Problem-Solving Based Epistemic Learning Pattern: Optimizing Mathematical Representation Ability of Prospective Teachers and Pharmacists

Background/purpose. Although mathematical representation ability is a significant ability and an interesting topic to study, quite a few researchers have studied this ability, and even fewer have examined it through the implementation of epistemic learning patterns based on problem-solving. In fact, this learning pattern is epistemic and makes problems the core situation for students in constructing concepts or solutions. Therefore, this study aimed to optimize students’ mathematical representation abilities through the implementation of this learning pattern.

Materials/methods. This study employed a didactical research design to achieve the research objectives. Participants were 56 prospective mathematics teachers and pharmacists (14 men and 42 women) aged between 20 and 24 years. The main instrument was the researcher, with several additional instruments, such as lecture design, mathematical representation ability forms, and documentation studies. Data were analyzed using qualitative data analysis methods.

Results. The results of the study revealed that all prospective teacher participants used verbal representation forms, and most others used symbolic and verbal representation forms when solving problems. All prospective pharmacist participants did not use visual representation forms but used symbolic and verbal representation forms when solving mathematical problems. This finding depended on the form of the task given.

Conclusion. The results of this study concluded that problem-solving-based epistemic learning patterns could be used during lectures to optimize students’ mathematical representation abilities, noting that the form of the assignment should be designed in a way that facilitates visual representation.

Keywords: epistemic learning patterns, mathematical representation ability, problem-solving

References

Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215–241. https://doi.org/10.1023/A:1024312321077

Arefaine, N., Michael, K., & Assefa, S. (2022). GeoGebra assisted multiple representations for enhancing students’ representation translation abilities in calculus. Asian Journal of Education and Training, 8(4), 121–130. https://doi.org/10.20448/edu.v8i4.4309

Arias, F., & Araya, A. (2009). Analysis of the didactical contracts in 10th grade math classes. Quaderni Di Ricerca in Didattica (Matematica), 4(19), 155–163. http://www.math.unipa.it/~grim/TSG24_ICIMI_Arias-Araya_QRDM_Supl4_09.pdf

Arslan, S., Baran, D., & Okumus, S. (2011). Brousseau’s theory of didactical situations in mathematics and an application of adidactical situations. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 5(1), 204–224. https://www.academia.edu/813560/Brousseaus_Theory_of_Didactical_Situations_in_Mathematics_and_An_Application_of_Adidactical_Situations

Bajo-Benito, J. M., Gavilán-Izquierdo, J. M., & Sánchez-Matamoros García, G. (2023). The concept of number sequence in graphical representations for secondary school students. European Journal of Educational Research, 12(1), 159–172. https://doi.org/10.12973/eu-jer.12.1.159

Barham, A. I. (2020). Investigating the development of pre-service teachers’ problem-solving strategies via problem-solving mathematics classes. European Journal of Educational Research, 9(1), 129–141. https://doi.org/10.12973/eu-jer.9.1.129

Benavides-lahnstein, A. I., & Ryder, J. (2019). School teachers’ conceptions of environmental education: Reinterpreting a typology through a thematic analysis. Environmental Education Research, 26(1), 43–60. https://doi.org/10.1080/13504622.2019.1687649

Bencivenga, R. (2017). The ‘digital curious’: first steps towards a new typology for mapping adults’ relationships with others when using ICT. European Journal for Research on the Education and Learning of Adults, 8(1), 55–76. https://doi.org/10.3384/rela.2000-7426.rela9117

Bronkhorst, H., Roorda, G., Suhre, C., & Goedhart, M. (2021). Student development in logical reasoning: Results of an intervention guiding students through different modes of visual and formal representation. Canadian Journal of Science, Mathematics and Technology Education, 21(2), 378–399. https://doi.org/10.1007/s42330-021-00148-4

Brousseau, G. (2002). Theory of didactical situations in mathematics. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2

Cooper, J. L., & Alibali, M. W. (2012). Visual representations in mathematics problem-solving: effects of diagrams and illustrations. Proceeding of the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 281–288. https://files.eric.ed.gov/fulltext/ED584910.pdf

Dockendorff, M., & Solar, H. (2018). ICT integration in mathematics initial teacher training and its impact on visualization: The case of GeoGebra. International Journal of Mathematical Education in Science and Technology, 49(1), 66–84. https://doi.org/10.1080/0020739X.2017.1341060

