Main Article Content

Abstract

Semiotics is defined as using signs to represent mathematical concepts in problem-solving. The mathematical semiotic process involves creating meaning from the triadic relationship between the representamen (R), object (O), and interpretant (I). Mathematical semiotics play an essential role in the cognitive processes of individuals as they formulate and communicate mathematical ideas. Therefore, this study aims to describe the stages of the semiotic process of junior high school students solving integers-related mathematical problems. In this qualitative analysis, the participant is a seventh-grade student categorized as pseudo-semiotic. The research instrument is a test on integers and interviews. The results demonstrate that the semiosis related to integers involves the representamen, object, and interpretant stages. For a subject with a pseudo-semiotic type, this meaning-making process requires the construction of a comprehensive understanding of the concept. Furthermore, the understanding is developed using various instruments, resulting in connection conflicts between different components of the semiotic system. Connection conflict occurs because of the mismatched relationship between the elements of semiosis: representamen, object, and interpretant. A pseudo-semiotic subject only has a superficial understanding of mathematical concepts, making it challenging to establish accurate connections between symbols and their underlying meanings. Consequently, this hinders the ability to understand mathematics profoundly and apply the concepts in real-life situations.

Keywords

Integers Mathematical activity Semiotic perspective

Article Details

References

  1. Akhtar, Z. (2018). Students’ misconceptions about locating integers and decimals on number line. International Journal of Innovation in Teaching and Learning, 4(1), 1-16. https://doi.org/10.35993/ijitl.v4i1.314

  2. Alshwaikh, J. (2010). Geometrical diagrams as representation and communication: A functional analytic framework. Research in Mathematics Education, 12(1), 69-70. https://doi.org/10.1080/14794800903569881

  3. Ardina, F. R., & Sa’dijah, C. (2016). Analisis lembar kerja siswa dalam meningkatkan komunikasi matematis tulis siswa [Analysis of student worksheets in improving students' written mathematical communication]. Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan, 1(2), 171-180.

  4. Arzarello, F., & Sabena, C. (2011). Semiotic and theoretic control in argumentation and proof activities. Educational Studies in Mathematics, 77(2), 189-206. https://doi.org/10.1007/s10649-010-9280-3

  5. Bishop, J. P., Lamb, L. L., Philipp, R. A., Whitacre, I., & Schappelle, B. P. (2014). Using order to reason about negative numbers: the case of Violet. Educational Studies in Mathematics, 86(1), 39-59. https://doi.org/10.1007/s10649-013-9519-x

  6. Bofferding, L. (2014). Negative integer understanding: Characterizing first graders' mental models. Journal for Research in Mathematics Education, 45(2), 194-245. https://doi.org/10.5951/jresematheduc.45.2.0194

  7. Bofferding, L., & Wessman-Enzinger, N. (2017). Subtraction involving negative numbers: Connecting to whole number reasoning. The Mathematics Enthusiast, 14(1), 241-262. https://doi.org/10.54870/1551-3440.1396

  8. Bosse, M. J., Lynch-Davis, K., Adu-Gyamfi, K., & Chandler, K. (2016). Using integer manipulatives: Representational determinism. International Journal for Mathematics Teaching and Learning, 17(3), 1-20. https://doi.org/10.4256/ijmtl.v17i3.37

  9. Brier, S. (2018). Transdisciplinarity across the qualitative and quantitative science through C.S. Peirce’s semiotic concept of habit. Open Information Science, 2(1), 102-114. https://doi.org/10.1515/opis-2018-0008

  10. Cetin, H. (2019). Explaining the concept and operations of integer in primary school mathematics teaching: Opposite model sample. Universal Journal of Educational Research, 7(2), 365-370. https://doi.org/10.13189/ujer.2019.070208

  11. Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage.

