Transformations of students’ cognitive processes when solving PISA-like problems: A commognitive analysis
DOI:
https://doi.org/10.29408/jel.v12i1.30715Keywords:
cognitive process, commognitive, mathematical literacy, PISA-like mathematical problemsAbstract
The mathematical literacy of Indonesian students in PISA 2022 was categorized as low, highlighting the importance of understanding students’ cognitive processes in mathematical problem solving. This study examines transformations in the cognitive processes of a 15-year-old Indonesian student when solving PISA-like problems using Sfard’s commognitive framework. A qualitative approach was employed to capture detailed learning dynamics. The participant was a 15-year-old student from a randomly selected junior high school in Rembang Regency, Central Java Province, Indonesia, purposefully selected based on the mathematics teacher’s nomination for strong mathematical ability and clear evidence of cognitive shifts during problem solving. The tasks were developed by the researcher and adapted to relevant Indonesian contexts. Qualitative data—including written work, observations, and semi-structured interviews—were analyzed using mathematical literacy processes (formulating, employing, interpreting, and evaluating) and mapped onto four commognitive components: Word Use (WU), Visual Mediators (VM), Routines (R), and Narratives (N). Findings show that reflective self-evaluation supports cognitive restructuring, enabling movement from procedural errors toward coherent reasoning through shifts in WU, VM, and R. The study underscores the need for instructional designs that foster meta-level discourse, reflective thinking, and flexible visual re-representation to strengthen students’ mathematical reasoning.
References
Albab, I. U., Albab, I. U., Hartono, Y., & Darmawijoyo, D. (2014). Kemajuan belajar siswa pada geometri transformasi menggunakan aktivitas refleksi geometri [Students’ learning progress in transformation geometry through geometric reflection activities. Jurnal Cakrawala Pendidikan, 33(3). https://doi.org/10.21831/cp.v3i3.2378
Alvidrez, M., Louie, N., & Tchoshanov, M. (2022). From mistakes, we learn? mathematics teachers’ epistemological and positional framing of mistakes. Journal of Mathematics Teacher Education, 1–26. https://doi.org/10.1007/s10857-022-09553-4
Andrews, P. (2015). Mathematics, PISA, and culture: An unpredictable relationship. Journal of Educational Change, 16(3), 251 – 280. https://doi.org/10.1007/s10833-015-9248-2
Annizar, A. M., Maulyda, M. A., Khairunnisa, G. F., & Hijriani, L. (2020). Kemampuan pemecahan masalah matematis siswa dalam menyelesaikan soal pisa pada topik geometri [Students’ mathematical problem-solving ability in completing PISA tasks on the topic of geometry]. Jurnal Elemen, 6(1), 39–55. https://doi.org/10.29408/jel.v6i1.1688
Asmara, A. S., Waluya, S. B., Suyitno, H., Junaedi, I., & Ardiyanti, Y. (2024). Developing patterns of students’ mathematical literacy processes: insights from cognitive load theory and design-based research. Infinity Journal, 13(1), 197 – 214. https://doi.org/10.22460/infinity.v13i1.p197-214
Barwell, R. (2016). Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic. Educational Studies in Mathematics, 92(3), 331 – 345. https://doi.org/10.1007/s10649-015-9641-z
Bayirli, E. G., Kaygun, A., & Öz, E. (2023). An analysis of PISA 2018 mathematics assessment for Asia-Pacific countries using educational data mining. Mathematics, 11(6). https://doi.org/10.3390/math11061318
Boaler. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. https://psycnet.apa.org/record/2016-07883-000
Borji, V., Radmehr, F., & Font, V. (2021). The impact of procedural and conceptual teaching on students’ mathematical performance over time. International Journal of Mathematical Education in Science and Technology, 52(3), 404–426. https://doi.org/10.1080/0020739X.2019.1688404
