Development of the Descriptive-Relational-Graphical (DRG) Model for Eduinformatics
Fostering Relational Understanding through Representational Transformation in Data-Driven Mathematics Education
DOI:
https://doi.org/10.52731/liir.v007.484Keywords:
Descriptive-Relational-Graphical (DRG) Model, Representational transformation, Visualization, Relational understanding, Mathematical learning, Eduinformatics, Data-driven education, OECD Learning Compass 2030Abstract
The Organization for Economic Co-operation and Development (OECD) Learning Compass 2030 envisions education as cultivating transformative competencies for navigating uncertain futures. This study proposes the Descriptive-Relational-Graphical (DRG) Model as a comprehensive framework for understanding mathematical learning through representational transformation. The DRG Model integrates three complementary modes: descriptive language for articulation through natural expression, relational language for quantitative and logical structures, and graphical language for spatial visualization. This framework emerged from data-driven education research within Eduinformatics, an interdisciplinary field integrating educational sciences with informatics methodologies. Building on Ainsworth's DeFT framework, Duval's semiotic representation theory, and Skemp's distinction between instrumental and relational understanding, this study demonstrates that mathematical learning develops through recursive movement across representational systems. Visualization functions as a central mediating pathway connecting internal cognition with external representation. Analysis of geometric examples illustrates how bidirectional transformations among descriptive, relational, and graphical representations foster relational understanding—comprehending both what to do and why. The DRG Model supports OECD Learning Compass 2030 goals by enhancing learner autonomy, metacognitive reflection, and agency in mathematics education and beyond.
References
T. A. Hughson and B. E. Wood, “The OECD Learning Compass 2030 and the future of disciplinary learning: a Bernsteinian critique,” J. Educ. Pol., vol. 37, no. 4, pp. 634–654, July 2022, doi: 10.1080/02680939.2020.1865573.
OECD, The Future of Education as Envisioned by the OECD Education 2030 Project (Japanese) ISBN:4623090442. Minerva Shobo, 2020.
S. Ainsworth, “DeFT: A conceptual framework for considering learning with multiple representations,” Learn. Instr., vol. 16, no. 3, pp. 183–198, June 2006, doi: 10.1016/j.learninstruc.2006.03.001.
R. Duval, “Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning,” 1999, [Online]. Available: https://eric.ed.gov/?id=ed466379
K. Takamatsu, S. Matsumoto, N. Honda, Y. Ishige, S. Matsumoto, H. Kawasaki, I. Noda, K. Bannaka, T. Gozu, K. Murakami, T. Sakai, R. Kozaki, A. Kishida, H. Ito, K. Akashi, S. Hama, G. Prescott, M. Uchida, et al., “Lifelong sustainable inquiry-based community learning (LSiCL) based on eduinformatics,” in Lecture Notes in Networks and Systems, Singapore: Springer Nature Singapore, 2025, pp. 415–424. doi: 10.1007/978-981-97-9559-8_36.
J. S. Bruner, “The process of education,” 2009, [Online]. Available: https://books.google.co.jp/books?hl=ja&lr=lang_ja|lang_en&id=S6FKW90QY40C&oi=fnd&pg=PR29&dq=The+Process+of+Education.+Cambridge&ots=leiWmc25wX&sig=AVZ1pFEv34hZ_JzcInBDmfIjTHg
R. R. Skemp, “Relational understanding and instrumental understanding,” Mathematics teaching, vol. 77, no. 1, pp. 20–26, 1976, [Online]. Available: http://davidtall.com/skemp/pdfs/instrumental-relational.pdf
T. Kirimura, K. Mitsunari, T. Kunisaki, T. Gozu, K. Takamatsu, K. Bannaka, and Y. Nakata, “Effectiveness of first year experience’s course ‘Manaburu’ at Kobe Tokiwa University for university students by using textual analysis,” Bulletin of Kobe Tokiwa University, vol. 11, pp. 193–208, 2018, doi: 10.20608/00000972.
