Success Indicators of Mathematical Problem-Solving Performance Among Malaysian Matriculation Students

Suriati Abu Bakar, Nur Raidah Salim, Ahmad Fauzi Mohd Ayub, Kathiresan Gopal

Abstract


This study identifies the success indicators of mathematical problem-solving performances among Malaysian matriculation students divided into four indicators: mathematical beliefs, mathematics attitudes, mathematics self-efficacy and metacognitive skills. For this purpose, 368 matriculation students from three matriculation colleges were selected as respondents using proportioned stratified sampling. This study utilized a descriptive correlational design approach. A set of questionnaires and a mathematics test were used as the instruments. Independent variables were measured using a questionnaire, while mathematical problem-solving performance was measured using a mathematics test. The findings show students had a high level in mathematics beliefs, attitude towards mathematics, mathematics self-efficacy and metacognitive skills. Statistical tests to determine success indicators predicting mathematical problem-solving performance revealed that mathematics self-efficacy does not contribute significantly to these variables and that metacognitive skills make the most decisive contribution, followed by mathematics attitude and mathematics beliefs. Hence, this study suggests that problem-solving should be included as an essential part of the mathematics matriculation syllabus to enable students to improve their problem-solving abilities.

https://doi.org/10.26803/ijlter.20.3.7


Keywords


mathematics beliefs; mathematics attitude; mathematics self-efficacy and metacognitive skills; problem-solving performance

Full Text:

PDF

References


Abdullah, A. H., Rahman, S. N. S. A., & Hamzah, M. H. (2017). Metacognitive skills of Malaysian students in non-routine mathematical problem-solving. Bolema: Boletim de Educação Matemática, 31(57), 310-322. https://doi.org/10.1590/1980-4415v31n57a15

Abedalaziz, N., & Akmar, S. N. (2012). Epistemology beliefs about mathematical problem solving among Malaysian students. OIDA International Journal of Sustainable Development, 5(1), 59–74.

Ajisuksmo, C., & Saputri, G. (2017) The Influence of Attitudes towards Mathematics, and Metacognitive Awareness on Mathematics Achievements. Creative Education, 8, 486-497. http://doi.org/10.4236/ce.2017.83037

Amalia, E., Surya, E., & Syahputra, E. (2017). The effectiveness of using problem-based learning (PBL) in mathematics problem-solving ability for junior high school students. International Journal of Advance Research and Innovative Ideas in Education, 3(2), 3402-3406.

Ary, D., Jacobs, L. C., Sorensen, C. K., & Walker, D. (2014). Introduction to research in education (9th ed.). Belmont, CA: Wadsworth, Cengage Learning.

Ayop, R. A., & Ahmad Tarmizi, R. (2015). Pre-university Students’ Difficulties in Problem Solving by Using Q-methodology. Jurnal Pendidikan Sains dan Matematik Malaysia, 5(2), 1–11.

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W.H. Freeman.

Barrett, L. L. (2016). Development and Validation of the Mathematical Problem-solving Dispositions and Beliefs Scale. [PhD Dissertations, Kennesaw State University].

Barlett, J. E., Kotrlik, J. W., & Higgins, C. C. (2001). Organizational research: Determining appropriate sample size in survey research. Information Technology, Learning, and Performance Journal, 19(1), 43-50.

Buzzai, C., Filippello, P., Puglisi, B., Mafodda, A. V., & Sorrenti, L. (2020). The relationship between mathematical achievement, mathematical anxiety, perfectionism, and metacognitive abilities in Italian students. Mediterranean Journal of Clinical Psychology, 8(3).1-18

Boğar, Y. (2018). Exploring 6th grade students’scientific epistemological beliefs and metacognitive awareness regarding achievement level [Doctoral dissertation, Middle East Technical University].

Deng, F., Tay, E. G., Toh, T. L., Leong, Y. H., Quek, K. S., Toh, P. C., ... & Ho, F. H. (2015). Enhancing Student Beliefs about Mathematical Problem Solving: Effects of a Problem-Solving based Intervention. Research in Mathematical Education, 19(1), 19-41.

Denscombe, M. (2010). The Good Research Guide for Small-Scale Social Research Project (4th ed.). New York: Open University Press.

Doménech-Betoret, F., Abellán-Roselló, L., & Gómez-Artiga, A. (2017). Self-efficacy, Satisfaction, and Academic Achievement: The Mediator Role of Students’ Expectancy-Value Beliefs. Frontiers in Psychology, 8(2), 1–12. https://doi.org/10.3389/fpsyg.2017.01193

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2016). How to design and evaluate research in education (9th ed.). New York: McGraw Hill Higher Education.

