Analyzing Indonesian Mathematics Textbooks on Linear Inequalities Through the Lens of the Anthropological Theory of the Didactic

Authors

  • Muhammad Daut Siagian Universitas Singaperbangsa Karawang
  • Rosliana Siregar Universitas Islam Sumatera Utara
  • Suwanto Universitas Negeri Medan

DOI:

https://doi.org/10.21831/jrpm.v13i2.95587

Keywords:

Mathematics textbooks, Inequalities, ATD

Abstract

This study aims to analyze how the concept of inequality is presented in secondary school mathematics textbooks through the lens of the Anthropological Theory of the Didactic (ATD). Using a mathematical praxeology analysis that includes types of tasks (T), techniques (τ), technology (θ), and theory (Θ), this study examines the characteristics of tasks and techniques developed in 10th-grade mathematics textbooks in Indonesia. The analysis results show that the praxeology presented is unbalanced, with a dominance of procedural techniques and minimal explicitness of the technology and theory underlying the inequality concept. The concept of inequality is reduced to a procedural tool for ordering or symbolic modeling, while the epistemic foundations of the ordering property of real numbers and the conceptual distinction between equality and inequality are not presented as learning objects. From the perspective of didactic transposition, these findings indicate an epistemic impoverishment in the process of transforming scholarly knowledge into knowledge to be taught. This study contributes to the ATD literature and textbook studies by demonstrating how the absence of technology and theory in textbook praxeology potentially creates epistemological learning obstacles, and strengthens the argument for the need for a more balanced and reflective reconstruction of praxeology design in the teaching of inequality.

References

Amade-Escot, C. (2023). Daryl Siedentop’s Legacy and the French Didactique Tradition: Influences and Convergences. Quest, 75(1), 74–85. https://doi.org/10.1080/00336297.2022.2150662

Asami-Johansson, Y. (2021). The didactic notion of “mathematical activity” in japanese teachers’ professional scholarship: A case study of an open lesson. Journal of Research in Mathematics Education, 10(1), 88–112. https://doi.org/10.17583/redimat.2021.4598

Bagni, G. T. (2005). Inequalities and equations: History and didactics. In M. Bosch (Ed.), Proceedings of CERME (Vol. 4, hlm. 652–662).

Bartle, R. G., & Sherbert, D. R. (1983). Introduction to real analysis. New Jersey: John Wiley & Sons, Inc.

Bosch, M., & Chevallard, Y. (1999). The sensitivity of mathematical activity for ostensive. Research in Maths Didactics, 19, 77–123.

Bosch, M., & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, (58), 51–65.

Botty, H. M. R. H., Yusof, H. J. H. M., Shahrill, M., & Mahadi, M. A. (2015). Exploring students’ understanding on ‘inequalities.’ Mediterranean Journal of Social Sciences, 6(5), 218–227. https://doi.org/10.5901/mjss.2015.v6n5s1p218

Cavadas, B. (2019). From the contracting earth to continental drift: Wegener's influence on portuguese and spanish science textbooks through the twentieth century. Earth Sciences History, 38(1), 74–93. https://doi.org/10.17704/1944-6178-38.1.74

Chevallard, Y. (1986). La transposition didactique: du savoir savant au savoir enseigné. Revue française de pédagogie, 76(1), 89–91.

Chevallard, Y. (1992). A theoretical approach to curricula. Journal für Mathematik-Didaktik: Zeitschrift der Gesellschaft für Didaktik der Mathematik (GDM), 13(2), 215–230. https://doi.org/10.1007/BF03338779

Chevallard, Y. (1994). Ostensifs et non-ostensifs dans l’activité mathématique. Intervention au Séminaire de l’Associazione Mathesis, 190–200.

Chevallard, Y. (2006). Step towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the IV Congress of the European Society for Research in Mathematics Education (hlm. 21–30). La Pensée Sauvage.

Chevallard, Y. (2007). Readjusting didactics to a changing epistemiology. European Educational Research Journal, 6(2), 131–134. https://doi.org/10.2304/eerj.2007.6.2.131

Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: An attempt at a principled approach. Hiroshima Journal of Mathematics Education, 12, 71–114.

Chevallard, Y., & Bosch, M. (2014). Didactic transposition in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (hlm. 170–174). London: Springer Dordrecht Heidelberg New York London. https://doi.org/10.1145/1869746.1869759

Chevallard, Y., & Sensevy, G. (2014). Anthropological approaches in mathematics education, French perspectives. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (hlm. 38–43). Dordrecht: Springer.

Crooks, N. M., & Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review, 34(4), 344–377. http://dx.doi.org/10.1016/j.dr.2014.10.001

El-Khateeb, M. M. A. (2016). Errors analysis of solving linear inequalities among the preparatory year students at king saud university. Journal of Education and Practice, 7(12), 124–133.

Florensa, I., Bosch, M., & Gascón, J. (2015). The epistemological dimension in didactics: Two problematic issues. CERME 9 - Ninth Congress of the European Society for Research in MathematicsEducation, 2635–2641. Prague, Czech Republic: Charles University, Faculty of Education.

Gellert, U., Barbé, J., & Espinoza, L. (2013). Towards a local integration of theories: Codes and praxeologies in the case of computer-based instruction. Educational Studies in Mathematics, 82(2), 303–321. https://doi.org/10.1007/s10649-012-9427-5

Hattikudur, S., & Alibali, M. W. (2010). Learning about the equal sign: does comparing with inequality symbols help?. Journal of experimental child psychology, 107(1), 15–30. https://doi.org/10.1016/j.jecp.2010.03.004

Kazarinoff, N. D. (1961). Geometric inequalities. New York: Random House.

