Journal of Pedagogical Sociology and Psychology
An investigation of mathematical problem-solving skills based on students’ prior mathematical knowledge and cognitive style
Ahmad Dzulfikar 1 2 * , Tatang Herman 1
More Detail
1 Universitas Pendidikan Indonesia, Indonesia
2 Universitas Islam Negeri K.H. Abdurrahman Wahid Pekalongan, Indonesia
* Corresponding Author
Open Access Full Text (PDF)
ARTICLE INFO

Journal of Pedagogical Sociology and Psychology, 2023 - Volume 5 Issue 3, pp. 186-194
https://doi.org/10.33902/jpsp.202319689

Article Type: Research Article

Published Online: 20 Oct 2023

Views: 655 | Downloads: 449

ABSTRACT
Several prior research concluded that students' mathematical problem-solving skills (MPSS) were deemed inadequate. The research necessitated additional research into the components that govern it. This study explored the differences in MPSS between students based on their basic mathematics knowledge and cognitive style. This study was conducted using a survey and quantitative analysis utilizing inferential statistics. Cluster sampling was used to choose 182 students from a junior high school in Bandung, Indonesia. There were 91 male and 91 female pupils in the sample. Valid and reliable mathematical prior knowledge tests, MPSS tests, and the Group Embedded Figure Test (GEFT) were used as data mining instruments in this work. The acquired data were analyzed using JASP software and a two-way ANOVA test. This study found that, first, there is no difference in MPSS based on prior knowledge of mathematics. Second, there are moderate differences in MPSS based on cognitive style. Third, there is no interaction between the effects of prior knowledge of mathematics and cognitive style on MPSS. This study concludes that cognitive style is the most influential factor influencing students' MPSS.
KEYWORDS
cognitive style mathematical problem-solving skills prior mathematical knowledge two-way ANOVA
SUPPLEMENTARY FILES
In-text citation: (Dzulfikar & Herman, 2023)
Reference: Dzulfikar, A., & Herman, T. (2023). An investigation of mathematical problem-solving skills based on students’ prior mathematical knowledge and cognitive style. Journal of Pedagogical Sociology and Psychology, 5(3), 186-194. https://doi.org/10.33902/jpsp.202319689
In-text citation: (1), (2), (3), etc.
Reference: Dzulfikar A, Herman T. An investigation of mathematical problem-solving skills based on students’ prior mathematical knowledge and cognitive style. Journal of Pedagogical Sociology and Psychology. 2023;5(3), 186-194. https://doi.org/10.33902/jpsp.202319689
In-text citation: (1), (2), (3), etc.
Reference: Dzulfikar A, Herman T. An investigation of mathematical problem-solving skills based on students’ prior mathematical knowledge and cognitive style. Journal of Pedagogical Sociology and Psychology. 2023;5(3):186-94. https://doi.org/10.33902/jpsp.202319689
In-text citation: (Dzulfikar and Herman, 2023)
Reference: Dzulfikar, Ahmad, and Tatang Herman. "An investigation of mathematical problem-solving skills based on students’ prior mathematical knowledge and cognitive style". Journal of Pedagogical Sociology and Psychology 2023 5 no. 3 (2023): 186-194. https://doi.org/10.33902/jpsp.202319689
In-text citation: (Dzulfikar and Herman, 2023)
Reference: Dzulfikar, A., and Herman, T. (2023). An investigation of mathematical problem-solving skills based on students’ prior mathematical knowledge and cognitive style. Journal of Pedagogical Sociology and Psychology, 5(3), pp. 186-194. https://doi.org/10.33902/jpsp.202319689
In-text citation: (Dzulfikar and Herman, 2023)
Reference: Dzulfikar, Ahmad et al. "An investigation of mathematical problem-solving skills based on students’ prior mathematical knowledge and cognitive style". Journal of Pedagogical Sociology and Psychology, vol. 5, no. 3, 2023, pp. 186-194. https://doi.org/10.33902/jpsp.202319689
REFERENCES
  • Ary, D., Jacobs, L. C., Sorensen, C., & Walker, D. A. (2014). Introduction to Research in Education. Cengage Learning.
  • Aydın Güç, F., & Daltaban, D. (2021). An investigation of the use of specific problem-solving strategies by mathematics teachers in lessons. Journal of Pedagogical Research, 5(1), 126–140. https://doi.org/10.33902/jpr.2021067307
