Main Article Content
Abstract
Mathematics textbooks are essential tools for facilitating the achievement of learning objectives, yet their use varies across classrooms, even when the same mathematical concepts are being taught. This study aims to investigate students' understanding of geometrical similarity through praxeological analysis within the framework of the Anthropological Theory of the Didactic (ATD). The analysis identifies differences in the structuring of geometrical similarity tasks between Indonesian and Singaporean textbooks. According to ATD praxeology, mathematical content is analyzed through the "praxis" and "logos" blocks, where praxis encompasses task types (T) and techniques (τ), while logos involves technology (θ) and theory (Θ). The findings highlight distinct priorities in how geometrical similarity is presented in textbooks from both countries, with implications for students’ conceptual and procedural understanding. Specifically, the absence of pantograph tasks in Singaporean textbooks and the lack of scale factor exercises in Indonesian textbooks reflect differences in knowledge construction and task emphasis. These variations impact students' ability to relate textbook knowledge to real-world applications. The study underscores the significance of incorporating a diverse range of task designs and practical experiences to enhance students' geometric reasoning abilities. A well-structured textbook not only supports students in achieving learning objectives but also fosters a continuous process of building, connecting, and deepening their mathematical understanding.
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References
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References
Abdullah, A. H., & Shin, B. (2019). A Comparative Study of Quadrilaterals Topic Content in Mathematics Textbooks between Malaysia and South Korea. Journal on Mathematics Education, 10(3), 315–340. https://doi.org/10.22342/jme.10.3.7572.315-340
Amaral, R. B., & Hollebrands, K. (2017). An analysis of context-based similarity tasks in textbooks from Brazil and the United States. International Journal of Mathematical Education in Science and Technology, 48(8), 1166–1184. https://doi.org/10.1080/0020739X.2017.1315188
Audi, R. (2010). Epistemology: A contemporary introduction to the theory of knowledge. Routledge. https://doi.org/10.4324/9780203846469
Basu, M., Koellner, K., Jacobs, J. K., & Seago, N. (2022). Understanding Similarity through Dilations of Nonstandard Shapes. Mathematics Teacher: Learning and Teaching PK-12, 115(9), 642–649. https://doi.org/10.5951/mtlt.2021.0284
Bosch, M., & Gascón, J. (2014). Introduction to the Anthropological Theory of the Didactic (ATD). In Networking of theories as a research practice in mathematics education (pp. 67–83). Springer. https://doi.org/10.1007/978-3-319-05389-9_5
Chaachoua, H., Bessot, A., Romo, A., & Castela, C. (2019). Developments and functionalities in the praxeological model. Working with the Anthropological Theory of the Didactic in Mathematics Education: A Comprehensive Casebook, 41. https://doi.org/10.4324/9780429198168-4
Chevallard, Y., & Bosch, M. (2020a). Anthropological theory of the didactic (ATD). Encyclopedia of Mathematics Education, 53–61. https://doi.org/10.1007/978-3-030-15789-0_100034
Chevallard, Y., & Bosch, M. (2020b). Didactic transposition in mathematics education. Encyclopedia of Mathematics Education, 214–218. https://doi.org/10.1007/978-3-030-15789-0_48
Chevallard, Y., Bosch, M., & Kim, S. (2015). What is a theory according to the anthropological theory of the didactic? CERME 9-Ninth Congress of the European Society for Research in Mathematics Education, 2614–2620. Retrieved from https://hal.science/hal-01289424
