logo logo European Journal of Educational Research

EU-JER is is a, peer reviewed, online academic research journal.

Subscribe to

Receive Email Alerts

for special events, calls for papers, and professional development opportunities.

Subscribe

Publisher (HQ)

Eurasian Society of Educational Research
Eurasian Society of Educational Research
7321 Parkway Drive South, Hanover, MD 21076, USA
Eurasian Society of Educational Research
Headquarters
7321 Parkway Drive South, Hanover, MD 21076, USA
apos theory cognitive style problem solving reflective

Problem-Solving Process of Students with a Reflective Cognitive Style Based on the Action-Process-Object-Schema Theory

Ratri Rahayu , Kartono , Dwijanto , Arief Agoestanto

The skill to solve mathematical problems facilitates students to develop their basic skills to solve problems in daily life. This study analyzes stude.

T

The skill to solve mathematical problems facilitates students to develop their basic skills to solve problems in daily life. This study analyzes students' problem-solving process with a reflective cognitive style in constructing probability problems using action, process, object, and schema theory (APOS). The explanatory method was used in this qualitative study. The participants were mathematics students at the Department of Mathematics, Universitas Negeri Semarang. The researchers collected the data with the cognitive style test using the Matching Familiar Figure Test (MFFT), used a valid problem-solving skill test, and the interview questions. The data analysis techniques used were processing and preparing the data for analysis, extensive reading of the data, coding all data, applying the coding process, describing the data, and interpreting the data. The results showed that (1) the problem-solving process of students with symbolic representation was characterized by the use of mathematical symbols to support the problem-solving process in the problem representation phase; (2) the problem-solving process of students with symbolic-visual representation was characterized by the use of symbols, notations, numbers, and visual representation in the form of diagrams in the problem representation phase.

Keywords: APOS theory, cognitive style, problem-solving, reflective.

cloud_download PDF
Cite
Article Metrics
Views
501
Download
530
Citations
Crossref
2

Scopus
2

References

Aljarrah, A. (2020). Describing collective creative acts in a mathematical problem-solving environment. Journal of Mathematical Behavior, 60, Article 100819. https://doi.org/10.1016/j.jmathb.2020.100819

Altun, A., & Cakan, M. (2006). Undergraduate students’ academic achievement, field dependent/independent cognitive styles and attitude toward computers. Educational Technology & Society, 9(1), 289–297. https://cutt.ly/uNNTe0H  

Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). APOS theory. Springer. https://doi.org/10.1007/978-1-4614-7966-6

Arum, D. P., Kusmayadi, T. A., & Pramudya, I. (2018). Students’ difficulties in probabilistic problem-solving. Journal of Physics: Conference Series, 983, Article 012098. https://doi.org/10.1088/1742-6596/983/1/012098

Atteh, E., Andam, E., & Denteh, W. O. (2017). Problem solving framework for mathematics discipline. Asian Research Journal of Mathematics, 4(4), 1–11. https://doi.org/10.9734/arjom/2017/32586

Avcu, S., & Avcu, R. (2010). Pre-service elementary mathematics teacher’s use of strategies in mathematical problem solving. Procedia - Social and Behavioral Sciences, 9, 1282–1286. https://doi.org/10.1016/j.sbspro.2010.12.321

Bintoro, H. S., Sukestiyarno, Y. L., Mulyono, & Walid. (2021). The spatial thinking process of the field-independent students based on action-process-object-schema theory. European Journal of Educational Research, 10(4), 1807–1823. https://doi.org/10.12973/eu-jer.10.4.1807

Boonen, A. J. H., Van Wesel, F., Jolles, J., & Van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001

Borji, V., Font, V., Alamolhodaei, H., & Sánchez, A. (2018). Application of the complementarities of two theories , apos and osa , for the analysis of the university students ’ understanding on the graph of the function and its derivative. EURASIA Journal of Mathematics, Science and Technology Education, 14(6), 2301–2315. https://doi.org/10.29333/ejmste/89514

Branca, N. A. (1980). Problem solving as a goal, process and basic skill. In D. Krulik (Ed.), Problem Solving in School Mathematics. National Council of Teachers of Mathematics.

