Students’ commognition in solving linear programming question
DOI:
https://doi.org/10.29408/jel.v12i2.34184Keywords:
cognition, commognition, communication, linear programmingAbstract
Although mathematical communication is considered important, students' ability to express mathematical ideas effectively is still not good. Therefore, this research is going to use commognitive framework that provides a valuable lens for analyzing and enhancing students' mathematical communication skills. The purpose of this study is to describe students' commognition in solving linear programming problem. The researcher selected six students for interviews based on the consistency of their answers then selected two students from the six students who had been interviewed. Commognition analysis shows striking differences in mathematical thinking and communication between DAJ and ED subjects as student with high and low commognitive ability. Student with high commognitive ability tends to be more comprehensive and exploratory. In contrast, student with low commognitive ability is relatively more limited and procedural. This implies that teachers can not judge understanding only from whether students reach the correct answer. They must also attend to how students talk, write, and represent mathematics, since these discursive moves reveal whether their routines are genuinely conceptual or merely imitative. As a result, it is advised that future studies include a group discussion, better developed question types, and more specified student criteria.
References
Akçakoca, T., Sağ, G. Y., & Argün, Z. (2024). Rituals and explorations in students’ mathematical discourses: The case of polynomial inequalities. Participatory Educational Research (PER), 11(1), 178–197. https://doi.org/10.17275/per.24.11.11.1
Bİber, M. (2023). Constructing mental models: mathematical communication and discourses in conceptual understanding. Journal of Necmettin Erbakan University Ereğli Faculty of Education, 5, 271–305. https://doi.org/10.51119/ereegf.2023.45
Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. Manhattan, New York: Springer
Campos, I. S., Almeida, L. S., Ferreira, A. I., Martinez, L. F., & Ramalho, G. (2013). Cognitive processes and math performance: A study with children at third grade of basic education. European Journal of Psychology of Education, 28(2), 421–436. https://doi.org/10.1007/s10212-012-0121-x
Caspi, S., & Sfard, A. (2012). Spontaneous meta-arithmetic as a first step toward school algebra. International Journal of Educational Research, 51-52, 45-65. https://doi.org/10.1016/j.ijer.2011.12.006
Chan, M. C. E., Moate, J., Clarke, D., Cunnington, R., Díez-Palomar, J., Friesen, M., Haataja, E., Hošpesová, A., Kuntze, S., Nieminen, J. H., Novotná, J., Ochôa, X., Sherwell, C., Trần, D., & Tuohilamp., L. (2022). Learning research in a laboratory classroom: A reflection on complementarity and commensurability among multiple analytical accounts. ZDM-Mathematics Education, 54. https://doi.org/10.1007/s11858-022-01330-0
Ching, M., Chan, E., & Sfard, A. (2020). On learning that could have happened: The same tale in two cities. Journal of Mathematical Behavior, 60(1). https://doi.org/10.1016/j.jmathb.2020.100815
Creswell, J. W. (2009). Research design: qualitative, quantitative, and mixed methods approaches (3rd ed.). Sage Publications, Inc.
Daher, W. (2012). Characteristics of middle school students learning actions in outdoor mathematical activities with the cellular phone. Teaching Mathematics and Its Applications, 31(3), 133-152. https://doi.org/10.1093/teamat/hrr018
Habibi, F., Sukma, D., & Padang, U. N. (2023). Improving Self-Concept through Effective Interpersonal Communication. Jurnal Iqra’ : Kajian Ilmu Pendidikan, 8(2), 1–16. https://doi.org/10.25217/ji.v8i2.2710
Heldeman, P. D., Flores, K. A., Sevler, L. M., Trouton, K. E. (2017). Effectiveness and Adoption of a Drawing-to-Learn Study Tool for Recall and Problem Solving: Minute Sketches with Folded Lists. CBE-Life Sciences Education, 16(2), 1-13. https://doi.org/10.1187/cbe.16-03-0116.
