Main Article Content
Abstract
Educational research has consistently highlighted that learning obstacles stem not only from the design of learning situations but also from curriculum structures and textbooks, which are pivotal learning resources. Despite the growing body of literature, limited studies focus on the specific challenges posed by the design of learning materials, particularly in early algebra within the Indonesian context. This study addresses the gap by analyzing the grade VII mathematics textbook in the Merdeka Curriculum, with a focus on linear equations with one variable, to uncover learning obstacles in early algebra. Utilizing Didactical Design Research (DDR), a qualitative approach, the research examines the praxeological components of the textbook—tasks (T), techniques (τ), technology (θ), and theory (Θ). The findings indicate three primary categories of learning obstacles: ontogenic, epistemological, and didactic. Notably, the analysis reveals that the design of linear equation content in the textbook is non-systemic and lacks epistemic coherence, posing significant challenges for learners. This study contributes to the understanding of curriculum design by identifying specific obstacles in the Merdeka Curriculum's grade VII mathematics textbook and underscores the need for more systematic and epistemically aligned textbook development. Future research should extend this analysis to other textbooks across various grade levels to determine if these findings are consistent within the broader curriculum framework.
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References
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- Al-Daami, K. K., & Wallace, G. (2007). Curriculum reform in a global context: A study of teachers in Jordan. Journal of Curriculum Studies, 39(3), 339–360. https://doi.org/10.1080/00220270601057790.
- Arslan, S., Baran, D., & Okumus, S. (2011). Brousseau’s Theory of Didactical Situations in mathematics and an application of adidactical situations. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 5(1), 204-224.
- Astriani. L., Mujib. A., & Firmansyah. (2022). Didactic design for overcoming learning obstacles in mathematics of junior high school students. International Journal of Educational Research Excellence (IJERE), 1(1), 58–62. https://doi.org/10.55299/ijere.v1i1.97
- Barbosa, E. J. T., & Lima, A. P. D. A. B. (2020). Teacher's Praxeologies: Comparative Analysis of the Textbook in Teaching First-Degree Polynomial Equations. Educação Matemática Pesquisa, 22(4), 224-231. https://doi.org/10.23925/1983-3156.2020v22i4p224-231
- Blanton, M. L. (2008). Algebra and the elementary classroom: Transforming thinking, transforming practice. Heinemann Educational Books.
- Bondi, W. (2008). Curriculum Development: A Guide to Practice. United States: Merril.
- Bosch, M., & Gascón, J. (2014). Introduction to the Anthropological Theory of the Didactic (ATD). Networking of theories as a research practice in mathematics education, 67-83. Springer Cham. https://doi.org/10.1007/978-3-319-05389-9
- Bosch, M., Hausberger, T., Hochmuth, R., Kondratieva, M., & Winsløw, C. (2021). External didactic transposition in undergraduate mathematics. International Journal of Research in Undergraduate Mathematics Education, 7(1), 140-162. https://doi.org/10.1007/s40753-020-00132-7
- Brousseau, G. (2002). Epistemological obstacles, problems, and didactical engineering. Theory of didactical situations in mathematics. Didactique Des MathEmatiques, 1970-1990, (1 983), 79–117. https://doi.org/10.1007/0-306-47211-2_6
- 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
- Creswell, J. W. (2016). Research design: Pendekatan metode kualitatif, kuantitatif, dan campuran. Yogyakarta: Pustaka Pelajar, 5.
