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References
- Afriyani, D., Sa’Dijah, C., Subanji, S., & Muksar, M. (2019). Students’ construction error in translation among mathematical representations. Journal of Physics: Conference Series, 1157(3), 032098. https://doi.org/10.1088/1742-6596/1157/3/032098
- Akar, N., & Işıksal-Bostan, M. (2022). The didactic transposition of quadrilaterals: the case of 5th grade in Turkey. International Journal of Mathematical Education in Science and Technology, 55(3), 1–22. https://doi.org/10.1080/0020739X.2021.2022228
- Alves, F. R. V., Mangueira, M. C. dos S., Catarino, P. M. M. C., & Vieira, R. P. M. (2021). Didactic engineering to teach leonardo sequence: A study on a complexification process in a mathematics teaching degree course. International Electronic Journal of Mathematics Education, 16(3), em0655. https://doi.org/10.29333/iejme/11196
- Alwan, A. A. (2011). Misconception of heat and temperature among physics students. Procedia - Social and Behavioral Sciences, 12(1), 600–614. https://doi.org/10.1016/j.sbspro.2011.02.074
- Amade-Escot, C. (2006). Student learning within the didactique tradition. In D. Kirk, M. O’Sullivanx, & D. Macdonald (Eds.), Handbook of Research in Physical Education (pp. 347–365). SAGE Publication Ltd. https://doi.org/10.4135/9781848608009.n20
- Andini, W., & Suryadi, D. (2017). Student obstacles in solving algebraic thinking problems. Journal of Physics: Conference Series, 895(1), 2–8. https://doi.org/10.1088/1742-6596/895/1/012091
- As’ari, A. R., Tohir, M., Valentino, E., Imron, Z., & Taufiq, I. (2017). Matematika SMP/MTs kelas VII semester 1 [Junior high school mathematics grade VII semester 1] (A. Lukito, A. Mahmudi, T. M, N. Priatna, Y. Satria, & Widowati (eds.); Rev. 2017). Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud.
- Asher, N., & Hunter, J. (2021). Interpretive blindness and the impossibility of learning from testimony. In F. Dignum, A. Lomuscio, U. Endriss, & A. Nowé (Eds.), Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS (Vol. 3, pp. 1437–1439). International Foundation for Autonomous Agents and Multiagent Systems.
- Banks, F., Leach, J., & Moon, B. (2005). Extract from new understandings of teachers’ pedagogic knowledge. Curriculum Journal, 16(3), 331–340. https://doi.org/10.1080/09585170500256446
- Bardini, C., Pierce, R. U., & Stacey, K. (2004). Teaching linear functions in context with graphics calculators: Students’ responses and the impact of the approach on their use of algebraic symbols. International Journal of Science and Mathematics Education, 2(3), 353–376. https://doi.org/10.1007/s10763-004-8075-3
- Bingolbali, E., Demir, G., & Monaghan, J. D. (2021). Knowledge of sets: A didactic phenomenon. International Journal of Science and Mathematics Education, 19(6), 1187–1208. https://doi.org/10.1007/s10763-020-10106-5
- Bolden, D. S., & Newton, L. D. (2008). Primary teachers’ epistemological beliefs: some perceived barriers to investigative teaching in primary mathematics. Educational Studies, 34(5), 419–432. https://doi.org/10.1080/03055690802287595
- Bray, W. S. (2011). A collective case study of the influence of teachers’ beliefs and knowledge on error-handling practices during class discussion of mathematics. Journal for Research in Mathematics Education, 42(1), 2–38. https://doi.org/10.5951/jresematheduc.42.1.0002
- Brousseau, G. (1976). Les obstacles épistémologiques et les problèmes en mathématiques. In W. Vanhamme & J. Vanhamme (Eds.), La problématique et l’enseignement des mathématiques. Comptes rendus de la XXVIIIe rencontre organisée par la Commission Internationale pour l’Etude et l’Amélioration de l’Enseignement des Mathématiques (Vol. 4, pp. 101–117). HAL Open Science. https://hal.science/hal-00516569
- Brousseau, G. (2002). The didactical contract: The teacher, the student and the milieu. In N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds.), Theory of Didactical Situations in Mathematics (Vol. 19, pp. 226--249). Springer Netherlands. https://doi.org/10.1007/0-306-47211-2_13
- Brousseau, G., & Warfield, V. (2020). Didactic transposition in mathematics education. In Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-94-007-4978-8_89
- Brown, S. A. (2008). Exploring epistemological obstacles to the development of mathematics induction. In K. A. Keene, S. Larsen, K. Marrongelle, V. Mesa, C. Rasmussen, N. Speer, K. Weber, & M. Zandieh (Eds.), Proceedings of the 11th Conference for Research on Undergraduate Mathematics Education (pp. 1–19). San Diego State University. http://sigmaa.maa.org/rume/crume2008/Proceedings/Proceedings.html
- Buford, C., & Cloos, C. M. (2018). A dilemma for the knowledge despite falsehood strategy. Episteme, 15(2), 166–182. https://doi.org/10.1017/epi.2016.53
- Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2015). Children’s mathematics: Cognitively guided instruction (2nd ed.). Heinemann. http://www.amazon.com/dp/0325001375
- Catrambone, R. (1994). Improving examples to improve transfer to novel problems. Memory & Cognition, 22(5), 606–615. https://doi.org/10.3758/BF03198399
- Chevallard, Y. (1989). On didatic transposition theory: some introductory notes. International Symposium on Selected Domains of Research and Development in Mathematics Education, 51–62. http://yves.chevallard.free.fr/spip/spip/article.php3?id_article=122
- Chevallard, Y., & Bosch, M. (2020). Didactic transposition in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 214--218). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0_48
- Creswell, J., & Guetterman, T. (2018). Educational Research: Planning, conducting, and evaluating quantitative and qualitative research (6th Edition). Pearson Education, Inc.
