Uncovering Critical Thinking and Mathematical Representation Skills of Pre-Service Elementary Teachers Through Cognitive Style

Achmad Salido; Sugiman Sugiman; Fery Muhamad  Firdaus; Agung Prihatmojo; Agus  Herwanto; Eka  Yuni Andari; Widiya Saputri  Wulandari; Lussy  Midani Rizki

doi:10.48161/qaj.v5n2a1505

Authors

Achmad Salido Department of Primary Education Doctoral, Faculty of Education and Psychology, Universitas Negeri Yogyakarta, Yog-yakarta, 55281, Indonesia; Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Sembilanbelas November Kolaka, Kolaka, 93517, Indonesia;
Sugiman Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta, Yogyakarta, 55281, Indonesia;
Fery Muhamad Firdaus Department of Primary School Education, Faculty of Education and Psychology, Universitas Negeri Yogyakarta, Yogya-karta, 55281, Indonesia;
Agung Prihatmojo Department of Primary Education Doctoral, Faculty of Education and Psychology, Universitas Negeri Yogyakarta, Yog-yakarta, 55281, Indonesia;
Agus Herwanto Universitas Negeri Department of Primary Education Magister, Faculty of Education and Psychology, Universitas Negeri Yogyakarta, Yog-yakarta, 55281, Indonesia;
Eka Yuni Andari Department of Primary Education Magister, Faculty of Education and Psychology, Universitas Negeri Yogyakarta, Yog-yakarta, 55281, Indonesia;
Widiya Saputri Wulandari Department of Primary Education Magister, Faculty of Education and Psychology, Universitas Negeri Yogyakarta, Yog-yakarta, 55281, Indonesia;
Lussy Midani Rizki Department of Mathematics Education Doctoral, Faculty of Mathematics and Science Education, Universitas Pendidikan Indonesia, Bandung, 40154, Indonesia;Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Pahlawan Tuanku Tambusai, Kampar, 28412, Indonesia.

DOI:

https://doi.org/10.48161/qaj.v5n2a1505

Abstract

This study examines the critical thinking and mathematical representation abilities of pre-service elementary school teachers’ students (PESTS) through the lens of field-dependent (FD) and field-independent (FI) cognitive styles. Using a qualitative descriptive approach, 39 participants completed the Group Embedded Figures Test (GEFT), problem-solving tasks, and semi-structured interviews to assess cognitive styles and representation skills. Results indicate that FD participants struggled with problem-solving, relying on prior experiences, providing superficial solutions, and using primarily symbolic and numerical representations with limited abstraction. In contrast, FI participants demonstrated more assertive critical thinking, systematically employing diverse representations including symbols, mathematical expressions, and verbal explanations to solve problems independently. These differences underscore the need for differentiated instruction, with the FD learners requiring structured support to enhance critical thinking and broaden their representation skills. The FI learners should be challenged with abstract and complex tasks to enhance their skills further. Personalized, adaptive learning strategies are essential to preparing future educators for the challenges of 21st-century teaching.

Downloads

Download data is not yet available.

Author Biographies

Achmad Salido , Department of Primary Education Doctoral, Faculty of Education and Psychology, Universitas Negeri Yogyakarta, Yog-yakarta, 55281, Indonesia; Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Sembilanbelas November Kolaka, Kolaka, 93517, Indonesia;

Achmad Salido M.Pd. (corresponding author) is a doctoral student in Elementary Education Study Program, Faculty of Education and Psychology, Universitas Negeri Yogyakarta, Indonesia. He is also a lecturer and researcher at Universitas Sembilanbelas November Kolaka, Indonesia. His main research interests are mathematics education and mathematical thinking.

Sugiman , Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta, Yogyakarta, 55281, Indonesia;

Dr Sugiman is a Professor at Universitas Negeri Yogyakarta, Indonesia. He obtained his doctorate degree from Universitas Pendidikan Indonesia. He actively engaged in diverse research endeavors and disseminated his findings through publication in reputable international journals. His main line of research is mathematics education

Lussy Midani Rizki , Department of Mathematics Education Doctoral, Faculty of Mathematics and Science Education, Universitas Pendidikan Indonesia, Bandung, 40154, Indonesia;Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Pahlawan Tuanku Tambusai, Kampar, 28412, Indonesia.

