Pre-service mathematics teacher conducting prospective analysis: A case study on practice didactical design research
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Abstract
This study aims to understand how pre-service mathematics teachers conduct prospective analyses comprehensively. A qualitative research method with a case study design was used. The participant was Mrs N, a pre-service mathematics teacher who conducted research using DDR methodology in a grade 9 junior high school in Sindang, Majalengka, involving 48 students. Data were collected by analyzing empirical evidence from Mrs. N's prospective analysis process by uncovering the various stages of a prospective analysis. An iterative approach was used to analyze the data by refining the research questions through discussions and regular meetings with Mrs. N. The process ensured adaptability to new insights and understandings from the empirical data. Our findings reveal that the teacher draws upon fundamental philosophical principles from didactical design research, including hermeneutics, phenomenology, and ethnomethodology. By embracing these approaches, the teacher gains valuable insights into conducting research within an interpretive paradigm, allowing for a deeper exploration of the meaning of concepts, the purpose of learning, and the cultural influences that shape the educational process. Additionally, our study sheds light on the emergence of transpositional didactics theory as the prospective teacher delves into understanding the meaning of the geometrics transformation concept.
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Ada, T., & Kurtuluş, A. (2010). Students’ misconceptions and errors in transformation geometry. International Journal of Mathematical Education in Science and Technology, 41(7), 901-909. https://doi.org/10.1080/0020739X.2010.486451
Ajinegara, M. W., & Soebagyo, J. (2022). Analisis bibliometrik tren penelitian media pembelajaran Google Classroom menggunakan aplikasi VOSViewer [Bibliometric analysis of Google Classroom learning media research trends using the VOSViewer application]. JNPM (Jurnal Nasional Pendidikan Matematika), 6(1), 193-210. https://doi.org/10.33603/jnpm.v6i1.5451
Albab, I. U., Hartono, Y., & Darmawijoyo, D. (2014). Kemajuan belajar siswa pada geometri transformasi menggunakan aktivitas refleksi geometri [Student learning progress in transformation geometry using geometric reflection activities]. Jurnal Cakrawala Pendidikan, 33(3), 338-348. https://doi.org/10.21831/cp.v3i3.2378
Allas, R., Leijen, Ä., & Toom, A. (2020). Guided reflection procedure as a method to facilitate student teachers’ perception of their teaching to support the construction of practical knowledge. Teachers and Teaching, 26(2), 166-192. https://doi.org/10.1080/13540602.2020.1758053
Aydın, U., & Ubuz, B. (2010). Structural model of metacognition and knowledge of geometry. Learning and Individual Differences, 20(5), 436-445. https://doi.org/10.1016/j.lindif.2010.06.002
Bai, L., Millwater, J., & Hudson, P. (2013). Factors that Influence Chinese TEFL academics’ research capacity building: An institutional case study. The Asia-Pacific Education Researcher, 22(2), 119-126. https://doi.org/10.1007/s40299-012-0004-6
Bakker, A. (2018). Design research in education: A practical guide for early career researchers (1st ed.). Routledge. https://doi.org/10.4324/9780203701010
Balbag, M. Z., Yenilmez, K., & Turgut, M. (2017). Personal professional development efforts scale for middle school mathematics teachers: An adaptation study. International Journal of Instruction, 10(4), 325-342. https://doi.org/10.12973/iji.2017.10419a
Bansilal, S., & Naidoo, J. (2012). Learners engaging with transformation geometry. South African Journal of Education, 32(1), 26-39. https://doi.org/10.15700/saje.v32n1a452
Bardini, C., Pierce, R., Vincent, J., & King, D. (2014). Undergraduate mathematics students' understanding of the concept of function. Journal on Mathematics Education, 5(2), 85-107. https://doi.org/10.22342/jme.5.2.1495.85-107