- 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), 417. https://doi.org/10.3390/math10030417
- de Mello, L. A. (2017). A propose of rules defining as a didactic transposition should occur or be achieved - The generalized didactic transposition theory. OSF Preprints, June. https://doi.org/https://doi.org/10.31219/osf.io/uzfhb
- De Sousa, R. T., & Alves, F. R. V. (2022). Didactic engineering and learning objects: A proposal for teaching parabolas in analytical geometry. Indonesian Journal of Science and Mathematics Education, 5(1), 1–16. https://doi.org/10.24042/ijsme.v5i1.11108
- Diana, N., Suryadi, D., & Dahlan, J. A. (2020). Analysis of students’ mathematical connection abilities in solving problem of circle material: Transposition study. Journal for the Education of Gifted Young Scientists, 8(2), 829–842. https://doi.org/10.17478/JEGYS.689673
- Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https://doi.org/10.1007/s10649-006-0400-z
- Ellis, G. W., & Turner, W. A. (2003). Helping students organize and retrieve their understanding of dynamics. ASEE Annual Conference Proceedings, 7535–7547. https://doi.org/10.18260/1-2--11592
- Enderton, H. B. (1977). Elements of set theory. Academic Press.
- Fauzi, I., & Suryadi, D. (2020). Learning obstacle the addition and subtraction of fraction in grade 5 elementary schools. MUDARRISA: Jurnal Kajian Pendidikan Islam, 12(1), 51–68. https://doi.org/10.18326/mdr.v12i1.51-68
- Ferdianto, F., & Hartinah, S. (2020). Analysis of the difficulty of students on visualization ability mathematics based on learning obstacles. In Y. R. Hidayat, T. Suciaty, U. Syaripudin, A. Sustikarini, G. S. Brajadenta, I. Saleh, I. Indrayanti, I. S. W. Atmaja, F. Ferdiyanto, & K. A. Rohman (Eds.), Proceedings of the International Conference on Agriculture, Social Sciences, Education, Technology and Health (ICASSETH 2019) (Vol. 429, Issue Icasseth 2019, pp. 227–231). Atlantis Press. https://doi.org/10.2991/assehr.k.200402.053
- Fischbein, E., & Baltsan, M. (1999). The mathematical concept of set and the “collection” model. Educational Studies in Mathematics, 37, 1–22. https://doi.org/https://doi.org/10.1023/A:1003421206945
- Furner, J. M., Yahya, N., & Duffy, M. Lou. (2005). Teach mathematics: Strategies to reach all students. Intervention in School and Clinic, 41(1), 16–23. https://doi.org/10.1177/10534512050410010501
- Ganal, N., & Guiab, M. (2014). Problems and difficulties encountered by students towards mastering learning competencies in mathematics. International Refereed Research Journal, 5(4), 25–37.
- Giunchiglia, F. (1993). Contextual reasoning. Epistemologia, Special Issue on I Linguaggi e Le Macchine, XVI, 345–364.
- Glaser, B. G., & Anselm, S. (2017). The discovery of grounded theory: Strategies for qualitative research (1st Edition). Routledge. https://doi.org/https://doi.org/10.4324/9780203793206
- Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. Cuoco & F. Curcio (Eds.), The Roles of Representation in School Mathematics (Issue 2001 Yearbook, pp. 1–23). National Council of Teachers of Mathematics
- Grandgirard, J., Poinsot, D., Krespi, L., Nénon, J. P., & Cortesero, A. M. (2003). Costs of secondary parasitism in the facultative hyperparasitoid Pachycrepoideus dubius: Does host size matter? Entomologia Experimentalis et Applicata, 103(3), 239–248. https://doi.org/https://doi.org/10.1046/j.1570-7458.2002.00982.x
- Guazzini, J. (2018). An epistemological approach to the symbol grounding problem. In V. C. Müller (Ed.), Philosophy and Theory of Artificial Intelligence 2017 (pp. 36–39). Springer International Publishing.
- Gunderson, E. A., Ramirez, G., Levine, S. C., & Beilock, S. L. (2012). The role of parents and teachers in the development of gender-related math attitudes. Sex Roles, 66(3–4), 153–166. https://doi.org/10.1007/s11199-011-9996-2
- 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), 1–13. https://doi.org/https://doi.org/10.29333/ejmste/12953
- Holmes, M. R. (1998). Elementary Set Theory with a Universal Set. Bruylant-Academia.
- Indonesia, G. of. (2018). Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 37 Tahun 2018.
- Jackson, E. (2008). Mathematics anxiety in student teachers. Practitioner Research in Higher Education, 2(1), 36–42. https://doi.org/10.4324/9781315643137-8
- Jamilah, J., Suryadi, D., & Priatna, N. (2020). Didactic transposition from scholarly knowledge of mathematics to school mathematics on sets theory. Journal of Physics: Conference Series, 1521(3), 032093. https://doi.org/10.1088/1742-6596/1521/3/032093
- Just, W., & Weese, M. (1996). Discovering Modern Set Theory. I. American Mathematical Society.
- Kunen, K. (1980). Set theory: An introduction to independence proofs. North—Holland.
