The Characteristics of Students Engaged in Spontaneous Problem-Posing

Authors

Syaiful Hadi , Cholis Sa’dijah , Sudirman , I Made Sulandra , Sri Rahayuningsih

DOI:

10.29303/jppipa.v10i2.6869

Published:

2024-02-28

Issue:

Vol. 10 No. 2 (2024): February

Keywords:

Originality Spontaneous, Problems-as-problematic, Problem-as-exercise, Spontaneous problem-posing

Research Articles

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How to Cite

Hadi, S., Sa’dijah, C. ., Sudirman, S., Sulandra, I. M. ., & Rahayuningsih, S. . (2024). The Characteristics of Students Engaged in Spontaneous Problem-Posing. Jurnal Penelitian Pendidikan IPA, 10(2), 964–972. https://doi.org/10.29303/jppipa.v10i2.6869
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Abstract

Spontaneous problem posing is a basic concept of spontaneous mathematical thinking and science learning. Students generate problems without systematic encouragement and pose problems based on the student's desire to develop their skills. As a result, they can serve as important markers of constructive mathematical and science engagement, particularly affective engagement, for problem solvers and their classroom communities. We used a qualitative approach to analyze student characteristics, especially in the affective domain, when presenting random problems. We used an observational approach and experience sampling in each class to observe students' engagement in spontaneous problem posing both individually and in groups. The findings revealed that each student showed different characteristics when presenting problems suddenly (spontaneous problem posing). The submission of the first subject problem was categorized as problem-as-exercise, satisfying the characteristics of spontaneous originality, where constructive emotional experiences impressed more on the teacher, while negative emotional experiences impressed more on oneself (self), classmates, and mathematical activities. The submission of the second subject problem is classified as a problematic problem, fulfilling the characteristics of spontaneous originality. Negative emotional experiences are more visible in me (myself), while constructive emotional experiences are more visible in teachers, classmates, and math activities

References

Aguillon, S. M., Siegmund, G.-F., Petipas, R. H., Drake, A. G., Cotner, S., & Ballen, C. J. (2020). Gender differences in student participation in an active-learning classroom. CBE—Life Sciences Education, 19(2), ar12. https://doi.org/10.1187/cbe.19-03-0048

Aubry, A., Gonthier, C., & Bourdin, B. (2021). Explaining the high working memory capacity of gifted children: Contributions of processing skills and executive control. Acta Psychologica, 218, 103358. https://doi.org/10.1016/j.actpsy.2021.103358

Beghetto, R. A. (2006). Creative self-efficacy: Correlates in middle and secondary students. Creativity Research Journal, 18(4), 447–457. https://doi.org/10.1207/s15326934crj1804_4

Bicer, A., Lee, Y., Perihan, C., Capraro, M. M., & Capraro, R. M. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics, 105(3), 457–485. https://doi.org/10.1007/s10649-020-09995-8

Bonotto, C., & Santo, L. D. (2015). On the Relationship Between Problem Posing, Problem Solving, and Creativity in the Primary School. In Mathematical Problem Posing: From Research to Effective Practice (pp. 1–569). Springer. https://doi.org/10.1007/978-1-4614-6258-3

Cai, J. (2003). Singaporean students’ mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719–737. https://doi.org/10.1080/00207390310001595401

Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57–69. https://doi.org/10.1007/s10649-012-9429-3

Çakır, A., & Akkoç, H. (2020). Correction to: Examining socio-mathematical norms related to problem posing: A case of a gifted and talented mathematics classroom (Educational Studies in Mathematics. Educational Studies in Mathematics, 105, 1(3), 19–34 ,. https://doi.org/10.1007/s10649-020-09965-0).

