Main Article Content
Abstract
The integration of three-dimensional geometry in secondary mathematics education plays a crucial role in developing students' spatial reasoning and problem-solving skills. However, textbooks often present limitations in structuring tasks, techniques, and justifications, which may lead to learning obstacles. Despite the importance of well-designed instructional materials, there is a lack of comprehensive studies analyzing Indonesian mathematics textbooks using both the praxeological framework and the learning obstacles perspective in didactic situations. Addressing this gap, this study examines a Grade XII mathematics textbook in Indonesia, focusing on three-dimensional geometry through a structured content analysis. The analysis categorizes tasks based on praxeological components, including types of tasks, solution techniques, technological justifications, and supporting theories, while also identifying potential learning obstacles related to the clarity of visual representations and contextual problem diversity. The findings reveal that the textbook includes 10 types of tasks, solved using 6 techniques, supported by 7 forms of technological reasoning, all grounded in three-dimensional geometry concepts. The presentation of tasks is systematically structured and balances conceptual and procedural aspects, minimizing significant didactic obstacles. However, epistemological obstacles were identified, primarily due to limited visualizations and a lack of diverse contextual tasks, which may hinder students’ flexibility in applying three-dimensional geometry concepts. These findings highlight the need for improved task design and enhanced visual representations to foster deeper conceptual understanding and adaptability in problem-solving. This study contributes to mathematics education research by providing empirical insights into textbook design and its impact on students' learning processes, offering recommendations for more effective instructional material development.
Keywords
Article Details

This work is licensed under a Creative Commons Attribution 4.0 International License.
References
- Artigue, M., & Bosch, M. (2014). Reflection on networking through the praxeological lens. Networking of Theories as a Research Practice in Mathematics Education, 249–265. https://doi.org/10.1007/978-3-319-05389-9
- Bosch, M. (2015). Doing research within the anthropological theory of the didactic: The case of school algebra. Selected Regular Lectures from the 12th International Congress on Mathematical Education, 51–69. https://doi.org/10.1007/978-3-319-17187-6
- Bosch, M., Chevallard, Y., Garcia, F. J., & Monaghan, J. (2020). Working with the anthropological theory of the didactic in mathematics education. In Working with the Anthropological Theory of the Didactic in Mathematics Education. Routledge Taylor & Francis Group. https://doi.org/10.4324/9780429198168
- 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. https://doi.org/10.1007/978-3-319-05389-9
- Bosch, M., Gascón, J., & Trigueros, M. (2017). Dialogue between theories interpreted as research praxeologies: the case of APOS and the ATD. Educational Studies in Mathematics, 95(1), 39–52. https://doi.org/10.1007/s10649-016-9734-3
- Brousseau, G. (2002). Theory of didactical situations in mathematics. In N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds.), Theory of Didactical Situations in Mathematics. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2
- Céspedes, M. J. C., Burgos, M., & Godino, J. D. (2022). Building a guide to analyse mathematics textbooks based on the didactical suitability theory. Educacao e Pesquisa, 48, 1–18. https://doi.org/10.1590/S1678-4634202248238787eng
- Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. Proceedings of the IV Congress of the European Society for Research in Mathematics Education, 21–30. https://doi.org/10.1093/0198248601.003.0007
- Chevallard, Y. (2007). Passé et présent de la théorie anthropologique du didactique. In Sociedad, escuela y matemáticas. Aportaciones de la Teoría Antropológica de lo Didáctico. http://yves.chevallard.free.fr/spip/spip/article.php3?id_article=134
- 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://www.jasme.jp/hjme/download/05_Yves%20Chevallard.pdf