Baumert, J., & Kunter, M. (2013). The COACTIV model of teachers’ professional competence. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers: Results from the COACTIV project (pp. 25-48). Springer US. https://doi.org/10.1007/978-1-4614-5149-5_2
Blömeke, S., Kaiser, G., König, J., & Jentsch, A. (2020). Profiles of mathematics teachers’ competence and their relation to instructional quality. Zdm, 52(2), 329-342. https://doi.org/10.1007/s11858-020-01128-y
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. (2006). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (Vol. 19). Springer Science & Business Media. https://doi.org/10.1007/0-306-47211-2
Carvalho, G. S., Silva, R., Lima, N., Coquet, E., & Clément, P. (2004). Portuguese primary school children's conceptions about digestion: identification of learning obstacles. International Journal of Science Education, 26(9), 1111-1130. https://doi.org/10.1080/0950069042000177235
Chevallard, Y. (2019). Introducing the anthropological theory of the didactic an attempt at a principled approach. Hiroshima journal of mathematics education, 12, 71-114. https://doi.org/10.24529/hjme.1205
Chevallard, Y., & Bosch, M. (2020). Anthropological Theory of the Didactic (ATD). In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 53-61). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0_100034
Christie, D., & Menter, I. (2009). Research capacity building in teacher education: Scottish collaborative approaches. Journal of Education for Teaching, 35(4), 337-354. https://doi.org/10.1080/02607470903220414
Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: the case of geometry. Journal of Mathematics Teacher Education, 14(2), 133-148. https://doi.org/10.1007/s10857-011-9173-0
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13. https://doi.org/10.3102/0013189x032001009
Corbin, J. M., & Strauss, A. (1990). Grounded theory research: Procedures, canons, and evaluative criteria. Qualitative Sociology, 13(1), 3-21. https://doi.org/10.1007/BF00988593
Costică, L. (2013). Epistemological and psychological fundamentals of the didactics of science. Procedia - Social and Behavioral Sciences, 92, 490-494. https://doi.org/10.1016/j.sbspro.2013.08.706
Costică, L. (2015). Elaborating a paradigm for the didactics of a discipline. Procedia - Social and Behavioral Sciences, 203, 35-41. https://doi.org/10.1016/j.sbspro.2015.08.256
Dodge, C. W. (2012). Euclidean geometry and transformations. Courier Corporation.
Dreyfus, Т., Hoyles, C., Gueudet, G., & Krainer, K. (2014). Solid findings: Concept images in students’ mathematical reasoning. Newsletter of the European Mathematical Society, 93, 50-52.
Dudeja, V., & Madhavi, V. (2018). Jelajah Matematika Jilid 3 SMP Kelas 9 Kurikulum 2013 Revisi 2016. Yudhistira Ghalia Indonesia.
Eccles, F. M. (1971). An introduction to transformational geometry. Addison-Wesley.
Edelson, D. C. (2002). Design research: What we learn when we engage in design. Journal of the Learning Sciences, 11(1), 105-121. https://doi.org/10.1207/S15327809JLS1101_4
Edwards, L. D. (1997). Exploring the territory before proof: Student‘s generalizations in a computer microworld for transformation geometry. International Journal of Computers for Mathematical Learning, 2(3), 187-215. https://doi.org/10.1023/A:1009711521492
Ellinger, A. D., Watkins, K. E., & Marsick, V. J. (2005). Case study research methods. In R. A. Swanson & E. F. Holton III (Eds.), Research in organizations: Foundations and methods of inquiry (pp. 327-350). Berrett-Koehler Publishers, Inc.
Engelke Infante, N., Murphy, K., Glenn, C., & Sealey, V. (2018). How concept images affect students’ interpretations of Newton's method. International Journal of Mathematical Education in Science and Technology, 49(5), 643-659. https://doi.org/10.1080/0020739X.2017.1410737
Fennema, E., & Franke, M. L. (1992). Teacher’s knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). National Council of Teachers of Mathematics.
Fuadiah, N. F., Suryadi, D., & Turmudi, T. (2019). Teaching and learning activities in classroom and their impact on student misunderstanding: A case study on negative integers. International Journal of Instruction, 12(1), 407-424.
Garfinkel, H. (2005). Ethnomethodological studies of work. Routledge.
