Integration of abstraction theory and TPACK framework in geometry learning to optimize prospective mathematics teachers’ spatial abilities
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Abstract
This study aims to optimize the spatial abilities of prospective mathematics teachers (PMTs) using an integrated geometry learning module based on abstraction theory and TPACK, and to reduce the gap in geometry learning by integrating these theories. Epistemic abstraction refers to mental actions, including recognizing, building with, and constructing. Meanwhile, TPACK is introduced to use technology as a medium for prospective teachers to design geometry lessons and help learners understand geometry while considering pedagogical principles. We employed a research and development design by Borg and Gall, involving 30 participants selected using purposive sampling. Spatial ability data were collected using the Purdue Spatial Test and descriptively analyzed to assess the optimization of PMTs' spatial abilities before and after implementing the integrated geometry learning module. Findings demonstrated that the percentage of PMTs with beginner-spatial abilities decreased from 80% to 26.66%, while the rate of PMTs with advanced spatial skills increased from 20% to 73.33%. We concluded that integrating abstraction theory and TPACK in geometry learning produced an integrated geometry learning module capable of optimizing the spatial abilities of prospective teachers both didactically and pedagogically.
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Abdul Hanid, M. F., Mohamad Said, M. N. H., Yahaya, N., & Abdullah, Z. (2022). Effects of augmented reality application integration with computational thinking in geometry topics. Education and Information Technologies, 27(7), 9485–9521. https://doi.org/10.1007/s10639-022-10994-w
Ariani, Y., Johar, R., & Marwan, M. (2019). Penggunaan software Cabri 3D untuk meningkatkan kemampuan spasial siswa sekolah menengah pertama [The use of Cabri 3D software to improve the spatial abilities of junior high school students]. Jurnal Peluang Vol, 7(2), 11–21.
Bergstrom, C., & Zhang, D. (2016). Geometry interventions for k-12 students with and without disabilities: A research synthesis. International Journal of Educational Research, 80, 134–154. https://doi.org/10.1016/j.ijer.2016.04.004
Bodner, G. M., & Guay, R. B. (1997). The purdue visualization of rotations test. The Chemical Educator, 2(4), 1–17. https://doi.org/10.1007/s00897970138a
Bokosmaty, S., Sweller, J., & Kalyuga, S. (2015). Learning geometry problem solving by studying worked examples. American Educational Research Journal, 52(2), 307–333. https://doi.org/10.3102/0002831214549450
Bretscher, N. (2022). Conceptualising TPACK within mathematics education: Teachers’ strategies for capitalising on transitions within and beyond dynamic geometry software. Digital Experiences in Mathematics Education, 9(2), 232–254. https://doi.org/10.1007/s40751-022-00115-0
Budiarto, M. T. (2005). Proses abstraksi siswa SMP kelas 1 dalam mengkonstruksi kubus dari rangkaian 6 persegi [The abstraction process of 1st grade junior high school students in constructing a cube from a series of 6 squares]. In Seminar Nasional Penelitian, Pendidikan dan Penerapan MIPA 2005, (pp. 29–39).
Budiarto, M. T., Fuad, Y., & Sahidin, L. (2021). Teacher’s specialized content knowledge on the concept of square: a vignette approach. Jurnal Pendidikan Matematika, 15(1), 1–22.
Dilling, F., Witzke, I., Hörnberger, K., & Trgalová, J. (2024). Co-designing teaching with digital technologies: a case study on mixed pre-service and in-service mathematics teacher design teams. ZDM – Mathematics Education, 56(4), 667–680. https://doi.org/10.1007/s11858-024-01623-6
Dintarini, M., Fuad, Y., & Budiarto, M. T. (2024). Examining undergraduate students' abstraction of conic sections in a dynamic geometry environment. Journal on Mathematics Education, 15(3), 717–734. https://doi.org/10.22342/jme.v15i3.pp717-734
Dreyfus, T. (2015). Constructing abstract mathematical knowledge in context. In S. J. Cho (Ed.), Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 115–133). Springer International Publishing. https://doi.org/10.1007/978-3-319-17187-6_7
Dreyfus, T., Hershkowitz, R., & Schwarz, B. (2015). The nested epistemic actions model for abstraction in context: Theory as methodological tool and methodological tool as theory. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 185–217). Springer Netherlands. https://doi.org/10.1007/978-94-017-9181-6_8
Drijvers, P., & Sinclair, N. (2023). The role of digital technologies in mathematics education: purposes and perspectives. ZDM – Mathematics Education, 56(2), 239–248. https://doi.org/10.1007/s11858-023-01535-x
Fiantika, F. R., ketut Budayasa, I., & Lukito, A. (2017). Komponen penting representasi internal pada berpikir spasial [An important component of internal representation in spatial thinking]. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah di Bidang Pendidikan Matematika, 3(1), 34–42.