Carmona-Medeiro, E., Mart’in-D’iaz, J. P., & Climent, N. (2024). Variables in planning and carrying out a problem-posing task in early childhood education. The Journal of Mathematical Behavior, 73, 101131. https://doi.org/10.1016/j.jmathb.2024.101131

Carrillo, J., & Cruz, J. (2016). Posing and Solving Mathematical Problems. In Posing and Solving Mathematical Problems (pp. 23–36). https://doi.org/10.1007/978-3-319-28023-3

Chen, L., Dooren, W., Chen, Q., & Verschaffel, L. (2011). An investigation on Chinese teachers’ realistic problem posing andProblem Solving ability and beliefs. International Journal of Science and Mathematics Education, 9(4), 919–948. https://doi.org/10.1007/s10763-010-9259-7

Chen, L., Dooren, W. V., & Verschaffel. (2015). Enhancing the Development of Chinese Fifth- Graders’ Problem-Posing and Problem- Solving Abilities, Beliefs, and Attitudes: A Design Experiment. In Enhancing the Development of Chinese Fifth- Graders’ Problem-Posing and Problem- Solving Abilities, Beliefs, and Attitudes: A Design Experiment (F.M. Singe. Springer Science+Business Media New York. https://doi.org/10.1007/978-1-4614-6258-3

Chin, C., & Osborne, J. (2008). Students’ questions: A potential resource for teaching and learning science. Studies in Science Education, 44(1), 1–39. https://doi.org/10.1080/03057260701828101

Cifarelli, V. V, & Sevim, V. (2015). Mathematical problem posing: From research to effective practice. In Research in Mathematics Education (pp. 1–569). Springer. https://doi.org/10.1007/978-1-4614-6258-3

Fonteles, F. P. G., Hirashima, T., Hayashi, Y., & Maeda, K. (2019). Application focused on structural comprehension of mathematics contextual problems for kindergarten students. Research and Practice in Technology Enhanced Learning, 14(1), 2. https://doi.org/10.1186/s41039-019-0096-1

Getzels, & J.W. (1979). Problem Finding: A Theoretical Note (Vol. 172, pp. 167–171). https://doi.org/10.1016/S0364-0213(79)80030-0

Harpen, X. Y., & Presmeg, N. C. (2013). An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics, 83(1), 117–132. https://doi.org/10.1007/s10649-012-9456-0

Headrick, L., Wiezel, A., Tarr, G., Zhang, X., Cullicott, C. E., Middleton, J. A., & Jansen, A. (2020). Engagement and affect patterns in high school mathematics classrooms that exhibit spontaneous problem posing: an exploratory framework and study. Educational Studies in Mathematics, 105, 435–456. https://doi.org/10.1007/s10649-020-09996-7

Jr, & Cai. (2016). Posing and Solving Mathematical Problems. In Can Mathematical Problem Solving Be Taught? Preliminary Answers from 30 Years of Research (pp. 117–135). https://doi.org/10.1007/978-3-319-28023-3_8

Konopczyński, M., & others. (2020). Rehabilitation pedagogy towards (re) socialization of youth in the “augmented reality†Commentary on the phenomenon of empathy and aggression on the Internet. Resocjalizacja Polska, 19(1), 9–32. Retrieved from https://www.ceeol.com/search/article-detail?id=910526

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., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. Journal of Mathematical Behavior, 31(1), 149–161. https://doi.org/10.1016/j.jmathb.2011.11.002

Lee, J.-E., & Lim, W. (2021). Preservice teachers’ eliciting and responding to student thinking in lesson plays. Mathematics, 9(22), 2842. https://doi.org/10.3390/math9222842

Lee, K. H., Boltz, M., Lee, H., & Algase, D. L. (2017). Does Social Interaction Matter Psychological Well-Being in Persons with Dementia? American Journal of Alzheimer’s Disease & Other Dementiasr, 32(4), 207–212. https://doi.org/10.1177/1533317517704301

Leikin, R. (2018). Part IV: Commentary – Characteristics of Mathematical Challenge in Problem-Based Approach to Teaching Mathematics. Springer International Publishing. https://doi.org/10.1007/978-3-319-92390-1_38

Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM - International Journal on Mathematics Education, 45(2), 159–166. https://doi.org/10.1007/s11858-012-0459-1