Ho, W. K., Hong, L. S., Tay, E. G., Leong, Y. H., & Ming, T. K. (2019, July). Passing a proof message: Student-teacher communication through a commognitive lens. Paper presented at 42nd Annual Conference of the Mathematics Education Research Group of Australasia. The Mathematics Education Research Group of Australasia Inc, Australia. https://repository.nie.edu.sg/bitstream/10497/21313/1/MERGA-2019-700.pdf
Iglesias-Sarmiento, V., & Deaño, M. (2011). Cognitive processing and mathematical achievement. Journal of Learning Disabilities, 44(6), 570–583. https://doi.org/10.1177/0022219411400749
Khadka, J. B. (2024). Role of mathematical communication for learning mathematics. Journal of Education Research and Innovation, 4(1), 68–76. https://doi.org/10.3126/jeri.v4i1.75791
Kieran, C. (2001). The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emergres. Educational Studies in Mathematics, 46, 187–228. https://doi.org/10.1007/0-306-48085-9_6
Kim, D., Choi, S., & Lim, W. (2017). Sfard’s commognitive framework as a method of discourse analysis in mathematics. International Journal of Cognitive and Language Sciences, 11(11), 448–452. https://web.archive.org/web/20201223111554/https://zenodo.org/record/1132727/files/10008184.pdf
Kosko, K. W. (2014). What students say about their mathematical thinking when they listen. School Science and Mathematics, 114(5), 214–223. https://doi.org/10.1111/ssm.12070
Kristiani, Y. D., Juandi, D., & Putri, R. I. I. (2024). Students’ mathematical communication skills on straight-line equation using PMRI and collaborative learning. Mathematics Education Journal, 18(2), 163–180. https://doi.org/10.22342/jpm.v18i2.pp163-180
Lestari, A. S. B., Nusantara, T., Susiswo, S., & Chandra, T. D. (2019). Imitation in students' mathematical communication to solve mathematical problems. IndoMath: Indonesia Mathematics Education, 2(2), 95. https://doi.org/10.30738/indomath.v2i2.4681
Lu, J., Wu, S., & Wang, Y. (2023). Visualizing the commognitive processes of collaborative problem solving in mathematics classrooms. The Asia-Pacific Education Researcher, 32(5), 615–628. https://doi.org/10.1007/s40299-022-00681-2
Makgakga, T. P. (2023). Twinned teachers’ mathematical discourse using problem-solving. Journal of Culture and Values in Education, 6(2), 138-157. https://doi.org/10.46303/jcve.2023.13
Matthews, P. G. (2024). Reflecting from the border between mathematics education research and cognitive psychology. Journal for Research in Mathematics Education, 55(2), 68-75. https://doi.org/10.5951/jresematheduc-2023-0229
Montague, M., Krawec, J., Enders, C., & Dietz, S. (2014). The effects of cognitive strategy instruction on math problem solving of middle-school students of varying ability. Journal of Educational Psychology, 106(2), 469–481. https://doi.org/10.1037/a0035176
Mpofu, S., & Pournara, C. (2018). Learner participation in the functions discourse: a focus on asymptotes of the hyperbola. African Journal of Research in Mathematics, Science and Technology Education, 22(1), 2–13. https://doi.org/10.1080/18117295.2017.1409170
Mwambazi, C. M., Mbewe, S., & Simui, F. (2025). Enhancing understanding of linear programming concepts through contextual education. International Journal of Research and Innovation in Social Science (IJRISS), 8(2454), 4469-4480. https://doi.org/10.47772/IJRISS
Nardi, E., Ryve, A., Stadler, E., & Viirman, O. (2014). Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of Calculus. Research in Mathematics Education, 16(2), 182-198. https://doi.org/10.1080/14794802.2014.918338
Nauli, N., Harisman, Y., Armiati, & Yerizon. (2024). Junior high school students’ habits of mind in solving mathematical problems. Mathematics Education Journal, 18(1), 39-58. https://doi.org/10.22342/jpm.v18i1.pp39-58
NCTM. (2000). Principles and Standards for School Mathematics. The National Council of Teachers of Mathematics, Inc
Pinto, A., Cooper, J. (2023). Boundary crossing in curriculum reform. Manhattan, New York: Springer
Pratiwi, W. D., Zulkardi, Putri, R. I. I., & Hiltrimartin, C. (2025). Students’ communication skill and algebraic thinking through commognitive framework in algebra learning. Mathematics Education Journal, 19(3), 413–436. https://jpm.ejournal.unsri.ac.id/index.php/jpm/article/view/88
Rahmawati, A., Cholily, Y. M., & Zukhrufurrohmah, Z. (2023). Analyzing students’ mathematical communication ability in solving numerical literacy problems. Mosharafa: Jurnal Pendidikan Matematika, 12(1), 59–70. https://doi.org/10.31980/mosharafa.v12i1.1938
Rahmawati, M. S., & Soekarta, R. (2021). Social Media-based e-learning and online assignments on algebraic materials. Jurnal Pendidikan Matematika, 15(2), 175–190. https://doi.org/10.22342/jpm.15.2.13714.175-190
Ratumanan, T. G., Ayal, C. S., & Tupamahu, P. Z. (2022). Mathematical representation ability of mathematics education study program students. Jurnal Pendidikan Matematika, 5(1), 50–59. https://doi.org/10.30598/jupitekvol5iss1pp50-59
Roberts, A., & Roux, K. le. (2019). A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equations. Phytagoras, 40(1). https://doi.org/https://doi.org/10.4102/pythagoras.v40i1.438