Kieran, C. (2007). Research on the learning and teaching of algebra. In A. Gutiérrez & P. Boero (Eds.), Handbook of Research on the Psychology of Mathematics Education (hlm. 256–258). Rotterdam: BRILL. https://doi.org/10.1163/9789087901509_015

Ligozat, F., Lundqvist, E., & Amade-Escot, C. (2017). Analysing the continuity of teaching and learning in classroom actions: When the joint action framework in didactics meets the pragmatist approach to classroom discourses. European Educational Research Journal, 17(1), 147-169. https://doi.org/10.1177/1474904117701923

Lim, K. H. (2006). Students’ mental acts of anticipating in solving problems involving algebraic inequalities and equations (Dissertation, University of California). University of California, San Diego.

Maudy, S., & Ruli, R. (2024). Learning obstacle instrument analysis of proportion concept with praxiology framework. Journal of Didactic Mathematics, 5(3), 194–210. https://doi.org/10.34007/jdm.v5i3.2435

Mokh, R. A., Othman, A., & Shahbari, J. A. (2019). Mistakes made by students with logical connectives when solving equations and inequalities, and how teachers assess these mistakes. International Journal of Research in Education and Science (IJRES), 5(2), 421–428.

Otero, M. R., & Llanos, C. (2021). The gap between studying a generating question and planning lessons based on it. In Trends in Mathematics (Vol. 13, pp. 67–76). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-76413-5_8

Pradipta, T. R., Turmudi, T., Hendriyanto, A., & Pramartha, I. N. B. . (2025). Praxeological analysis of number patterns through the anthropological theory of the didactic perspective. Indonesian Journal of Science and Mathematics Education, 8(3), 799-819. https://doi.org/10.24042/0rqrd137

Putra, Z. H. (2019). Praxeological change and the density of rational numbers: The case of pre-service teachers in Denmark and Indonesia. Eurasia Journal of Mathematics, Science and Technology Education, 15(5), em1711. https://doi.org/10.29333/ejmste/105867

Putra, Z. H., Dahnilsyah, & Aljarrah, A. (2021). A praxeological analysis of pre-service elementary teacher-designed mathematics comics. Journal on Mathematics Education, 12(3), 563-580. http://doi.org/10.22342/jme.12.3.14143.563-580

Rasmussen, K. (2016). Lesson study in prospective mathematics teacher education: didactic and paradidactic technology in the post-lesson reflection. Journal of Mathematics Teacher Education, 19(4), 301–324. https://doi.org/10.1007/s10857-015-9299-6

Rosyidi, A. H., & Kohar, A. W. (2018). Student teachers’ proof schemes on proof tasks involving inequality: Deductive or inductive? Journal of Physics: Conference Series, 947, 012028. https://doi.org/10.1088/1742-6596/947/1/012028

Siagian, M. D., Suryadi, D., Nurlaelah, E., & Prabawanto, S. (2022). Investigation of secondary students' epistemological obstacles in the inequality concept. Mathematics Teaching Research Journal, 14(4), 106–128. https://files.eric.ed.gov/fulltext/EJ1361657.pdf

Siagian, M.D. & Maudy, S.Y. (2025). Making and unmaking meaning: when students call inverses ‘zero makers'. For the Learning of Mathematics, 45(3).

Surma, T., Vanhees, C., Wils, M., Nijlunsing, J., Crato, N., Hattie, J., Muijs, D., Rata, E., Wiliam, D., & Kirschner, P. A. (2025). Knowledge and the curriculum. In Developing curriculum for deep thinking (pp. 37–73). SpringerBriefs in Education. Springer, Cham. https://doi.org/10.1007/978-3-031-74661-1_3

Tall, D. (2004). Reflections on reserach and teavhing of equations and inequalities. Proceedings of the 28th Conference of the International Group of Psychology of Mathematics Education, 1, 158–161. Bergen, Norway.

Tamba, K. P., & Saragih, M. J. (2020). Epistemological obstacles on the quadratic inequality. Al-Jabar: Jurnal Pendidikan Matematika, 11(2), 317–330. https://doi.org/10.24042/ajpm.v11i2.6858

Taqiyuddin, M., Sumiaty, E., & Jupri, A. (2017). Analysis of junior high school students’ attempt to solve a linear inequality problem. AIP Conference Proceedings, 1868(August). https://doi.org/10.1063/1.4995160

Tsamir, P., & Almog, N. (2001). Students’ strategies and difficulties: the case of algebraic inequalities. International Journal of Mathematical Education in Science and Technology, 32(4), 513–524. https://doi.org/10.1080/00207390110038277

Utami, N. S., Mizoguchi, T., Prabawanto, S., & Suryadi, D. (2025). A praxeological analysis of functions in lower secondary school: Comparing the textbooks in Japan and Indonesia. International Electronic Journal of Mathematics Education, 20(2), em0814. https://doi.org/10.29333/iejme/15818

Winsløw, C., Barquero, B., de Vleeschouwer, M., & Hardy, N. (2014). An institutional approach to university mathematics education: From dual vector spaces to questioning the world. Research in Mathematics Education, 16(2), 95–111. https://doi.org/10.1080/14794802.2014.918345

Published

2026-10-23

How to Cite

Siagian, M. D., Siregar, R., & Suwanto. (2026). Analyzing Indonesian Mathematics Textbooks on Linear Inequalities Through the Lens of the Anthropological Theory of the Didactic. Jurnal Riset Pendidikan Matematika, 13(2). https://doi.org/10.21831/jrpm.v13i2.95587