- Daher, W., Baya’a, N., & Jaber, O. (2022). Understanding prospective teachers’ task design considerations through the lens of the theory of didactical situations. Mathematics, 10(3). https://doi.org/10.3390/math10030417
- Eldridge, S. (1935). Textbooks, teachers, and students. American Journal of Sociology, 40(5), 637-645. https://doi.org/10.1086/216901
- Elkjær, M., & Jankvist, U. T. (2021). Designing tasks for a dynamic online environment: Applying research into students’ difficulties with linear equations. Mathematics, 9(5). https://doi.org/10.3390/math9050557
- Fan, L. (2013). Textbook research as scientific research: Towards a common ground on issues and methods of research on mathematics textbooks. ZDM - International Journal on Mathematics Education, 45(5), 765–777. https://doi.org/10.1007/s11858-013-0530-6
- Fardian, D., Suryadi, D., Prabawanto, S., & Hayuningrat, S. (2024). Research trends on early algebra in the middle school: A combined bibliometric and meta-analysis review. Jurnal Elemen, 10(2), 410-440. https://doi.org/10.29408/jel.v10i2.25539
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- Hadar, L. L. (2017). Opportunities to learn: Mathematics textbooks and students’ achievements. Studies in Educational Evaluation, 55(May), 153–166. https://doi.org/10.1016/j.stueduc.2017.10.002
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- Hendricson, W. D., & Kleffner, J. H. (2002). Assessing and helping challenging students: part one, why do some students have difficulty learning? Journal of Dental Education, 66(1), 43–61. https://doi.org/10.1002/j.0022-0337.2002.66.1.tb03507.x
- Hendriyanto, A., Suryadi, D., Dahlan, J. A., & Juandi, D. (2023). Praxeology review: Comparing Singaporean and Indonesian textbooks in introducing the concept of sets. Eurasia Journal of Mathematics, Science and Technology Education, 19(2). https://doi.org/10.29333/ejmste/12953
- Huang, X., Huang, R., & Bosch, M. (2021). Analyzing a teacher’s learning through cross-cultural collaboration: A praxeological perspective of mathematical knowledge for teaching. Educational Studies in Mathematics, 107(3), 427–446. https://doi.org/10.1007/s10649-021-10057-w
- Hussain, A., Jat, Z. G., Hassan, M., Hafeez, A., Iqbal, S., & Imran, M. (2022). Curriculum reforms in school education sector in Sindh; What has changed? Journal of Positive School Psychology, 6(9), 2675–2687. https://ssrn.com/abstract=4251678
- Insani, S. U., & Akbar, P. (2019). Development of open-ended based mathematics problem to measure high-level thinking ability. In Journal of Physics: Conference Series (Vol. 1315, No. 1, p. 012047). IOP Publishing. https://doi.org/10.1088/1742-6596/1315/1/012047
- Isnawan, M. G., Suryadi, D., Turmudi, T., & Marfuah, M. (2022). Parental obstacles during distance learning mathematics in Indonesia: A phenomenology study. European Journal of Educational Research, 11(2), 873-883. https://doi.org/10.12973/eu-jer.11.2.873
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- Johar, R., Sasalia, P., Desy, Ramli, M., & Walker, H. C. O. (2023). Preservice teachers’ noticing skills in relation to student misconceptions in algebra. European Journal of Educational Research, 12(2), 865–879. https://doi.org/10.12973/eu-jer.12.2.865
- Kajander, A., & Lovric, M. (2009). Mathematics textbooks and their potential role in supporting misconceptions. International Journal of Mathematical Education in Science and Technology, 40(2), 173–181. https://doi.org/10.1080/00207390701691558
- Kansanen, P., & Meri, M. (1999). The didactic relation in the teaching-studying-learning process. Didaktik/Fachdidaktik as Science (-s) of the Teaching profession, 2(1), 107-116.
- Kelly, A. V. (1983) The Curriculum. Theory and practice 4e, London: Paul Chapman.