Gravemeijer, K. (1994). Educational development and developmental research in mathematics education. Journal for Research in Mathematics Education JRME, 25(5), 443-471. https://doi.org/10.5951/jresematheduc.25.5.0443
Hausberger, T. (2017). The (homo)morphism concept: Didactic transposition, meta-discourse and thematisation. International Journal of Research in Undergraduate Mathematics Education, 3(3), 417-443. https://doi.org/10.1007/s40753-017-0052-7
Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M., Hollingsworth, H., Manaster, A., Wearne, D., & Gallimore, R. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27(2), 111-132. https://doi.org/10.3102/01623737027002111
Hitchcock, G., & Hughes, D. (1995). Research and the teacher: A qualitative introduction to school-based research (2nd ed.). Routledge. https://doi.org/10.4324/9780203424605
Huberman, M. (1983). Recipes for busy kitchens: A situational analysis of routine knowledge use in schools. Knowledge, 4(4), 478-510. https://doi.org/10.1177/0164025983004004002
Jiang, Z. (2008). Explorations and reasoning in the dynamic geometry environment In The Thirteenth Asian Technology Conference in Mathematics (ATCM) 2008, Suan Sunandha Rajabhat University, Bangkok, Thailand. https://atcm.mathandtech.org/EP2008/papers_full/2412008_15336.pdf
Kanselaar, G. (1993). Ontwikkelingsonderzoek bezien vanuit de rol van advocaat van de duivel. Ontwikkelingsonderzoek: theorie en praktijk, 63-66.
Keller-Schneider, M., Zhong, H. F., & Yeung, A. S. (2020). Competence and challenge in professional development: teacher perceptions at different stages of career. Journal of Education for Teaching, 46(1), 36-54. https://doi.org/10.1080/02607476.2019.1708626
Kozikoglu, I. (2017). Prospective teachers' cognitive constructs concerning ideal teacher qualifications: A phenomenological analysis based on repertory grid technique. International Journal of Instruction, 10(3), 63-78. https://doi.org/10.12973/iji.2017.1035a
Lloyd, G. M., Rice, C. L., & McCloskey, A. V. (2020). Opportunities for professional learning about mathematics instruction: the role of joint work in student-teaching triads. Journal of Mathematics Teacher Education, 23(5), 499-525. https://doi.org/10.1007/s10857-019-09439-y
Lo, W. Y. (2021). Pre-service teachers' prior learning experiences of mathematics and the influences on their beliefs about mathematics teaching. International Journal of Instruction, 14(1), 795-812. https://doi.org/10.29333/iji.2021.14148a
Lombard, F., & Weiss, L. (2018). Can didactic transposition and popularization explain transformations of genetic knowledge from research to classroom? Science & Education, 27(5), 523-545. https://doi.org/10.1007/s11191-018-9977-8
Maboya, M. J., Jita, L. C., & Chimbi, G. T. (2022). Reaping the rewards of professional development: Evidence from mathematics teachers' pedagogical practices. International Journal of Instruction, 15(1), 873-890. https://doi.org/10.29333/iji.2022.15150a
Maher, C. A., Sigley, R., Sullivan, P., & Wilkinson, L. C. (2018). An international perspective on knowledge in teaching mathematics. The Journal of Mathematical Behavior, 51, 71-79. https://doi.org/10.1016/j.jmathb.2018.05.002
Malatjie, F., & Machaba, F. (2019). Exploring mathematics learners’ conceptual understanding of coordinates and transformation geometry through concept mapping. Eurasia Journal of Mathematics, Science and Technology Education, 15(12), em1818. https://doi.org/10.29333/ejmste/110784
Martin, G. E. (2012). Transformation geometry: An introduction to symmetry. Springer Science & Business Media.
Marton, F. (1981). Phenomenography — Describing conceptions of the world around us. Instructional Science, 10(2), 177-200. https://doi.org/10.1007/BF00132516
Mellone, M., Ribeiro, M., Jakobsen, A., Carotenuto, G., Romano, P., & Pacelli, T. (2020). Mathematics teachers’ interpretative knowledge of students’ errors and non-standard reasoning. Research in Mathematics Education, 22(2), 154-167. https://doi.org/10.1080/14794802.2019.1710557
Merriam, S. B., & Tisdell, E. J. (2015). Qualitative research: A guide to design and implementation. John Wiley & Sons.