Chua, V. C. (2021). Improving learners’ productive disposition through realistic mathematics education, a teacher’s critical reflection of personal pedagogy. Reflective Practice, 22(6), 809 – 823. https://doi.org/10.1080/14623943.2021.1974373
Cooper, J., & Lavie, I. (2021). Bridging incommensurable discourses – A commognitive look at instructional design in the zone of proximal development. The Journal of Mathematical Behavior, 61, 100822. https://doi.org/10.1016/J.JMATHB.2020.100822
DeCaro, M. S. (2016). Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics. Memory and Cognition, 44(7), 1138–1148. https://doi.org/10.3758/s13421-016-0614-y
Fenanlampir, A., Batlolona, J. R., & Imelda, I. (2019). The struggle of Indonesian students in the context of TIMSS and PISA has not ended. International Journal of Civil Engineering and Technology, 10(2), 393–406. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85063559674&partnerID=40&md5=95e70ac6e2de86be429219d7273ae603
Heyd-Metzuyanim, E., & Graven, M. (2019). Rituals and explorations in mathematical teaching and learning: introduction to the special issue. Educational Studies in Mathematics, 101(2), 141–151. https://doi.org/10.1007/s10649-019-09890-x
Heyd-Metzuyanim, E., & Sfard, A. (2012). Identity struggles in the mathematics classroom: On learning mathematics as an interplay of mathematizing and identifying. International Journal of Educational Research, 51–52, 128–145. https://doi.org/10.1016/j.ijer.2011.12.015
Hough, S., & Solomon, Y. (2023). Teacher development for equitable mathematics classrooms: reflecting on experience in the context of performativity. Education Sciences, 13(10). https://doi.org/10.3390/educsci13100993
Kholid, M. N., Sa'Dijah, C., Hidayanto, E., & Permadi, H. (2022). Students’ reflective thinking pattern changes and characteristics of problem solving. Reflective Practice, 23(3), 319–341. https://doi.org/10.1080/14623943.2021.2025353
Koichu, B., Schwarz, B. B., Heyd-Metzuyanim, E., Tabach, M., & Yarden, A. (2022). Design practices and principles for promoting dialogic argumentation via interdisciplinarity. Learning, Culture and Social Interaction, 37. https://doi.org/10.1016/j.lcsi.2022.100657
Kolar, V. M., & Hodnik, T. (2021). Mathematical literacy from the perspective of solving contextual problems. European Journal of Educational Research, 10(1), 467 – 483. https://doi.org/10.12973/eu-jer.10.1.467
Kusuma, D., Wardono, W., & Cahyono, A. N. (2021). The characteristics of mathematical literacy based on students’ executive function. European Journal of Educational Research, 11(1), 193–206. https://doi.org/10.12973/eu-jer.11.1.193
Legesse, M., Luneta, K., & Ejigu, T. (2020). Analyzing the effects of mathematical discourse-based instruction on eleventh-grade students’ procedural and conceptual understanding of probability and statistics. Studies in Educational Evaluation, 67. https://doi.org/10.1016/j.stueduc.2020.100918
Lu, J., Wu, S., Wang, Y., & Zhang, Y. (2022). Visualizing the commognitive processes of collaborative problem solving in mathematics classrooms. Asia-Pacific Education Researcher, 1–14. https://doi.org/10.1007/s40299-022-00681-2
Manalo, E., & Kapur, M. (2018). The role of failure in promoting thinking skills and creativity: New findings and insights about how failure can be beneficial for learning. Thinking Skills and Creativity, 30, 1–6. https://doi.org/10.1016/j.tsc.2018.06.001
Nachlieli, T., & Heyd-Metzuyanim, E. (2022). Commognitive conflicts as a learning mechanism towards explorative pedagogical discourse. Journal of Mathematics Teacher Education, 25(3), 347–369. https://doi.org/10.1007/s10857-021-09495-3
OECD. (2023). PISA 2022 assessment and analytical framework. OECD Publishing. https://doi.org/10.1787/dfe0bf9c-en
Oktiningrum, W., & Hartono, Y. (2016). Developing PISA-like mathematics task with Indonesia natural and cultural heritage as context to assess students’ mathematical literacy. Journal on Mathematics Education, 7(1), 1–8. https://doi.org/10.22342/jme.7.1.2812.1-8
