From Multiplicative Growth to Institutionalized Exponential Knowledge: A Praxeological Analysis of Exponential Learning in a Secondary Mathematics Textbook

Laila Cantika; Septiani Yugni Maudy; Mulia Putra

doi:10.31949/dm.v8i2.18499

Authors

Laila Cantika Universitas Singaperbangsa Karawang, Indonesia
Septiani Yugni Maudy Universitas Singaperbangsa Karawang, Indonesia
Mulia Putra Universitas Singaperbangsa Karawang, Indonesia

DOI:

https://doi.org/10.31949/dm.v8i2.18499

Abstract

This study investigates the praxeological organization of exponent learning in a Grade 10 mathematics textbook through the lens of the Anthropological Theory of the Didactic (ATD). The study aims to examine how exponent knowledge is introduced, developed, and institutionalized through the relationships among tasks, techniques, technologies, and theories. A qualitative document analysis was conducted using the exponent chapter of the 2021 Indonesian Mathematics Electronic School Book. The analysis focused on Exploration 1.1, Exploration 1.2, and Exercise 1.1, which cover the initial development of concepts of exponents. Mathematical tasks were identified and reconstructed into local praxeologies, which were subsequently synthesized into a global praxeological organization. The findings reveal a coherent learning trajectory consisting of three successive phases. Exploration 1.1 constructs exponentiation through multiplicative growth situations, enabling students to develop meaning from repeated multiplication. Exploration 1.2 extends this understanding by identifying and generalizing the properties of exponents. Exercise 1.1 institutionalizes exponent knowledge by transforming exponent properties into tools for justification, equation solving, and symbolic simplification. The reconstructed global organization demonstrates a progression from meaning construction to formal mathematical practice. The analysis further shows that the visibility of the praxis block increases throughout the chapter, whereas technological explanations become less explicit during the institutionalization phase. These findings contribute to textbook research by illustrating how the sequencing of praxeological components shapes students' opportunities to construct, generalize, and apply mathematical knowledge. The study also highlights the value of ATD as a framework for examining the epistemological organization of mathematical content in school textbooks

Keywords:

Exponentiation, Praxeology, Mathematics textbook, Anthropological theory of the didactic, Mathematical knowledge

Downloads

Download data is not yet available.

References

Abou-Hayt, I. (2026). A critical look at the anthropological theory of the didactic. Research in Mathematics Education, 28(1), 3–24. https://doi.org/10.1080/14794802.2024.2344754

Amit, M., & Neria, D. (2008). Rising to the challenge: Using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM Mathematics Education, 40(1), 111–129. https://doi.org/10.1007/s11858-007-0069-5

Bani Irshid, M. M., Khasawneh, A. A., & Al-Barakat, A. A. (2023). The effect of conceptual understanding principles-based training program on enhancement of pedagogical knowledge of mathematics teachers. Eurasia Journal of Mathematics, Science and Technology Education, 19(6), Article em2277. https://doi.org/10.29333/ejmste/13215

Baroody, A. J. (2013). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 1–33). Routledge. https://doi.org/10.4324/9781410607218-1

Bittar, M. (2021). Overview of research on textbooks in Brazilian compulsory education. In B. Barquero, I. Florensa, P. Nicolás, & N. Ruiz-Munzón (Eds.), Extended abstracts spring 2019 (Vol. 13). Birkhäuser. https://doi.org/10.1007/978-3-030-76413-5_15

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

Bosch, M. (2015). Doing research within the anthropological theory of the didactic: The case of school algebra. In S. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 51–71). Springer. https://doi.org/10.1007/978-3-319-17187-6_4

Bosch, M., Chevallard, Y., García, F. J., & Monaghan, J. (2020). Working with the anthropological theory of the didactic in mathematics education. Routledge. https://doi.org/10.4324/9780429198168

Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27–40. https://doi.org/10.3316/QRJ0902027

Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM Mathematics Education, 40(1), 3–22. https://doi.org/10.1007/s11858-007-0067-7

Chevallard, Y. (2019). Introducing the anthropological theory of the didactic an attempt at a principled approach. Hiroshima journal of mathematics education, 12, 71-114. https://doi.org/10.24529/hjme.1205

Chevallard, Y. (2022). Challenges and advances in teacher education within the anthropological theory of the didactic. In Y. Chevallard et al. (Eds.), Advances in the anthropological theory of the didactic. Birkhäuser. https://doi.org/10.1007/978-3-030-76791-4_7

Chevallard, Y., Bosch, M. (2020). Didactic Transposition in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_48

Ciccione, L., Sablé-Meyer, M., & Dehaene, S. (2022). Analyzing the misperception of exponential growth in graphs. Cognition, 225, Article 105112. https://doi.org/10.1016/j.cognition.2022.105112

Confrey, J. (1991). The concept of exponential functions: A student’s perspective. In L. P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 124–159). Springer. https://doi.org/10.1007/978-1-4612-3178-3_8

Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26(2–3), 135–164. https://doi.org/10.1007/BF01273661

Ernest, P. (2003). Constructing mathematical knowledge: Epistemology and mathematics education. Routledge. https://doi.org/10.4324/9780203454206

Gascón, J. (2024). Contributions of the anthropological theory of the didactic to the epistemological programme of research in mathematics education. ZDM–Mathematics Education, 56, 1319–1330. https://doi.org/10.1007/s11858-024-01563-1

Guba, E. G., & Lincoln, Y. S. (1994). Competing paradigms in qualitative research. Handbook of qualitative research, 2(163-194), 105. https://miguelangelmartinez.net/IMG/pdf/1994_Guba_Lincoln_Paradigms_Quali_Research_chapter.pdf

Hackenberg, A. J. (2010). Students’ reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383–432. https://doi.org/10.1080/07370008.2010.511565