- Laevers, F. (2005). The curriculum as means to raise the quality of early childhood education. implications for policy. International Journal of Phytoremediation, 21(1), 17–29. https://doi.org/10.1080/13502930585209531
- López, A. C., Jiménez, E. S., & López, A. M. (2024). La ecuación lineal en un libro de texto oficial en República Dominicana (2013-2023): enseñanza. EDUCATECONCIENCIA, 32(3). https://doi.org/10.58299/edutec.v32i3.760
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- Ligozat, F., Amade-Escot, C., & Östman, L. (2015). Beyond subject specific approaches of teaching and learning: comparative didactics. Interchange, 46(4), 313–321. https://doi.org/10.1007/s10780-015-9260-8
- Mengistie, S. M. (2020). Enhancing students’ understanding of linear equation with one variable through teaching. International Journal of Trends in Mathematics Education Research, 3(2), 69–80. https://doi.org/10.33122/ijtmer.v3i2.148
- Németh, Á. E. (2017). Teaching graphs for contestants in lower-secondary-school-age. Olympiads in Informatics, 11, 41–53. https://doi.org/10.15388/ioi.2017.04
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- Palló, G. (2006). Encyclopedia as textbook. Science and Education, 15(7–8), 779–799. https://doi.org/10.1007/s11191-004-1998-9
- Pinto, E., & Cañadas, M. C. (2021). Generalizations of third and fifth graders within a functional approach to early algebra. Mathematics Education Research Journal, 33(1), 113–134. https://doi.org/10.1007/s13394-019-00300-2
- Putri, A. D., Yerizon, Y., Arnellis, A., & Suherman, S. (2024). Development of realistic mathematics education-based teaching materials to increase students’ mathematical literacy ability. In AIP Conference Proceedings (Vol. 3024, No. 1). https://doi.org/10.1063/5.0204587
- Putri, A. H., & Suhardi, S. (2023). The Influence of the Political System on Education Curriculum Policy in Indonesia. AL-ISHLAH: Jurnal Pendidikan, 15(4), 4384-4392. https://doi.org/10.35445/alishlah.v15i4.3184
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- Smith, K. B. (1997). Exploration and visualization: making critical connections about linear systems of equations. School Science and Mathematics, 97(1), 13–19. https://doi.org/10.1111/j.1949-8594.1997.tb17335.x
- Sulastri, R., Suryadi, D., Prabawanto, S., & Cahya, E. (2022). Epistemological obstacles on limit and functions concepts-a phenomenological study in online learning. Mathematics Teaching-Research Journal, 14(5), 84–106. https://eric.ed.gov/?id=EJ1382285
- Suryadi, D. (2019). Landasan filosofis penelitian desain didaktis (DDR). Pusat Pengembangan DDR Indonesia.
- Suryadi, D., Itoh, T., & Isnarto. (2023). A prospective mathematics teacher’s lesson planning: An in-depth analysis from the anthropological theory of the didactic. Journal on Mathematics Education, 14(4), 723–740. https://doi.org/10.22342/jme.v14i4.pp723-740
- Takeuchi, H., & Shinno, Y. (2020). Comparing the lower secondary textbooks of Japan and England: A praxeological analysis of symmetry and transformations in geometry. International Journal of Science and Mathematics Education. 18(4), 791–810. https://doi.org/10.1007/s10763-019-09982-3
- Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315–327. https://doi.org/10.1016/j.stueduc.2005.11.005
- Utami, N. S., Prabawanto, S., & Suryadi, D. (2023). How students generate patterns in learning algebra? A focus on functional thinking in secondary school students. European Journal of Educational Research, 12(2), 913–925. https://doi.org/10.12973/eu-jer.12.2.913
- Utami, N. S., Prabawanto, S., & Suryadi, D. (2024). How do Indonesian students learn function concepts? A praxeological analysis of textbook. Journal on Mathematics Education, 15(2), 451–472. https://doi.org/10.22342/jme.v15i2.pp451-472
- Watanabe, T. (2011). Shiki: A critical foundation for school algebra in Japanese elementary school mathematics. In Early algebraization: A global dialogue from multiple perspectives (pp. 109-124). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_7
- Wickman, P. O. (2012). Using pragmatism to develop didactics in Sweden. Zeitschrift Fur Erziehungswissenschaft, 15(3), 483–501. https://doi.org/10.1007/s11618-012-0287-7
- Wijayanti, D., & Winslow, C. (2017). Mathematical practice in textbooks analysis: Praxeological reference models, the case of proportion. Journal of Research in Mathematics Education, 6(3), 307–330. https://doi.org/10.17583/redimat.2017.2078
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References
Adelman, H. S., Reyna, C., Collins, R., Onghai, J., & Taylor, L. (1999). Fundamental concerns about policy for addressing barriers to student learning. Reading and Writing Quarterly, 15(4), 327–349. https://doi.org/10.1080/105735699278134.