K. Takamatsu, K. Murakami, T. Kirimura, K. Bannaka, I. Noda, L. R.-J. Wei, K. Mitsunari, M. Seki, E. Matsumoto, M. Bohgaki, A. Imanishi, M. Omori, R. Adachi, M. Yamasaki, H. Sakamoto, K. Takao, J. Asahi, T. Nakamura, et al., “‘Eduinformatics’: A new education field promotion,” Bulletin of kobe Tokiwa University, vol. 11, pp. 27–44, 2018, doi: 10.20608/00000958.
K. Takamatsu, Y. Kozaki, K. Murakami, A. Sugiura, K. Bannaka, K. Mitsunari, M. Omori, and Y. Nakata, “Review of Recent Eduinformatics Research,” in 2019 IIAI International Congress on Applied Information Technology (IIAI-AIT), 2019, pp. 27–32.
K. Takamatsu, K. Murakami, R.-J. W. Lim, and Y. Nakata, “Novel visualization for curriculum in silico using syllabus by a combination of cosine similarity, multidimensional scaling methods, and scatter plot: Dynamic curriculum mapping (DCM) for syllabus,” Bulletin of Kobe Tokiwa University, vol. 10, pp. 99–106, 2017, doi: 10.20608/00000396.
K. Takamatsu, T. Kirimura, K. Bannaka, I. Noda, M. Omori, R. Adachi, K. Mitsunari, T. Nakamura, and Y. Nakata, “A new way of visualizing curricula using competencies: Cosine similarity, multidimensional scaling methods, and scatter plotting,” Advanced Applied Informatics (IIAI-AAI), 2016 5th IIAI International Congress on. IEEE, p. accepted, 2017.
K. Takamatsu, K. Murkami, Y. Kozaki, K. Bannaka, I. Noda, M. Yamasaki, R.-J. W. Lim, K. Mitsunari, N. Tadashi, and Y. Nakata, “A Novel Curriculum Visualization Method Using a Combination of Competencies, Cosine Similarity, Multidimensional Scaling Methods, and Scatter Plotting,” IEE: Information Engineering Express, vol. 5, no. 1, pp. 127–143, 2019.
K. Takamatsu, Y. Kozaki, K. Murakami, K. Bannaka, I. Noda, W. Lim Raphael-Joel, K. Mitsunari, T. Nakamura, and Y. Nakata, “A New Way of Visualizing Curricula Using Competencies : Cosine Similarity and t-SNE,” in Advanced Applied Informatics (IIAI-AAI), 2018 7th International Institute of Applied Informatics (IIAI) International Congress on. Institute of Electrical and Electronics Engineers (IEEE), 2018, pp. 390–395. doi: 10.1109/IIAI-AAI.2018.00084.
K. Takamatsu, Y. Kozaki, K. Murakami, E. Matsumoto, M. Bohgaki, M. Seki, A. Imanishi, K. Bannaka, I. Noda, K. Mitsunari, and Y. Nakata, “Web-based Radar Chart System of Tokiwa Competencies in Eduinformatics,” in International Conference on Education, Psychology, and Learning (ICEPL2018), 2018, pp. 30–37.
Y. Nakata, E. Matsumoto, M. Bohgaki, M. Seki, A. Imanishi, T. Kirimura, K. Bannaka, I. Noda, K. Mitsunari, and K. Takamatsu, “Construction of a Prototype of a Method for Advising Students Regarding Courses Using Competencies,” 23rd International Conference on Teaching, Education & Learning (ICTEL), 2017.
I. Noda, K. Takamatsu, K. Nishiyama, K. Bannaka, Y. Saruwatari, T. Kirimura, Y. Nakata, and M. Omori, “New visualization of competency-based education ( CBE ) in higher education institutional research ( IR ),” in Advanced Applied Informatics (IIAI-AAI), 2020 9th International Institute of Applied Informatics (IIAI) International Congress on. Institute of Electrical and Electronics Engineers (IEEE), 2020, pp. 391–396. doi: 10.1109/IIAI-AAI50415.2020.00085.
