From Theory to Practice: Exploring the Use of Physical Visualization Objects in Rural Mathematics Classrooms

  • Abongile Happy Ngwabe Department of Mathematics, Science and Technology Education, Faculty of Education, Walter Sisulu University, South Africa
Keywords: Physical visualisation objects, Reflective practice theory, Instrumental genesis, Mathematics education, Preservice teachers

Abstract

Physical visualization objects play a critical role in mathematics education, particularly in rural settings where access to digital resources is limited. This study explores how preservice teachers in rural schools utilize physical visualization objects in mathematics lessons, highlighting their impact on teaching and learning. Guided by Instrumental Genesis Theory and Reflective Practice Theory, the study examines how preservice teachers transform physical objects into instructional tools and adapt their teaching strategies through reflective practice. Adopting a qualitative case study design within an interpretive paradigm, the study involved ten final-year preservice mathematics teachers undertaking teaching practice in rural schools. Data were collected through classroom observations and written reflections and analyzed using thematic analysis to examine preservice teachers’ use of physical visualization objects in mathematics instruction. Findings reveal that physical visualization objects enhance conceptual understanding, learner engagement, and teaching effectiveness. However, challenges such as classroom management, time constraints, and limited access to materials were reported. The study emphasizes the need for structured teacher training to optimize the pedagogical use of physical visualization objects. Future research should investigate the long-term impact of physical visualizations on learner achievement and explore their integration across diverse educational contexts, especially in resource-constrained environments.

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References

Ahiaku, P. K. A., Uleanya, C., & Muyambi, G. C. (2025). Rural schools and tech use for sustainability: The challenge of disconnection. Education and Information Technologies 30 (9), 12557–12571. https://doi.org/10.1007/s10639-024-13311-9

Ajani, O. A., & Ngema, T. (2024). Addressing digital competence gaps in pre-service teacher education: Challenges and strategies for rural schools. International Journal of Development and Sustainability, 13(10), 895–908. https://isdsnet.com/ijds-v13n10-04.pdf

Andresen, M. (2023). The influence of ready-made tools on students’ learning by modelling with differential equations systems. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1141019

Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245–274. https://doi.org/10.1023/A:1022103903080

Aruleba, K., & Jere, N. (2022). Exploring digital transforming challenges in rural areas of South Africa through a systematic review of empirical studies. Scientific African, 16, e01190. https://doi.org/10.1016/j.sciaf.2022.e01190

Braun, V., & Clarke, V. (2021). One size fits all? What counts as quality practice in (reflexive) thematic analysis? Qualitative Research in Psychology, 18(3), 328–352. https://doi.org/10.1080/14780887.2020.1769238

Buentello-Montoya, D. A., Lomelí-Plascencia, M. G., & Medina-Herrera, L. M. (2021). The role of reality enhancing technologies in teaching and learning of mathematics. Computers & Electrical Engineering, 94, 107287. https://doi.org/10.1016/j.compeleceng.2021.107287

Byrne, E. M., Jensen, H., Thomsen, B. S., & Ramchandani, P. G. (2023). Educational interventions involving physical manipulatives for improving children’s learning and development: A scoping review. Review of Education, 11(2), e3400. https://doi.org/10.1002/rev3.3400

Camaño, D., & Turmo, M. (2019). Promoting social creativity in science education with digital technology to overcome inequalities: A scoping review. Frontiers in Psychology, 10. https://doi.org/10.3389/fpsyg.2019.01474

Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. https://doi.org/10.1037/a0031084

Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education (8th ed.). Routledge. https://doi.org/10.4324/9781315456539

Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). SAGE Publications.

Farrell, T. S. C. (2015). Promoting teacher reflection in second language education: A framework for TESOL professionals. Routledge.

Flores, M., & Hinton, V. (2022). Use of the concrete–representational–abstract instructional sequence to improve mathematical outcomes for elementary students with EBD. Beyond Behavior, 31(1), 16–28. https://doi.org/10.1177/10742956211072421

Flores, M., Hinton, V., & Schweck, K. (2023). Using CRA-I to teach fraction and decimal concepts to students with learning disabilities. Learning Disability Quarterly, 47(1), 44–58. https://doi.org/10.1177/07319487231176545

Fokuo, M. O., Opuku-Mensah, N., Asamoah, R., Nyarko, J., Agyeman, K. D., Owusu-Mintah, C., & Asare, S. (2023). The use of visualization tools in teaching mathematics in college of education: A systematic review. Online Journal of Mathematics, Science and Technology Education, 4(1). https://ojomste.com/index.php/1/article/view/24

Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction. Educational Psychology Review, 26(1), 9–25. https://doi.org/10.1007/s10648-014-9249-3