Al-Daami, K. K., & Wallace, G. (2007). Curriculum reform in a global context: A study of teachers in Jordan. Journal of Curriculum Studies, 39(3), 339–360. https://doi.org/10.1080/00220270601057790.
Arslan, S., Baran, D., & Okumus, S. (2011). Brousseau’s Theory of Didactical Situations in mathematics and an application of adidactical situations. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 5(1), 204-224.
Astriani. L., Mujib. A., & Firmansyah. (2022). Didactic design for overcoming learning obstacles in mathematics of junior high school students. International Journal of Educational Research Excellence (IJERE), 1(1), 58–62. https://doi.org/10.55299/ijere.v1i1.97
Barbosa, E. J. T., & Lima, A. P. D. A. B. (2020). Teacher's Praxeologies: Comparative Analysis of the Textbook in Teaching First-Degree Polynomial Equations. Educação Matemática Pesquisa, 22(4), 224-231. https://doi.org/10.23925/1983-3156.2020v22i4p224-231
Blanton, M. L. (2008). Algebra and the elementary classroom: Transforming thinking, transforming practice. Heinemann Educational Books.
Bondi, W. (2008). Curriculum Development: A Guide to Practice. United States: Merril.
Bosch, M., & Gascón, J. (2014). Introduction to the Anthropological Theory of the Didactic (ATD). Networking of theories as a research practice in mathematics education, 67-83. Springer Cham. https://doi.org/10.1007/978-3-319-05389-9
Bosch, M., Hausberger, T., Hochmuth, R., Kondratieva, M., & Winsløw, C. (2021). External didactic transposition in undergraduate mathematics. International Journal of Research in Undergraduate Mathematics Education, 7(1), 140-162. https://doi.org/10.1007/s40753-020-00132-7
Brousseau, G. (2002). Epistemological obstacles, problems, and didactical engineering. Theory of didactical situations in mathematics. Didactique Des MathEmatiques, 1970-1990, (1 983), 79–117. https://doi.org/10.1007/0-306-47211-2_6
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
Creswell, J. W. (2016). Research design: Pendekatan metode kualitatif, kuantitatif, dan campuran. Yogyakarta: Pustaka Pelajar, 5.
Daher, W., Baya’a, N., & Jaber, O. (2022). Understanding prospective teachers’ task design considerations through the lens of the theory of didactical situations. Mathematics, 10(3). https://doi.org/10.3390/math10030417
Eldridge, S. (1935). Textbooks, teachers, and students. American Journal of Sociology, 40(5), 637-645. https://doi.org/10.1086/216901
Elkjær, M., & Jankvist, U. T. (2021). Designing tasks for a dynamic online environment: Applying research into students’ difficulties with linear equations. Mathematics, 9(5). https://doi.org/10.3390/math9050557
Fan, L. (2013). Textbook research as scientific research: Towards a common ground on issues and methods of research on mathematics textbooks. ZDM - International Journal on Mathematics Education, 45(5), 765–777. https://doi.org/10.1007/s11858-013-0530-6
Fardian, D., Suryadi, D., Prabawanto, S., & Hayuningrat, S. (2024). Research trends on early algebra in the middle school: A combined bibliometric and meta-analysis review. Jurnal Elemen, 10(2), 410-440. https://doi.org/10.29408/jel.v10i2.25539