Cahyono, B., Kartono, Waluyo, B., & Mulyono. (2019). Analysis critical thinking skills in solving problems algebra in terms of cognitive style and gender. Journal of Physics: Conference Series, 1321, Article 022115. https://doi.org/10.1088/1742-6596/1321/2/022115

Cartwright, K. (2020). Analyzing students’ communication and representation of mathematical fluency during group tasks. Journal of Mathematical Behavior, 60, Article 100821. https://doi.org/10.1016/j.jmathb.2020.100821

Cataloglu, E., & Ates, S. (2014). The effects of cognitive styles on naive impetus theory application degrees of pre-service science teacher. International Journal of Science and Mathematics Education, 12, 699–719. https://doi.org/10.1007/s10763-013-9430-z

Chagwiza, C. J., Sunzuma, G., & Mutambara, L. H. N. (2021). Exploring Zimbabwean a-level mathematics learners’ understanding of the determinant concept. European Journal of Mathematics and Science Education, 2(2), 85-100. https://doi.org/10.12973/ejmse.2.2.85  

Colbert, J., Brown, R., Choi, S., & Thomas, S. (2008). An investigation of the impacts of teacher-driven professional development on pedagogy and student learning. Teacher Education Quarterly, 35(2), 135–154.

Cresswell, J. W. (2014). Research design. Sage Publications, Inc.

Docktor, J. L., Dornfeld, J., Frodermann, E., Heller, K., Hsu, L., Jackson, K. A., Mason, A., Ryan, Q. X., & Yang, J. (2016). Assessing student written problem solutions: A problem-solving rubric with application to introductory physics. Physical Review Physics Education Research, 12(1), 1-18. https://doi.org/10.1103/PhysRevPhysEducRes.12.010130

Drijvers, P., Kodde-Buitenhuis, H., & Doorman, M. (2019). Assessing mathematical thinking as part of curriculum reform in the netherlands. Educational Studies in Mathematics, 102, 435–456. https://doi.org/10.1007/s10649-019-09905-7

Dubinsky, E. D., & Mcdonald, M. A. (2001). APOS : A constructivist theory of learning in undergraduate mathematics education research. In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study (pp. 275–282). Kluwer Academic. https://doi.org/10.1007/0-306-47231-7_25

Estrada, A., Batanero, C., & Diaz, C. (2018). Exploring teachers’ attitudes towards probability and its teaching. In C. Batanero & E. J. Chernoff (Eds.), Teaching and learning stochastics (pp. 313–332). Springer. https://doi.org/10.1007/978-3-319-72871-1_18

Gök, T., & Sýlay, I. (2010). The Effects of problem solving strategies on students’ achievement, attitude and motivation. Latin-American Journal of Physics Education, 4(1), 7–21. https://cutt.ly/9NNTuW2   

Gravemeijer, K., Stephan, M., Julie, C., Lin, F. L., & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education, 15, 105–123. https://doi.org/10.1007/s10763-017-9814-6

Güner, P., & Erbay, H. N. (2021). Prospective mathematics teachers’ thinking styles and problem-solving skills. Thinking Skills and Creativity, 40, Article 100827. https://doi.org/10.1016/j.tsc.2021.100827

Hidayatullah, A. (2019). Comparison of processes construct concept of SOLO theory And APOS theory in mathematics learning. Humanities & Social Sciences Reviews, 7(3), 432–437. https://doi.org/10.18510/hssr.2019.7363

Hoogland, K., de Koning, J., Bakker, A., Pepin, B. E. U., & Gravemeijer, K. (2018). Changing representation in contextual mathematical problems from descriptive to depictive: The effect on students’ performance. Studies in Educational Evaluation, 58, 122–131. https://doi.org/10.1016/j.stueduc.2018.06.004

Ifelunni, C. O., Ezema, V. S., Ugwu, G. C., Eze, C. O., & Ncheke, D. C. (2022). Cognitive Styles as a correlate of pupils’ academic achievement in South-East, Nigeria. International Journal of Social Science And Human Research, 5(1), 159–166. https://doi.org/10.47191/ijsshr/v5-i1-24

Inglis, M. (2015). Review of APOS Theory. International Journal of Research in Undergraduate Mathematics Education, 1, 413–417. https://doi.org/10.1007/s40753-015-0015-9

Junarti, Sukestiyarno, Y. L., Mulyono, & Dwidayanti, N. K. (2020). The Process of structure sense of group prerequisite material: A case in Indonesian context. European Journal of Educational Research, 9(3), 1047–1061. https://doi.org/10.12973/eu-jer.9.3.1047

Kagan, J. (1965). Impulsive and reflective children. In J. D. Krumboltz (Ed.), Learning and the educational process (pp. 133-161). Rand Mc Nally.

