Pre-University Students’ Difficulties in Problem Solving by Using Q-Methodology
Keywords:
Mathematics problem solving,, Mathematics difficulties, Q-methodology, PQMethod 2.33Abstract
Problem solving is very important in learning mathematics. During mathematical problem solving, all the mathematical concepts and skills are important particularly in their applications as well as in making decisions. However, students were reported to have difficulties in mathematics problem solving eventhough they were in the post-secondary education level. This level is less researched compared to those of the primary and secondary education levels. The focus of this paper is to present the students’ viewpoints on their difficulties in solving mathematics problems from cognitive ability aspect. The study was carried out using Q-Methodology which is a systematic study of subjectivity in order to have a clearer understanding in studying subjective viewpoints. Data were analyzed using factor analysis of the PQMethod Program. Findings showed the respondents lacked in mathematical cognition such as resource, heuristic and control. The understanding on how these factors influence problem solving is expected to give effective guidelines in preparing diagnostic instruments and learning modules by teachers in order to develop students’ mathematics skills.
Downloads
References
Bayat, S., & Tarmizi, R. A. (2010). Assessing Cognitive and Metacognitive Strategies during Algebra Problem Solving Among University Students. Procedia - Social and Behavioral Sciences, 8, 403–410. doi: 10.1016/j.sbspro.2010.12.056.
Brown, S.R. (1993). A primer on Q methodology. Operant Subjectivity. 16(3/4): 91-138.
Chow, T. (2011). Students’ difficulties, conceptions and attitudes towards learning algebra: an intervention study to improve teaching and learning. Retrieved from http://espace.library.curtin.edu.au/cgi-bin/espace.pdf?file=/2012/07/06/file_1/186423.
Davis, C., & Michelle, C. (2011). Q methodology in audience research: bridging the qualitative/quantitative “divide”? Participations: Journal of Audience and …, 8(2), 559–593. Retrieved from http://www.participations.org/Volume8/Issue2/4aDavisMichelle.pdf.
Krawec, J., Huang, J., Montague, M., Kressler, B., & de Alba, A. M. (2012). The Effects of Cognitive Strategy Instruction on Knowledge of Math Problem-Solving Processes of Middle School Students With Learning Disabilities. Learning Disability Quarterly, 0731948712463368.
Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26, 49–63. doi: 10.1023/A:1003088013286.
McKeown, B.F & Thomas, D.D. (1988). Q methodology: Quantitative application in the social sciences series. Ministry of Education Malaysia. (2003). Integrated Curriculum for Secondary Schools. Retrieved from http://apps2.moe.gov.my/kurikulum/sp_hsp/mate/kbsm/Syllabus%20Maths%20for%20Sec.pdf.
Nadirah, M. N., Yusof, H., Fatimah, S., Zabidi, H. A., Rahimah, J., & Ezrinda, M. Z. (2012). Preliminary Study of Student Performance on Algebraic Concepts and Differentiation.
Ong, H., & Lim, J. (2014). Identifying Factors Influencing Mathematical Problem Solving among Matriculation Students in Penang. Pertanika Journal of Social Sciences & Humanities, 22(3), 393–408.
Polya, G. (1945). How to Solve It: A New Aspect of Mathematical Method. American Mathematical Monthly. doi: 10.2307/2306109.
Polya, G. (1981). Mathematical Discovery on Understanding Learning and Teaching Problem Solving. NewYork: John Wiley and sons.
Phonapichat, P., Wongwanich, S., & Sujiva, S. (2014). An Analysis of Elementary School Students’ Difficulties in Mathematical Problem Solving. Procedia - Social and Behavioral Sciences, 116(2012), 3169–3174. doi: 10.1016/j.sbspro.2014.01.728.
Samo, M. (2009). About the Symbols, Letters and Signs in Algebra and How Do These Affect Their Learning of Algebra: A Case Study in a Government Girls Secondary School Karachi. … Journal for Mathematics Teaching and Learning. Retrieved from http://eric.ed.gov/?id=EJ904876.
Schoenfeld, A. H. (1985). Mathematical problem solving. Research Ideas for the Classroom High School Mathematics (pp. 1–22). Retrieved from http://jwilson.coe.uga.edu/emt725/PSsyn/Pssyn.html.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Handbook of Research on Mathematics Teaching and Learning, 334–370. Retrieved from http://gse.berkeley.edu/faculty/AHSchoenfeld/Schoenfeld_MathThinking.pdf.
Sharma, M. (2012). Improving Mathematics Instruction For All: Vertical Acceleration, 4608(508), 1–29. Tarmizi, R. A. (2010). Visualizing Student’s Difficulties in Learning Calculus. Procedia - Social and Behavioral Sciences, 8, 377–383. doi: 10.1016/j.sbspro.2010.12.053.
Tambychik, T., & Meerah, T. S. M. (2010). Students’ Difficulties in Mathematics Problem-Solving: What do they Say? Procedia - Social and Behavioral Sciences, 8, 142–151. doi: 10.1016/j.sbspro.2010.12.020.
Watts, S.; Stenner, P. (2005). Doing Q methodology:Theory, method, and interpretation. Qualitative Research in Psychology.
Watts, S., & Stenner, P. (2012). Doing Q methodological research: theory, method & interpretation. SAGE.
Yeo, K. (2009). Secondary 2 Students’ Difficulties in Solving Non-Routine Problems. International Journal for Mathematics Teaching and …, 1–30. Retrieved from http://eric.ed.gov/?id=EJ904874.
Yong, H. T., & Kiong, L. N. (2005). Metacognitive aspect of mathematics problem solving. In Third East Asia Regional Conference on Mathematics Education (ICMI Regional Conference), Shanghai, Nanjing and Hangzhou, China. Retrieved from http://math.ecnu.edu.cn/earcome3/TSG4.htm4.
Yunus, A. S., Hamzah, R., Tarmizi, R. A., Abu, R., & Nor, S. (2006). Problem Solving Abilities of Malaysian University Students. International Journal of Teaching and Learning in Higher Education, 17, 86–96. Retrieved from http://www.isetl.org/ijtlhe/
Zahrah Abd Kadir, Jamaliah Bejor, Rohana Nathiman, Badariah Moamed & Jaafar Khamis. (2003). Meningkatkan Kemahiran Membentuk Ungkapan Kuadratik. Jurnal Penyelidikan Pendidikan Jld., 7 (2003), pp. 12–19.
Zakaria, E., & Yusoff, N. (2009). Attitudes and Problem-Solving Skills in Algebra Among Malaysian Matriculation College Students. European Journal of Social Sciences, Volume 8,, 232–245