Fardian, D., & Dasari, D. (2023). The effects of problem-based learning on mathematical proficiency: A combined bibliometric analysis and meta-analysis review. Journal of Didactic Studies, 1(2), 99–113. https://doi.org/10.17509/jds.v1i2.65591
Grigg, J. (2012). School enrollment changes and student achievement growth: A case study in educational disruption and continuity. Sociology of Education, 85(4), 388–404. https://doi.org/10.1177/0038040712441374
Hadar, L. L. (2017). Opportunities to learn: Mathematics textbooks and students’ achievements. Studies in Educational Evaluation, 55(May), 153–166. https://doi.org/10.1016/j.stueduc.2017.10.002
Hansson, S. O. (2006). How to define: a tutorial. Princípios: Revista de Filosofia (UFRN), 13(19–20), 05–30. https://periodicos.ufrn.br/principios/article/view/50
Hendricson, W. D., & Kleffner, J. H. (2002). Assessing and helping challenging students: part one, why do some students have difficulty learning? Journal of Dental Education, 66(1), 43–61. https://doi.org/10.1002/j.0022-0337.2002.66.1.tb03507.x
Hendriyanto, A., Suryadi, D., Dahlan, J. A., & Juandi, D. (2023). Praxeology review: Comparing Singaporean and Indonesian textbooks in introducing the concept of sets. Eurasia Journal of Mathematics, Science and Technology Education, 19(2). https://doi.org/10.29333/ejmste/12953
Huang, X., Huang, R., & Bosch, M. (2021). Analyzing a teacher’s learning through cross-cultural collaboration: A praxeological perspective of mathematical knowledge for teaching. Educational Studies in Mathematics, 107(3), 427–446. https://doi.org/10.1007/s10649-021-10057-w
Hussain, A., Jat, Z. G., Hassan, M., Hafeez, A., Iqbal, S., & Imran, M. (2022). Curriculum reforms in school education sector in Sindh; What has changed? Journal of Positive School Psychology, 6(9), 2675–2687. https://ssrn.com/abstract=4251678
Insani, S. U., & Akbar, P. (2019). Development of open-ended based mathematics problem to measure high-level thinking ability. In Journal of Physics: Conference Series (Vol. 1315, No. 1, p. 012047). IOP Publishing. https://doi.org/10.1088/1742-6596/1315/1/012047
Isnawan, M. G., Suryadi, D., Turmudi, T., & Marfuah, M. (2022). Parental obstacles during distance learning mathematics in Indonesia: A phenomenology study. European Journal of Educational Research, 11(2), 873-883. https://doi.org/10.12973/eu-jer.11.2.873
Istanti, D. J. (2014). Dinamika Kebijakan Kurikulum Pendidikan di Indonesia Pasca Reformasi. JIPP: Jurnal Ilmu Politik Dan Ilmu Pemerintahan, 05(02), 140–156. https://doi.org/10.37058/jipp.v5i2.1537
Johar, R., Sasalia, P., Desy, Ramli, M., & Walker, H. C. O. (2023). Preservice teachers’ noticing skills in relation to student misconceptions in algebra. European Journal of Educational Research, 12(2), 865–879. https://doi.org/10.12973/eu-jer.12.2.865
Kajander, A., & Lovric, M. (2009). Mathematics textbooks and their potential role in supporting misconceptions. International Journal of Mathematical Education in Science and Technology, 40(2), 173–181. https://doi.org/10.1080/00207390701691558
Kansanen, P., & Meri, M. (1999). The didactic relation in the teaching-studying-learning process. Didaktik/Fachdidaktik as Science (-s) of the Teaching profession, 2(1), 107-116.
Kelly, A. V. (1983) The Curriculum. Theory and practice 4e, London: Paul Chapman.