- Laborde, C. (2014). Didactical situation. In R. Gunstone (Ed.), Encyclopedia of Science Education (pp. 1–5). Springer Netherlands. https://doi.org/10.1007/978-94-007-6165-0_404-1
- Lanigan, M. (2021). Impediments to adult learner engagement in higher education mathematics learning: Obstacles to creating a classroom culture of enquiry. In M. Kingston & P. Grimes (Eds.), Proceedings of the Eighth Conference on Research in Mathematics Education in Ireland (pp. 252–259). Dublin City University. https://doi.org/10.5281/zenodo.5573968
- Laurens, T., Batlolona, F. A., Batlolona, J. R., & Leasa, M. (2017). How does realistic mathematics education (RME) improve students’ mathematics cognitive achievement? Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 569–578. https://doi.org/10.12973/ejmste/76959
- Linchevski, L., & Vinner, S. (1988). The naive concept of sets in elementary teachers. In A. Borbas (Ed.), Proceedings of the 12th International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 471–478). Veprem OOK Print House.
- Lipschutz, S. (1986). Set theory and related topics (Asian Stud). Scaum’s Outline Series, McGraw-Hill Book Company.
- Loewenberg Ball, D., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
- Lutfi, M. K., Juandi, D., & Jupri, A. (2021). Students’ ontogenic obstacle on the topic of triangle and quadrilateral. Journal of Physics: Conference Series, 1806(1), 012108. https://doi.org/10.1088/1742-6596/1806/1/012108
- Maarif, S., Perbowo, K. S., & Kusharyadi, R. (2021). Depicting epistemological obstacles in understanding the concept of sequence and series. IndoMath: Indonesia Mathematics Education, 4(1), 66–80. https://doi.org/10.30738/indomath.v4i1.9339
- Maddy, P. (2003). Realism in Mathematics. Oxford University Press.
- Marasabessy, R. (2021). Study of mathematical reasoning ability for mathematics learning in schools: A literature review. Indonesian Journal of Teaching in Science, 1(1), 79–90. https://doi.org/10.17509/ijotis.v1i2.37950
- Marquet, P. (2011). Obstacles to the use of ICTs in training and consequences for the development of e-learning and m-learning. Education, Knowledge and Economy, 4(3), 183–192. https://doi.org/10.1080/17496896.2010.556483
- Miller, S. P., & Hudson, P. J. (2007). Using evidence-based practices to build mathematics competence related to conceptual, procedural, and declarative knowledge. Learning Disabilities Research & Practice, 22(1), 47–57. https://doi.org/10.1111/j.1540-5826.2007.00230.x
- Modestou, M., & Gagatsis, A. (2007). Students’ Improper Proportional Reasoning: A result of the epistemological obstacle of “linearity.” Educational Psychology, 27(1), 75–92. https://doi.org/10.1080/01443410601061462
- Moru, E. K. (2009). Epistemological obstacles in coming to understand the limit of a function at undergraduate level: A case from the national university of lesotho. International Journal of Science and Mathematics Education, 7(3), 431–454. https://doi.org/10.1007/s10763-008-9143-x
- Muilenburg, L. Y., & Berge, Z. L. (2005). Students barriers to online learning: A factor analytic study. Distance Education, 26(1), 29–48. https://doi.org/10.1080/01587910500081269
- Mutambara, L. H. N., & Tsakeni, M. (2022). Cognitive obstacles in the learning of complex number concepts: A case study of in-service undergraduate physics student-teachers in Zimbabwe. Eurasia Journal of Mathematics, Science and Technology Education, 18(10), 1–15. https://doi.org/10.29333/ejmste/12418
- Naderifar, M., Goli, H., & Ghaljaie, F. (2017). Snowball sampling: A purposeful method of sampling in qualitative research. Studies in Development of Medical Education, 14(3). https://doi.org/10.5812/sdme.67670
- Nicol, D. (2010). From monologue to dialogue: Improving written feedback processes in mass higher education. Assessment and Evaluation in Higher Education, 35(5), 501–517. https://doi.org/10.1080/02602931003786559
- Nokes, T. J., & Ross, B. H. (2007). Facilitating conceptual learning through analogy and explanation. AIP Conference Proceedings, 951(1), 7–10. https://doi.org/10.1063/1.2820952
- Noto, M. S., Pramuditya, S. A., & Handayani, V. D. (2020). Exploration of learning obstacle based on mathematical understanding of algebra in junior high school. Eduma: Mathematics Education Learning and Teaching, 9(1), 14–20. https://doi.org/10.24235/eduma.v9i1.5946
- Peet, A. (2016). Testimony and the epistemic uncertainty of interpretation. Philosophical Studies, 173(2), 395–416. https://doi.org/10.1007/s11098-015-0498-x
- Perrine, T. (2014). In defense of non-reductionism in the epistemology of testimony. Synthese, 191(14), 3227–3237. https://doi.org/10.1007/s11229-014-0443-0
- Pinheiro, A. L. V., Rachelli, J., & Porta, L. D. (2022). Study of round bodies: Conceptions and praxis of a didactic sequence in light of Guy Brousseau’s theory. Acta Scientiae, 24(6), 634–665. https://doi.org/10.17648/acta.scientiae.7402
