Analyzing the Use of Snowball Throwing Model to Enhance Comprehension of Linear Functions: A Qualitative Study
Abstract
This study aims to explore the teaching and learning process of linear functions through the implementation of the Snowball Throwing learning model. A qualitative approach was employed, with data collected via observations, in-depth interviews, and documentation of the learning activities. The findings reveal that the Snowball Throwing model’s syntax—including the delivery of material, group formation, group leader explanations, question writing and throwing, as well as group discussion and evaluation—creates an active and collaborative learning environment. This process encourages students to develop key indicators of mathematical conceptual understanding: the ability to restate the concept of linear functions in their own words, classify objects according to the concept’s characteristics, and provide accurate examples and non-examples. Moreover, students demonstrate the ability to represent the concept in various mathematical forms, such as graphs and algebraic expressions, and apply the concept effectively in solving contextual problems. The interactive question-and-answer sessions and group discussions prove effective in strengthening conceptual understanding and clarifying misconceptions. This study recommends the use of the Snowball Throwing model as a participatory teaching strategy to enhance student engagement and improve the quality of mathematical conceptual understanding, particularly in the topic of linear functions.
References
Adu-Gyamfi, K., & Bossé, M. J. (2014). Processes and reasoning in representations of linear functions. International Journal of Science and Mathematics Education, 12(1), 167–192. https://doi.org/10.1007/S10763-013-9416-X
Anggoro, A., & Prabawanto, S. (2019). Undergraduate students’ conceptual understanding on rational inequalities. Journal of Physics: Conference Series, 1211(1). https://doi.org/10.1088/1742-6596/1211/1/012064
Aygör, N., & Ozdag, H. (2012). Misconceptions in Linear Algebra: the Case of Undergraduate Students. Procedia - Social and Behavioral Sciences, 46, 2989–2994. https://doi.org/10.1016/J.SBSPRO.2012.05.602
Catarino, P., & Vasco, P. (2014). Scilab in linear algebra. Applied Mathematical Sciences, 25–28, 1391–1399. https://doi.org/10.12988/AMS.2014.4148
Crawford, K. (1996). Vygotskian approaches in human development in the information era. Educational Studies in Mathematics, 31(1–2), 43–62. https://doi.org/10.1007/BF00143926
Creswell, J. W., & Guetterman, T. C. (2019). Educational research: planning, conducting, and evaluating quantitative and qualitative research. Pearson.
Gidalevich, S., & Kramarski, B. (2019). The value of fixed versus faded self-regulatory scaffolds on fourth graders’ mathematical problem solving. Instructional Science, 47(1), 39–68. https://doi.org/10.1007/S11251-018-9475-Z
Hodnik Čadež, T., & Manfreda Kolar, V. (2015). Comparison of Types of Generalizations and Problem-Solving Schemas Used to Solve a Mathematical Problem. Educational Studies in Mathematics, 89(2), 283–306. https://doi.org/10.1007/S10649-015-9598-Y
Indraswari, N. F. (2022). Snowball throwing based on lesson study to improve college student’s algebraic reasoning in solving problems generating functions. Math Didactic: Jurnal Pendidikan Matematika, 8(3), 169–181. https://doi.org/10.33654/MATH.V8I3.1932
Jong, S. De. (2019). Metacognitive reflection and insight therapy (MERIT) for patients with schizophrenia. Psychological Medicine, 49(2), 303–313. https://doi.org/10.1017/S0033291718000855
Karlina, K., & Amelia, F. (2019). Efektivitas Model Pembelajaran Kooperatif Tipe Snowball Throwing Terhadap Hasil Belajar Matematika Siswa. Cahaya Pendidikan, 5(1). https://doi.org/10.33373/CHYPEND.V5I1.1830
Lysaker, P. H. (2020). Metacognitive reflection and insight therapy: A recovery-oriented treatment approach for psychosis. In Psychology Research and Behavior Management (Vol. 13, pp. 331–341). https://doi.org/10.2147/PRBM.S198628
Ma’sum, M. H. R., & Nurkolis, N. (2018). Improve Mathematical Learning Creativities of Junior High School Students Through Snowball Throwing Type of Cooperative Learning Model. (JIML) JOURNAL OF Innovative Mathematics Learning, 1(3), 302. https://doi.org/10.22460/JIML.V1I3.P302-306