Choi, K. M., & Park, H.-J. (2013). A comparative analysis of geometry education on curriculum standards, textbook structure, and textbook items between the US and Korea. Eurasia Journal of Mathematics, Science and Technology Education, 9(4), 379–391. https://doi.org/10.12973/eurasia.2013.947a
Citrini, C. (2015). The Role of Geometry in Reasoning and Teaching. In The Visual Language of Technique: Volume 3-Heritage and Expectations in Education (pp. 77–91). Springer. https://doi.org/10.1007/978-3-319-05326-4_8
Clements, D. H., & Sarama, J. (2020). Learning and teaching early math: The learning trajectories approach. Routledge. https://doi.org/10.4324/9781003083528
Clivaz, S., & Miyakawa, T. (2020). The effects of culture on mathematics lessons: an international comparative study of a collaboratively designed lesson. Educational Studies in Mathematics, 105(1), 53–70. https://doi.org/10.1007/s10649-020-09980-1
Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers’ learning. The Elementary School Journal, 103(3), 287–311. https://doi.org/10.1086/499727
Cornelius, K. E., & Owiny, R. L. (2024). How Can I Ensure My Lessons Are Logically Sequenced? In The Practical Guide to High-Leverage Practices in Special Education (pp. 173–186). Routledge. https://doi.org/10.4324/9781003525844
Creswell, J. W. (2018). Mixed Methods Procedures. In Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. SAGE Publications Ltd. Retrieved from https://books.google.co.id/books?id=4uB76IC_pOQC&printsec=copyright&hl=id#v=onepage&q&f=false
DeJarnette, A. F., Lausell, S. L. R., & González, G. (2015). Shadow puppets: Exploring a context for similarity and dilations. The Mathematics Teacher, 109(1), 20–27. https://doi.org/10.5951/mathteacher.109.1.0020
Dixon, R. A., & Brown, R. A. (2012). Transfer of Learning: Connecting Concepts during Problem Solving. Journal of Technology Education, 24(1), 2–17. https://doi.org/10.21061/jte.v24i1.a.1
Flick, U. (2018). Designing qualitative research. (Vols. 1-0). SAGE Publications Ltd, https://doi.org/10.4135/9781529622737
Friesen, N., Henriksson, C., & Saevi, T. (2012). Hermeneutic phenomenology in education: Method and practice (M. Friesen, C. Henriksson, & T. Saevi (eds.); Vol. 4). Sense Publisher. https://doi.org/10.1007/978-94-6091-834-6
Glasnovic Gracin, D. (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
Gravemeijer, K. P. E. (2014). Transforming mathematics education: The role of textbooks and teachers. In Transforming mathematics instruction (pp. 153–172). Springer. https://doi.org/10.1007/978-3-319-04993-9_10
Guillen, D. E. F. (2019). Qualitative research: Hermeneutical phenomenological method. Propósitos y Representaciones, 7(1), 201–229. https://doi.org/10.20511/pyr2019.v7n1.267
Hidayah, M., & Forgasz, H. (2020). A Comparison of Mathematical Tasks Types Used in Indonesian and Australian Textbooks Based on Geometry Contents. Journal on Mathematics Education, 11(3), 385–404. https://doi.org/10.22342/jme.11.3.11754.385-404
Hodgen, J. (2010). Knowing and identity: A situated theory of mathematics knowledge in teaching. In Mathematical knowledge in teaching (pp. 27–42). Springer. https://doi.org/10.1007/978-90-481-9766-8_3
Hong, D. S., & Choi, K. M. (2018). Reasoning and Proving Opportunities in Textbooks: A Comparative Analysis. International Journal of Research in Education and Science, 4(1), 82–97. https://doi.org/10.21890/ijres.382937
Islam, M. (2020). Data analysis: types, process, methods, techniques and tools. International Journal on Data Science and Technology, 6(1), 10–15. https://doi.org/10.11648/j.ijdst.20200601.12
Jupri, A., Sispiyati, R., & Chin, K. E. (2021). An investigation of students algebraic proficiency from a structure sense perspective. Journal on Mathematics Education, 12(1), 315–340. https://doi.org/10.22342/jme.12.1.13125.147-158
Kang, W., & Kilpatrick, J. (1992). Didactic transposition in mathematics textbooks. For the Learning of Mathematics, 12(1), 2–7. Retrieved from https://api.semanticscholar.org/CorpusID:58900546