- Prabowo, A., Suryadi, D., Dasari, D., Juandi, D., & Junaedi, I. (2022). Learning obstacles in the making of lesson plans by prospective mathematics teacher students. Education Research International, 2022, 1–15. https://doi.org/10.1155/2022/2896860
- Pratiwi, V., Herman, T., & Suryadi, D. (2019). Algebraic thinking obstacles of elementary school students: A Hermeneutics-phenomenology study. Journal of Physics: Conference Series, 1157(3), 032115. https://doi.org/10.1088/1742-6596/1157/3/032115
- Prediger, S. (2008). The relevance of didactic categories for analysing obstacles in conceptual change: Revisiting the case of multiplication of fractions. Learning and Instruction, 18(1), 3–17. https://doi.org/https://doi.org/10.1016/j.learninstruc.2006.08.001
- Quintero, A. H. (1983). Conceptual understanding in solving two-step word problems with a ratio. Journal for Research in Mathematics Education, 14(2), 102–112. https://doi.org/10.5951/jresematheduc.14.2.0102
- Ramos-Rodríguez, E., Fernández-Ahumada, E., & Morales-Soto, A. (2022). Effective teacher professional development programs. A case study focusing on the development of mathematical modeling skills. Education Sciences, 12(1), 2. https://doi.org/10.3390/educsci12010002
- Rønning, F. (2021). Opportunities for language enhancement in a learning environment designed on the basis of the theory of didactical situations. ZDM - Mathematics Education, 53(2), 305–316. https://doi.org/10.1007/s11858-020-01199-x
- Schneuwly, B. (2021). “Didactiques” is not (entirely) “Didaktik”: The origin and atmosphere of a recent academic field. In Didaktik and Curriculum in Ongoing Dialogue. Routledge. https://doi.org/10.4324/9781003099390-9
- Scotland, J. (2012). Exploring the philosophical underpinnings of research: Relating ontology and epistemology to the methodology and methods of the scientific, interpretive, and critical research paradigms. English Language Teaching, 5(9), 9–16. https://doi.org/10.5539/elt.v5n9p9
- Serradó, A., Cardeñoso, J. M., & Azcárate, P. (2005). Obstacles in the learning of probabilistic knowledge: Influence from the textbooks. Statistics Education Research Journal, 4(2), 59–81. https://doi.org/10.52041/serj.v4i2.515
- Sierpińska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18(4), 371–397. https://doi.org/10.1007/BF00240986
- 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
- Simamora, R. E., Saragih, S., & Hasratuddin, H. (2018). Improving students’ mathematical problem-solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1), 61–72. https://doi.org/10.12973/iejme/3966
- Šipuš, Ž. M., Bašić, M., Doorman, M., Špalj, E., & Antoliš, S. (2022). MERIA – Conflict lines: Experience with two innovative teaching materials. Center for Educational Policy Studies Journal, 12(1), 103–124. https://doi.org/10.26529/cepsj.987
- Sitorus, J., & Masrayati. (2016). Students’ creative thinking process stages: Implementation of realistic mathematics education. Thinking Skills and Creativity, 22, 111–120. https://doi.org/10.1016/j.tsc.2016.09.007
- Skilling, K., Bobis, J., & Martin, A. J. (2021). The “ins and outs” of student engagement in mathematics: shifts in engagement factors among high and low achievers. Mathematics Education Research Journal, 33(3), 469–493. https://doi.org/10.1007/s13394-020-00313-2
- Smith, C., & Morgan, C. (2016). Curricular orientations to real-world contexts in mathematics. Curriculum Journal, 27(1), 24–45. https://doi.org/10.1080/09585176.2016.1139498
- Sterenberg, G. (2008). Investigating teachers’ images of mathematics. Journal of Mathematics Teacher Education, 11(2), 89–105. https://doi.org/10.1007/s10857-007-9062-8
- Sullivan, P., Tobias, S., & McDonough, A. (2006). Perhaps the decision of some students not to engage in learning mathematics in school is deliberate. Educational Studies in Mathematics, 62(1), 81–99. https://doi.org/10.1007/s10649-006-1348-8
- Supandi, S., Suyitno, H., Sukestiyarno, Y. L., & Dwijanto, D. (2021). Learning barriers and student creativity in solving math problems. Journal of Physics: Conference Series, 1918(4), 042088. https://doi.org/10.1088/1742-6596/1918/4/042088
- Suryadi, D. (2019a). Landasan filosofis penelitian desain didaktis (DDR) [Philosophical foundation of didactical design research (DDR)]. Gapura Press.
- Suryadi, D. (2019b). Penelitian desain didaktis (DDR) dan implementasinya [Didactic design research (DDR) and its implementation]. Gapura Press.
- Tutticci, N., Coyer, F., Lewis, P. A., & Ryan, M. (2017). Validation of a reflective thinking instrument for third-year undergraduate nursing students participating in high-fidelity simulation. Reflective Practice, 18(2), 219–231. https://doi.org/10.1080/14623943.2016.1268115
- Vassallo, N. (2001). Contexts and philosophical problems of knowledge. In V. Akman, P. Bouquet, R. Thomason, & R. Young (Eds.), Modeling and Using Context. CONTEXT 2001 (pp. 353–366). Springer Berlin Heidelberg.