Laevers, F. (2005). The curriculum as means to raise the quality of early childhood education. implications for policy. International Journal of Phytoremediation, 21(1), 17–29. https://doi.org/10.1080/13502930585209531
López, A. C., Jiménez, E. S., & López, A. M. (2024). La ecuación lineal en un libro de texto oficial en República Dominicana (2013-2023): enseñanza. EDUCATECONCIENCIA, 32(3). https://doi.org/10.58299/edutec.v32i3.760
Li, Y., Chen, X., & An, S. (2009). Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: The case of fraction division. ZDM - International Journal on Mathematics Education, 41(6), 809–826. https://doi.org/10.1007/s11858-009-0177-5
Ligozat, F., Amade-Escot, C., & Östman, L. (2015). Beyond subject specific approaches of teaching and learning: comparative didactics. Interchange, 46(4), 313–321. https://doi.org/10.1007/s10780-015-9260-8
Mengistie, S. M. (2020). Enhancing students’ understanding of linear equation with one variable through teaching. International Journal of Trends in Mathematics Education Research, 3(2), 69–80. https://doi.org/10.33122/ijtmer.v3i2.148
Németh, Á. E. (2017). Teaching graphs for contestants in lower-secondary-school-age. Olympiads in Informatics, 11, 41–53. https://doi.org/10.15388/ioi.2017.04
Nurlaily, V. A., Soegiyanto, H., & Usodo, B. (2019). Elementary school teacher’s obstacles in the implementation of problem-based learning model in mathematics learning. Journal on Mathematics Education, 10(2), 229–238. https://doi.org/10.22342/jme.10.2.5386.229-238
Palló, G. (2006). Encyclopedia as textbook. Science and Education, 15(7–8), 779–799. https://doi.org/10.1007/s11191-004-1998-9
Pinto, E., & Cañadas, M. C. (2021). Generalizations of third and fifth graders within a functional approach to early algebra. Mathematics Education Research Journal, 33(1), 113–134. https://doi.org/10.1007/s13394-019-00300-2
Putri, A. D., Yerizon, Y., Arnellis, A., & Suherman, S. (2024). Development of realistic mathematics education-based teaching materials to increase students’ mathematical literacy ability. In AIP Conference Proceedings (Vol. 3024, No. 1). https://doi.org/10.1063/5.0204587
Putri, A. H., & Suhardi, S. (2023). The Influence of the Political System on Education Curriculum Policy in Indonesia. AL-ISHLAH: Jurnal Pendidikan, 15(4), 4384-4392. https://doi.org/10.35445/alishlah.v15i4.3184
Robinson, T. J., Fischer, L., Wiley, D., & Hilton, J. (2014). The impact of open textbooks on secondary science learning outcomes. Educational Researcher, 43(7), 341–351. https://doi.org/10.3102/0013189X14550275
Smith, K. B. (1997). Exploration and visualization: making critical connections about linear systems of equations. School Science and Mathematics, 97(1), 13–19. https://doi.org/10.1111/j.1949-8594.1997.tb17335.x
Sulastri, R., Suryadi, D., Prabawanto, S., & Cahya, E. (2022). Epistemological obstacles on limit and functions concepts-a phenomenological study in online learning. Mathematics Teaching-Research Journal, 14(5), 84–106. https://eric.ed.gov/?id=EJ1382285
Suryadi, D. (2019). Landasan filosofis penelitian desain didaktis (DDR). Pusat Pengembangan DDR Indonesia.
Suryadi, D., Itoh, T., & Isnarto. (2023). A prospective mathematics teacher’s lesson planning: An in-depth analysis from the anthropological theory of the didactic. Journal on Mathematics Education, 14(4), 723–740. https://doi.org/10.22342/jme.v14i4.pp723-740
Takeuchi, H., & Shinno, Y. (2020). Comparing the lower secondary textbooks of Japan and England: A praxeological analysis of symmetry and transformations in geometry. International Journal of Science and Mathematics Education. 18(4), 791–810. https://doi.org/10.1007/s10763-019-09982-3
Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315–327. https://doi.org/10.1016/j.stueduc.2005.11.005
Utami, N. S., Prabawanto, S., & Suryadi, D. (2023). How students generate patterns in learning algebra? A focus on functional thinking in secondary school students. European Journal of Educational Research, 12(2), 913–925. https://doi.org/10.12973/eu-jer.12.2.913
Utami, N. S., Prabawanto, S., & Suryadi, D. (2024). How do Indonesian students learn function concepts? A praxeological analysis of textbook. Journal on Mathematics Education, 15(2), 451–472. https://doi.org/10.22342/jme.v15i2.pp451-472
Watanabe, T. (2011). Shiki: A critical foundation for school algebra in Japanese elementary school mathematics. In Early algebraization: A global dialogue from multiple perspectives (pp. 109-124). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_7
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Wijayanti, D., & Winslow, C. (2017). Mathematical practice in textbooks analysis: Praxeological reference models, the case of proportion. Journal of Research in Mathematics Education, 6(3), 307–330. https://doi.org/10.17583/redimat.2017.2078
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