  12. Dimmel, J. K., & Herbst, P. G. (2015). The semiotic structure of geometry diagrams: How textbook diagrams convey meaning. Journal for Research in Mathematics Education (JRME), 46(2), 147-195. https://doi.org/10.5951/jresematheduc.46.2.0147

  13. Eco, U. (1978). A Theory of semiotics Boomington. Indiana University.

  14. Fuadiah, N. F., Suryadi, D., & Turmudi, T. (2017). Analysis of didactical contracts on teaching mathematics: A design experiment on a lesson of negative integers operations. Infinity Journal, 6(2), 157-168. https://doi.org/10.22460/infinity.v6i2.p157-168

  15. Fuadiah, N. F., Suryadi, D., & Turmudi, T. (2017). Some difficulties in understanding negative numbers faced by students: A qualitative study applied at secondary schools in Indonesia. International Education Studies, 10(1), 24-38. https://doi.org/10.5539/ies.v10n1p24

  16. Hoed, B. H. (2014). Semiotik & dinamika sosial budaya [Semiotics & socio-cultural dynamics] (2nd ed.). Komunitas Bambu.

  17. Hoffmann, M. H. G. (2006). What Is a “semiotic perspective”, and what could it be? Some comments on the contributions to this special issue. Educational Studies in Mathematics, 61(1), 279-291. https://doi.org/10.1007/s10649-006-1456-5

  18. Hundeland, P. S., Carlsen, M., & Erfjord, I. (2014). Children’s engagement with mathematics in kindergarten mediated by the use of digital tools. In U. Kortenkamp, B. Brandt, C. Benz, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early mathematics learning: Selected papers of the POEM 2012 conference (pp. 207-221). Springer New York. https://doi.org/10.1007/978-1-4614-4678-1_13

  19. Kadarisma, G., Fitriani, N., & Amelia, R. (2020). Relationship between misconception and mathematical abstraction of geometry at junior high school. Infinity Journal, 9(2), 213-222. https://doi.org/10.22460/infinity.v9i2.p213-222

  20. Kariadinata, R. (2021). Students’ reflective abstraction ability on linear algebra problem solving and relationship with prerequisite knowledge. Infinity Journal, 10(1), 1-16. https://doi.org/10.22460/infinity.v10i1.p1-16

  21. Khalid, M., & Embong, Z. (2020). Sources and possible causes of errors and misconceptions in operations of integers. International Electronic Journal of Mathematics Education, 15(2), em0568. https://doi.org/10.29333/iejme/6265

  22. Kralemann, B., & Lattmann, C. (2013). Models as icons: modeling models in the semiotic framework of Peirce’s theory of signs. Synthese, 190(16), 3397-3420. https://doi.org/10.1007/s11229-012-0176-x

  23. Kusmaryono, I., Ubaidah, N., & Basir, M. A. (2020). The role of scaffolding in the deconstructing of thinking structure: A case study of pseudo-thinking process. Infinity Journal, 9(2), 247-262. https://doi.org/10.22460/infinity.v9i2.p247-262

  24. Miller, J. (2015). Young indigenous students' engagement with growing pattern tasks: A semiotic perspective. In Proceedings of the 38th annual conference of the Mathematics Education Research Group of Australasia (pp. 421-428). Sunshine Coast

  25. Mudaly, V. (2014). A visualisation-based semiotic analysis of learners’ conceptual understanding of graphical functional relationships. African Journal of Research in Mathematics, Science and Technology Education, 18(1), 3-13. https://doi.org/10.1080/10288457.2014.889789

  26. Murtafiah, W., Lestari, N. D. S., Yahya, F. H., Apriandi, D., & Suprapto, E. (2023). How do students'decision-making ability in solving open-ended problems? Infinity Journal, 12(1), 133-150. https://doi.org/10.22460/infinity.v12i1.p133-150

  27. Murtianto, Y. H., Sutrisno, S., Nizaruddin, N., & Muhtarom, M. (2019). Effect of learning using mathematica software toward mathematical abstraction ability, motivation, and independence of students in analytic geometry. Infinity Journal, 8(2), 219-228. https://doi.org/10.22460/infinity.v8i2.p219-228

  28. Ningsih, E. F., Sugiman, S., Budiningsih, C. A., & Surwanti, D. (2023). Is communicating mathematics part of the ease of online learning factor? Infinity Journal, 12(1), 151-164. https://doi.org/10.22460/infinity.v12i1.p151-164

  29. Ostler, E. (2011). Teaching adaptive and strategic reasoning through formula derivation: beyond formal semiotics. International Journal of Mathematics Science Education, 4(2), 16-26.

