journal of Emerging Technologies in Learning (iJET), 2(3).

Kusmaryono, I., & Suyitno, H. (2016, February). The effect of constructivist learning using scientific approach on mathematical power and conceptual understanding of students grade IV. In Journal of Physics: Conference Series (Vol. 693, No. 1, p. 012019). IOP Publishing.

Lee, J., & Sabarudin, R. (2001). Impact of the graphics calculator on the Calculus curriculum-A study in the polytechnic context. In Proceedings of the Sixth Asian Technology Conference in Mathematics (ATCM 2001), ATCM Inc., USA (pp. 253-262).

Lutfi, M. (2016). Misconceptions in solving indefinite integrals for nonelementary functions using the Taylor series. Jurnal Ilmiah Matematika dan Terapan, 13(1).

Machromah, I. U. (2017). Process skill error: the majority student’s error in problem solving of integral calculus. Daya Matematis: Jurnal Inovasi Pendidikan Matematika, 5(3), 358-376.

Morin, L. L., Watson, S. M., Hester, P., & Raver, S. (2017). The use of a bar model drawing to teach word problem solving to students with mathematics difficulties. Learning Disability Quarterly, 40(2), 91-104.

Nursyahidah, F., & Albab, I. U. (2017). Investigating student difficulties on integral calculus based on critical thinking aspects. Jurnal Riset Pendidikan Matematika, 4(2), 211-218.

Ofori-Kusi, D. (2017). An investigation into the use of problem-solving heuristics to improve the teaching and learning of mathematics. Unpublished doctoral thesis. Pretoria: University of South Africa.

Renfro, A. (2014). Assessing the effects of a flipped classroom approach on student achievement, mathematical thinking, attitudes, and teacher perceptions in an undergraduate calculus class using a participatory action research approach. Robert Morris University.

Roberts, J. D., Chung, G. K., & Parks, C. B. (2016). Supporting children’s progress through the PBS KIDS learning analytics platform. Journal of Children and Media, 10(2), 257-266.

Robinson, L. M. (2016). An exploratory study of the factors related to successful mathematical problem solving on non-routine unconstrained tasks. Temple University.

Rokhimah, S., Suyitno, A., & Sukestiyarno, Y. L. (2015). Students error analysis in solving math word problems of social arithmetic material for 7th grade based on newman procedure. In Proceedings in International Conference on Conservation for Better Life (pp. 349-356).

Sánchez, M. R., & Vicente, S. (2015). Models and processes for solving arithmetic word problems proposed by Spanish mathematics textbooks/Modelos y procesos de resolución de problemas aritméticos verbales propuestos por los libros de texto de matemáticas españoles. Cultura y Educación, 27(4), 695-725.

Sağlam, Y. (2014). Visual preferences and teaching anxiety of preservice mathematics teachers. Procedia-Social and Behavioral Sciences, 141, 1270-1274.

Saygılı, S. (2017). Examining the problem solving skills and the strategies used by high school students in solving non-routine problems. E-International Journal of Educational Research, 8(2), 91-114.

Sealey, V. (2014). A framework for characterizing student understanding of Riemann sums and definite integrals. The Journal of Mathematical Behavior, 33, 230-245.

Serhan, D. (2015). Students' Understanding of the Definite Integral Concept. International Journal of Research in Education and Science, 1(1), 84-88.

Shea, P., & Bidjerano, T. (2010). Learning presence: Towards a theory of self-efficacy, self-regulation, and the development of a communities of inquiry in online and blended learning environments. Computers & education, 55(4), 1721-1731.

Solfitri, T., Siregar, H. M., & Syari, R. (2019, November). The Analysis of Students' Errors in Using Integration Techniques. In Proceedings of the UR International Conference on Educational Sciences (pp. 328-335).

Spooner, F., Saunders, A., Root, J., & Brosh, C. (2017). Promoting access to common core mathematics for students with severe disabilities through mathematical problem solving. Research and Practice for Persons with Severe Disabilities, 42(3), 171-186.

Sullivan, E., & Melvin, T. (2016). Enhancing student writing and computer programming with LATEX and Matlab in multivariable calculus. Primus, 26(6), 509-530.

Tatar, E., & Zengin, Y. (2016). Conceptual understanding of definite integral with Geogebra. Computers in the Schools, 33(2), 120-132.

Wagner, J. F. (2015). What the integral does: Physics students’ efforts at making sense of integration. In 2015 Physics education research Conference Proceedings (pp. 355-358).

Yavuz, G., Deringol-Karatas, Y., Arslan, C., & Erbay, H. N. (2015). Research Trends on Mathematical Problem Solving in Turkey: Master Thesis and Dissertations of 2006-2013 Period. Procedia-Social and Behavioral Sciences, 177, 114-117.

Yazid, N. A. M., & Atiqah, N. (2016). Amalan pembelajaran teradun pensyarah di Politeknik Sultan Salahuddin Abdul Aziz Shah (Doctoral dissertation, Universiti Tun Hussein Onn Malaysia).

Yew, W. T., & Zamri, S. N. A. S. (2018). Problem solving strategies of selected pre-service secondary school mathematics teachers in Malaysia. MOJES: Malaysian Online Journal of Educational Sciences, 4(2), 17-31.

Zakaria, E., & Salleh, T. S. (2015). Using technology in learning integral calculus. Mediterranean Journal of Social Sciences, 6(5), 144.

Wahyudi, A. T., Subanti, S., & Usodo, B. (2017, December). Behaviour analysis of students in solving mathematics word problem. In Journal of Physics: Conference Series (Vol. 943, No. 1, p. 012019). IOP Publishing.

West, J. G. (2013). Comparing the impact of traditional and modeling college algebra courses on student performance in survey of calculus. University of Arkansas.

White, H., & Sabarwal, S. (2014). Quasi-experimental design and methods. Methodological briefs: impact evaluation, 8(2014), 1-16.




How to Cite

Nurul Shida, Ahmad, N., & Sapari, J. (2022). Improving Problem Solving Skills Using Critical Thinking Learning Strategy in Integral Calculus. Asian Pendidikan, 2(2), 52-64.