Konold, C. (2017). Issues in assessing conceptual understanding in probability and statistics. Journal of Statistics Education, 3(1), 1-9. https://doi.org/10.1080/10691898.1995.11910479

Kozhevnikov. (2007). Cognitive Styles in the context of modern psychology: Toward an integrated framework of cognitive style. Psychological Bulletin, 133(3), 464–481. https://doi.org/10.1037/0033-2909.133.3.464

Krawec, J. L. (2014). Problem representation and mathematical problem solving of students of varying math ability. Journal of Learning Disabilities, 47(2), 103–115. https://doi.org/10.1177/0022219412436976

Lee, C. I. (2017). An appropriate prompts system based on the Polya method for mathematical problem-solving. Eurasia Journal of Mathematics, Science and Technology Education, 13(3), 893–910. https://doi.org/10.12973/eurasia.2017.00649a

Margunayasa, I. G., Dantes, N., Marhaeni, A. A. I., & Suastra, I. W. (2019). The effect of guided inquiry learning and cognitive style on science learning achievement. International Journal of Instruction, 12(1), 737–750. https://doi.org/10.29333/iji.2019.12147a

Marzano, R. J., Brandt, R. S., Hughes, A. S., Jones, B. F., Presseisen, B. Z., Rankin, S. C., & Suhor, C. (1988). Dimension of thinking: A framework for curriculum and instruction. Association for Supervision and Curriculum Development.

Masel, J., Humphrey, P. T., Blackburn, B., & Levine, J. A. (2015). Evidence-based medicine as a tool for undergraduate probability and statistics education. CBE Life Sciences Education, 14(4), 1–10. https://doi.org/10.1187/cbe.15-04-0079

Michalska, P., & Zajac, L. (2015). The measurement of cognitive style reflection-impulsivity in the adulthood-result of own study. Polskie Forum Psychlgiczne, 20(4), 1–6. https://s.id/1jqcw

Moll, V. F., Trigueros, M., Badillo, E., & Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educational Studies in Mathematics, 91, 107–122. https://doi.org/10.1007/s10649-015-9639-6

Mora, M. C. G., Vera-Monroy, S. P., Mejía-Camacho, A., & Rueda, W. J. G. (2021). Perception channels and cognitive styles: Opponents, followers or learning allies? Heliyon, 7, Article e06242. https://doi.org/10.1016/j.heliyon.2021.e06242

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Authur.

Olesova, A. P., & Borisova, U. S. (2016). Formation of professional-communicative competence of the future teachers in the conditions of the Yakut-Russian bilingualism. International Electronic Journal of Mathematics Education, 11(10), 3435–3445. https://cutt.ly/gNNTok4

Ott, N., Brünken, R., Vogel, M., & Malone, S. (2018). Multiple symbolic representations: The combination of formula and text supports problem solving in the mathematical field of propositional logic. Learning and Instruction, 58, 88–105. https://doi.org/10.1016/j.learninstruc.2018.04.010

Pakarinen, E., & Kikas, E. (2019). Child-centered and Teacher-directed practices in relation to calculation and word problem solving skills. Learning and Individual Differences, 70, 76–85. https://doi.org/10.1016/j.lindif.2019.01.008

Peng, A., Cao, L., & Yu, B. (2020). Reciprocal learning in mathematics problem posing and problem solving: an interactive study between Canadian and Chinese elementary school students. EURASIA Journal of Mathematics, Science and Technology Education, 16(12), 1–13. https://doi.org/10.29333/ejmste/9130

Pisarenko, V. F. (2018). The notion of probability and difficulties of interpretation. Herald of the Russian Academy of Sciences, 88(4), 289–293. https://doi.org/10.1134/S1019331618040056

Polya, G. (1971). How to solve it: a new aspect of mathematics method. Princeton University Press.