Lussy Midani Rizki is a doctoral student in Mathematics Education Study Program, Faculty of Mathematics and Science Education, Universitas Pendidikan Indonesia. She is also a lecturer and researcher at Universitas Pahlawan Tuanku Tambusai, Indonesia. Her main research interest is mathematics education

References

Facione, P. A. (2011). Critical thinking: What it is and why it counts. Insight Assessment, 1(1), 1–23.

Spector, J. M., & Ma, S. (2019). Inquiry and critical thinking skills for the next generation: from artificial intelligence back to human intelligence. Smart Learning Environments, 6(1), 1-11.

Kusaeri, & Aditomo, A. (2019). Pedagogical beliefs about critical thinking among Indonesian mathematics pre-service teachers. International Journal of Instruction, 12(1), 573–590.

Sosa-Gutierrez, F., Apaza, H. M. V., Valdivia-Yábar, S. V., & Condori-Castillo, W. W. (2024). Critical thinking and teaching mathematics: An analysis from education. International Journal of Religion, 5(9), 958–976.

Setiana, D. S., Purwoko, R. Y., & Sugiman. (2021). The application of mathematics learning model to stimulate mathematical critical thinking skills of senior high school students. European Journal of Educational Research, 10(1), 509–523.

Fonseca, L., & Arezes, S. (2017). A didactic proposal to develop critical thinking in mathematics: The case of Tomás. Journal of the European Teacher Education Network, 12, 37–48.

Pentang, J. T., Bautista, R. M., Viernes, M. D. D., Caubang, M. G. M., Tidalgo, A. M. L., Morizo, S. B., Sercenia, J. C., & Bucad, M. L. (2023). Demystifying the relationship between confidence and critical thinking in mathematics among preservice teachers in West Philippines. European Journal of Educational Research, 12(4), 1743–1754.

Afriansyah, E. A., Herman, T., Turmudi, & Dahlan, J. A. (2021). Critical thinking skills in mathematics. Journal of Physics: Conference Series, 1778(1).

Karakoç, M. (2016). The significance of critical thinking ability in terms of education. International Journal of Humanities and Social Science, 6(7), 81–84.

Cartwright, K. (2023). Interpreting young children’s multiplicative strategies through their drawn representations. Mathematics Education Research Journal, 36(2), 367-397.

Putra, F. G., Lengkana, D., Sutiarso, S., Nurhanurawati, Saregar, A., Diani, R., Widyawati, S., Suparman, Imama, K., & Umam, R. (2024). Mathematical representation: A bibliometric mapping of the research literature (2013–2022). Infinity Journal, 13(1), 1–26.

Cendekiawaty, T., & Sugiman, S. (2020). Realistic mathematics education: An alternative to improve students’ understanding of fraction concept. Journal of Physics: Conference Series, 1581(1).

Duma’, S. Y., Sa’dijah, C., Hidayanto, E., & Irawati, S. (2023). Analytic geometry problems are completed by symbolic visualization of representation: A case of a future teacher. Journal of Higher Education Theory and Practice, 23(20), 55–64.

Sokolowski, A. (2018). The effects of using representations in elementary mathematics: Meta-analysis of research. IAFOR Journal of Education, 6(3), 129–152.

Rianasari, V. F., & Apriani, M. S. (2019). Pre-service mathematics teachers’ knowledge about higher-order thinking skills. Journal of Physics: Conference Series, 1366(012083), 1–9.

Arifuddin, A. (2020). The analysis of critical thinking skills of primary school teacher candidates in solving mathematical problems. Al Ibtida: Jurnal Pendidikan Guru MI, 7(1), 46–55.

Farokhah, L., Herman, T., & Jupri, A. (2019). Students’ ability of mathematical representation on statistics topic in elementary school. Journal of Physics: Conference Series, 1157(3).

Li, C., Mu, X., Tan, Y., Gu, C., Hu, B. Y., & Fan, C. (2020). Do field-dependent individuals tend to have lower creativity than field-independent ones? The role of informational cues in electronic brainstorming. Interactive Learning Environments, 31(2), 1106-1125.