- Chevallard, Y., & Bosch, M. (2014). Didactic transposition in mathematics education. Encyclopedia of Mathematics Education, 1984, 170–174. https://doi.org/10.1007/978-94-007-4978-8_48
- Chevallard, Y., & Bosch, M. (2019). Anthropological Theory of the Didactic (ATD). Encyclopedia of Mathematics Education, 1–8. https://doi.org/10.1007/978-3-319-77487-9_100034-1
- Chevallard, Y., & Sensevy, G. (2014). Anthropological approaches in mathematics education, french perspectives. Encyclopedia of Mathematics Education, 38–43. https://doi.org/10.1007/978-94-007-4978-8_9
- 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
- Fan, L., Mailizar, M., Alafaleq, M., & Wang, Y. (2018). A comparative study on the presentation of geometric proof in secondary mathematics textbooks in China, Indonesia, and Saudi Arabia. 53–65. https://doi.org/10.1007/978-3-319-73253-4_3
- Fujita, T., & Jones, K. (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81–91. https://doi.org/10.1016/j.ijer.2013.09.014
- González-Martín, A. S., Giraldo, V., & Souto, A. M. (2013). The introduction of real numbers in secondary education: An institutional analysis of textbooks. Research in Mathematics Education, 15(3), 230–248. https://doi.org/10.1080/14794802.2013.803778
- Gracin, D. G. (2018). Requirements in mathematics textbooks: a five-dimensional analysis of textbook exercises and examples. International Journal of Mathematical Education in Science and Technology, 49(7), 1003–1024. https://doi.org/10.1080/0020739X.2018.1431849
- Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks in england, france and germany: Some challenges for England. Research in Mathematics Education, 4(1), 127–144. https://doi.org/10.1080/14794800008520106
- Hardy, G. . H. . (1925). What Is Geometry ? ( Presidential Address to the Mathematical Association , 1925 ). 12(175), 309–316.
- Hariyani, M., Herman, T., Suryadi, D., & Prabawanto, S. (2022). Exploration of student learning obstacles in solving fraction problems in elementary school. International Journal of Educational Methodology, 8(3), 505-515. https://doi.org/10.12973/ijem.8.3.505
- 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), em2229. https://doi.org/10.29333/ejmste/12953
- Jablonski, S., & Ludwig, M. (2023). Teaching and learning of geometry—a literature review on current developments in theory and practice. Education Sciences, 13(7), 682. https://doi.org/10.3390/educsci13070682
- Jessen, B., Bos, R., Doorman, M., & Winsløw, C. (2023). Lesson study in mathematics with TDS and RME as theoretical support: two cases from the European TIME project. International Journal for Lesson and Learning Studies, 12(1), 52–64. https://doi.org/10.1108/IJLLS-01-2022-0009
- Kusumah, Y. S., Kustiawati, D., & Herman, T. (2020). The effect of geogebra in three-dimensional geometry learning on students’ mathematical communication ability. International Journal of Instruction, 13(2), 895–908. https://doi.org/10.29333/iji.2020.13260a
- Leung, A., & Bolite-Frant, J. (2015). Designing mathematics tasks: The role of tools. In New ICMI Study Series. https://doi.org/10.1007/978-3-319-09629-2_6
- Miftah, R., Amalina, A. N., & Kurniawati, L. (2022). Didactical design of mathematical reasoning on three dimensional in high school. Journal of Physics: Conference Series, 2157(1). https://doi.org/10.1088/1742-6596/2157/1/012043
- Pansell, A. (2023). Mathematical knowledge for teaching as a didactic praxeology. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1165977
- Pepin, B., Gueudet, G., & Trouche, L. (2013). Investigating textbooks as crucial interfaces between culture, policy and teacher curricular practice: Two contrasted case studies in France and Norway. ZDM - International Journal on Mathematics Education, 45(5), 685–698. https://doi.org/10.1007/s11858-013-0526-2
- Prihandhika, A., Prabawanto, S., Turmudi, T., & Suryadi, D. (2020). Epistemological obstacles: An overview of thinking process on derivative concepts by APOS theory and clinical interview. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032028