  30. Palayukan, H., Purwanto, P., Subanji, S., & Sisworo, S. (2022). Semiotics in integers: How can the semiosis connections occur in problem solving? Webology, 19(2), 98-111.

  31. Pino-Fan, L. R., Guzmán, I., Font, V., & Duval, R. (2017). Analysis of the underlying cognitive activity in the resolution of a task on derivability of the the absolute-value function: two theoretical perspectives. Pna, 11(2), 97-124. https://doi.org/10.30827/pna.v11i2.6076

  32. Presmeg, N. (2006). Research on visualization in learning and teaching mathematics: Emergence from psychology. In Á. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205-235). Brill. https://doi.org/10.1163/9789087901127_009

  33. Presmeg, N., Radford, L., Roth, W.-M., & Kadunz, G. (2016). Semiotics in mathematics education. Springer Nature. https://doi.org/10.1007/978-3-319-31370-2

  34. Purwasih, R., Turmudi, T., Dahlan, J. A., & Irawan, E. (2023). Semiotic perspective in mathematics problem-solving. Journal of Didactic Studies, 1(1), 36-46.

  35. Rachmawati, L. N., Cholily, Y. M., & Zukhrufurrohmah, Z. (2021). Mathematics communication mistakes in solving HOTs problems. Infinity Journal, 10(1), 69-80. https://doi.org/10.22460/infinity.v10i1.p69-80

  36. Sa’dijah, C., Rahayuningsih, S., Sukoriyanto, S., Qohar, A., & Pujarama, W. (2021). Concept understanding layers of seventh graders based on communication ability in solving fraction problems. AIP Conference Proceedings, 2330(1). https://doi.org/10.1063/5.0043725

  37. Santi, G. (2011). Objectification and semiotic function. Educational Studies in Mathematics, 77(2), 285-311. https://doi.org/10.1007/s10649-010-9296-8

  38. Schindler, M., Hußmann, S., Nilsson, P., & Bakker, A. (2017). Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Mathematics Education Research Journal, 29(4), 471-492. https://doi.org/10.1007/s13394-017-0202-x

  39. Semetsky, I. (2016). Edusemiotics – A handbook. Springer. https://doi.org/10.1007/978-981-10-1495-6

  40. Setambah, M. A. B., Jaafar, A. N., Saad, M. I. M., & Yaakob, M. F. M. (2021). Fraction cipher: A way to enhance student ability in addition and subtraction fraction. Infinity Journal, 10(1), 81-92. https://doi.org/10.22460/infinity.v10i1.p81-92

  41. Skemp, R. R. (2012). The psychology of learning mathematics: Expanded American edition. Routledge.

  42. Suryaningrum, C. W., & Ningtyas, Y. D. W. K. (2019). Multiple representations in semiotic reasoning. Journal of Physics: Conference Series, 1315(1), 012064. https://doi.org/10.1088/1742-6596/1315/1/012064

  43. Suryaningrum, C. W., Purwanto, P., Subanji, S., Susanto, H., Ningtyas, Y. D. W. K., & Irfan, M. (2020). Semiotic reasoning emerges in constructing properties of a rectangle: A study of adversity quotient. Journal on Mathematics Education, 11(1), 95-110. https://doi.org/10.22342/jme.11.1.9766.95-110

  44. Vlassis, J. (2008). The role of mathematical symbols in the development of number conceptualization: The case of the minus sign. Philosophical Psychology, 21(4), 555-570. https://doi.org/10.1080/09515080802285552

  45. Whitacre, I., Bishop, J. P., Lamb, L. L. C., Philipp, R. A., Schappelle, B. P., & Lewis, M. L. (2012). Happy and sad thoughts: An exploration of children's integer reasoning. The Journal of Mathematical Behavior, 31(3), 356-365. https://doi.org/10.1016/j.jmathb.2012.03.001

  46. Widjaja, W., Stacey, K., & Steinle, V. (2011). Locating negative decimals on the number line: Insights into the thinking of pre-service primary teachers. The Journal of Mathematical Behavior, 30(1), 80-91. https://doi.org/10.1016/j.jmathb.2010.11.004

  47. Yung, H. I., & Paas, F. (2015). Effects of computer-based visual representation on mathematics learning and cognitive load. Educational Technology & Society, 18(4), 70-77.