Izzatin, M., Waluyo, S. B., Rochmad, & Wardono. (2020). Students’ cognitive style in mathematical thinking process. Journal of Physics: Conference Series, 1613(1).

Kholid, M. N., Hamida, P. S., Pradana, L. N., & Maharani, S. (2020). Students‘ critical thinking depends on their cognitive style. International Journal of Scientific and Technology Research, 9(1), 1045–1049

Son, A. L., Darhim, D., & Fatimah, S. (2020). Students ’ mathematical problem -solving ability based on teaching models intervention and cognitive style. Journal on Mathematics Education, 11(2), 209–222.

Giancola, M., Palmiero, M., & D’amico, S. (2022). Field dependent–independent cognitive style and creativity from the process and product-oriented approaches: A systematic review. Creativity Studies, 15(2), 542–559.

Lee, M. Y., & Lee, J.-E. (2019). Pre-service teachers’ perceptions of the use of representations and suggestions for students’ incorrect use. Eurasia Journal of Mathematics, Science and Technology Education, 15(9), 1–21.

Saputro, A. D., Atun, S., Wilujeng, I., Ariyanto, A., & Arifin, S. (2020). Enhancing pre-service elementary teachers’ self-efficacy and critical thinking using problem-based learning. European Journal of Educational Research, 9(2), 765–773.

van Garderen, D., Scheuermann, A., Sadler, K., Hopkins, S., & Hirt, S. M. (2021). Preparing pre-service teachers to use visual representations as strategy to solve mathematics problems: what did they learn?. Teacher Education and Special Education, 44(4), 319-339.

Domingo, J. G., Ibañez, E. D., Subia, G. S., Pentang, J. T., Gamit, A. M., Pascual, L. E., Mina, J. C., Tomas, A. V., & Liangco, M. M. (2021). Cognitive skills achievement in mathematics of the elementary pre-service teachers using piaget’s seven logical operations. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12(4), 435–440.

Kivunja, C. (2014). Do you want your students to be job-ready with 21st century skills? Change pedagogies: A pedagogical paradigm shift from Vygotskyian social constructivism to critical thinking, problem solving and Siemens’ digital connectivism. International Journal of Higher Education, 3(3), 81–91.

Ariza, M. R., Armenteros, A. Q., & Castro, A. E. (2024). Promoting critical thinking through mathematics and science teacher education: the case of argumentation and graphs interpretation about climate change. European Journal of Teacher Education, 47(1), 41–59.

Maharani, S., Nusantara, T., As’ari, A. R., & Qohar, A. (2019). Analyticity and systematicity students of mathematics education on solving non-routine problems. Mathematics and Statistics, 7(2), 50–55.

Gashan, A. K. (2015). Exploring saudi pre-service teachers’ knowledge of critical thinking skills and their teaching perceptions. International Journal of Education and Literacy Studies, 3(1), 26–33.

Duangngern, P., Kwangmuang, P., & Nguyen, L. T. (2023). Next normal teaching and learning: perceptions and readiness of pre-service teachers to promote critical and creative thinking. IIAI Letters on Institutional Research, 3.

Wang, Q., & Abdullah, A. H. (2024). Enhancing Students’ Critical Thinking Through Mathematics in Higher Education: A Systemic Review. SAGE Open, 14(3), 21582440241275651.

Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17(2), 137–165.

Firdaus, F. M., Azizah, I. N., Pritin, S., Damayanti, O., & Annisa, F. C. (2022). The development of articulate storyline-based learning media to improve 5th grade students’ mathematical representation ability. Al Ibtida: Jurnal Pendidikan Guru MI, 9(1), 55-73.

Ahmad, Akhsani, L., & Mohamed, Z. (2023). The profile of students’ mathematical representation competence, self-confidence, and habits of mind through problem-based learning models. Infinity Journal, 12(2), 323–338.

Syah, A., Harizahayu, H., Haddar, G. Al, Annisah, A., & Pratiwi, E. Y. R. (2023). Improving students’ mathematical problem-solving ability through the use of external representations. Journal on Education, 5(2), 5313–5323.