Muhammad, I., Marchy, F., Naser, A. d. m., & Turmudi, T. (2023). Analisis bibliometrik: Tren penelitian etnomatematika dalam pembelajaran matematika di indonesia (2017–2022) [Bibliometric analysis: Ethnomathematics research trends in mathematics learning in Indonesia (2017–2022)]. JIPM (Jurnal Ilmiah Pendidikan Matematika), 11(2), 267-279. https://doi.org/10.25273/jipm.v11i2.14085
Musyrifah, E., Dahlan, J. A., Cahya, E., & Hafiz, M. (2022). Analisis learning obstacles mahasiswa calon guru matematika pada konsep turunan [Analysis of learning obstacles for prospective mathematics teacher students on the concept of derivatives]. FIBONACCI: Jurnal Pendidikan Matematika Dan Matematika, 8(2), 187-196. https://doi.org/10.24853/fbc.8.2.187-196
Nurwahyu, B., & Tinungki, G. M. (2020). Students' concept image and its impact on reasoning towards the concept of the derivative. European Journal of Educational Research, 9(4), 1723-1734. https://doi.org/10.12973/eu-jer.9.4.1723
Oancea, A., Fancourt, N., Robson, J., Thompson, I., Childs, A., & Nuseibeh, N. (2021). Research capacity-building in teacher education. Oxford Review of Education, 47(1), 98-119. https://doi.org/10.1080/03054985.2020.1842184
Østergaard, K. (2015). A model of theory-practice relations in mathematics teacher education CERME 9-Ninth Congress of the European Society for Research in Mathematics Education, https://hal.science/hal-01289643
Pesti, C., Győri, J. n. G., & Kopp, E. (2018). Student teachers as future researchers: How do Hungarian and Austrian initial teacher education systems address the issue of teachers as researchers? Center for educational policy studies journal, 8(3), 35-57. https://doi.org/10.26529/cepsj.518
Portnoy, N., Grundmeier, T. A., & Graham, K. J. (2006). Students’ understanding of mathematical objects in the context of transformational geometry: Implications for constructing and understanding proofs. The Journal of Mathematical Behavior, 25(3), 196-207. https://doi.org/10.1016/j.jmathb.2006.09.002
Raiula, T., Alasa, V., Takiveikata, S., & Qabale, I. (2023). Quality instruction through four components of the mathematical knowledge for teaching (MKT) and teaching experience in Fiji. International Journal of Instruction, 16(1), 1021-1036. https://doi.org/10.29333/iji.2023.16156a
Ramli, F., Shafie, N., & Tarmizi, R. A. (2013). Exploring student's in-depth learning difficulties in mathematics through teachers’ perspective. Procedia - Social and Behavioral Sciences, 97, 339-345. https://doi.org/10.1016/j.sbspro.2013.10.243
Reynolds, R., Howley, P., Southgate, E., & Brown, J. (2016). Just add hours? An assessment of pre-service teachers’ perception of the value of professional experience in attaining teacher competencies. Asia-Pacific Journal of Teacher Education, 44(5), 455-469. https://doi.org/10.1080/1359866X.2015.1086971
Rohimah, S. M. (2017). Analisis learning obstacles pada materi persamaan dan pertidaksamaan linear satu variabel [Analysis of learning obstacles in the material of linear equations and inequalities in one variable]. Jurnal Penelitian dan Pembelajaran Matematika, 10(1), 132-141. https://doi.org/10.30870/jppm.v10i1.1293
Rösken, B., & Rolka, K. (2007). Integrating intuition: The role of concept image and concept definition for students’ learning of integral calculus. The Montana Mathematics Enthusiast, 3, 181-204.