Patton, M. Q. (2015). Four triangulation processes for enhancing credibility. In Qualitative research and evaluation methods: Integrating theory and practice. Sage Publication. https://uk.sagepub.com/en-gb/eur/qualitative-research-evaluation-methods/book232962
Presmeg, N. (2016). Commognition as a lens for research. Educ Stud Math, 91, 423–430. https://doi.org/10.1007/s10649-015-9676-1
Putri. (2020). Designing PISA-like mathematics task using asian games context. Journal on Mathematics Education, 11(1), 135–144. https://doi.org/10.22342/jme.11.1.9786.135-144
Putri, O. R. U., & Alfani, I. (2020). Mathematical connection process of students with high mathematics ability in solving PISA problems. European Journal of Educational Research, 9(4), 1527–1537. https://doi.org/10.12973/eu-jer.9.4.1527
Retnowati, E., Fathoni, Y., & Chen, O. (2018). Mathematics problem solving skill acquisition: Learning by Problem Posing or by Problem Solving? Jurnal Cakrawala Pendidikan, 37(1). https://doi.org/10.21831/cp.v37i1.18787
Safura, N. A., Aisyah, N., Hiltrimartin, C., & Indaryanti. (2018). Student’s mathematical value in mathematics learning using non-routine problem. Jurnal Cakrawala Pendidikan, 37(3), 400–412. https://doi.org/10.21831/cp.v38i3.19032
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: making sense of mathematics learning from a commognitive standpoint. Journal of the Learning Sciences, 16(4), 565–613. https://doi.org/10.1080/10508400701525253
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944
Stacey, K. (2011). The PISA view of mathematical literacy in Indonesia. Journal on Mathematics Education, 2(2), 95–126. https://doi.org/10.22342/jme.2.2.746.95-126
Stacey, K., & Turner, R. (2015). The evolution and key concepts of the PISA mathematics frameworks. In Assessing Mathematical Literacy: The PISA Experience (pp. 5–33). https://doi.org/10.1007/978-3-319-10121-7_1
Stovner, R. B., & Klette, K. (2022). Teacher feedback on procedural skills, conceptual understanding, and mathematical practices: A video study in lower secondary mathematics classrooms. Teaching and Teacher Education, 110. https://doi.org/10.1016/j.tate.2021.103593
Tabach, M., & Nachlieli, T. (2016). Communicational perspectives on learning and teaching mathematics: prologue. Educational Studies in Mathematics, 91(3), 299–306. https://doi.org/10.1007/S10649-015-9638-7
Thien, L. M., Darmawan, I. G. N., & Ong, M. Y. (2015). Affective characteristics and mathematics performance in Indonesia, Malaysia, and Thailand: what can PISA 2012 data tell us? Large-Scale Assessments in Education, 3(1). https://doi.org/10.1186/s40536-015-0013-z
Wijaya, A., Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. Mathematics Enthusiast, 11(3), 555–584. https://doi.org/10.54870/1551-3440.1317
Wijaya, T. T., Hidayat, W., Hermita, N., Alim, J. A., & Talib, C. A. (2024). Exploring contributing factors to PISA 2022 mathematics achievement: insights from indonesian teachers. Infinity Journal, 13(1), 139–156. https://doi.org/10.22460/infinity.v13i1.p139-156
Wijayanto, Z., Sukestiyarno, W., K, & Pujiastuti, E. (2024). Analysis of mathematical literacy through the lens of students’ spatial geometry aptitude. Jurnal Cakrawala Pendidikan, 43(3), 746–755. https://doi.org/10.21831/cp.v43i3.65013
Yin. (2018). Case study research and applications sixth edition. Sage Publication. https://uk.sagepub.com/en-gb/eur/case-study-research-and-applications/book250150
Zayyadi, M., Nusantara, T., Subanji, S., Hidayanto, E., & Sulandra, I. M. (2019). A commognitive framework: The process of solving mathematical problems of middle school students. International Journal of Learning Teaching and Educational Research, 18(2), 89–102. https://doi.org/10.26803/ijlter.18.2.7
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