Journal Screenshot

International Journal of Academic Research in Accounting, Finance and Management Sciences

Open Access Journal

ISSN: 2225-8329

The Effect of a Problem-Solving Approach on Students’ Heuristics Knowledge Development

Nurul Akmal Md Nasir, Parmjit Singh

http://dx.doi.org/10.6007/IJARAFMS/v13-i2/18025

Open access

Various current studies have shown that high school leavers have a major bridge to gap between the expectations of tertiary level cognitive requirements and their current thinking repertoire in mathematics learning. This study investigates if cognitive strategy or heuristics were the stumbling blocks (other than content knowledge) in inhibiting students’ mathematical thinking development. Thus, this three-phase study was undertaken to examine the effect of the problem-solving approach (PSA) on students’ heuristic knowledge development in solving non-routine problems. This study employed a quasi-experimental design, comprising 49 first-year college students majoring in mathematics. The first phase findings show that students' lack the repertoire of heuristic knowledge that, to a large extent, inhibited their ability to solve problems. The second phase findings show a positive impact of PSA on students' cognitive heuristic ability in solving problems. The third phase found a significant relationship between heuristic knowledge and the math thinking scores. These heuristics allowed them to generate necessary ‘tools’ in the absence of the requisite knowledge in seeking solutions to the problems. The findings suggest that college students need to be provided more opportunities to develop their heuristic knowledge and to connect with core math content to bridge the gap with the cognitive requirements of college mathematics.

