Profile of Student Algebraic Thinking with Polya's Problem-Solving Strategy: Study on Male Students with Field Independent Cognitive Style

Nur Hardiani

doi:10.31764/jtam.v6i2.6915

Profile of Student Algebraic Thinking with Polya's Problem-Solving Strategy: Study on Male Students with Field Independent Cognitive Style

Nur Hardiani

Abstract

This study aims to describe the profile of students' algebraic thinking with Polya's problem solving strategy in completing a linear program conducted on male students with field independent cognitive style. This research is exploratory research with qualitative approaches. In accordance with the purpose of the study, the subject (single subject) were male student with field independent cognitive style. Single subject were screened from 119 participants (male students in grade X) at a high school in the city of Mataram, Indonesia. The criteria for determining a single subject are male students with field independent cognitive style, and having the highest math scores on linear algebra material. The research instrument consisted of the main instrument (researcher/human instrument) which interacted directly with the subject to explore the subject's algebraic thinking profile, and research aid instruments consisting of the GEFT test, mathematical ability test, linear programming tasks, and interview guidelines. Through Polya's problem solving, the students' algebraic thinking profile has been described, where the subject has represented mathematical ideas using algebraic expressions, the subject interprets algebraic expressions; the subject uses symbolic representations, formulations, and expressions of equations using algebraic conventions; and the subject can interpret the solution.

Keywords

Algebraic thinking profile; Polya's problem solving; Field independent cognitive style;

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References

Adamuz-Povedano, N., Fernández-Ahumada, E., García-Pérez, M. T., & Montejo-Gámez, J. (2021). Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education. Mathematics, 9(5), 518. https://doi.org/10.3390/math9050518

Armstrong, S. J., Cools, E., & Sadler-Smith, E. (2012). Role of Cognitive Styles in Business and Management: Reviewing 40 Years of Research. International Journal of Management Reviews, 14(3), 238–262. https://doi.org/10.1111/j.1468-2370.2011.00315.x

Ashar, S., Permadi, H., & Susanto, H. (2021). Algebraic thinking process analysis of senior high school students in solving absolute value mathematics problem. AIP Conference Proceedings, 2330(1), 040038. https://doi.org/10.1063/5.0043365

Bandura, A. (1982). Self-efficacy mechanism in human agency. American Psychologist, 37(2), 122–147. https://doi.org/10.1037/0003-066X.37.2.122

Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J., Palm, T., & Palmberg, B. (2014). Developing mathematical competence: From the intended to the enacted curriculum. The Journal of Mathematical Behavior, 33, 72–87. https://doi.org/10.1016/j.jmathb.2013.10.001

Cai, J., & Knuth, E. (2011). Preface to Part I. In J. Cai & E. Knuth (Eds.), Early Algebraization: A Global Dialogue from Multiple Perspectives (pp. 3–4). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_1

Chimoni, M., & Pitta-Pantazi, D. (2017). Parsing the notion of algebraic thinking within a cognitive perspective. Educational Psychology, 37(10), 1186–1205. https://doi.org/10.1080/01443410.2017.1347252

Danişman, Ş., & Erginer, E. (2017). The predictive power of fifth graders’ learning styles on their mathematical reasoning and spatial ability. Cogent Education, 4(1), 1266830. https://doi.org/10.1080/2331186X.2016.1266830

Evendi, E., & Verawati, N. N. S. P. (2021). Evaluation of Student Learning Outcomes in Problem-Based Learning: Study of Its Implementation and Reflection of Successful Factors. Jurnal Penelitian Pendidikan IPA, 7(SpecialIssue), 69–76. https://doi.org/10.29303/jppipa.v7iSpecialIssue.1099

Faulkner, F., Breen, C., Prendergast, M., & Carr, M. (2021). Profiling mathematical procedural and problem-solving skills of undergraduate students following a new mathematics curriculum. International Journal of Mathematical Education in Science and Technology, 0(0), 1–30. https://doi.org/10.1080/0020739X.2021.1953625

Fuchs, L. S., Compton, D. L., Fuchs, D., Powell, S. R., Schumacher, R. F., Hamlett, C. L., Vernier, E., Namkung, J. M., & Vukovic, R. K. (2012). Contributions of domain-general cognitive resources and different forms of arithmetic development to pre-algebraic knowledge. Developmental Psychology, 48(5), 1315–1326. https://doi.org/10.1037/a0027475

George, B., Desmidt, S., Cools, E., & Prinzie, A. (2018). Cognitive styles, user acceptance and commitment to strategic plans in public organizations: An empirical analysis. Public Management Review, 20(3), 340–359. https://doi.org/10.1080/14719037.2017.1285112

Gijsbers, D., de Putter-Smits, L., & Pepin, B. (2020). Changing students’ beliefs about the relevance of mathematics in an advanced secondary mathematics class. International Journal of Mathematical Education in Science and Technology, 51(1), 87–102. https://doi.org/10.1080/0020739X.2019.1682698

Hardiani, N., Budayasa, I. K., & Juniati, D. (2018). Algebraic Thinking in Solving Linier Program at High School Level: Female Student’s Field Independent Cognitive Style. Journal of Physics: Conference Series, 947, 012051. https://doi.org/10.1088/1742-6596/947/1/012051

Kurniawan, M. R., & Mashuri, M. (2021). Analyzing the Influence of Concept Understanding and Self Efficacy on Student’s Algebraic Thinking Ability in Flipped Classroom Learning Model. Unnes Journal of Mathematics Education, 10(3), 231–243. https://doi.org/10.15294/ujme.v10i3.54144

Lew, H. (2004). Developing Algebraic Thinking in Early Grades: Case Study of Korean Elementary School Mathematics1. The Mathematics Educator, 8, 88–106.