Hassan, I., & Mitchelmore, M. (2006). The role of abstraction in learning about rates of change. In Mathematics Education Research Group of Australasia Conference (29th: 2006), (pp. 278–285).
Hershkowitz, R., Hadas, N., Dreyfus, T., & Schwarz, B. (2007). Abstracting processes, from individuals’ constructing of knowledge to a group’s “shared knowledge”. Mathematics Education Research Journal, 19(2), 41–68. https://doi.org/10.1007/BF03217455
Hodiyanto, H., Budiarto, M. T., Ekawati, R., Susanti, G., Kim, J., & Bongtiwon, D. M. R. (2025). Trends of abstraction research in mathematics education: A bibliometric analysis. Infinity Journal, 14(1), 125–142. https://doi.org/10.22460/infinity.v14i1.p125-142
Hodiyanto, H., Budiarto, M. T., Ekawati, R., Susanti, G., Kim, J., & Bonyah, E. (2024). How abstraction of a pre-service teacher in constructing relationships among quadrilaterals. Journal on Mathematics Education, 15(2), 339–362. https://doi.org/10.22342/jme.v15i2.pp339-362
Hollebrands, K., & Okumuş, S. (2018). Secondary mathematics teachers’ instrumental integration in technology-rich geometry classrooms. The Journal of Mathematical Behavior, 49, 82–94. https://doi.org/10.1016/j.jmathb.2017.10.003
In’am, A., & Hajar, S. (2017). Learning geometry through discovery learning using a scientific approach. International Journal of Instruction, 10(1), 55–70. https://doi.org/10.12973/iji.2017.1014a
Ishartono, N., Nurcahyo, A., & Dwi Setyono, I. (2019). Guided discovery: an alternative teaching method to reduce students’ rote learning behavior in studying geometric transformation. Journal of Physics: Conference Series, 1265(1), 012019. https://doi.org/10.1088/1742-6596/1265/1/012019
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
Kong, S.-C., & Lai, M. (2021). A proposed computational thinking teacher development framework for k-12 guided by the TPACK model. Journal of Computers in Education, 9(3), 379–402. https://doi.org/10.1007/s40692-021-00207-7
Lacey, N. (1994). Abstraction in Context. Oxford Journal of Legal Studies, 14(2), 255–267. https://doi.org/10.1093/ojls/14.2.255
Lane, D., & Sorby, S. (2021). Bridging the gap: blending spatial skills instruction into a technology teacher preparation programme. International Journal of Technology and Design Education, 32(4), 2195–2215. https://doi.org/10.1007/s10798-021-09691-5
Lumbanbatu, G. T. F., Lubis, A. D., Lumban Tobing, S. I. M., Simangunsong, P. S., & Perangin Angin, L. M. (2023). Analysis of the application of Bruner's theory in improving mathematics learning outcomes in geometry materials at SD Negeri 14 Sei Meranti. Journal of Educational Analytics, 2(2), 295–306. https://doi.org/10.55927/jeda.v2i2.4422
Mandala, A. S., Anwar, L., Sa'dijah, C., & Zulnaidi, H. (2025). Development of mobile augmented reality-based geometry learning games to facilitate spatial reasoning. Infinity Journal, 14(2), 323–348. https://doi.org/10.22460/infinity.v14i2.p323-348
Ng, O.-L., Shi, L., & Ting, F. (2020). Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: dynamic geometry and 3D printing. International journal of STEM education, 7(1), 50. https://doi.org/10.1186/s40594-020-00244-1
Nindiasari, H., Pranata, M. F., Sukirwan, S., Sugiman, S., Fathurrohman, M., Ruhimat, A., & Yuhana, Y. (2024). The use of augmented reality to improve students' geometry concept problem-solving skills through the STEAM approach. Infinity Journal, 13(1), 119–138. https://doi.org/10.22460/infinity.v13i1.p119-138
Olofson, M. W., Swallow, M. J. C., & Neumann, M. D. (2016). TPACKing: A constructivist framing of TPACK to analyze teachers' construction of knowledge. Computers & Education, 95, 188–201. https://doi.org/10.1016/j.compedu.2015.12.010
Pagiling, S. L., Nur'aini, K. D., & Mokoagow, E. I. (2024). The novice mathematics teachers' technological pedagogical content knowledge: A case study. Southeast Asian Mathematics Education Journal, 13(2), 126–140. https://doi.org/10.46517/seamej.v13i2.201
Pamungkas, A. S., Khaerunnisa, E., & Fajriyanti, T. (2023). Development of web-based e-LKPD to develop high school students' numeracy on geometry. Union: Jurnal Ilmiah Pendidikan Matematika, 11(3), 538–550. https://doi.org/10.30738/union.v11i3.16091
Petko, D., Mishra, P., & Koehler, M. J. (2025). TPACK in context: An updated model. Computers and Education Open, 8, 100244. https://doi.org/10.1016/j.caeo.2025.100244
Radu, I., Doherty, E., DiQuollo, K., McCarthy, B., & Tiu, M. (2015). Cyberchase shape quest. In Proceedings of the 14th International Conference on Interaction Design and Children, (pp. 430–433). https://doi.org/10.1145/2771839.2771871
Reinke, L. T. (2019). Toward an analytical framework for contextual problem-based mathematics instruction. Mathematical thinking and learning, 21(4), 265–284. https://doi.org/10.1080/10986065.2019.1576004
Saeed, A., Foaud, L., & Fattouh, L. (2017). Techniques used to improve spatial visualization skills of students in engineering graphics course: A survey. International Journal of Advanced Computer Science and Applications, 8(3), 91–100. https://doi.org/10.14569/ijacsa.2017.080315
Sahrudin, A. (2024). Abstraksi aksi epistemik spasial rendah dan tinggi dalam mengkonstruk jaring-jaring kubus [Abstraction of low and high spatial epistemic actions in constructing cube nets]. Pena Persada Kerta Utama.