- Vergnaud, G. (2009). The theory of conceptual fields. Human Development, 52(2), 83–94. https://doi.org/10.1159/000202727
- Wang, Z., Hart, S. A., Kovas, Y., Lukowski, S., Soden, B., Thompson, L. A., Plomin, R., McLoughlin, G., Bartlett, C. W., Lyons, I. M., & Petrill, S. A. (2014). Who is afraid of math? Two sources of genetic variance for mathematical anxiety. Journal of Child Psychology and Psychiatry, 55(9), 1056–1064. https://doi.org/https://doi.org/10.1111/jcpp.12224
- Wilhelmi, M. R., Godino, J. D., & Lacasta, E. (2021). Didactic effectiveness of mathematical definitions: The case of the absolute value. International Electronic Journal of Mathematics Education, 2(2), 72–90. https://doi.org/10.29333/iejme/176
- Wood, M. B. (2013). Mathematical micro-identities: Moment-to-moment positioning and learning in a fourth-grade classroom. Journal for Research in Mathematics Education, 44(5), 775–808. https://doi.org/10.5951/jresematheduc.44.5.0775
- Yorulmaz, A., Uysal, H., & Çokçaliskan, H. (2021). Pre-service primary school teachers’ metacognitive awareness and beliefs about mathematical problem solving. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(3), 239–259. https://doi.org/10.23917/jramathedu.v6i3.14349
- Yuen, A. H. K., Law, N., & Wong, K. C. (2003). ICT implementation and school leadership: Case studies of ICT integration in teaching and learning. Journal of Educational Administration, 41(2), 158–170. https://doi.org/10.1108/09578230310464666
References
Afriyani, D., Sa’Dijah, C., Subanji, S., & Muksar, M. (2019). Students’ construction error in translation among mathematical representations. Journal of Physics: Conference Series, 1157(3), 032098. https://doi.org/10.1088/1742-6596/1157/3/032098
Akar, N., & Işıksal-Bostan, M. (2022). The didactic transposition of quadrilaterals: the case of 5th grade in Turkey. International Journal of Mathematical Education in Science and Technology, 55(3), 1–22. https://doi.org/10.1080/0020739X.2021.2022228
Alves, F. R. V., Mangueira, M. C. dos S., Catarino, P. M. M. C., & Vieira, R. P. M. (2021). Didactic engineering to teach leonardo sequence: A study on a complexification process in a mathematics teaching degree course. International Electronic Journal of Mathematics Education, 16(3), em0655. https://doi.org/10.29333/iejme/11196
Alwan, A. A. (2011). Misconception of heat and temperature among physics students. Procedia - Social and Behavioral Sciences, 12(1), 600–614. https://doi.org/10.1016/j.sbspro.2011.02.074
Amade-Escot, C. (2006). Student learning within the didactique tradition. In D. Kirk, M. O’Sullivanx, & D. Macdonald (Eds.), Handbook of Research in Physical Education (pp. 347–365). SAGE Publication Ltd. https://doi.org/10.4135/9781848608009.n20
Andini, W., & Suryadi, D. (2017). Student obstacles in solving algebraic thinking problems. Journal of Physics: Conference Series, 895(1), 2–8. https://doi.org/10.1088/1742-6596/895/1/012091
As’ari, A. R., Tohir, M., Valentino, E., Imron, Z., & Taufiq, I. (2017). Matematika SMP/MTs kelas VII semester 1 [Junior high school mathematics grade VII semester 1] (A. Lukito, A. Mahmudi, T. M, N. Priatna, Y. Satria, & Widowati (eds.); Rev. 2017). Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud.
Asher, N., & Hunter, J. (2021). Interpretive blindness and the impossibility of learning from testimony. In F. Dignum, A. Lomuscio, U. Endriss, & A. Nowé (Eds.), Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS (Vol. 3, pp. 1437–1439). International Foundation for Autonomous Agents and Multiagent Systems.
Banks, F., Leach, J., & Moon, B. (2005). Extract from new understandings of teachers’ pedagogic knowledge. Curriculum Journal, 16(3), 331–340. https://doi.org/10.1080/09585170500256446
Bardini, C., Pierce, R. U., & Stacey, K. (2004). Teaching linear functions in context with graphics calculators: Students’ responses and the impact of the approach on their use of algebraic symbols. International Journal of Science and Mathematics Education, 2(3), 353–376. https://doi.org/10.1007/s10763-004-8075-3
Bingolbali, E., Demir, G., & Monaghan, J. D. (2021). Knowledge of sets: A didactic phenomenon. International Journal of Science and Mathematics Education, 19(6), 1187–1208. https://doi.org/10.1007/s10763-020-10106-5
Bolden, D. S., & Newton, L. D. (2008). Primary teachers’ epistemological beliefs: some perceived barriers to investigative teaching in primary mathematics. Educational Studies, 34(5), 419–432. https://doi.org/10.1080/03055690802287595
Bray, W. S. (2011). A collective case study of the influence of teachers’ beliefs and knowledge on error-handling practices during class discussion of mathematics. Journal for Research in Mathematics Education, 42(1), 2–38. https://doi.org/10.5951/jresematheduc.42.1.0002
Brousseau, G. (1976). Les obstacles épistémologiques et les problèmes en mathématiques. In W. Vanhamme & J. Vanhamme (Eds.), La problématique et l’enseignement des mathématiques. Comptes rendus de la XXVIIIe rencontre organisée par la Commission Internationale pour l’Etude et l’Amélioration de l’Enseignement des Mathématiques (Vol. 4, pp. 101–117). HAL Open Science. https://hal.science/hal-00516569
Brousseau, G. (2002). The didactical contract: The teacher, the student and the milieu. In N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds.), Theory of Didactical Situations in Mathematics (Vol. 19, pp. 226--249). Springer Netherlands. https://doi.org/10.1007/0-306-47211-2_13
Brousseau, G., & Warfield, V. (2020). Didactic transposition in mathematics education. In Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-94-007-4978-8_89
Brown, S. A. (2008). Exploring epistemological obstacles to the development of mathematics induction. In K. A. Keene, S. Larsen, K. Marrongelle, V. Mesa, C. Rasmussen, N. Speer, K. Weber, & M. Zandieh (Eds.), Proceedings of the 11th Conference for Research on Undergraduate Mathematics Education (pp. 1–19). San Diego State University. http://sigmaa.maa.org/rume/crume2008/Proceedings/Proceedings.html
Buford, C., & Cloos, C. M. (2018). A dilemma for the knowledge despite falsehood strategy. Episteme, 15(2), 166–182. https://doi.org/10.1017/epi.2016.53
Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2015). Children’s mathematics: Cognitively guided instruction (2nd ed.). Heinemann. http://www.amazon.com/dp/0325001375
Catrambone, R. (1994). Improving examples to improve transfer to novel problems. Memory & Cognition, 22(5), 606–615. https://doi.org/10.3758/BF03198399
Chevallard, Y. (1989). On didatic transposition theory: some introductory notes. International Symposium on Selected Domains of Research and Development in Mathematics Education, 51–62. http://yves.chevallard.free.fr/spip/spip/article.php3?id_article=122
Chevallard, Y., & Bosch, M. (2020). Didactic transposition in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 214--218). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0_48
Creswell, J., & Guetterman, T. (2018). Educational Research: Planning, conducting, and evaluating quantitative and qualitative research (6th Edition). Pearson Education, Inc.