Ofridaningsih, O., Sumartono, S., & Mokh. Anang, H. (2023). The Effectiveness of Snowball Throwing Cooperative Learning Model on Students’ Mathematics Learning Outcomes. Journal of Education Technology and Inovation, 6(1), 17–23. https://doi.org/10.31537/JETI.V6I1.1102
Park, S., & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Science Education, 38(3), 261–284. https://doi.org/10.1007/S11165-007-9049-6
Perdana, D. C., & Isrokatun, I. (2019). Problem-based learning and ethnomathematics on mathematical understanding. Journal of Physics: Conference Series, 1318(1). https://doi.org/10.1088/1742-6596/1318/1/012134
Puspitarini, A., Sukmarani, D., Rahmawati, P., & Mir’ati, K. (2023). Improving Mathematics Learning Outcomes Through The Snowball Throwing Model Assisted By The Mystical Box Media (Fun Mystery Box of Fractions). Indonesian Journal of Educational Development (IJED), 4(3), 373–379. https://doi.org/10.59672/IJED.V4I3.3292
Ratna Herawati, Ellen Proborini, & Wiwin Astuti. (2024). Understanding of Linear Algebra Concepts through the TAPPS (Thinking Aloud Pair Problem Solving) Learning Model at the Faculty of Computer Science, Dharma AUB University of Surakarta. International Journal of Educational Research, 1(2), 56–62. https://doi.org/10.62951/IJER.V1I2.26
Sartika, S. F., Setiani, A., & Nurcahyono, N. A. (2020). Penerapan Model Pembelajaran Snowball Throwing Untuk Meningkatkan Kemampuan Pemahaman Matematis Siswa. De Fermat : Jurnal Pendidikan Matematika, 3(1), 1–8. https://doi.org/10.36277/DEFERMAT.V3I1.45
Schmittau, J. (2005). The Development of Algebraic Thinking: A Vygotskian Perspective. ZDM - International Journal on Mathematics Education, 37(1), 16–22. https://doi.org/10.1007/BF02655893
Serhan, D. (2019). Web-Based Homework Systems: Students’ Perceptions of Course Interaction and Learning in Mathematics. International Journal on Social and Education Sciences, 1(2), 57–62. https://doi.org/10.46328/IJONSES.18
Thonhongsa, P., Srithammasatn, S., & Poonputta, A. (2024). Impact of activity-based learning on understanding linear and quadratic functions: An evaluation of student performance and satisfaction in a Thai high school. International Journal of Advanced and Applied Sciences, 11(6), 139–146. https://doi.org/10.21833/IJAAS.2024.06.015
Walshaw, M. (2017). Understanding mathematical development through Vygotsky. Research in Mathematics Education, 19(3), 293–309. https://doi.org/10.1080/14794802.2017.1379728
Wedastuti, N. K., Sunismi, S., & Faradiba, S. (2022). Scaffolding in Mathematics Learning Social Arithmetic Material to Improve Students’ Mathematical Thinking. QALAMUNA: Jurnal Pendidikan, Sosial, Dan Agama, 14(2), 455–470. https://doi.org/10.37680/QALAMUNA.V14I2.3421
Xu, X., Liu, B., Chang, J., & Gong, D. (2010). The discussion of starting experimental courses in the teaching of linear algrbra. ICIMA 2010 - 2010 2nd International Conference on Industrial Mechatronics and Automation, 1, 562–565. https://doi.org/10.1109/ICINDMA.2010.5538091
Zandieh, M., Ellis, J., & Rasmussen, C. (2017). A characterization of a unified notion of mathematical function: the case of high school function and linear transformation. Educational Studies in Mathematics, 95(1), 21–38. https://doi.org/10.1007/S10649-016-9737-0
Copyright (c) 2025 Journal of Education and Learning Mathematics Research (JELMaR)
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Copyright of the published articles will be transferred to the journal as the publisher of the manuscripts. Therefore, the author confirms that the copyright has been managed by the journal.
- Authors can publish papers separately, arrange non-exclusive distribution of manuscripts that have been published in this journal into other versions by acknowledging that the manuscripts have been published for the first time in Journal of Education and Learning Mathematics Research (JELMaR).
- The copyright follows Creative Commons Attribution–ShareAlike License (CC BY SA): This license allows to Share — copy and redistribute the material in any medium or format, Adapt — remix, transform, and build upon the material, for any purpose, even commercially.
.jpg)