Gopal, K., Salim, N. R., & Ayub, A. F. M. (2018, November). Influence of Self-efficacy and Attitudes Towards Statistics on Undergraduates’ Statistics Engagement in A Malaysian Public University. In Journal of Physics: Conference Series (Vol. 1132, No. 1, p. 012042).

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate Data Analysis (7th ed.). New Jersey, USA: Pearson Prentice Hall.

Hinojosa, L. M. M., Rodriguez, M. C., & Paez, C. A. O. (2020). Measurement of Metacognition: Adaptation of Metacognitive State Inventory in Spanish to Mexican University Students. European Journal of Educational Research, 9(1), 413-421.

Hinton, P. R., McMurray, I., & Brownlow, C. (2014). SPSS Explained (2nd ed.). New York: Routledge.

Kahramanoglu, R., & Deniz, T. (2017). An investigation of The Relationship Between Middle School Students’ Metacognitive Skills, Mathematics Self-Efficacy, and Mathematics Achievement. Inonu University Journal of the Faculty of Education, 18(3), 189-200. https://doi.org/10.17679/inuefd.334285

Kamalimoghaddam, H., Ahmad Tarmizi, R., Ayub, A. F. M., & Jaafar, W. M. W. (2016). The Influences of Mathematics Beliefs on Mathematics Achievement Through Mathematics Self-Efficacy: A Structural Equation Model. Communication in Mathematical Modeling and Applications, 51(1), 44–51.

Kandemir, M. A., & AkbaÅŸ-Perkmen, R. (2017). Examining Validity of Sources of Mathematics Self-Efficacy Scale in Turkey. European Journal of Education Studies. 3(11), 69-88. https://doi.org/10.5281/zenodo.1041845.

Kasimu, O., & Imoro, M. (2017). Students’ Attitudes Towards Mathematics: The Case of Private and Public Junior High Schools in The East Mamprusi District, Ghana. IOSR Journal of Research & Method in Education (IOSR-JRME), 7(5), 38-43. https://doi.org/10.9790/7388-0705063843

Khalid, M. (2017). Fostering problem solving and performance assessment among Malaysian mathematics teachers. Sains Humanika, 9(1–2), 51–55. https://doi.org/10.11113/sh.v9n1-2.1098

Kloosterman, P., Raymond, A. M., & Emenaker, C. (1996). Students' Beliefs about Mathematics: A three-year Study. The Elementary School Journal, 97(1), 39-56.

Kloosterman, P., & Stage, F. K. (1992). Measuring Beliefs about Mathematical Problem Solving. School Science and Mathematics, 92(3), 109-115.

Lee, J. H., Abdullah, F. A. P., & Bunyamin, M. A. H. (2013). Aplikasi konsep fizik dalam menyelesaikan masalah yang berasaskan STEM bagi pelajar tingkatan enam atas. In 2nd International Seminar on Quality and Affordable Education (pp. 470–481). Universiti Teknologi Malaysia, Malaysia.

Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem Solving in Mathematics Education. Switzerland: Springer International Publishing.

Lodico, M. G., Spaulding, D. T., & Voegtle, K. H. (2010). Methods in Educational Research: From theory to practice (Vol. 28). John Wiley & Sons.

Loh, M. Y., & Lee, N. H. (2019). The Impact of Various Methods in Evaluating Metacognitive Strategies in Mathematical Problem Solving. In Mathematical Problem Solving (pp. 155-176). Springer, Cham. ttps://doi.org/10.1007/978-3-030-10472-6_8

Mason, J. (2016). Part 1 Reaction: Problem Posing and Solving Today. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and Solving Mathematical Problems (pp. 109–113). Switzerland: Springer. https://doi.org/10.1007/978-3-319-28023-3_7

Mills, G. E., & Gay, L. R. (2016). Educational Research: Competencies for Analysis and Applications (11th. ed.). Boston: Pearson Education.

Ministry of Education Malaysia. (2013). Malaysia Education Blueprint 2013-2025 (Preschool to Post-Secondary Education). Education. Putrajaya: Ministry of Education Malaysia.

Ministry of Education Malaysia. (2016). Malaysian Education Blueprint (2013-2015) Annual Report 2015. Putrajaya: Ministry of Education Malaysia.

NCTM. (2010). Why is teaching with problem solving necessary to student learning? National Council of Teachers of Mathematics, 13(12), 1–6. https://doi.org/10.1016/S2213-8587(14)70016-6

Ong, H. C., & Lim, J. S. (2014). Identifying factors influencing mathematical problem solving among matriculation students in Penang. Pertanika Journal of Social Science and Humanities, 22(1), 393–408.