  • Bahar, A., & June Maker, C. (2015). Cognitive backgrounds of problem solving: A comparison of open-ended vs. closed mathematics problems. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1531–1546. https://doi.org/10.12973/eurasia.2015.1410a
  • Bakar, K. A. A., Supriyati, Y., & Hanafi, I. (2019). The evaluation of admission student policy based on zoning system for acceleration education quality in Indonesia. Journal of Management Info, 6(2), 19–24. https://doi.org/10.31580/jmi.v6i2.883
  • Bakar, S. A., Salim, N. R., Ayub, A. F. M., & Gopal, K. (2021). Success indicators of mathematical problem-solving performance among Malaysian matriculation students. International Journal of Learning, Teaching and Educational Research, 20(3), 97–116. https://doi.org/10.26803/ijlter.20.3.7
  • Fraillig, J. L., Murphy, L. A., & Fuson, K. C. (1999). Advancing children’s mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30(2), 148–170. https://doi.org/https://doi.org/10.2307/749608
  • Gavaz, H. O., Yazgan, Y., & Arslan, Ç. (2021). Non-routine problem solving and strategy flexibility: A quasi-experimental study. Journal of Pedagogical Research, 5(3), 40–54. https://doi.org/10.33902/jpr.2021370581
  • Güner, P., & Erbay, H. N. (2021). Prospective mathematics teachers’ thinking styles and problem-solving skills. Thinking Skills and Creativity, 40, 100827. https://doi.org/10.1016/j.tsc.2021.100827
  • Kemendikbud. (2018). Sistem zonasi: Strategi pemerataan pendidikan yang bermutu dan berkeadilan [Zoning system: Strategy for equal distribution of quality and fair education]. Indonesian Ministry of Education and Culture.
  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Addding it up: helping children learn mathematics. National Research Council.
  • Kuhfeld, M., Ruzek, E., Lewis, K., Soland, J., Johnson, A., Tarasawa, B., & Dworkin, L. (2021). Understanding the initial educational impacts of COVID-19 on communities of color. NWEA Research.
  • Kuhfeld, M., Soland, J., Lewis, K., Ruzek, E., & Johnson, A. (2022). The COVID-19 school year: Learning and recovery across 2020-2021. AERA Open, 8(1), 1–15. https://doi.org/10.1177/23328584221099306
  • Kuhfeld, M., & Tarasawa, B. (2020). The COVID-19 slide: What summer learning loss can tell us about the potential impact of school closures on student academic achievement. NWEA Research.
  • Lee, C. Y., & Chen, M. P. (2009). A computer game as a context for non-routine mathematical problem solving: The effects of type of question prompt and level of prior knowledge. Computers and Education, 52(3), 530–542. https://doi.org/10.1016/j.compedu.2008.10.008
  • Lewis, K., Kuhfeld, M., Ruzek, E., & Mceachin, A. (2021). Learning during COVID-19: Reading and math achievement in the 2020-21 school year. NWEA Research.
  • Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem Solving in Mathematics Education. Springer. https://doi.org/10.1007/978-94-007-4978-8_129
  • Marchiş, I. (2013). Relation between students’ attitude towards mathematics and their problem solving skills. PedActa, 3(2), 59–66.
  • Masalimova, A. R., Mikhaylovsky, M. N., Grinenko, A. V., Smirnova, M. E., Andryushchenko, L. B., Kochkina, M. A., & Kochetkov, I. G. (2019). The interrelation between cognitive styles and copying strategies among student youth. Eurasia Journal of Mathematics, Science and Technology Education, 15(4), 1–7. https://doi.org/10.29333/ejmste/103565
  • Maya, R., & Sumarmo, U. (2011). Mathematical understanding and proving abilities : Experiment with undergraduate student by using modified moore learning approach. Journal on Mathematics Education, 2(2), 231–250.
  • Mefoh, P. C., Nwoke, M. B., Chukwuorji, J. B. C., & Chijioke, A. O. (2017). Effect of cognitive style and gender on adolescents’ problem solving ability. Thinking Skills and Creativity, 25, 47–52. https://doi.org/10.1016/j.tsc.2017.03.002
  • Mogari, D., & Lupahla, N. (2013). Mapping a group of northern namibian grade 12 learners’ Algebraic non-routine problem solving skills. African Journal of Research in Mathematics, Science and Technology Education, 17(1–2), 94–105. https://doi.org/10.1080/10288457.2013.826974
  • Mulbar, U., Rahman, A., & Ahmar, A. S. (2017). Analysis of the ability in mathematical problem-solving based on SOLO taxonomy and cognitive style. World Transactions on Engineering and Technology Education, 15(1), 68–73. https://doi.org/10.26858/wtetev15i1y2017p6873