Adams, C. (2014). High School Graduates Feel Unprepared for College and Work, Survey Finds. http://blogs.edweek.org/edweek/college_bound/2014/12/high_school_grads_unprepared_for_future.html. Accessed 4 March 2022
Apostol, E. M. D. (2017). Problem Solving Heuristics on Non-Routine Problems of College Students. 5(3), 338–343. https://doi.org/10.12691/education-5-3-16
Bowyer, J., & Darlington, E. (2016). “Applications, applications, applications”: Lecturers’ perceptions of students’ mathematical preparedness for STEMM and Social Science degrees Executive Summary. (July), 1–29.
Borsuk, A. J. (2016). Too many students unprepared for college. Retrieved on December 15, 2016, from http://www.jsonline.com/story/news/ education/2016/10/08/borsuk-too-many-students-unprepared- college/91750628/
Bruder, R. (2016). Role of Heuristics for Problem Solving. In Problem solving in mathematics education (pp. 230–233). https://doi.org/10.1080/14794802.2020.1731577
Devlin, K. (2012). Introduction to Mathematical Thinking. Keith Devlin, 331 Poe St, Unit 4 Palo Alto, CA 94301 USA
Duch, B. J. (2001). Writing problems for deeper understanding. In B. J. Duch, S. E. Groh, & D. E. Allen (Eds.), The Power of Problem-Based Learning: A Practical “How To” for Teaching Undergraduate Courses in Any Discipline. Falmer Press.
Educomics (2021). Why Singaporean Students are So Good at Math. Educomics. https://www.educomics.org/why-singaporean-students-are-so-good-at-math/.
Halim, A. (2020). Pentaksiran PISA: Di Mana Kedudukan Malaysia Untuk Literasi Matematik Dalam Kalangan Negara Asia Tenggara? Majalah Sains. https://www.majalahsains.com/pentaksiran-pisa-di-mana-kedudukan-malaysia-untuk-literasi-matematik-dalam-kalangan-negara-asia-tenggara/
Halim, A., Johari, S., & Norhasniza, I. (2014). PISA 2012: Di mana kedudukan Malaysia untuk subjek Matematik? Prosiding Seminar Antarabangsa Kelestarian Insan (INSAN2014), (9-10 April 2016), 1–17.
Hashemi, N., Abu, M. S., & Kashefi, H. (2019). Undergraduate Students’ Difficulties in Solving Derivative and Integral Mathematical Problems. Sains Humanika, 11(2), 65–74. https://doi.org/10.11113/sh.v11n2.1477
Hoon, T. S., Narayanan, G., Aris, S. R. B. S., Ibrahim, N., & Isa, B. Bin. (2022). Science, Technology, Engineering, and Mathematics (STEM) Education in University: Pre-service Teachers’ Perceptions. Asian Journal of University Education, 18(3), 637–648. https://doi.org/10.24191/ajue.v18i3.18951
Hoon, Teoh S, Singh, P., Han, C. T., Nasir, N. A. M., Rasid, N. S. M., & Yusof, M. M. M. (2018). Mathematical Thinking Attainment among University Students. Journal of Economic & Management Perspectives, 12(1), 623–629. Retrieved from https://search.proquest.com/docview/2266299685?accountid=169659
Isa, C. M. M., Lian, O. C., Pao, L. C., Mohd Saman, H., Che Ibrahim, C. K. I., & Yusof, Z. (2021). Effective Implementation of Complex Engineering Problems and Complex Engineering Activities in Malaysian Engineering Curricular. Asian Journal of University Education, 17(4), 170–178. https://doi.org/10.24191/ajue.v17i4.16219
Isa, C. M. M., Mohammad, N. I. A., Saad, N. H., & Preece, C. N. (2021). Programme Outcome Attributes related to Complex Engineering Problem Capability: Perceptions of Engineering Students in Malaysia. Asian Journal of University Education, 17(4), 95–105. https://doi.org/10.24191/ajue.v17i4.16220
Kusdinar, U., Sukestiyarno, S., Isnarto, I., & Istiandaru, A. (2017). Krulik and Rudnik Model Heuristic Strategy in Mathematics Problem Solving. International Journal on Emerging Mathematics Education, 1(2), 205. https://doi.org/10.12928/ijeme.v1i2.5708
Lau, P. N. K. (2005). Mathematical Problem Solving: Interdependence of Problems, Problem Solving and Metacognition. In Improving Teaching and Learning of Mathematics: From Research to Practice (pp. 165–198).
Lester, F. K., & Mau, S. T. (1993). Teaching mathematics via problem solving: A course for prospective elementary teachers. For the Learning of Mathematics, 13(2), 8–11.
Liu, P.-H., & Niess, M. L. (2006). An Exploratory Study of College Students’ Views of Mathematical Thinking in a Historical Approach Calculus Course. Mathematical Thinking and Learning, 8(4), 373–406. https://doi.org/10.1207/s15327833mtl0804_2
Marilyn Ten On (December 2, 2021). Decline in Malaysia’s education performance worrying. https://www.theborneopost.com/2021/12/02/decline-in-msias-education-performance-worrying-says-psb-man/
Nasir, N. A. M., Singh, P., Narayanan, G., Han, C. T., Rasid, N. S., & Hoon, T. S. (2021). An Analysis of Undergraduate Students Ability in Solving Non-Routine Problems. Review of International Geographical Education Online, 11(4), 861–872. https://doi.org/10.33403/rigeo.8006800
Polya, G. (1973). How to Solve It (Second). Princeton, New Jersey: Princeton University Press.
Posamentier, A. S., & Krulik, S. (2008). Problem Solving in Mathematics: Powerful Strategies to Deepen Understanding. California, United States of America: A SAGE Company.
Salleh, M. F. M., Rauf, R. A. A., Saat, R. M., & Ismail, M. H. (2022). Novice Chemistry Teachers’ Instructional Strategies in Teaching Mixed-Ability Classrooms. Asian Journal of University Education, 18(2), 510–525. https://doi.org/10.24191/ajue.v18i2.18066
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics Schoenfeld, A. H. … of Research on Mathematics Teaching and Learning, 334–370. Retrieved from
http://cimm.ucr.ac.cr/ciaem/articulos/universitario/aprendizaje/Learning to think mathematically: problem solving, metacognition, and sense-making in mathematics. 1992*Schoenfeld, Alan*Schoenfeld. Learning to think mathematically...1992.pdf
Singh, P., Rasid, S., Nasir, N. A. M., Hoon, T. S., & Han, C. T. (2017). How Well Do University Level Courses Prepare Students to Mathematical Thinkers? The Social Sciences, 12(9), 1516–1521.
Singh, P., Teoh, S. H., Cheong, T. H., Md Rasid, N. S., Kor, L. K., & Md Nasir, N. A. (2018). The Use of Problem-Solving Heuristics Approach in Enhancing STEM Students Development of Mathematical Thinking. International Electronic Journal of Mathematics Education, 13(3), 289–303. https://doi.org/10.12973/iejme/3921
Singh, P., Hoon, T. S., Rasid, N. S., Nasir, N. A. M., Han, C. T., & Rahman, N. A. (2016). Teaching and Learning of College Mathematics and Student Mathematical Thinking: Are the Lines of the Same Track?. Asian Journal of University Education, 12(2), 65–78.
Sonia, R. (2021). Not a Surprise That Our Students Are Weak in Science and Maths. Prec Edu Services. https://www.studyinchina.com.my/web/page/our-students-are-weak-in-science-and-maths/
Tambunan, H. (2018). Impact of Heuristic Strategy on Students’ Mathematics Ability in High Order Thinking. International Electronic Journal of Mathematics Education, 13(3), 321–328. https://doi.org/10.12973/iejme/3928
Tiong, J. Y. S. (2006). Top-Down Approach to Teaching Problem Solving Heuristics in Mathematics. Singapore.
Toh, T. L., Chan, C. M. E., Tay, E. G., Leong, Y. H., Quek, K. S., Toh, P. C., & Dong, F. (2019). Problem Solving in the Singapore School Mathematics Curriculum. In Algorithms and Complexity in Mathematics, Epistemology, and Science: Proceedings of 2015 and 2016 ACMES Conferences (pp. 141–164). https://doi.org/10.1007/978-981-13-3573-0_7.
Treffinger, D. J., Selby, E. C., & Isaksen, S. G. (2008). Understanding individual problem-solving style: A key to learning and applying creative problem solving. Learning and Individual Differences, 18(4), 390–401. https://doi.org/10.1016/j.lindif.2007.11.007
Smith, J. P. (1973). The Effect of General Versus Specific Heuristics in Mathematical Problem-Solving Tasks.
Suraya, A. (2015). Developing students' mathematical thinking: How far have we come? http://www.educ.upm.edu.my/dokumen/FKKDI1_BULETINEDUC.pdf. Accessed 4 March 2022.
Watters, S., & Logan, P. (2006). “ I can solve problems .” Glasgow City Council, Education Services.
Wilson, P. S. (1993). Mathematical Problem Solving. Research Ideas for the Classroom: High School Mathematics. New York: MacMillan.
Yunus, A. S. M. (2015). Developing Students’ Mathematical Thinking: How Far Have We Come. Serdang: Universiti Puta Malaysia Press. doi: 10.1007/978-981-13-3573-0_7

In-Text Citation: (Nasir & Singh, 2023)
To Cite this Article: Nasir, N. A. M., & Singh, P. (2023). The Effect of a Problem-Solving Approach on Students’ Heuristics Knowledge Development. International Journal of Academic Research in Accounting Finance and Management Sciences, 13(2), 827–842.