Christine Wulandari Suryaningrum, Purwanto Purwanto, Subanji Subanji, Hery Susanto, Yoga Dwi Windy Kusuma Ningtyas, Muhammad Irfan


Semiotics is simply defined as the sign-using to represent a mathematical concept in a problem-solving. Semiotic reasoning of constructing concept is a process of drawing a conclusion based on object, representamen (sign), and interpretant. This paper aims to describe the phases of semiotic reasoning of elementary students in constructing the properties of a rectangle. The participants of the present qualitative study are three elementary students classified into three levels of Adversity Quotient (AQ): quitter/AQ low, champer/AQ medium, and climber/AQ high. The results show three participants identify object by observing objects around them. In creating sign stage, they made the same sign that was a rectangular image. However, in three last stages, namely interpret sign, find out properties of sign, and discover properties of a rectangle, they made different ways. The quitter found two characteristics of rectangular objects then derived it to be a rectangle’s properties. The champer found four characteristics of the objects then it was derived to be two properties of a rectangle. By contrast, Climber found six characteristics of the sign and derived all of these to be four properties of a rectangle. In addition, Climber could determine the properties of a rectangle correctly.


Reasoning; Semiotic; Semiotic Reasoning; Construction Concept; Adversity Quotient (AQ)

Full Text:



Ahamad, S.N.S.H., Li, H.C., Shahrill, M., & Prahmana, R.C.I. (2018). Implementation of problem-based learning in geometry lessons. Journal of Physics: Conference Series, 943(1), 012008.

Ali, R.H., & Aslaadi, S. (2016) A cognitive semiotic study of students ' reading a textless image versus a verbal image. Advances in Laguage and Literary Studies, 7(5), 1-13.

Arzarello, F., & Sabena, C. (2011). Semiotic and theoretic control in argumentation and proof activities. Educational Studies in Mathematics, 77(2-3), 189-206.

Bjuland, R. (2012) The mediating role of a teacher’s use of semiotic resources in pupils’ early algebraic reasoning. ZDM, 44(5), 665-675.

Brier, S. (2015). Cybersemiotics and the reasoning powers of the universe : philosophy of information in a semiotic- systemic transdisciplinary approach. Green Letters Studies in Ecocriticism, 19(3), 280-292.

Campos, D.G. (2010). Peirce’s philosophy of mathematical education: Fostering reasoning abilities for mathematical inquiry. Studies in Philosophy and Education, 29(5), 421-439.

Creswell, J.W. (2015). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. Educational Research (Vol. 4).

Deledalle, G. (2013). Peirce and semiotic–An introduction. KODIKAS/CODE. Ars Semeiotica, 36(3-4), 185-191.

Eco, U. (1976). A Theory of Semiotics. Bloomington: Indiana University.

Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Edication, 9(1), 3-20.

Godino, J.D., Font, V., Wilhelmi, M.R., & Lurduy, O. (2011). Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects. Educational Studies in Mathematics, 77(2-3), 247-265.

Hardiarti, S. (2017). Ethnomatematics: The application of quadrilateral plane figure in muaro Jambi temple [in Bahasa]. Aksioma, 8(2), 99-110.

Hendroanto, A., van Galen, F., van Eerde, D., Prahmana, R.C.I., Setyawan, F., & Istiandaru, A. (2018). Photography activities for developing students’ spatial orientation and spatial visualization. Journal of Physics: Conference Series, 943(1), 012029.

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.

Metro-Roland, M. (2009). Interpreting meaning : An application of Peircean semiotics to tourism. Tourism Geographies, 11(2), 270-279.

Miller, J. (2015). Young indigenous students’ engagement with growing pattern tasks: A semiotic perspective. Proceeding of the 38th Annual Conference of the Mathematic Education Reseacrh Group of Australasia, 421-428.

Ng, O.L., & Sinclair, N. (2015). Young children reasoning about symmetry in a dynamic geometry environment. ZDM, 47(3), 421-434.

Ostler, E. (2011). Teaching adaptive and strategic reasoning through. International Journal of Mathematics Science Education, 4(2), 16-26.

Panchal, C. (2013). A study of abstract reasoning of the students of standard IX of Ahmedabad city. International Journal for Research in Education, 2(3), 30-34.

Parcell, W.C., & Parcell, L.M. (2009). Evaluating and communicating geologic reasoning with semiotics and certainty estimation. Journal of Geoscience Education, 57(5), 379-389.

Peirce, C.S. (1931). The Collected Papers of Charles Sanders Peirce. Cambridge: Harvard University Press.

Presmeg, N. (2016). Semiotics in theory and practice in mathematics education. ICME-13.

Priss, U. (2016). A semiotic-conceptual analysis of conceptual learning. In International Conference on Conceptual Structures (pp. 122-136). Cham: Springer.

Radford, L., & Schubring, G. (2008). Semiotics in Mathematics Education. Rotterdam: Sense Publishers.

Sáenz-Ludlow, A., & Kadunz, G. (2016). Semiotics as a Tool for Learning Mathematics. Rotterdam: Sense Publishers.

Sarbo, J.J., & Yang, J.H. (2015). A semiotic approach to critical reasoning. In International Conference on Informatics and Semiotics in Organisations (pp. 10-19). Cham: Springer.

Schreiber, C. (2013). Semiotic processes in chat-based problem-solving situations. Educational Studies in Mathematics, 82(1), 51-73.

Semetsky, I. (2013). The Edusemiotics of Images. Rotterdam: Sense Publishers.

Sendera, H., Yakin, M., & Totu, A. (2014). The semiotic perspectives of peirce and saussure: A brief comparative study. Procedia-Social and Behavioral Sciences, 155(October), 4–8.

Stjernfelt, F. (2015). Dicisigns Peirce’s semiotic doctrine of propositions. Synthese: An International Journal for Epistemology, Methodology and Philosophy of Science, 192(4), 1019-1054.

Stoltz, P.G. (2004). Adversity Quotient: Reverse the Threats into Opportunities Fifth Edition [in Bahasa]. Jakarta: Grasindo.

Syah, M. (2010). Learning Psychology [in Bahasa]. Jakarta: Rajagrafindo Persada.

Turgut, M. (2017) Students’ reasoning on linear transformations in a DGS: A semiotic perspective. CERME 10 (pp. 01946324). Dublin, Ireland.

Türkcan, B. (2013). Semiotic approach to the analysis of children’s drawings. Educational Science: Theory & Practice, 13(1), 600-607.

Usiskin. (1982). Van Hiele Levels and Achievement in Secondary School Geometri. Chicago: The University of Chicago.

Uslucan, H.H. (2004). Charles Sanders Peirce and the semiotic foundation of self and reason. Mind, Culture, and activity, 11(2), 96-108.

West, D.E. (2015). Embodied experience and the semiosis of abductive reasoning. Southern Semiotic Review, 5(1), 53-59.

Yang, C., & Hsu, T. (2015). Applying semiotic theories to graphic design education: An empirical study on poster design teaching. International Education Studies, 8(12), 117-129.



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139

p-ISSN: 2087-8885 | e-ISSN: 2407-0610
Journal on Mathematics Education is licensed under a Creative Commons Attribution 4.0 International License

View My Stats