Sahrudin, A. (2024). Inovasi adaptasi kurikulum merdeka dalam pembelajaran matematika [Innovation of independent curriculum adaptation in mathematics learning]. Pena Persada Kerta Utama.
Sahrudin, A., Budiarto, M. T., & Manuharawati, M. (2021). The abstraction of junior high school student in learning geometry. Journal of Physics: Conference Series, 1918(4), 042072. https://doi.org/10.1088/1742-6596/1918/4/042072
Sahrudin, A., Budiarto, M. T., & Manuharawati, M. (2022). Epistemic action of junior high school students with low spatial ability in constructing cube nets. International Journal of Educational Methodology, 8(2), 221–230. https://doi.org/10.12973/ijem.8.2.221
Scheiner, T. (2015). New light on old horizon: Constructing mathematical concepts, underlying abstraction processes, and sense making strategies. Educational Studies in Mathematics, 91(2), 165–183. https://doi.org/10.1007/s10649-015-9665-4
Simsek, A., & Clark-Wilson, A. (2024). Adopting a framework for investigating mathematics teachers’ technology-integrated classroom teaching practice: Structuring features of classroom practice. International Journal of Science and Mathematics Education, 23(3), 589–616. https://doi.org/10.1007/s10763-024-10480-4
Sudirman, S., García-García, J., Rodríguez-Nieto, C. A., & Son, A. L. (2024). Exploring junior high school students' geometry self-efficacy in solving 3D geometry problems through 5E instructional model intervention: A grounded theory study. Infinity Journal, 13(1), 215–232. https://doi.org/10.22460/infinity.v13i1.p215-232
Sulistyowati, F., Budiyono, B., & Slamet, I. (2017). Problem solving reasoning and problem based instruction in geometry learning. Journal of Physics: Conference Series, 895, 012045. https://doi.org/10.1088/1742-6596/895/1/012045
Sumen, O. O. (2019). Primary school students' abstraction levels of whole-half-quarter concepts according to RBC theory. Journal on Mathematics Education, 10(2), 251–264. https://doi.org/10.22342/jme.10.2.7488.251-264
Thissen, A., Koch, M., Becker, N., & Spinath, F. M. (2018). Construct your own response. European Journal of Psychological Assessment, 34(5), 304–311. https://doi.org/10.1027/1015-5759/a000342
Weinhandl, R., Kleinferchner, L. M., Schobersberger, C., Schwarzbauer, K., Houghton, T., Lindenbauer, E., Anđić, B., Lavicza, Z., & Hohenwarter, M. (2023). Utilising personas as a methodological approach to support prospective mathematics teachers’ adaptation and development of digital mathematics learning resources. Journal of Mathematics Teacher Education, 28(4), 775–805. https://doi.org/10.1007/s10857-023-09607-1
Yilmaz, R., & Argun, Z. (2017). Role of visualization in mathematical abstraction: The case of congruence concept. International Journal of Education in Mathematics, Science and Technology, 6(1), 41–57. https://doi.org/10.18404/ijemst.328337
Yurt, E., & Tünkler, V. (2016). A study on the spatial abilities of prospective social studies teachers: A mixed method research. Educational Sciences: Theory & Practice, 16(3), 965–986.
Zurn-Birkhimer, S., Serrano Anazco, M., Holloway, B., & Baker, R. (2018). Work in progress: Online training in spatial reasoning for first-year female engineering students. In 2018 ASEE Annual Conference & Exposition Proceedings, (pp. 21783). https://doi.org/10.18260/1-2--31298