MacDonald, A. (2020). Mathematics education beliefs and practices of Under 3s educators in Australia. European Early Childhood Education Research Journal, 28(5), 758–769. https://doi.org/10.1080/1350293X.2020.1817246

Midgett, C. W., & Eddins, S. K. (2001). NCTM’s Principles and Standards for School Mathematics: Implications for Administrators. NASSP Bulletin, 85(623), 35–42. https://doi.org/10.1177/019263650108562305

Muniroh, A., Usodo, B., & Subanti, S. (2017). Algebraic Form Problem Solving Based on Student Abstraction Ability. Journal of Physics: Conference Series, 895, 012038. https://doi.org/10.1088/1742-6596/895/1/012038

Nisak, A. R. Z., As’ari, A. R., Rahardi, R., & Subanji, S. (2020). The Relationship of Student’s Algrebraic Thinking and Cognitive Learning Style. IndoMath: Indonesia Mathematics Education, 3(2), 70–77.

Niss, M., Bruder, R., Planas, N., Turner, R., & Villa-Ochoa, J. A. (2016). Survey team on: Conceptualisation of the role of competencies, knowing and knowledge in mathematics education research. ZDM, 48(5), 611–632. https://doi.org/10.1007/s11858-016-0799-3

Nu, A. T. (2019). Algebra Thinking Process on Vocational School Students in Completing Line Problems. KOLOKIUM, 7(2), 75–87. https://doi.org/10.24036/kolokium-pls.v7i2.350

Nuryah, M., Ferdianto, F., & Supriyadi, S. (2020). Analisis Kesalahan Siswa dalam Menyelesaikan Soal Persamaan dan Pertidaksamaan Nilai Mutlak Berdasarkan Langkah Penyelesaian Polya. Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, 4(1), 63. https://doi.org/10.31331/medivesveteran.v4i1.983

Pedemonte, B. (2008). Argumentation and algebraic proof. ZDM, 40(3), 385–400. https://doi.org/10.1007/s11858-008-0085-0

Pendlington, S. (2005). Mathematics Is Not Easy: The Importance of Teaching Children to Struggle. Research in Mathematics Education, 7(1), 3–17. https://doi.org/10.1080/14794800008520142

Pinnock, E. (2021). Teaching and learning algebraic thinking with 5-to 12-year-olds: The global evolution of and emerging field of research and practice. Research in Mathematics Education, 23(2), 226–230. https://doi.org/10.1080/14794802.2020.1725613

Polya, G. (1945). How to Solve It: A New Aspect of Mathematical Method. Princeton University Press. https://doi.org/10.1515/9781400828678

Pratiwi, V., Farokhah, L., & Abidin, Z. (2019). A Lesson Design of Algebraic Thinking in Elementary School as an Efforts to Develop Mathematical Literation in Industrial Era 4.0. PrimaryEdu - Journal of Primary Education, 3(2), 61–75. https://doi.org/10.22460/pej.v3i2.1376

Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM, 40(1), 83–96. https://doi.org/10.1007/s11858-007-0061-0

Rayner, S., & Cools, E. (2011). Style Differences in Cognition, Learning, and Management: Theory, Research and Practice. Routledge.

Sukmawati, A., Sutawidjaja, A., & Siswono, T. (2018). Algebraic Thinking of Elementary Students in Solving Mathematical Word Problems: Case of Male Field Dependent and Independent Student. Proceedings of the International Conference on Teacher Training and Education 2018 (ICTTE 2018). International Conference on Teacher Training and Education 2018 (ICTTE 2018), Surakarta, Indonesia. https://doi.org/10.2991/ictte-18.2018.20

Tsaqifah, S. (2020). Analisis kesalahan siswa dalam menyelesaikan masalah matematika ditinjau dari kemampuan berpikir aljabar. Prosiding Seminar Nasional Matematika Dan Pendidikan Matematika, 5, 401–407.

Viator, R. E., Harp, N. L., Rinaldo, S. B., & Marquardt, B. B. (2020). The mediating effect of reflective-analytic cognitive style on rational thought. Thinking & Reasoning, 26(3), 381–413. https://doi.org/10.1080/13546783.2019.1634151

Witkin, H. A. (1967). A Cognitive-Style Approach to Cross-Cultural Research. International Journal of Psychology, 2(4), 233–250. https://doi.org/10.1080/00207596708247220

Witkin, H. A., Moore, C. A., Goodenough, D., & Cox, P. W. (1977). Field-Dependent and Field-Independent Cognitive Styles and Their Educational Implications. Review of Educational Research, 47(1), 1–64. https://doi.org/10.3102/00346543047001001

DOI: https://doi.org/10.31764/jtam.v6i2.6915