- Putra, Z. H. (2017). Anthropological theory of the didactic : A new research anthropological theory of the didactic : a new research perspective. Proceeding of the second international conference on education, technology, and sciences: Integrating technology and sciences into early and primary education, June, 142–149. https://researchprofiles.ku.dk/da/publications/anthropological-theory-of-the-didactic-a-new-research-perspective
- Putra, Z. H. (2020). Didactic transposition of rational numbers: A case from a textbook analysis and prospective elementary teachers’ mathematical and didactic knowledge. Journal of Elementary Education, 13(4), 365–394. https://doi.org/10.18690/rei.13.4.365-394.2020
- Rahimah, D., & Visnovska, J. (2021). Analysis of mathematics textbook use: An argument for combining horizontal, vertical, and contextual analyses. Journal of Physics: Conference Series, 1731(1). https://doi.org/10.1088/1742-6596/1731/1/012048
- Sari, I. P., Suryadi, D., Herman, T., Dahlan, J. A., & Supriyadi, E. (2024). Learning obstacles on fractions: A scoping review. Infinity Journal, 13(2), 377–392. https://doi.org/10.22460/infinity.v13i2.p377-392
- Schneider, M. (2014). Epistemological obstacles in mathematics education. Encyclopedia of Mathematics Education, 90(3), 214–217. https://doi.org/10.1007/978-94-007-4978-8_57
- Schubring, G., & Fan, L. (2018). Recent advances in mathematics textbook research and development: an overview. ZDM - Mathematics Education, 50(5), 765–771. https://doi.org/10.1007/s11858-018-0979-4
- Sievert, H., van den Ham, A. K., Niedermeyer, I., & Heinze, A. (2019). Effects of mathematics textbooks on the development of primary school children’s adaptive expertise in arithmetic. Learning and Individual Differences, 74(January), 101716. https://doi.org/10.1016/j.lindif.2019.02.006
- Stylianides, G. J. (2014). Textbook analyses on reasoning-and-proving: Significance and methodological challenges. International Journal of Educational Research, 64, 63–70. https://doi.org/10.1016/j.ijer.2014.01.002
- Suryadi, D. (2019). Penelitian desain didaktis (DDR) dan implementasinya. Gapura Press
- Suryadi, D. (2023). Jalan epistemik menghasilkan pengetahuan melalui Didactical Design Research (DDR). Pusat Pengembangan DDR Indonesia (PUSBANGDDRINDO)
- 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
- van den Ham, A. K., & Heinze, A. (2018). Does the textbook matter? Longitudinal effects of textbook choice on primary school students’ achievement in mathematics. Studies in Educational Evaluation, 59(July), 133–140. https://doi.org/10.1016/j.stueduc.2018.07.005
- Yenil, T., Arslan, Ç., & Tapan Broutin, M. S. (2023). Triangle inequality concept teaching: The theory of didactic situations case. Journal of Pedagogical Research, 7(4), 14–29. https://doi.org/10.33902/JPR.202318961
- 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
- Zhang, Q. (2021). Opportunities to learn three-dimensional shapes in primary mathematics: The case of content analysis of primary mathematics textbooks in Hong Kong. Eurasia Journal of Mathematics, Science and Technology Education, 17(6), 1–15. https://doi.org/10.29333/ejmste/10884
- Zhang, Y., & Savard, A. (2023). Defining computational thinking as an evident tool in problem-solving: Comparative research on Chinese and Canadian mathematics textbooks. ECNU Review of Education. https://doi.org/10.1177/20965311231158393
References
Artigue, M., & Bosch, M. (2014). Reflection on networking through the praxeological lens. Networking of Theories as a Research Practice in Mathematics Education, 249–265. https://doi.org/10.1007/978-3-319-05389-9
Bosch, M. (2015). Doing research within the anthropological theory of the didactic: The case of school algebra. Selected Regular Lectures from the 12th International Congress on Mathematical Education, 51–69. https://doi.org/10.1007/978-3-319-17187-6
Bosch, M., Chevallard, Y., Garcia, F. J., & Monaghan, J. (2020). Working with the anthropological theory of the didactic in mathematics education. In Working with the Anthropological Theory of the Didactic in Mathematics Education. Routledge Taylor & Francis Group. https://doi.org/10.4324/9780429198168
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. https://doi.org/10.1007/978-3-319-05389-9
Bosch, M., Gascón, J., & Trigueros, M. (2017). Dialogue between theories interpreted as research praxeologies: the case of APOS and the ATD. Educational Studies in Mathematics, 95(1), 39–52. https://doi.org/10.1007/s10649-016-9734-3