Lepik, M., Grevholm, B., & Viholainen, A. (2015). Using textbooks in the mathematics classroom–the teachers’ view. Nordic Studies in Mathematics Education, 20(3–4), 129–156. https://doi.org/10.15388/ActPaed.2015.35.9193
Lundberg, A. L. V., & Kilhamn, C. (2018). Transposition of Knowledge: Encountering Proportionality in an Algebra Task. International Journal of Science and Mathematics Education, 16(3), 559–579. https://doi.org/10.1007/s10763-016-9781-3
Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Routledge. https://doi.org/10.4324/9781003009443
Miyakawa, T., & Winsløw, C. (2019). Paradidactic infrastructure for sharing and documenting mathematics teacher knowledge: a case study of “practice research” in Japan. Journal of Mathematics Teacher Education, 22(3), 281–303. https://doi.org/10.1007/s10857-017-9394-y
O’Halloran, K. L., Beezer, R. A., & Farmer, D. W. (2018). A new generation of mathematics textbook research and development. ZDM, 50(5), 863–879. https://doi.org/10.1007/s11858-018-0959-8
OECD. (2023). PISA 2022 Results (Volume I): The State of Learning and Equity in Education (PISA). OECD Publishing. https://doi.org/10.1787/53f23881-en
Pansell, A., & Bjorklund Boistrup, L. (2018). Mathematics teachers’ teaching practices in relation to textbooks: exploring praxeologies. The Mathematics Enthusiast, 15(3), 541–562. https://doi.org/10.54870/1551-3440.1444
Pernia-Espinoza, A., Sanz-Garcia, A., Martinez-de-Pison-Ascacibar, F. J., Peciña-Marqueta, S., & Blanco-Fernandez, J. (2020). Technical projects with social commitment for teaching-learning intervention in STEM students. 2020 IEEE Global Engineering Education Conference (EDUCON), 579–586. https://doi.org/10.1109/EDUCON45650.2020.9125176
Peterson, A., Dumont, H., Lafuente, M., & Law, N. (2018). Understanding innovative pedagogies: Key themes to analyse new approaches to teaching and learning. https://doi.org/10.1787/19939019
Prediger, S., Barzel, B., Hußmann, S., & Leuders, T. (2021). Towards a research base for textbooks as teacher support: The case of engaging students in active knowledge organization in the KOSIMA project. ZDM–Mathematics Education, 53(6), 1233–1248. https://doi.org/10.1007/s11858-021-01245-2
Rezat, S., Fan, L., & Pepin, B. (2021). Mathematics textbooks and curriculum resources as instruments for change. ZDM – Mathematics Education, 53(6), 1189–1206. https://doi.org/10.1007/s11858-021-01309-3
Rodríguez-Nieto, C. A., Cervantes-Barraza, J. A., & Moll, V. F. (2023). Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories. Eurasia Journal of Mathematics, Science and Technology Education, 19(5), em2264. https://doi.org/10.29333/ejmste/13157
Sherman, M. F., Cayton, C., Walkington, C., & Funsch, A. (2020). An analysis of secondary mathematics textbooks with regard to technology integration. Journal for Research in Mathematics Education, 51(3), 361–374. https://doi.org/10.5951/jresemtheduc-2020-0005
Shi, L., Dong, L., Zhao, W., & Tan, D. (2023). Improving middle school students’ geometry problem solving ability through hands-on experience: An fNIRS study. Frontiers in Psychology, 14, 1126047. https://doi.org/10.3389/fpsyg.2023.1126047
Shinno, Y., & Mizoguchi, T. (2021). Theoretical approaches to teachers’ lesson designs involving the adaptation of mathematics textbooks: two cases from kyouzai kenkyuu in Japan. ZDM - Mathematics Education, 53(6), 1387–1402. https://doi.org/10.1007/s11858-021-01269-8
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, 101716. https://doi.org/10.1016/j.lindif.2019.02.006
Subchan, S., Winarni, W., Mufid, M. S., Fahim, K., & Syaifudin, W. H. (2018). Matematika SMP Kelas IX. Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud. Retrieved from https://buku.kemdikbud.go.id/katalog/Buku-Matematika-Kelas-IX
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
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