Moses, R. N., & Mohamad, M. (2019). Challenges Faced by Students and Teachers on Writing Skills in ESL Contexts: A Literature Review. Creative Education, 10(13), 3385–3391. https://doi.org/10.4236/ce.2019.1013260

Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2023). Teacher efforts towards the development of students’ mathematical reasoning skills. Heliyon, 9(4), 14789. https://doi.org/10.1016/j.heliyon.2023.e14789

Rahayuningsih, S., Sirajuddin, S., & Ikram, M. (2021). Using open-ended problem-solving tests to identify students’ mathematical creative thinking ability. Participatory Educational Research, 8(3), 285–299. https://doi.org/10.17275/per.21.66.8.3

Reiss, K., & Törner, G. (2007). Problem solving in the mathematics classroom: The German perspective. ZDM - International Journal on Mathematics Education, 39(5–6), 431–441. https://doi.org/10.1007/s11858-007-0040-5

Rosli, R., Capraro, M. M., & Capraro, R. M. (2014). The effects of problem posing on student mathematical learning: A meta-analysis. International Education Studies, 7(13), 227–241. https://doi.org/10.5539/ies.v7n13p227

Schifter, D., & Russell, S. J. (2022). The centrality of student-generated representation in investigating generalizations about the operations. ZDM – Mathematics Education, 54(6), 1289–1302. https://doi.org/10.1007/s11858-022-01379-x

Schindler, M., & Bakker, A. (2020). Affective field during collaborative problem posing and problem solving: A case study. Educational Studies in Mathematics, 105(3), 303–324. https://doi.org/10.1007/s10649-020-09973-0

Schoenfeld, A. H. (2016). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint. Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202

Sengupta-Irving, T., & Enyedy, N. (2015). Why Engaging in Mathematical Practices May Explain Stronger Outcomes in Affect and Engagement: Comparing Student-Driven With Highly Guided Inquiry. Journal of the Learning Sciences, 24(4), 550–592. https://doi.org/10.1080/10508406.2014.928214

Singer, F. M., F, N., E., & Cai, J. (2015). Mathematical problem posing: From research to effective practice. In Mathematical Problem Posing: From Research to Effective Practice. https://doi.org/10.1007/978-1-4614-6258-3

Voica, C., Singer, F. M., & Stan, E. (2020). How are motivation and self-efficacy interacting in problem-solving and problem-posing? Educational Studies in Mathematics, 105, 487–517. https://doi.org/10.1007/s10649-020-10005-0

Weber, K., & Leikin, R. (2016). Recent advances in research on problem solving and problem posing. In The Second Handbook of Research on the Psychology of Mathematics Education: The Journey Continues, did (pp. 353–382). https://doi.org/10.1007/978-94-6300-561-6_10

Widodo, S. A., Pangesti, A. D., Istiqomah, I., Kuncoro, K. S., & Arigiyati, T. A. (2020). Thinking process of concrete student in solving two-dimensional problems. Jurnal Pendidikan Matematika, 14(2), 117–128. https://doi.org/10.22342/jpm.14.2.9460.117-128

Zhang, L., Stylianides, A. J., & Stylianides, G. J. (2023). Identifying competent problem posers and exploring their characteristics. The Journal of Mathematical Behavior, 72, 101086. https://doi.org/10.1016/j.jmathb.2023.101086

Author Biographies

Syaiful Hadi, UIN Sayyid Ali Rahmatullah, Tulungagung

Department of Mathematics Education

Cholis Sa’dijah, Universitas Negeri Malang

Department of Mathematics Education

Sudirman, Universitas Negeri Malang

Department of Mathematics Education

I Made Sulandra, Universitas Negeri Malang

Department of Mathematics Education

Sri Rahayuningsih, Universitas Negeri Malang

Department of Primary Education

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Copyright (c) 2024 Syaiful Hadi, Cholis Sa’dijah, Sudirman, I Made Sulandra, Sri Rahayuningsih

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