Brousseau, G. (2002). Theory of didactical situations in mathematics. In N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds.), Theory of Didactical Situations in Mathematics. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2
Céspedes, M. J. C., Burgos, M., & Godino, J. D. (2022). Building a guide to analyse mathematics textbooks based on the didactical suitability theory. Educacao e Pesquisa, 48, 1–18. https://doi.org/10.1590/S1678-4634202248238787eng
Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. Proceedings of the IV Congress of the European Society for Research in Mathematics Education, 21–30. https://doi.org/10.1093/0198248601.003.0007
Chevallard, Y. (2007). Passé et présent de la théorie anthropologique du didactique. In Sociedad, escuela y matemáticas. Aportaciones de la Teoría Antropológica de lo Didáctico. http://yves.chevallard.free.fr/spip/spip/article.php3?id_article=134
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://www.jasme.jp/hjme/download/05_Yves%20Chevallard.pdf
Chevallard, Y., & Bosch, M. (2014). Didactic transposition in mathematics education. Encyclopedia of Mathematics Education, 1984, 170–174. https://doi.org/10.1007/978-94-007-4978-8_48
Chevallard, Y., & Bosch, M. (2019). Anthropological Theory of the Didactic (ATD). Encyclopedia of Mathematics Education, 1–8. https://doi.org/10.1007/978-3-319-77487-9_100034-1
Chevallard, Y., & Sensevy, G. (2014). Anthropological approaches in mathematics education, french perspectives. Encyclopedia of Mathematics Education, 38–43. https://doi.org/10.1007/978-94-007-4978-8_9
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
Fan, L., Mailizar, M., Alafaleq, M., & Wang, Y. (2018). A comparative study on the presentation of geometric proof in secondary mathematics textbooks in China, Indonesia, and Saudi Arabia. 53–65. https://doi.org/10.1007/978-3-319-73253-4_3
Fujita, T., & Jones, K. (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81–91. https://doi.org/10.1016/j.ijer.2013.09.014
González-Martín, A. S., Giraldo, V., & Souto, A. M. (2013). The introduction of real numbers in secondary education: An institutional analysis of textbooks. Research in Mathematics Education, 15(3), 230–248. https://doi.org/10.1080/14794802.2013.803778
Gracin, D. G. (2018). Requirements in mathematics textbooks: a five-dimensional analysis of textbook exercises and examples. International Journal of Mathematical Education in Science and Technology, 49(7), 1003–1024. https://doi.org/10.1080/0020739X.2018.1431849
Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks in england, france and germany: Some challenges for England. Research in Mathematics Education, 4(1), 127–144. https://doi.org/10.1080/14794800008520106
Hardy, G. . H. . (1925). What Is Geometry ? ( Presidential Address to the Mathematical Association , 1925 ). 12(175), 309–316.
Hariyani, M., Herman, T., Suryadi, D., & Prabawanto, S. (2022). Exploration of student learning obstacles in solving fraction problems in elementary school. International Journal of Educational Methodology, 8(3), 505-515. https://doi.org/10.12973/ijem.8.3.505
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), em2229. https://doi.org/10.29333/ejmste/12953
Jablonski, S., & Ludwig, M. (2023). Teaching and learning of geometry—a literature review on current developments in theory and practice. Education Sciences, 13(7), 682. https://doi.org/10.3390/educsci13070682
Jessen, B., Bos, R., Doorman, M., & Winsløw, C. (2023). Lesson study in mathematics with TDS and RME as theoretical support: two cases from the European TIME project. International Journal for Lesson and Learning Studies, 12(1), 52–64. https://doi.org/10.1108/IJLLS-01-2022-0009
Kusumah, Y. S., Kustiawati, D., & Herman, T. (2020). The effect of geogebra in three-dimensional geometry learning on students’ mathematical communication ability. International Journal of Instruction, 13(2), 895–908. https://doi.org/10.29333/iji.2020.13260a
Leung, A., & Bolite-Frant, J. (2015). Designing mathematics tasks: The role of tools. In New ICMI Study Series. https://doi.org/10.1007/978-3-319-09629-2_6