Pujiastuti, E., Waluya, B., & Mulyono. (2018). Tracing for the problem-solving ability in advanced calculus class based on modification of SAVI model at Universitas Negeri Semarang. Journal of Physics: Conference Series, 983, Article 012081. https://doi.org/10.1088/1742-6596/983/1/012081

Rahayu, R., & Kartono. (2014). The Effect of mathematical disposition on PMRI toward problem solving ability based on Ideal problem solver. International Journal of Science and Research, 3(10), 1315–1318. https://cutt.ly/gNNTaxa

Rozencwajg, P., & Corroyer, D. (2005). Cognitive processes in the reflective-impulsive cognitive style. The Journal of Genetic Psychology, 166(4), 451–463. https://doi.org/10.3200/GNTP.166.4.451-466

Selçuk, G. S., Çalişkan, S., & Erol, M. (2008). The effects of problem solving instruction on physics achievement, problem solving performance, and strategy use. Latin-American Journal of Physics Education, 2(3), 151–166. https://cutt.ly/jNNTdm6

Sezgin-Memnun, D., Ozbilen, O., & Dinc, E. (2019). A qualitative research on the difficulties and failures about probability concepts of high school students. Journal of Educational Issues, 5(1), 1–19. https://doi.org/10.5296/jei.v5i1.14146

Son, A. L., & 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

Suarsana, I. M., Lestari, I. A. P. D., & Mertasari, N. M. S. (2019). The Effect of online problem posing on students ’ problem-solving abilitiy in mathematics. International Journal of Instruction, 12(1), 809–820. https://doi.org/10.29333/iji.2019.12152a

Subanji, & Nusantara, T. (2016). Thinking process of pseudo construction in mathematics concepts. International Education Studies, 9(2), 17–31. https://doi.org/10.5539/ies.v9n2p17

Sudarsono, Kartono, Mulyono, & Mariani, S. (2022). The effect of STEM Model based on bima’s local cultural on problem solving ability. International Journal of Instruction, 15(2), 83–96. https://doi.org/10.29333/iji.2022.1525a

Sumaji, Sa’dijah, C., Susiswo, & Sisworo. (2020). Mathematical communication process of junior high school students in solving problems based on APOS Theory. Journal for the Education of Gifted Young Scientists, 8(1), 197–221. https://doi.org/10.17478/jegys.652055

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

Sutarto, Nusantara, T., Subanji, Hastuti, I. D., & Dafik. (2018). Global conjecturing process in pattern generalization problem global conjecturing process in pattern generalization problem. Journal of Physics: Conference Series, 1008, Article 012060. https://doi.org/10.1088/1742-6596/1008/1/012060

Tam, Y. P., Wong, T. T. Y., & Chan, W. W. L. (2019). The relation between spatial skills and mathematical abilities: The mediating role of mental number line representation. Contemporary Educational Psychology, 56, 14–24. https://doi.org/10.1016/j.cedpsych.2018.10.007

Tobia, V., Bonifacci, P., & Marzocchi, G. M. (2021). Symbolic versus non-symbolic training for improving early numeracy in preschoolers at risk of developing difficulties in mathematics. Research in Developmental Disabilities, 111, Article 103893. https://doi.org/10.1016/j.ridd.2021.103893

Triliana, T., & Asih, E. C. M. (2019). Analysis of students’ errors in solving probability based on Newman’s error analysis. Journal of Physics: Conference Series, 1211, Article 012061. https://doi.org/10.1088/1742-6596/1211/1/012061

Warli. (2013). Kreativitas siswa SMP yang bergaya kognitif reflektif atau impulsif dalam memecahkan masalah geometri [The creativity of junior high school students with reflective or impulsive cognitive style in solving geometric problems]. Paedagogi. Jurnal Pendidikan dan Pembelajaran, 20(2), 190-201. https://cutt.ly/ONNTg3W    

Wulandari, T. S. H., Astuti, H. P., & Cintamulya, I. (2020). Analysis of Students’ critical thinking abilities using the pdeode strategy in terms of cognitive style through online learning. Procedia of Social Sciences and Humanities, 1, 19–26. https://doi.org/doi.org/10.21070/pssh.v1i.3

 

...