Guan, H., Li, J., Rao, Y., Chen, R., & Xu, Z. (2024). Comparative effects of dynamic geometry system and physical manipulatives on inquiry-based math learning for students in junior high school. Education and Information Technologies, 29, 21477–21499. https://doi.org/10.1007/s10639-024-12663-6

Haspekian, M. (2023). Algebra education and digital resources: A long-distance relationship? In Mathematics education in the digital age (pp. 1–33). Springer. https://doi.org/10.1007/978-3-030-95060-6_16-1

Hatlevik, I. (2011). The theory–practice relationship: Reflective skills and theoretical knowledge as key factors in bridging the gap between theory and practice in initial nursing education. Journal of Advanced Nursing, 68(4), 868–877. https://doi.org/10.1111/j.1365-2648.2011.05789.x

Justo, E., Delgado, A., Llorente-Cejudo, C., Aguilar, R., & Cabero-Almenara, J. (2022). The effectiveness of physical and virtual manipulatives on learning and motivation in structural engineering. Journal of Engineering Education, 111(4), 813–851. https://doi.org/10.1002/jee.20482

Korthagen, F. A. J. (2017). Inconvenient truths about teacher learning: Towards professional development 3.0. Teachers and Teaching, 23(4), 387–405. https://doi.org/10.1080/13540602.2016.1211523

Lagrange, J.-B. (2005). Articulation between technical and conceptual work in technology-rich learning environments: The case of symbolic calculators. ZDM, 37(5), 373–381. https://doi.org/10.1007/BF02652806

Lanyasunya, R. (2023). Relationship between selected economic factors and enrolment of girls in rural public primary schools in Samburu County, Kenya. Journal of Policy and Development Studies, 5(1), 376–382. https://doi.org/10.51317/ecjeds.v5i1.454

Long, H., Bouck, E., & Kelly, H. (2022). An evidence-based practice synthesis of virtual manipulatives for students with ASD and IDD. Focus on Autism and Other Developmental Disabilities, 38(3), 147–157. https://doi.org/10.1177/10883576221121654

López, N. (2017). The instrumental genesis process in future primary teachers using dynamic geometry software. International Journal of Mathematical Education in Science and Technology, 49(4), 481–500. https://doi.org/10.1080/0020739X.2017.1377302

Manches, A., & O’Malley, C. (2012). Tangibles for learning: A representational analysis of physical manipulation. Personal and Ubiquitous Computing, 16(4), 405–419. https://doi.org/10.1007/s00779-011-0406-0

Marlina, R. (2024). Theoretical frameworks of self-efficacy in collaborative science learning practices: A systematic literature review. JPBI (Jurnal Pendidikan Biologi Indonesia), 10(2), 602–615. https://doi.org/10.22219/jpbi.v10i2.33628

Mirza, H., & Bellalem, F. (2023). Ethical considerations in qualitative research: Summary guidelines for novice social science researchers. Social Studies and Research Journal, 11(1), 441–449. https://asjp.cerist.dz/en/article/220704

Mokgwathi, M., Graham, M., & Villiers, J. (2023). Promoting and hindering factors in mathematics teaching in South African high schools. Acta Didactica Napocensia, 16(1), 82–98. https://doi.org/10.24193/adn.16.1.6

Muzangwa, J., & Ogbonnaya, U. I. (2022). Undergraduate mathematics education students’ visual representations of multivariable functions. Edumatica: Jurnal Pendidikan Matematika, 12(3), 212–221. https://doi.org/10.22437/edumatica.v12i03.15712

Ng’ambi, D., & Bozalek, V. (2016). Learning with technologies in resource-constrained environments. In The Wiley handbook of learning technology (pp. 200–220). https://doi.org/10.1002/9781118736494.ch12

Özbey, N., & Özmantar, M. (2023). Material features that determine the activity preferences of mathematics teachers. E-Kafkas Eğitim Araştırmaları Dergisi, 10(1), 18–36. https://doi.org/10.30900/kafkasegt.1163539

Palinkas, L. A., Horwitz, S. M., Green, C. A., Wisdom, J. P., Duan, N., & Hoagwood, K. (2015). Purposeful sampling for qualitative data collection and analysis in mixed method implementation research. Administration and Policy in Mental Health and Mental Health Services Research, 42(5), 533–544. https://doi.org/10.1007/s10488-013-0528-y

Park, J., Bryant, D. P., & Shin, M. (2021). Effects of interventions using virtual manipulatives for students with learning disabilities: A synthesis of single-case research. Journal of Learning Disabilities, 55(4), 325–337. https://doi.org/10.1177/00222194211006336

Pati, R., & Garud, N. (2021). Role of feedback on innovative outcomes: Moderating role of resource-constrained environments. IEEE Transactions on Engineering Management, 68(3), 685–698. https://doi.org/10.1109/TEM.2020.3015129