Ismayanti, S., Jatisunda, M. G., & Hoon, T. S. (2025). Didactic transposition of trigonometric ratios: A comparative study of school and university textbooks. Journal on Mathematics Education, 16(4), 1283–1312. https://doi.org/10.22342/jme.v16i4.pp1283-1312

Jatisunda, M. G., Hoon, T. S., Jamilah, J., & Rohimatunissa, D. (2025). Praxeological analysis of junior secondary students’ epistemological obstacles in algebraic operations. Journal of Research and Advances in Mathematics Education, 10(4), 218–230. https://doi.org/10.23917/jramathedu.v10i4.13374

Keazer, L., & Phaiah, J. (2023). Analyzing prospective elementary teachers’ evidence of conceptual understanding and procedural fluency. Investigations in Mathematics Learning, 15(2), 135–148. https://doi.org/10.1080/19477503.2022.2139112

Kieran, C. (2013). The false dichotomy in mathematics education between conceptual understanding and procedural skills: An example from algebra. In K. Leatham (Ed.), Vital directions for mathematics education research (pp. 153–171). Springer. https://doi.org/10.1007/978-1-4614-6977-3_7

Kowiyah, K., Mulyawati, I., & Umam, K. (2019). Conceptual understanding and mathematical representation analysis of realistic mathematics education based on personality types. Al-Jabar: Jurnal Pendidikan Matematika, 10(2), 201–210. https://doi.org/10.24042/ajpm.v10i2.4605

Pansell, A. (2023). Mathematical knowledge for teaching as a didactic praxeology. Frontiers in Education, 8, Article 1165977. https://doi.org/10.3389/feduc.2023.1165977

Pepin, B., Gueudet, G. (2020). Curriculum Resources and Textbooks in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_40

Peters, J. (2022). Modifying exercises in mathematics service courses for engineers based on subject-specific analyses of engineering mathematical practices. In R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, & C. Winsløw (Eds.), Practice-oriented research in tertiary mathematics education (Advances in Mathematics Education). Springer. https://doi.org/10.1007/978-3-031-14175-1_28

Polly, D., & Martin, C. S. (2025). Build procedural fluency from conceptual understanding. https://doi.org/10.1108/978-1-83708-512-520251042

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. International Journal of Science and Mathematics Education, 8(3), 799–819. https://doi.org/10.24042/0rqrd137

Rivera, F. D. (2018). Pattern generalization processing of elementary students: Cognitive factors affecting the development of exact mathematical structures. Eurasia Journal of Mathematics, Science and Technology Education, 14(9), Article em1586. https://doi.org/10.29333/ejmste/92554

Şenay, Ş. C. (2024). Analysis of misconceptions and errors regarding exponential and radical expressions through the theory of reducing abstraction. Research on Education and Psychology, 8(2), 281–295. https://doi.org/10.54535/rep.1520588

Suarka, N. K. S. D., & Kusumah, Y. S. (2024). Students' learning obstacles in exponential: A case study in Indonesian higher education students. Jurnal Pendidikan MIPA, 25(2), 530–541. https://doi.org/10.23960/jpmipa/v25i2.pp530-541

Sunzuma, G. (2026). Cultural Activities in Secondary School Mathematics Textbooks in Zimbabwe: Toward a Contextualized Curriculum. In: Ampadu, E., Jojo, Z., Hartell, E., Sunzuma, G., Mensah, F.S. (eds) Mathematics for All. Springer, Cham. https://doi.org/10.1007/978-3-032-22072-1_6

Susanto, D., Kurniawan, T., Sihombing, S. K., Salim, E., Magdalena, M., Radjawane, R., Salmah, U., & Wardani, A. K. (2021). Matematika. Pusat Kurikulum dan Perbukuan, Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi. https://buku.kemdikbud.go.id

Syafiqoh, N., Amin, S. M., & Siswono, T. Y. E. (2018). Analysis of student’s understanding of exponential concept: A perspective of Pirie-Kieren theory. Journal of Physics: Conference Series, 1108(1), Article 012022. https://doi.org/10.1088/1742-6596/1108/1/012022

Ulusoy, F. (2019). Serious obstacles hindering middle school students’ understanding of integer exponents. International Journal of Research in Education and Science, 5(1), 52–69. https://files.eric.ed.gov/fulltext/EJ1198050.pdf

Vinner, S. (2020). Concept development in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Springer. https://doi.org/10.1007/978-3-030-15789-0_29

Weber, E., Walkington, C., & McGalliard, W. (2015). Expanding notions of learning trajectories in mathematics education. Mathematical Thinking and Learning, 17(4), 253–272. https://doi.org/10.1080/10986065.2015.1083836

Wijayanti, D., & Aufa, D. N. (2020). Picturing textbook on exponent equations based on praxeology organization. In Proceedings of the 2nd Social and Humaniora Research Symposium (SoRes 2019) (pp. 494–498). Atlantis Press. https://doi.org/10.2991/assehr.k.200225.107

Yunianta, T. N. H., Suryadi, D., Dasari, D., & Herman, T. (2023). Textbook praxeological-didactical analysis: Lessons learned from the Indonesian mathematics textbook. Journal on Mathematics Education, 14(3), 503–524. https://doi.org/10.22342/jme.v14i3.pp503-524

Zamanabadi, S., & Rafiepour, A. (2026). Application of anthropological theory of didactic in teaching of mathematics. Mathematics and Society, 11(1), 25–41. https://doi.org/10.22108/msci.2025.143082.1718

Zeynivandnezhad, F., Saralar-Aras, I., & Halai, A. (2024). A refined framework for qualitative content analysis of mathematics textbooks. Eurasia Journal of Mathematics, Science and Technology Education, 20(3), em2412. https://doi.org/10.29333/ejmste/14284