Miftah, R., Amalina, A. N., & Kurniawati, L. (2022). Didactical design of mathematical reasoning on three dimensional in high school. Journal of Physics: Conference Series, 2157(1). https://doi.org/10.1088/1742-6596/2157/1/012043
Pansell, A. (2023). Mathematical knowledge for teaching as a didactic praxeology. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1165977
Pepin, B., Gueudet, G., & Trouche, L. (2013). Investigating textbooks as crucial interfaces between culture, policy and teacher curricular practice: Two contrasted case studies in France and Norway. ZDM - International Journal on Mathematics Education, 45(5), 685–698. https://doi.org/10.1007/s11858-013-0526-2
Prihandhika, A., Prabawanto, S., Turmudi, T., & Suryadi, D. (2020). Epistemological obstacles: An overview of thinking process on derivative concepts by APOS theory and clinical interview. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032028
Putra, Z. H. (2017). Anthropological theory of the didactic : A new research anthropological theory of the didactic : a new research perspective. Proceeding of the second international conference on education, technology, and sciences: Integrating technology and sciences into early and primary education, June, 142–149. https://researchprofiles.ku.dk/da/publications/anthropological-theory-of-the-didactic-a-new-research-perspective
Putra, Z. H. (2020). Didactic transposition of rational numbers: A case from a textbook analysis and prospective elementary teachers’ mathematical and didactic knowledge. Journal of Elementary Education, 13(4), 365–394. https://doi.org/10.18690/rei.13.4.365-394.2020
Rahimah, D., & Visnovska, J. (2021). Analysis of mathematics textbook use: An argument for combining horizontal, vertical, and contextual analyses. Journal of Physics: Conference Series, 1731(1). https://doi.org/10.1088/1742-6596/1731/1/012048
Sari, I. P., Suryadi, D., Herman, T., Dahlan, J. A., & Supriyadi, E. (2024). Learning obstacles on fractions: A scoping review. Infinity Journal, 13(2), 377–392. https://doi.org/10.22460/infinity.v13i2.p377-392
Schneider, M. (2014). Epistemological obstacles in mathematics education. Encyclopedia of Mathematics Education, 90(3), 214–217. https://doi.org/10.1007/978-94-007-4978-8_57
Schubring, G., & Fan, L. (2018). Recent advances in mathematics textbook research and development: an overview. ZDM - Mathematics Education, 50(5), 765–771. https://doi.org/10.1007/s11858-018-0979-4
Sievert, H., van den Ham, A. K., Niedermeyer, I., & Heinze, A. (2019). Effects of mathematics textbooks on the development of primary school children’s adaptive expertise in arithmetic. Learning and Individual Differences, 74(January), 101716. https://doi.org/10.1016/j.lindif.2019.02.006
Stylianides, G. J. (2014). Textbook analyses on reasoning-and-proving: Significance and methodological challenges. International Journal of Educational Research, 64, 63–70. https://doi.org/10.1016/j.ijer.2014.01.002
Suryadi, D. (2019). Penelitian desain didaktis (DDR) dan implementasinya. Gapura Press
Suryadi, D. (2023). Jalan epistemik menghasilkan pengetahuan melalui Didactical Design Research (DDR). Pusat Pengembangan DDR Indonesia (PUSBANGDDRINDO)
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
van den Ham, A. K., & Heinze, A. (2018). Does the textbook matter? Longitudinal effects of textbook choice on primary school students’ achievement in mathematics. Studies in Educational Evaluation, 59(July), 133–140. https://doi.org/10.1016/j.stueduc.2018.07.005
Yenil, T., Arslan, Ç., & Tapan Broutin, M. S. (2023). Triangle inequality concept teaching: The theory of didactic situations case. Journal of Pedagogical Research, 7(4), 14–29. https://doi.org/10.33902/JPR.202318961
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
Zhang, Q. (2021). Opportunities to learn three-dimensional shapes in primary mathematics: The case of content analysis of primary mathematics textbooks in Hong Kong. Eurasia Journal of Mathematics, Science and Technology Education, 17(6), 1–15. https://doi.org/10.29333/ejmste/10884
Zhang, Y., & Savard, A. (2023). Defining computational thinking as an evident tool in problem-solving: Comparative research on Chinese and Canadian mathematics textbooks. ECNU Review of Education. https://doi.org/10.1177/20965311231158393