El Messaoudi, M. (2024). The impact of a blended learning model on undergraduate university students’ digital literacy skills: empirical evidence from higher education. Educational Process International Journal, 13(4). https://doi.org/10.22521/edupij.2024.134.5

Fernández-Cézar, R., Prada-Núñez, R., & Pinto, N. S. (2024). Collaborative online international learning: Experiences in higher education. Educational Process International Journal, 13(4). https://doi.org/10.22521/edupij.2024.134.1

Guo, W. (2023). Solving word problems involving triangles by transitional engineering students: learning outcomes and implications. European Journal of Science and Mathematics Education, 11(2), 249–258. https://doi.org/10.30935/scimath/12582

Hadiastuti, D. I., & Soedjoko, E. (2019). Analysis of mathematical representation ability based on students’ thinking style in solving open-ended problems. Unnes Journal of Mathematics Education, 8(3), 195–201. https://doi.org/10.15294/ujme.v8i3.34189

Idawati, I., Setyosari, P., Kuswandi, D., & Ulfa, S. (2020). The effects of problem-solving method and cognitive flexibility in improving university students’ metacognitive skills. Journal for the Education of Gifted Young Scientists, 657–680. https://doi.org/10.17478/jegys.652212

Isnawan, M. G. (2023). Pola pembelajaran epistemik: Sebuah pemikiran awal untuk pendidikan. Nashir Al-Kutub Indonesia.

Isnawan, M. G., Alsulami, N. M., & Sudirman, S. (2024a). Optimizing prospective teachers’ representational abilities through didactical design-based lesson study. International Journal of Evaluation and Research in Education (IJERE), 13(6), 4004. https://doi.org/10.11591/ijere.v13i6.29826

Isnawan, M. G., Alsulami, N. M., Yanuarto, W. N., & Sukarma, I. K. (2024b). Exploring the use of mobile technologies in Indonesian mathematics lectures. Jurnal Matematika Kreatif-Inovatif, 15(2), 528–547. https://doi.org/10.15294/s3jcep43

Joubert, J., Callaghan, R., & Engelbrecht, J. (2020). Lesson study in a blended approach to support isolated teachers in teaching with technology. ZDM-Mathematics Education, 52(5), 907–925. https://doi.org/10.1007/s11858-020-01161-x

Jupri, A., & Sispiyati, R. (2021). Symbol sense characteristics for designing mathematics tasks. Journal of Physics: Conference Series, 1806(1). https://doi.org/10.1088/1742-6596/1806/1/012051

Khasanah, K., & Lestari, A. (2021). The effect of Quizizz and learning independence on mathematics learning outcomes. Tadris: Jurnal Keguruan Dan Ilmu Tarbiyah, 6(1), 63–74. https://doi.org/10.24042/tadris.v6i1.7288

Lillo, E. A. G. (2023). Tutors’ and students’ views on learning and feedback in problem-based learning. European Journal of Educational Research, 12(2), 705–717. https://doi.org/10.12973/eu-jer.12.2.705

Lutfi, J. S., & Juandi, D. (2023). Mathematical representation ability: a systematic literature review. Union: Jurnal Ilmiah Pendidikan Matematika, 11(1), 124–135. https://doi.org/10.30738/union.v11i1.14048

Marfuah, M., Suryadi, D., Turmudi, T., & Isnawan, M. G. (2022). Providing online learning situations for in-service mathematics teachers’ external transposition knowledge during Covid-19 pandemic: case of Indonesia. Electronic Journal of E-Learning, 20(1), 69–84. https://doi.org/10.34190/ejel.20.1.2388

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook. (3rd ed.). SAGE Publications, Inc. https://id.id1lib.org/book/3593988/83e08f

Mudhofir, A. (2021). Effect of problem-based learning model combination flipped classroom against problem solving ability. The International Journal of High Education Scientists (IJHES), 2(2), 11–26. www.ijhes.com

Nindiasari, H., Pranata, M. F., Sukirwan, S., Sugiman, S., Fathurrohman, M., Ruhimat, A., & Yuhana, Y. (2024). The use of augmented reality to improve students’ geometry concept problem-solving skills through the steam approach. Infinity Journal, 13(1), 119–138. https://doi.org/10.22460/infinity.v13i1.p119-138