Ramírez, L., & Céspedes, V. (2021). Development of a learning model of quadric surfaces with augmented reality and didactic engineering. International Journal of Interactive Mobile Technologies (iJIM), 15(22), 142. https://doi.org/10.3991/ijim.v15i22.25341

Resch, K., & Schrittesser, I. (2021). Using the service-learning approach to bridge the gap between theory and practice in teacher education. International Journal of Inclusive Education, 27(10), 1118–1132. https://doi.org/10.1080/13603116.2021.1882053

Rizos, I., & Foykas, E. (2023). Utilization of “Byrne’s Euclid” in the teaching of geometry to students with special learning difficulties: A qualitative research. European Journal of Education and Pedagogy, 4(2), 139–148. https://doi.org/10.24018/ejedu.2023.4.2.623

Roorda, G., Vos, P., Drijvers, P., & Goedhart, M. (2016). Solving rate of change tasks with a graphing calculator: A case study on instrumental genesis. Digital Experiences in Mathematics Education, 2(3), 228–252. https://doi.org/10.1007/s40751-016-0022-8

Satsangi, R., & Sigmon, S. (2023). Teaching multiplicative thinking with virtual representations to children with mathematics difficulty. Remedial and Special Education, 45(4), 216–229. https://doi.org/10.1177/07419325231206483

Schön, D. A. (1983). The reflective practitioner: How professionals think in action. Basic Books.

Schön, D. A. (1987). Educating the reflective practitioner: Toward a new design for teaching and learning in the professions. Jossey-Bass.

Smith, C., & Cekiso, M. (2020). Teachers’ understanding and use of visual tools in their numeracy classrooms: A case study of two primary schools in Gauteng. South African Journal of Childhood Education, 10(1). https://doi.org/10.4102/sajce.v10i1.887

Stocker, M., Burmester, M., & Allen, M. (2014). Optimisation of simulated team training through the application of learning theories: A debate for a conceptual framework. BMC Medical Education, 14(1). https://doi.org/10.1186/1472-6920-14-69

Stodter, A., Cope, E., & Townsend, R. (2021). Reflective conversations as a basis for sport coaches’ learning: A theory-informed pedagogic design for educating reflective practitioners. Professional Development in Education, 50(4), 700–715. https://doi.org/10.1080/19415257.2021.1902836

Takyi, B., Korankye, S., & Akolbila, V. (2026). Innovating within constraints: Basic school teachers’ experiences with pedagogical reform. International Journal of Instruction, 19(2), 219–236. https://doi.org/10.29333/iji.2026.19212a

Tiwari, S., Obradović, D., Rathour, L., Mishra, L., & Mishra, V. (2021). Visualization in mathematics teaching. Journal of Advances in Mathematics, 20, 431–439. https://doi.org/10.24297/jam.v20i.9136

Trottier, D. (2024). Debriefing experiential learning in counselor education. Counselor Education and Supervision, 63(2), 145–160. https://doi.org/10.1002/ceas.12299

Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307. https://doi.org/10.1007/s10758-004-3468-5

Umuhoza, C., & Uworwabayeho, A. (2021). Teacher’s use of instructional materials in teaching and learning mathematics in Rwandan primary schools. African Journal of Teacher Education, 10(2), 1–16. https://doi.org/10.21083/ajote.v10i2.6659

Viberg, O., Grönlund, Å., & Andersson, A. (2023). Integrating digital technology in mathematics education: A Swedish case study. Interactive Learning Environments, 31(1), 232–243. https://doi.org/10.1080/10494820.2020.1770801

Wulandari, Y. A., Nusantara, T., Subanji, & Rahardjo, S. (2022). Developing students’ understanding through manipulative-based instruction: A case study in a rural Indonesian school. International Journal of Instruction, 15(2), 1–16. https://doi.org/10.29333/iji.2022.1521a

Yeo, S., & Webel, C. (2024). Elementary students’ fraction reasoning: A measurement approach to fractions in a dynamic environment. Mathematical Thinking and Learning, 26(1), 20–46. https://doi.org/10.1080/10986065.2022.2025639

Žakelj, A., & Klančar, A. (2022). The role of visual representations in geometry learning. European Journal of Educational Research, 11(3), 1393–1411. https://doi.org/10.12973/eu-jer.11.3.1393

Zou, P., Luo, Y., Krolak, K., Hu, J., Liu, L., Lin, Y., … Sun, W. (2019). Students’ experiences on learning therapeutic relationship: A narrative inquiry. Canadian Journal of Nursing Research, 53(1), 78–87. https://doi.org/10.1177/0844562119873760

Published
2026-04-29
How to Cite
Ngwabe, A. H. (2026). From Theory to Practice: Exploring the Use of Physical Visualization Objects in Rural Mathematics Classrooms. Studies in Learning and Teaching, 7(1), 108-124. https://doi.org/10.46627/silet.v7i1.764
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Articles
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