Man, Y. L., Asikin, M., & Sugiman, S. (2022). Systematic literature review: Students’ mathematical representation ability in mathematics learning. Daya Matematis : Jurnal Inovasi Pendidikan Matematika, 10(1), 36–44.

Isyam, Y. A. N., & Hidayati, K. (2022). Students’ mathematical representation in solving mathematical problems. AIP Conference Proceedings, 2575(1), 80026.

Hariyani, M., & Andriani, M. (2023). The Importance of Mathematical Representation Ability for Elementary School Students: A Literature Review and Its Implications. Syekh Nurjati International Conference on Elementary Education (SICEE), 1, 38–46.

Eroles, M. O., & Ching, D. A. (2021). Mental representation and critical thinking in problem solving. In 1st IIARI Research Competitions. Institute of Industry and Academic Research Incorporated.

Dinçer, B. (2022). The relationship between multiple representations and thinking structures: example of the integral concept. Journal for the Education of Gifted Young Scientists, 10(4), 563–571.

Sobirin, J. H., Setiawan, Y. E., & Faradiba, S. S. (2023). Mathematical representations based on field-dependent and field-independent cognitive styles. Journal of Mathematics Education, 8(2), 137–149.

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.

Hasbullah, H., & Sajiman, S. U. (2020). The differences of cognitive style fields-independent and dependent on students’ mathematical problem solving abilities. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(2), 387–394.

Setiawan, A., Degeng, I. N. S., Sa’dijah, C., & Praherdhiono, H. (2021). Collaborative problem-solving strategies and cognitive style: The impact and interaction on students’ mathematical reasoning abilities. Psychology and Education Journal, 58(2), 841–848.

Listiagfiroh, W., & Ellianawati, E. (2019). A problem based learning: Practicing students’ critical thinking skills with cognitive style dependent fields and independent fields. Jurnal Penelitian & Pengembangan Pendidikan Fisika, 5(2), 169–176.

Bakar, Z. A., & Ali, R. (2018). Interchangeable concept of cognitive styles and learning styles: A conceptual analysis. Journal of Education and Learning (EduLearn), 12(2), 179–187.

Hedayat Panah, A. (2010). Study and investigation of the problems and learning disorders of students by various cognitive styles in mathematics course at Rasht Shahid Chamran higher education center. Journal of Mathematics and Computer Science, 01(03), 216–229.

Facione, P. A., Facione, N. C., Riegel, F., Martini, J. G., & Crossetti, M. da G. O. (2021). Holistic critical thinking in times of covid-19 pandemic: unveiling fundamental skills to clinical nursing practice. Revista Gaucha de Enfermagem, 42(3), 3–5.

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis A Methods Sourcebook Edition 3. SAGE Publications, Inc.

Amini, N. U., Maimunah, M., & Roza, Y. (2019). Analysis students’ critical thinking skills in terms of cognitive style. Matematika Dan Pembelajaran, 7(2), 51–69.

Salwah, S., Ashari, N. W., & Ma’Rufi, M. (2020). Mathematical critical thinking ability of students grade VII in solving one variable linear equation questions based on their cognitive style. Journal of Physics: Conference Series, 1470 (1), 1–6.

Sutama, S., Anif, S., Prayitno, H. J., Narimo, S., Fuadi, D., Sari, D. P., & Adnan, M. (2021). Metacognition of junior high school students in mathematics problem solving based on cognitive style. Asian Journal of University Education, 17(1), 134–144.

Nasrullah, N. (2023). Students’ mathematical representation ability in terms of field dependent and field independent cognitive styles of Quadrilateral Flat material. International Journal of Trends in Mathematics Education Research, 6(2), 113–117.

Afifah, D. S. N., & Ningrum, R. L. (2018). Critical thinking of field dependent student’s in problem solving. International Journal on Teaching and Learning Mathematics, 1(1), 31–38.

Hardiansyah, F., Armadi, A., AR, M. M., & Wardi, M. (2024). Analysis of field dependent and field independent cognitive styles in solving science problems in elementary schools. Jurnal Penelitian Pendidikan IPA, 10(3), 240–247.

Budayasa, I. K., & Juniati, D. (2019). The influence of cognitive style on mathematical communication of prospective math teachers in solving problems. Journal of Physics: Conference Series, 1417(1).