O’Neil, H. F., & Abedi, J. (1996). Reliability and Validity of A State Metacognitive Inventory: Potential for Alternative Assessment. Journal of Educational Research, 89(4), 234–245. https://doi.org/10.1080/00220671.1996.9941208

Özcan, Z. Ç., & Gümüş, A. E. (2019). A modeling study to explain mathematical problem-solving performance through metacognition, self-efficacy, motivation, and anxiety. Australian Journal of Education, 63(1), 116-134. https://doi.org/10.1177/0004944119840073

Öztürk, M., Akkan, Y., & Kaplan, A. (2020). Reading comprehension, Mathematics self-efficacy perception, and Mathematics attitude as correlates of students’ non-routine Mathematics problem-solving skills in Turkey. International Journal of Mathematical Education in Science and Technology, 51(7), 1042-1058. https://doi.org/10.1080/0020739X.2019.1648893

Pallant, J. (2020). SPSS survival manual: A step-by-step guide to data analysis using IBM SPSS. Routledge.

Peteros, E., Columna, D., Etcuban, J. O., Almerino, Jr., P., & Almerino, J. G. (2019). Attitude and Academic Achievement of High School Students in Mathematics Under the Conditional Cash Transfer Program. International Electronic Journal of Mathematics Education, 14(3), 583-597. https://doi.org/10.29333/iejme/5770

Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd. ed.). Princeton, NJ: Princeton University Press.

Prendergast, M., Breen, C., Bray, A., Faulkner, F., Carroll, B., Quinn, D., & Carr, M. (2018). Investigating secondary students beliefs about mathematical problem-solving. International Journal of Mathematical Education in Science and Technology, 49(8), 1203-1218. https://doi.org/10.1080/0020739X.2018.1440325

Rincon, G. A., Cézar, R. F., & Hernandez, C. F. (2020, March). Beliefs about mathematics and academic performance: A descriptive-correlational analysis. In Journal of Physics: Conference Series (Vol. 1514, No. 1, p. 012021). IOP Publishing. https://doi.org/10.1088/1742-6596/1514/1/012021

Salkind, N. J. (2012). Exploring Research (8th. ed.). New Jersey: Pearson Education, Inc.

Salim, N. R., Gopal, K., & Ayub, A. F. M. (2018, June). The influence of statistics self-efficacy towards statistics engagement among undergraduate students. In AIP Conference Proceedings (Vol. 1974, No. 1, p. 050005). AIP Publishing LLC. https://doi.org/10.1063/1.5041705

Simegn, E. M., & Asfaw, Z. G. (2018). Assessing the Influence of Attitude Towards Mathematics on Achievement of Grade 10 and 12 Female Students in Comparison with Their Male Counterparts: Wolkite, Ethiopia. International Journal of Secondary Education, 5(5), 56. https://doi.org/10.11648/j.ijsedu.20170505.11

Stylianides, A. J., & Stylianides, G. J. (2014). Impacting positively on students’ mathematical problem solving beliefs: An instructional intervention of short duration. Journal of Mathematical Behavior, 33(1), 8–29. https://doi.org/10.1016/j.jmathb.2013.08.005

Tambunan, H. (2019). The Effectiveness of the Problem Solving Strategy and the Scientific Approach to Students' Mathematical Capabilities in High Order Thinking Skills. International Electronic Journal of Mathematics Education, 14(2), 293-302. https://doi.org/10.29333/iejme/5715

Tarmizi, R. A., Kargar, M., & Saadati, F. (2015). Correlates of Mathematics Attitude and Problem Solving Behaviour among Teheran, Republic of Iran Year 10 Students. Jurnal Pendidikan Sains Dan Matematik Malaysia, 5(1), 18–34.

Tapia, M., & Marsh, G. E. I. (2004). An Instrument to Measure Mathematics Attitudes. Academic Exchange Quarterly, 8(2), 16–21.

Usher, E. L., & Pajares, F. (2009). Sources of Self-efficacy in Mathematics: A validation study. Contemporary Educational Psychology, 34(1), 89–101.

Veenman, M. V., & van Cleef, D. (2019). Measuring Metacognitive Skills for Mathematics: Students’ Self-reports Versus Online Assessment Methods. ZDM, 51(4), 691-701. https://doi.org/10.1007/s11858-018-1006-5

Wang, G., Zhang, S., & Cai, J. (2019). Chinese High School Students’ Mathematics-Related Beliefs and Their Perceived Mathematics Achievement: A Focus on Teachers’ Praise. EURASIA Journal of Mathematics, Science and Technology Education, 15(7), 1-12. https://doi.org/10.29333/ejmste/105875

Warner, S., & Kaur, A. (2017). The perceptions of teachers and students on a 21st Century mathematics instructional model. International Electronic Journal of Mathematics Education, 12(2), 193-215.


Refbacks

  • There are currently no refbacks.


e-ISSN: 1694-2116

p-ISSN: 1694-2493