  • NCTM. (2000). Principles and Standards for School Mathematics. NCTM.
  • Nur, A. S., & Palobo, M. (2018). Profil kemampuan pemecahan masalah matematika siswa ditinjau dari perbedaan gaya kognitif dan gender [Profile of students' mathematical problem solving abilities in terms of differences in cognitive style and gender]. Kreano, Jurnal Matematika Kreatif-Inovatif, 9(2), 139–148. https://doi.org/https://doi.org/10.15294/kreano.v9i2.15067
  • OECD. (2019). Country Note PISA 2018 Results: Indonesia. Author.
  • Patrinos, H., Vegas, E., & Carter-Rau, R. (2022). An analysis of COVID-19 student learning loss. World Bank Group.
  • Peng, A., Ezeife, A., & Yu, B. (2020). Reciprocal learning in mathematics problem posing and problem solving: An interactive study between two Canadian and Chinese elementary schools. Eurasia Journal of Mathematics, Science and Technology Education, 16(12), 1–13. https://doi.org/10.5206/cie-eci.v47i1.9323
  • 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. https://doi.org/10.1016/j.sbspro.2014.01.728
  • Piaget, J. (2003). The Psychology of Intelligence. Taylor & Francis.
  • Schoenfeld, A. H. (1982). Measures of problem-solving performance and of problem-solving instruction. Journal for Research in Mathematics Education, 13(1), 31–49. https://doi.org/10.2307/748435
  • Simamora, R. E., Saragih, S., & Hasratuddin, H. (2018). Improving students’ mathematical problem solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1), 61–72. https://doi.org/10.12973/iejme/3966
  • Son, A. L., Darhim, & Fatimah, S. (2020). Students’ mathematical problem-solving ability based on teaching models intervention and cognitive style. Journal on Mathematics Education, 11(2), 209–222. https://doi.org/10.22342/jme.11.2.10744.209-222
  • Sumarmo, U. (2012). Pendidikan karakter serta pengembangan berfikir dan disposisi matematik dalam pembelajaran matematika [Character education and development of mathematical thinking and disposition in mathematics learning]. Seminar Pendidikan Matematika Di NTT.
  • Sumirattana, S., Makanong, A., & Thipkong, S. (2017). Using realistic mathematics education and the DAPIC problem-solving process to enhance secondary school students’ mathematical literacy. Kasetsart Journal of Social Sciences, 38(3), 307–315. https://doi.org/10.1016/j.kjss.2016.06.001
  • Surya, E., Putri, F. A., & Mukhtar. (2017). Improving mathematical problem-solving ability and self-confidence of high school students through contextual learning model. Journal on Mathematics Education, 8(1), 85–94. https://doi.org/10.22342/jme.8.1.3324.85-94
  • Suryadi, D. (2012). Membangun budaya baru dalam berpikir matematika [Building a new culture in mathematical thinking]. Rizqi Press.
  • Suryadi, D., & Herman, T. (2008). Eksplorasi matematika: pembelajaran pemecahan masalah [Mathematical exploration: problem solving learning]. Karya Duta Wahana.
  • Swanson, H. L., Arizmendi, G. D., & Li, J. T. (2021). Working memory growth predicts mathematical problem-solving growth among emergent bilingual children. Journal of Experimental Child Psychology, 201, 104988. https://doi.org/10.1016/j.jecp.2020.104988
  • 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.
  • Ulya, H., Kartono, & Retnoningsih, A. (2014). Analysis of mathematics problem solving ability of junior high school students viewed from students’ cognitive style. International Journal of Education and Research, 2(2), 63–71.
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. B. (2020). Elementary and middle school mathematics: teaching developmentally. Pearson.
  • Wapner, S. (2009). Introductory remarks. In M. Bertini, L. Pizzamiglio, & S. Wapner (Eds.), Field dependence in psychological theory, research and application: two symposia in memory of Herman A. Witkin (pp. 1–4). Routledge. https://doi.org/10.3168/jds.S0022-0302(60)90360-X
  • 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
  • Witkin, H. A., Moore, C. A., Oltman, P. K., Goodenough, D. R., Friedman, F., Owen, D. R., & Raskin, E. (1977). Role of the field-dependent and field-independent cognitive styles in academic evolution: A longitudinal study. Journal of Educational Psychology, 69(3), 197–211. https://doi.org/10.1037/0022-0663.69.3.197
LICENSE
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.