Exploring a Teacher’s Knowledge in Constructing Mathematical Lateral Thinking Problems to Teach Creativity
DOI:
https://doi.org/10.12928/ijeme.v9i1.30886Keywords:
lateral thinking, mathematics problem, students' creativity, teacher's knowledgeAbstract
This study examined the process of constructing mathematical problems to teach creativity using the concept of lateral thinking. It employed a case study design and involved a senior junior high school mathematics teacher who has won mathematics learning innovation competitions. The teacher has understood what is meant by mathematical creativity and lateral thinking, and has proven his mathematical ability and lateral thinking ability. He was asked to create his own math problems, teach creativity, and assess students' math learning outcomes using the problems. The findings of this study highlight three key relationships: (1) the connection between mathematical content knowledge and problem-structuring ability, (2) the influence of training experience on methods for teaching creativity, and (3) the interrelationship among content knowledge, training experience, and assessment practices. These highlight the importance of integrating content knowledge and pedagogical approaches in mathematics learning to enhance creative problem-solving skills.
References
Amador, J. M., Rogers, M. A. P., Hudson, R., Phillips, A., Carter, I., Galindo, E., & Akerson, V. L. (2022). Novice teachers’ pedagogical content knowledge for planning and implementing mathematics and science lessons. Teaching and Teacher Education, 115, 103736.
Bicer, A. (2021). Multiple representations and mathematical creativity. Thinking Skills and Creativity, 42, 100960. https://doi.org/10.1016/j.tsc.2021.100960
Bicer, A., Chamberlin, S., & Perihan, C. (2021). A Meta‐Analysis of the Relationship between Mathematics Achievement and Creativity. The Journal of Creative Behavior, 55(3), 569–590. https://doi.org/10.1002/jocb.474
Cai, J., & Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102, 101391. https://doi.org/10.1016/j.ijer.2019.01.001
De Bono, E. (1969). Information processing and new ideas—Lateral and vertical thinking. The Journal of Creative Behavior, 3(3), 159–171.
De Bono, E. (2018). The Teaching of Creative Thinking. https://www.debono.com/teaching-creative-thinking-1
De Bono, E. (2020). Lateral Thinking: A course based on the work of Dr. Edward de Bono. Edward de Bono Ltd. https://www.lateralthinking.com/flipbook
English, L. D. (2020). Teaching and learning through mathematical problem posing: Commentary. International Journal of Educational Research, 102, 101451. https://doi.org/10.1016/j.ijer.2019.06.014
Gencturk, Y. C., & Tolar, T. (2022). Mathematics teaching expertise: A study of the dimensionality of content knowledge, pedagogical content knowledge, and content-specific noticing skills. Teaching and Teacher Education, 114, 103696. https://doi.org/10.1016/j.tate.2022.103696
Heard, J., Krstic, S., & Richardson, S. (2023). Evidencing creativity in educational settings. Journal of Creativity, 33(1), 100046. https://doi.org/10.1016/j.yjoc.2023.100046
Julita. (2019). Improving mathematical lateral thinking ability of high school students through quantum learning based on creative problem solving. Journal of Physics: Conference Series, 1315(1). https://doi.org/10.1088/1742-6596/1315/1/012061
Kontorovich, I. (2020). Problem-posing triggers or where do mathematics competition problems come from? Educational Studies in Mathematics, 105(3), 389–406. https://doi.org/10.1007/s10649-020-09964-1
Kontorovich, I., & Koichu, B. (2016). A CASE STUDY OF AN EXPERT PROBLEM POSER FOR MATHEMATICS COMPETITIONS. International Journal of Science and Mathematics Education, 14(1), 81–99. https://doi.org/10.1007/s10763-013-9467-z
Lai, E. R. (2011). Critical thinking: A literature review. Pearson’s Research Reports, 6(1), 40–41.
Leikin, R., & Sriraman, B. (2022). Empirical research on creativity in mathematics (education): From the wastelands of psychology to the current state of the art. ZDM, 54(1), 1–17. https://doi.org/10.1007/s11858-022-01340-y
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (Edition 3). Sage.
Montes, M., Chico, J., Martín-Díaz, J. P., & Badillo, E. (2024). Mathematics teachers’ specialized knowledge mobilized through problem transformation. The Journal of Mathematical Behavior, 73, 101132. https://doi.org/10.1016/j.jmathb.2024.101132
Nggaba, M. E., Herman, T., & Prabawanto, S. (2018). Students’ lateral mathematical thinking ability on trigonometric problems. International Conference on Mathematics and Science Education of Universitas Pendidikan Indonesia, 3, 756–762.