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), 417. https://doi.org/10.3390/math10030417
de Mello, L. A. (2017). A propose of rules defining as a didactic transposition should occur or be achieved - The generalized didactic transposition theory. OSF Preprints, June. https://doi.org/https://doi.org/10.31219/osf.io/uzfhb
De Sousa, R. T., & Alves, F. R. V. (2022). Didactic engineering and learning objects: A proposal for teaching parabolas in analytical geometry. Indonesian Journal of Science and Mathematics Education, 5(1), 1–16. https://doi.org/10.24042/ijsme.v5i1.11108
Diana, N., Suryadi, D., & Dahlan, J. A. (2020). Analysis of students’ mathematical connection abilities in solving problem of circle material: Transposition study. Journal for the Education of Gifted Young Scientists, 8(2), 829–842. https://doi.org/10.17478/JEGYS.689673
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https://doi.org/10.1007/s10649-006-0400-z
Ellis, G. W., & Turner, W. A. (2003). Helping students organize and retrieve their understanding of dynamics. ASEE Annual Conference Proceedings, 7535–7547. https://doi.org/10.18260/1-2--11592
Enderton, H. B. (1977). Elements of set theory. Academic Press.
Fauzi, I., & Suryadi, D. (2020). Learning obstacle the addition and subtraction of fraction in grade 5 elementary schools. MUDARRISA: Jurnal Kajian Pendidikan Islam, 12(1), 51–68. https://doi.org/10.18326/mdr.v12i1.51-68
Ferdianto, F., & Hartinah, S. (2020). Analysis of the difficulty of students on visualization ability mathematics based on learning obstacles. In Y. R. Hidayat, T. Suciaty, U. Syaripudin, A. Sustikarini, G. S. Brajadenta, I. Saleh, I. Indrayanti, I. S. W. Atmaja, F. Ferdiyanto, & K. A. Rohman (Eds.), Proceedings of the International Conference on Agriculture, Social Sciences, Education, Technology and Health (ICASSETH 2019) (Vol. 429, Issue Icasseth 2019, pp. 227–231). Atlantis Press. https://doi.org/10.2991/assehr.k.200402.053
Fischbein, E., & Baltsan, M. (1999). The mathematical concept of set and the “collection” model. Educational Studies in Mathematics, 37, 1–22. https://doi.org/https://doi.org/10.1023/A:1003421206945
Furner, J. M., Yahya, N., & Duffy, M. Lou. (2005). Teach mathematics: Strategies to reach all students. Intervention in School and Clinic, 41(1), 16–23. https://doi.org/10.1177/10534512050410010501
Ganal, N., & Guiab, M. (2014). Problems and difficulties encountered by students towards mastering learning competencies in mathematics. International Refereed Research Journal, 5(4), 25–37.
Giunchiglia, F. (1993). Contextual reasoning. Epistemologia, Special Issue on I Linguaggi e Le Macchine, XVI, 345–364.
Glaser, B. G., & Anselm, S. (2017). The discovery of grounded theory: Strategies for qualitative research (1st Edition). Routledge. https://doi.org/https://doi.org/10.4324/9780203793206
Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. Cuoco & F. Curcio (Eds.), The Roles of Representation in School Mathematics (Issue 2001 Yearbook, pp. 1–23). National Council of Teachers of Mathematics
Grandgirard, J., Poinsot, D., Krespi, L., Nénon, J. P., & Cortesero, A. M. (2003). Costs of secondary parasitism in the facultative hyperparasitoid Pachycrepoideus dubius: Does host size matter? Entomologia Experimentalis et Applicata, 103(3), 239–248. https://doi.org/https://doi.org/10.1046/j.1570-7458.2002.00982.x
Guazzini, J. (2018). An epistemological approach to the symbol grounding problem. In V. C. Müller (Ed.), Philosophy and Theory of Artificial Intelligence 2017 (pp. 36–39). Springer International Publishing.
Gunderson, E. A., Ramirez, G., Levine, S. C., & Beilock, S. L. (2012). The role of parents and teachers in the development of gender-related math attitudes. Sex Roles, 66(3–4), 153–166. https://doi.org/10.1007/s11199-011-9996-2
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), 1–13. https://doi.org/https://doi.org/10.29333/ejmste/12953
Holmes, M. R. (1998). Elementary Set Theory with a Universal Set. Bruylant-Academia.
Indonesia, G. of. (2018). Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 37 Tahun 2018.
Jackson, E. (2008). Mathematics anxiety in student teachers. Practitioner Research in Higher Education, 2(1), 36–42. https://doi.org/10.4324/9781315643137-8
Jamilah, J., Suryadi, D., & Priatna, N. (2020). Didactic transposition from scholarly knowledge of mathematics to school mathematics on sets theory. Journal of Physics: Conference Series, 1521(3), 032093. https://doi.org/10.1088/1742-6596/1521/3/032093
Just, W., & Weese, M. (1996). Discovering Modern Set Theory. I. American Mathematical Society.
Kunen, K. (1980). Set theory: An introduction to independence proofs. North—Holland.