Rohid, N., Suryaman, & Rusmawati (2019). Students’ mathematical communication skills (mcs) in solving mathematics problems : A case in indonesian context. Anatolian Journal of Education, 4(2), 19–30. https://doi.org/10.29333/aje.2019.423a
Sánchez, V., García, M., & Escudero, I. (2013). An analytical framework for analyzing student teachers’ verbal interaction in learning situations. Instructional Science, 41(2), 247–269. https://doi.org/10.1007/s11251-012-9226-5
Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1–3), 13–57. https://doi.org/10.1023/a:1014097416157
Sfard, A. (2006). Participationist discourse on mathematics learning. New Mathematics Education Research and Practice, 153–170. BRILL. https://doi.org/10.1163/9789087903510_015
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. Cambridge, Cambridgeshire: Cambridge University Press
Sfard, A. (2015). Learning, commognition and mathematics. In D. Scott & E. Hargreaves (Eds.). The Sage Handbook of Learning. London: Sage, pp. 129-138
Shinno, Y., & Fujita, T. (2021). Characterizing how and when a way of proving develops in a primary mathematics classroom: A commognitive approach. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739x.2021.1941365
Sukasno, Zulkardi, Putri, R. I. I., & Somakim. (2024). Students’ cognitive processes in understanding fractions through the tourist context. Mathematics Education Journal, 18(1), 27–38. https://doi.org/10.22342/jpm.v18i1.pp27-38
Supardi, L., Zayyadi, M., Lanya, H., Hasanah, S. I., Hidayati, S. N. (2021). Commognitive Analysis Of Students' Errors In Solving High Order Thinking Skills Problems. Turkish Journal of Computer and Mathematics Education, 21(6), 950-961. https://doi.org/10.17762/TURCOMAT.V12I6.2373
Susilowati, I., Cholily, Y. M., Rosyadi, A. A. P., & In'am, A. (2025). Examination of students' written mathematical communication skills in addressing gender-based open-ended problems. Kalamatika: Journal of Mathematics Education, 10(2), 117-136. https://doi.org/10.22236/KALAMATIKA.vol10no2.2025pp117-136
Sutarto, S. (2017). Cognitive theory and its implications in learning. Islamic counseling: Jurnal Bimbingan Konseling Islam, 1(2), 1–26. https://doi.org/10.29240/jbk.v1i2.331
Tabacaru, C. D. (2016). Verbal and nonverbal communication of students with severe and profound disabilities. Research in Pedagogy, 6(2), 111-119. https://doi.org/10.17810/2015.39
Tasara, I. (2017, 11 November). Commognitive analysis of a teacher’s mathematical discourse on the derivative. Paper presented at the 37th Meeting of the British Society for Research into Learning Mathematics (BSRLM 2017), Liverpool Hope University, UK. https://www.bsrlm.org.uk/wp-content/uploads/2017/12/BSRLM-CP-37-3-12.pdf
Thinwiangthong, S., Inprasitha, M., & Loipha, S. (2012). Adaptation of lesson study and open approach for sustainable development of students’ mathematical learning process. Psychology, 03(10), 906–911. https://doi.org/10.4236/psych.2012.310136
Tong, D. H., Uyen, B. P, Quoc, N. V. A. (2021). The improvement of 10th students’ mathematical communication skills through learning ellipse topics. Heliyon, 7(11). https://doi.org/10.1016/j.heliyon.2021.e08282
Valenta, A., Rø, K. & Klock, S. I. (2024). A framework for reasoning in school mathematics: analyzing the development of mathematical claims. Educational Studies in Mathematics, 116, 91-111. https://doi.org/10.1007/s10649-024-10309-5.
Viirman, O. (2015). Explanation, motivation and question posing routines in university mathematics teachers’ pedagogical discourse: A commognitive analysis. International Journal of Mathematical Education in Science and Technology, 46(8), 1165–1181. https://doi.org/10.1080/0020739X.2015.1034206
Wong, V., Fujita, T., Hill, A., & Ruffle, S. (2025). Patterns of student discourse in solving quantitative science problems problems. International Journal of Science Education. https://doi.org/10.1080/09500693.2025.2488399
Yerizon, Y., & Arnawa, I. M., Arnellis, A., Tasman, F., Yarman, Y., Hevardani, K. A. (2025). Analysis of students’ errors in drawing function graphs in three-dimensional space based on APOS theory. Salud, Ciencia y Tecnología, 5. https://doi.org/10.56294/saludcyt20251833
Zayyadi, M., Nusantara, T., Hidayanto, E., Sulandra, I. M., & Sa’Dijah, C. (2020). Content and pedagogical knowledge of prospective teachers in mathematics learning: Commognitive. Journal for the Education of Gifted Young Scientists, 8(1), 515-532. https://doi.org/10.17478/jegys.642131
Zayyadi, M., Nusantara, T., Subanji, 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
Zulfah, Z., Nusantara, T., Hanafi, Y., & Arifin, S. (2025). Students’ commognitive processes in solving problem-based learning-oriented student worksheets. AL-ISHLAH: Jurnal Pendidikan, 17(2), 2194–2202. https://doi.org/10.35445/alishlah.v17i2.7457
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Achmad Ghozi Khoiruddin, Ali Shodikin, Evangelista Lus Windyana Palupi

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with the Jurnal Elemen agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).
- Authors are able to enter into separate, additional contractual arrangements for the distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License