Rrustemi, J., & Kurteshi, V. (2023). Pedagogical practice as a foundation course for the development of professional skills. International Journal of Instruction, 16(2), 1135-1150. https://doi.org/10.29333/iji.2023.16260a
Scriven, M. (1991). Can research-based teacher evaluation be saved? In R. L. Schwab (Ed.), Research-based teacher evaluation: A special issue of the journal of personnel evaluation in education (pp. 19-32). Springer Netherlands. https://doi.org/10.1007/978-94-011-3884-0_2
Shriki, A., & Lavy, I. (2012). Perceptions of Israeli mathematics teachers regarding their professional development needs. Professional Development in Education, 38(3), 411-433. https://doi.org/10.1080/19415257.2011.626062
Siahaan, M. M. L., Fitriani, F., & Leli, A. R. D. L. (2023). A study of learning obstacles: Determining solutions of a system of linear equation using Gauss-Jordan method. Mosharafa: Jurnal Pendidikan Matematika, 12(1), 25-34. https://doi.org/10.31980/mosharafa.v12i1.748
Steffe, L. P., & Thompson, P. W. (2012). Teaching experiment methodology underlying principles and essential elements. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267-306). Routledge.
Subchan, W., Mufid, M. S. u., Fahim, K., & Syaifudin, W. H. (2018). Buku guru matematika untuk SMP/MTs kelas IX. Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud.
Suharta, I. G. P., & Suarjana, I. M. (2018). A case study on mathematical literacy of prospective elementary school teachers. International Journal of Instruction, 11(2), 413-424. https://doi.org/10.12973/iji.2018.11228a
Sullivan, P. (2011). Teaching mathematics: Using research-informed strategies. Australian Council for Educational Research (ACER).
Supinah, R., & Soebagyo, J. (2022). Analisis bibliometrik terhadap tren penggunaan ICT pada pembelajaran matematika [Bibliometric analysis of trends in ICT use in mathematics learning]. JNPM (Jurnal Nasional Pendidikan Matematika), 6(2), 276-290. https://doi.org/10.33603/jnpm.v6i2.6153
Suryadi, D. (2019). Landasan filosofis penelitian desain didaktis (DDR) [Philosophical foundations of didactic design research (DDR)].
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169. https://doi.org/10.1007/BF00305619
Tanang, H., & Abu, B. (2014). Teacher professionalism and professional development practices in south Sulawesi, Indonesia. Journal of Curriculum and Teaching, 3(2), 25-42. https://doi.org/10.5430/jct.v3n2p25
Tichenor, M. S., & Tichenor, J. M. (2005). Understanding teachers' perspectives on professionalism. Professional Educator, 27, 89-95.
Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: triangles, circles, and cylinders. Zdm, 47(3), 497-509. https://doi.org/10.1007/s11858-014-0641-8
Umble, R. N., & Han, Z. (2015). Transformational plane geometry (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/b17787
Uriarte Jr, F. A. (2008). Introduction to knowledge management: A brief introduction to the basic elements of knowledge management for non-practitioners interested in understanding the subject. Asean Foundation.
Vergnaud, G. (2009). The theory of conceptual fields. Human development, 52(2), 83-94. https://doi.org/10.1159/000202727
Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293-305. https://doi.org/10.1080/0020739830140305
Vinner, S. (2002). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 65-81). Springer Netherlands. https://doi.org/10.1007/0-306-47203-1_5
Warshauer, H. K., Starkey, C., Herrera, C. A., & Smith, S. (2021). Developing prospective teachers’ noticing and notions of productive struggle with video analysis in a mathematics content course. Journal of Mathematics Teacher Education, 24(1), 89-121. https://doi.org/10.1007/s10857-019-09451-2
Yaakob, M. F. M., Don, Y., Sufi, I., & Yusof, M. R. (2020). Teachers' professional development level across cohort of generations in Malaysia. International Journal of Instruction, 13(4), 443-456. https://doi.org/10.29333/iji.2020.13428a
Yanik, H. B. (2011). Prospective middle school mathematics teachers’ preconceptions of geometric translations. Educational Studies in Mathematics, 78(2), 231-260. https://doi.org/10.1007/s10649-011-9324-3
Yanik, H. B., & Flores, A. (2009). Understanding rigid geometric transformations: Jeff's learning path for translation. The Journal of Mathematical Behavior, 28(1), 41-57. https://doi.org/10.1016/j.jmathb.2009.04.003
Yin, R. K. (2009). Case study research: Design and methods (4th ed.). SAGE Publications, Inc.