Poulos, A. (2020). A CASE STUDY OF A STUDENT WHO CREATED PROBLEMS FOR A MATHEMATICS COMPETITION. THE TEACHING OF MATHEMATICS, XXIII(2), 109–116.
Schoenfeld, A. H. (Ed.). (1987). Cognitive science and mathematics education (Online-Ausg). Lawrence Erlbaum Associates.
Schoevers, E. M., Kroesbergen, E. H., Moerbeek, M., & Leseman, P. P. M. (2022). The relation between creativity and students’ performance on different types of geometrical problems in elementary education. ZDM--Mathematics Education, 54(1), 133–147.
Shodiq, L. J., Faizati, P. S. D., & Utomo, B. T. (2022). Exploration of mathematics teacher knowledge in lateral thinking techniques to develop creative thinking skills. 020059. https://doi.org/10.1063/5.0096057
Shodiq, L. J., Juniati, D., & Susanah. (2023). Influence of personal background on lateral thinking skill of prospective mathematics teachers. 020011. https://doi.org/10.1063/5.0154628
Shodiq, L. J., Juniati, D., & Susanah. (2024a). Noticing differences in numerical methods class with lateral thinking-based assignments. 020037. https://doi.org/10.1063/5.0194654
Shodiq, L. J., Juniati, D., & Susanah, S. (2024b). Differentiated Instruction Based on Lateral Thinking Techniques for Enhancing Mathematical Creativity. City University of New York, 16(5), 240–264.
Shodiq, L. J., Juniati, D., & Susanah, S. (2025). Teaching creativity through mathematical lateral thinking problems: A pilot study. Eurasia Journal of Mathematics, Science and Technology Education, 21(2), em2574. https://doi.org/10.29333/ejmste/15913
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zdm, 29(3), 75–80.
Stahnke, R., & Blömeke, S. (2021). Novice and expert teachers’ situation-specific skills regarding classroom management: What do they perceive, interpret and suggest? Teaching and Teacher Education, 98, 103243. https://doi.org/10.1016/J.TATE.2020.103243
Susilawati, W., Karyadinata, R., & ... (2019). Cognitive conflict strategy to the improvement of students’ lateral mathematical thinking ability. Journal of Physics …. https://doi.org/10.1088/1742-6596/1175/1/012174
Tamsah, H., Ilyas, J. B., & Yusriadi, Y. (2021). Create Teaching Creativity through Training Management, Effectiveness Training, and Teacher Quality in the Covid-19 Pandemic. Journal of Ethnic and Cultural Studies, 8(4), 18–35. https://doi.org/10.29333/ejecs/800
Vale, I., & Barbosa, A. (2024). Exploring the creative potential of mathematical tasks in teacher education. International Electronic Journal of Mathematics Education, 19(4), em0790. https://doi.org/10.29333/iejme/15075
Vincent-Lancrin, S., González-Sancho, C., Bouckaert, M., De Luca, F., Fernández-Barrerra, M., Jacotin, G., Urgel, J., & Vidal, Q. (2019). Fostering Students’ Creativity and Critical Thinking: What it Means in School. OECD. https://doi.org/10.1787/62212c37-en
Vistro-Yu, C. P. (2009). Using Innovation Techniques to Generate ‘New’ Problems. In B. Kaur, B. H. Yeap, & M. Kapur, Mathematical Problem Solving (pp. 185–207). WORLD SCIENTIFIC. https://doi.org/10.1142/9789814277228_0010
White, R. E., & Cooper, K. (2022). Case Study Research. In R. E. White & K. Cooper, Qualitative Research in the Post-Modern Era (pp. 233–285). Springer International Publishing. https://doi.org/10.1007/978-3-030-85124-8_7
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Lukman Jakfar Shodiq, Dwi Juniati, Susanah Susanah, Ainnur Rohmania
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal. Please also carefully read the International Journal on Emerging Mathematics Education (IJEME) Author Guidelines at http://journal.uad.ac.id/index.php/IJEME/about/submissions#authorGuidelines
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities, tacitly or explicitly, of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Copyright
Authors who publish with the International Journal on Emerging Mathematics Education (IJEME) agree to the following terms:
- Authors retain copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Ciptaan disebarluaskan di bawah Lisensi Creative Commons Atribusi-BerbagiSerupa 4.0 Internasional.