Laborde, C. (2014). Didactical situation. In R. Gunstone (Ed.), Encyclopedia of Science Education (pp. 1–5). Springer Netherlands. https://doi.org/10.1007/978-94-007-6165-0_404-1
Lanigan, M. (2021). Impediments to adult learner engagement in higher education mathematics learning: Obstacles to creating a classroom culture of enquiry. In M. Kingston & P. Grimes (Eds.), Proceedings of the Eighth Conference on Research in Mathematics Education in Ireland (pp. 252–259). Dublin City University. https://doi.org/10.5281/zenodo.5573968
Laurens, T., Batlolona, F. A., Batlolona, J. R., & Leasa, M. (2017). How does realistic mathematics education (RME) improve students’ mathematics cognitive achievement? Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 569–578. https://doi.org/10.12973/ejmste/76959
Linchevski, L., & Vinner, S. (1988). The naive concept of sets in elementary teachers. In A. Borbas (Ed.), Proceedings of the 12th International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 471–478). Veprem OOK Print House.
Lipschutz, S. (1986). Set theory and related topics (Asian Stud). Scaum’s Outline Series, McGraw-Hill Book Company.
Loewenberg Ball, D., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
Lutfi, M. K., Juandi, D., & Jupri, A. (2021). Students’ ontogenic obstacle on the topic of triangle and quadrilateral. Journal of Physics: Conference Series, 1806(1), 012108. https://doi.org/10.1088/1742-6596/1806/1/012108
Maarif, S., Perbowo, K. S., & Kusharyadi, R. (2021). Depicting epistemological obstacles in understanding the concept of sequence and series. IndoMath: Indonesia Mathematics Education, 4(1), 66–80. https://doi.org/10.30738/indomath.v4i1.9339
Maddy, P. (2003). Realism in Mathematics. Oxford University Press.
Marasabessy, R. (2021). Study of mathematical reasoning ability for mathematics learning in schools: A literature review. Indonesian Journal of Teaching in Science, 1(1), 79–90. https://doi.org/10.17509/ijotis.v1i2.37950
Marquet, P. (2011). Obstacles to the use of ICTs in training and consequences for the development of e-learning and m-learning. Education, Knowledge and Economy, 4(3), 183–192. https://doi.org/10.1080/17496896.2010.556483
Miller, S. P., & Hudson, P. J. (2007). Using evidence-based practices to build mathematics competence related to conceptual, procedural, and declarative knowledge. Learning Disabilities Research & Practice, 22(1), 47–57. https://doi.org/10.1111/j.1540-5826.2007.00230.x
Modestou, M., & Gagatsis, A. (2007). Students’ Improper Proportional Reasoning: A result of the epistemological obstacle of “linearity.” Educational Psychology, 27(1), 75–92. https://doi.org/10.1080/01443410601061462
Moru, E. K. (2009). Epistemological obstacles in coming to understand the limit of a function at undergraduate level: A case from the national university of lesotho. International Journal of Science and Mathematics Education, 7(3), 431–454. https://doi.org/10.1007/s10763-008-9143-x
Muilenburg, L. Y., & Berge, Z. L. (2005). Students barriers to online learning: A factor analytic study. Distance Education, 26(1), 29–48. https://doi.org/10.1080/01587910500081269
Mutambara, L. H. N., & Tsakeni, M. (2022). Cognitive obstacles in the learning of complex number concepts: A case study of in-service undergraduate physics student-teachers in Zimbabwe. Eurasia Journal of Mathematics, Science and Technology Education, 18(10), 1–15. https://doi.org/10.29333/ejmste/12418
Naderifar, M., Goli, H., & Ghaljaie, F. (2017). Snowball sampling: A purposeful method of sampling in qualitative research. Studies in Development of Medical Education, 14(3). https://doi.org/10.5812/sdme.67670
Nicol, D. (2010). From monologue to dialogue: Improving written feedback processes in mass higher education. Assessment and Evaluation in Higher Education, 35(5), 501–517. https://doi.org/10.1080/02602931003786559
Nokes, T. J., & Ross, B. H. (2007). Facilitating conceptual learning through analogy and explanation. AIP Conference Proceedings, 951(1), 7–10. https://doi.org/10.1063/1.2820952
Noto, M. S., Pramuditya, S. A., & Handayani, V. D. (2020). Exploration of learning obstacle based on mathematical understanding of algebra in junior high school. Eduma: Mathematics Education Learning and Teaching, 9(1), 14–20. https://doi.org/10.24235/eduma.v9i1.5946
Peet, A. (2016). Testimony and the epistemic uncertainty of interpretation. Philosophical Studies, 173(2), 395–416. https://doi.org/10.1007/s11098-015-0498-x
Perrine, T. (2014). In defense of non-reductionism in the epistemology of testimony. Synthese, 191(14), 3227–3237. https://doi.org/10.1007/s11229-014-0443-0
Pinheiro, A. L. V., Rachelli, J., & Porta, L. D. (2022). Study of round bodies: Conceptions and praxis of a didactic sequence in light of Guy Brousseau’s theory. Acta Scientiae, 24(6), 634–665. https://doi.org/10.17648/acta.scientiae.7402
Prabowo, A., Suryadi, D., Dasari, D., Juandi, D., & Junaedi, I. (2022). Learning obstacles in the making of lesson plans by prospective mathematics teacher students. Education Research International, 2022, 1–15. https://doi.org/10.1155/2022/2896860
Pratiwi, V., Herman, T., & Suryadi, D. (2019). Algebraic thinking obstacles of elementary school students: A Hermeneutics-phenomenology study. Journal of Physics: Conference Series, 1157(3), 032115. https://doi.org/10.1088/1742-6596/1157/3/032115
Prediger, S. (2008). The relevance of didactic categories for analysing obstacles in conceptual change: Revisiting the case of multiplication of fractions. Learning and Instruction, 18(1), 3–17. https://doi.org/https://doi.org/10.1016/j.learninstruc.2006.08.001