Novitasari, P., Usodo, B., & Fitriana, L. (2021). Visual, symbolic, and verbal mathematics representation abilities in junior high school’s students. IOP Conference Series: Earth and Environmental Science, 1808(1). https://doi.org/10.1088/1742-6596/1808/1/012046

Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic analysis: striving to meet the trustworthiness criteria. International Journal of Qualitative Methods, 16, 1–13. https://doi.org/10.1177/1609406917733847

Prabowo, A., Suryadi, D., Dasari, D., Juandi, D., & Junaedi, I. (2022). Learning obstacles in the making of lesson plans by prospective mathematics teacher students. Education Research International, 2022, 1–15. https://doi.org/10.1155/2022/2896860

Putra, F. G., Lengkana, D., Sutiarso, S., Nurhanurawati, N., Saregar, A., Diani, R., Widyawati, S., Suparman, S., Imama, K., & Umam, R. (2024). Mathematical representation: a bibliometric mapping of the research literature (2013–2022). Infinity Journal, 13(1), 1–26. https://doi.org/10.22460/infinity.v13i1.p1-26

Putra, R. W. Y., Sunyono, S., Haenilah, E. Y., Hariri, H., Sutiarso, S., Nurhanurawati, N., & Supriadi, N. (2023). Systematic literature review on the recent three-year trend mathematical representation ability in Scopus database. Infinity Journal, 12(2), 243–260. https://doi.org/10.22460/infinity.v12i2.p243-260

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

Rahmawati, D., & Anwar, R. B. (2020). Translation of mathematical representation: Characteristics of verbal representation unpacking. Journal of Education and Learning (EduLearn), 14(2), 162–167. https://doi.org/10.11591/edulearn.v14i2.9538

Rønning, F. (2021). Opportunities for language enhancement in a learning environment designed on the basis of the theory of didactical situations. ZDM-Mathematics Education, 53(2), 305–316. https://doi.org/10.1007/s11858-020-01199-x

Septiani, D., Riyadi, & Triyanto. (2020). Students’ verbal representation abilities in solving geometry problems. Journal of Physics: Conference Series, 1594(1). https://doi.org/10.1088/1742-6596/1594/1/012046

Son, J.-W., & Lee, J.-E. (2016). Pre-service teachers’ understanding of fraction multiplication, representational knowledge, and computational skills. Mathematics Teacher Education and Development, 18(2), 5–28. https://eric.ed.gov/?id=EJ1113959

Stieff, M., Scopelitis, S., Lira, M. E., & Desutter, D. (2016). Improving representational competence with concrete models. Science Education, 100(2), 344–363. https://doi.org/10.1002/sce.21203

Sukarma, I. K., Isnawan, M. G., & Alsulami, N. M. (2024). Research on nonroutine problems: A hybrid didactical design for overcoming student learning obstacles. Human Behavior and Emerging Technologies, 2024(Article ID 5552365), 1–12. https://doi.org/10.1155/2024/5552365

Supriadi, S. (2019). Didactic design of sundanese ethnomathematics learning for primary school students. International Journal of Learning, Teaching and Educational Research, 18(11), 154–175. https://doi.org/10.26803/ijlter.18.11.9

Suryadi, D. (2019a). Landasan filosofis penelitian desain didaktis (DDR). Pusat Pengembangan DDR Indonesia.

Suryadi, D. (2019b). Penelitian desain didaktis (DDR) dan implementasinya. Gapura Press.

Tossavainen, T., & Faarinen, E. C. (2019). Swedish fifth and sixth graders’ motivational values and the use of ict in mathematics education. Eurasia Journal of Mathematics, Science and Technology Education, 15(12). https://doi.org/10.29333/ejmste/108533

Ünal, Z. E., Ala, A. M., Kartal, G., Özel, S., & Geary, D. C. (2023). Visual and symbolic representations as components of algebraic reasoning. Journal of Numerical Cognition, 9(2), 327–345. https://doi.org/10.5964/jnc.11151

Yanuarto, W. N., & Hastinasyah, P. D. (2022). Gamification: Quizizz in mathematical game learning for secondary students. Indonesian Journal of Mathematics Education, 5(2), 64–73. https://doi.org/10.31002/ijome.v5i2.6588

Zainudin, Z. A., & Zulkiply, N. (2023). Gamification in learning: Students’ motivation and cognitive engagement in learning business using Quizizz. Asian Journal of University Education, 19(4), 823–833. https://doi.org/10.24191/ajue.v19i4.24928

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