Quintero, A. H. (1983). Conceptual understanding in solving two-step word problems with a ratio. Journal for Research in Mathematics Education, 14(2), 102–112. https://doi.org/10.5951/jresematheduc.14.2.0102
Ramos-Rodríguez, E., Fernández-Ahumada, E., & Morales-Soto, A. (2022). Effective teacher professional development programs. A case study focusing on the development of mathematical modeling skills. Education Sciences, 12(1), 2. https://doi.org/10.3390/educsci12010002
Rønning, F. (2021). Opportunities for language enhancement in a learning environment designed on the basis of the theory of didactical situations. ZDM - Mathematics Education, 53(2), 305–316. https://doi.org/10.1007/s11858-020-01199-x
Schneuwly, B. (2021). “Didactiques” is not (entirely) “Didaktik”: The origin and atmosphere of a recent academic field. In Didaktik and Curriculum in Ongoing Dialogue. Routledge. https://doi.org/10.4324/9781003099390-9
Scotland, J. (2012). Exploring the philosophical underpinnings of research: Relating ontology and epistemology to the methodology and methods of the scientific, interpretive, and critical research paradigms. English Language Teaching, 5(9), 9–16. https://doi.org/10.5539/elt.v5n9p9
Serradó, A., Cardeñoso, J. M., & Azcárate, P. (2005). Obstacles in the learning of probabilistic knowledge: Influence from the textbooks. Statistics Education Research Journal, 4(2), 59–81. https://doi.org/10.52041/serj.v4i2.515
Sierpińska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18(4), 371–397. https://doi.org/10.1007/BF00240986
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
Simamora, R. E., Saragih, S., & Hasratuddin, H. (2018). Improving students’ mathematical problem-solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1), 61–72. https://doi.org/10.12973/iejme/3966
Šipuš, Ž. M., Bašić, M., Doorman, M., Špalj, E., & Antoliš, S. (2022). MERIA – Conflict lines: Experience with two innovative teaching materials. Center for Educational Policy Studies Journal, 12(1), 103–124. https://doi.org/10.26529/cepsj.987
Sitorus, J., & Masrayati. (2016). Students’ creative thinking process stages: Implementation of realistic mathematics education. Thinking Skills and Creativity, 22, 111–120. https://doi.org/10.1016/j.tsc.2016.09.007
Skilling, K., Bobis, J., & Martin, A. J. (2021). The “ins and outs” of student engagement in mathematics: shifts in engagement factors among high and low achievers. Mathematics Education Research Journal, 33(3), 469–493. https://doi.org/10.1007/s13394-020-00313-2
Smith, C., & Morgan, C. (2016). Curricular orientations to real-world contexts in mathematics. Curriculum Journal, 27(1), 24–45. https://doi.org/10.1080/09585176.2016.1139498
Sterenberg, G. (2008). Investigating teachers’ images of mathematics. Journal of Mathematics Teacher Education, 11(2), 89–105. https://doi.org/10.1007/s10857-007-9062-8
Sullivan, P., Tobias, S., & McDonough, A. (2006). Perhaps the decision of some students not to engage in learning mathematics in school is deliberate. Educational Studies in Mathematics, 62(1), 81–99. https://doi.org/10.1007/s10649-006-1348-8
Supandi, S., Suyitno, H., Sukestiyarno, Y. L., & Dwijanto, D. (2021). Learning barriers and student creativity in solving math problems. Journal of Physics: Conference Series, 1918(4), 042088. https://doi.org/10.1088/1742-6596/1918/4/042088
Suryadi, D. (2019a). Landasan filosofis penelitian desain didaktis (DDR) [Philosophical foundation of didactical design research (DDR)]. Gapura Press.
Suryadi, D. (2019b). Penelitian desain didaktis (DDR) dan implementasinya [Didactic design research (DDR) and its implementation]. Gapura Press.
Tutticci, N., Coyer, F., Lewis, P. A., & Ryan, M. (2017). Validation of a reflective thinking instrument for third-year undergraduate nursing students participating in high-fidelity simulation. Reflective Practice, 18(2), 219–231. https://doi.org/10.1080/14623943.2016.1268115
Vassallo, N. (2001). Contexts and philosophical problems of knowledge. In V. Akman, P. Bouquet, R. Thomason, & R. Young (Eds.), Modeling and Using Context. CONTEXT 2001 (pp. 353–366). Springer Berlin Heidelberg.
Vergnaud, G. (2009). The theory of conceptual fields. Human Development, 52(2), 83–94. https://doi.org/10.1159/000202727
Wang, Z., Hart, S. A., Kovas, Y., Lukowski, S., Soden, B., Thompson, L. A., Plomin, R., McLoughlin, G., Bartlett, C. W., Lyons, I. M., & Petrill, S. A. (2014). Who is afraid of math? Two sources of genetic variance for mathematical anxiety. Journal of Child Psychology and Psychiatry, 55(9), 1056–1064. https://doi.org/https://doi.org/10.1111/jcpp.12224
Wilhelmi, M. R., Godino, J. D., & Lacasta, E. (2021). Didactic effectiveness of mathematical definitions: The case of the absolute value. International Electronic Journal of Mathematics Education, 2(2), 72–90. https://doi.org/10.29333/iejme/176
Wood, M. B. (2013). Mathematical micro-identities: Moment-to-moment positioning and learning in a fourth-grade classroom. Journal for Research in Mathematics Education, 44(5), 775–808. https://doi.org/10.5951/jresematheduc.44.5.0775
Yorulmaz, A., Uysal, H., & Çokçaliskan, H. (2021). Pre-service primary school teachers’ metacognitive awareness and beliefs about mathematical problem solving. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(3), 239–259. https://doi.org/10.23917/jramathedu.v6i3.14349
Yuen, A. H. K., Law, N., & Wong, K. C. (2003). ICT implementation and school leadership: Case studies of ICT integration in teaching and learning. Journal of Educational Administration, 41(2), 158–170. https://doi.org/10.1108/09578230310464666