Case study in a grounded theory perspective: Students' reasoning abilities in Lithner's framework across self-regulated

##plugins.themes.bootstrap3.article.main##

Ginda Maruli Andi Siregar
Wahyudin Wahyudin
Tatang Herman

Abstract

Students' performance in understanding and developing algorithms from numerical methods is crucial because these concepts require them to engage in reasoning. DL-CA facilitates learning for fifth-semester bachelor students, specifically those in mathematics education, in comprehending numerical methods, algorithm concepts, and program development. Computer-assisted learning is appropriate for internalizing discovery learning and supporting autonomous study. The condition that differentiates individual learners is the level of self-regulated learning (SRL), which significantly enhances reasoning abilities by enabling goal setting, progress monitoring, and strategy adaptation, resulting in improved critical analysis and problem-solving skills. This grounded theory research investigates the reasoning outcomes of students in learning algorithm concepts for non-linear equation problems using computer-assisted discovery learning (DL-CA) through a web platform. It examines levels of self-regulated learning (SRL) and explores students' reasoning perspectives to describe differences in each level of SRL. Data analysis involved open coding through to categorization as essential steps in grounded theory, supported by method triangulation to enhance the validity and reliability of the findings. It was conducted using HyperRESEARCH output, a tool that aids in following comprehensive qualitative research procedures. The output suggests the following conjecture: The reasoning abilities of students in the high self-regulated learning (SRL) group encompass four categories: memorization, algorithm, plausibility, and mathematical foundation. In contrast, students in the medium and low SRL groups only demonstrate imitative reasoning abilities. Novel reasoning abilities are not sufficiently explained by these students, potentially due to limitations in the instruments or misunderstandings of the problems.

##plugins.themes.bootstrap3.article.details##


Section
Articles

References

Aisyah, N., Susanti, E., Meryansumayeka, M., Siswono, T. Y. E., & Maat, S. M. (2023). Proving geometry theorems: Student prospective teachers’ perseverance and mathematical reasoning. Infinity Journal, 12(2), 377-392. https://doi.org/10.22460/infinity.v12i2.p377-392

Anazifa, R. D., & Djukri, D. (2017). Project- based learning and problem- based learning: Are they effective to improve student’s thinking skills? Jurnal Pendidikan IPA Indonesia, 6(2), 346-355. https://doi.org/10.15294/jpii.v6i2.11100

Ancheta, C. M. D. (2022). An error analysis of students’ misconceptions and skill deficits in pre-calculus subjects. Journal for Educators, Teachers and Trainers, 13(5), 283-295. https://doi.org/10.47750/jett.2022.13.05.026

Angraini, L. M., Larsari, V. N., Muhammad, I., & Kania, N. (2023). Generalizations and analogical reasoning of junior high school viewed from Bruner's learning theory. Infinity Journal, 12(2), 291-306. https://doi.org/10.22460/infinity.v12i2.p291-306

Azmi, K. R., & Arfianti, K. (2021). Self regulated learning (SRL): Skills in improving learning motivation. KONSELI : Jurnal Bimbingan dan Konseling, 8(2), 199-206. https://doi.org/10.24042/kons.v8i2.9958

Carnevale, M., & Ahlfeld, R. (2019). Mathematical formulation. In F. Montomoli (Ed.), Uncertainty quantification in computational fluid dynamics and aircraft engines (pp. 67-155). Springer International Publishing. https://doi.org/10.1007/978-3-319-92943-9_3

Charmaz, K. (2014). Grounded theory in global perspective: Reviews by international researchers. Qualitative Inquiry, 20(9), 1074-1084. https://doi.org/10.1177/1077800414545235

Clark, R. C., & Mayer, R. E. (2016). E‐learning and the science of instruction: Proven guidelines for consumers and designers of multimedia learning. John Wiley & Sons. https://doi.org/10.1002/9781119239086

Cohen, L., Manion, L., & Morrison, K. (2002). Research methods in education. Routledge. https://doi.org/10.4324/9780203224342

Corazza, G. R., Lenti, M. V., & Howdle, P. D. (2021). Diagnostic reasoning in internal medicine: a practical reappraisal. Internal and emergency medicine, 16(2), 273-279. https://doi.org/10.1007/s11739-020-02580-0

Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage.

Dai, W., Li, Z., & Jia, N. (2022). Self-regulated learning, online mathematics learning engagement, and perceived academic control among Chinese junior high school students during the COVID-19 pandemic: A latent profile analysis and mediation analysis. Frontiers in psychology, 13. https://doi.org/10.3389/fpsyg.2022.1042843

Delima, N., Kusuma, D. A., & Paulus, E. (2024). The students' mathematics self-regulated learning and mathematics anxiety based on the use of chat GPT, music, study program, and academic achievement. Infinity Journal, 13(2), 349-362. https://doi.org/10.22460/infinity.v13i2.p349-362

Desti, R. M., Pertiwi, C. M., Sumarmo, U., & Hidayat, W. (2020). Improving student’s mathematical creative thinking and habits of mind using a problem-solving approach based on cognitive thinking stage. Journal of Physics: Conference Series, 1657(1), 012042. https://doi.org/10.1088/1742-6596/1657/1/012042

Dumas, A., Dantan, J.-Y., Gayton, N., Bles, T., & Loebl, R. (2015). An iterative statistical tolerance analysis procedure to deal with linearized behavior models. Journal of Zhejiang University-SCIENCE A, 16(5), 353-360. https://doi.org/10.1631/jzus.A1400221

Gibson, I. W. (2001). At the intersection of technology and pedagogy: considering styles of learning and teaching. Journal of Information Technology for Teacher Education, 10(1-2), 37-61. https://doi.org/10.1080/14759390100200102

Glaser, B., & Strauss, A. (2017). The discovery of grounded theory: Strategies for qualitative research. Routledge. https://doi.org/10.4324/9780203793206

Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81-112. https://doi.org/10.3102/003465430298487

Hidayat, W., Rohaeti, E. E., Ginanjar, A., & Putri, R. I. I. (2022). An ePub learning module and students' mathematical reasoning ability: A development study. Journal on Mathematics Education, 13(1), 103-118. https://doi.org/10.22342/jme.v13i1.pp103-118

Hidayat, W., Wahyudin, W., & Prabawanto, S. (2018). Improving students’ creative mathematical reasoning ability students through adversity quotient and argument driven inquiry learning. Journal of Physics: Conference Series, 948(1), 012005. https://doi.org/10.1088/1742-6596/948/1/012005

Hwang, Y., & Oh, J. (2021). The relationship between self-directed learning and problem-solving ability: The mediating role of academic self-efficacy and self-regulated learning among nursing students. International Journal of Environmental Research and Public Health, 18(4), 1738. https://doi.org/10.3390/ijerph18041738

Jordan, D. W., Smith, P., & Spector, D. (1999). Mathematical techniques: An introduction for the engineering, physical, and mathematical sciences, 2nd ed. American Journal of Physics, 67(2), 165-169. https://doi.org/10.1119/1.19219

Kollosche, D. (2021). Styles of reasoning for mathematics education. Educational Studies in Mathematics, 107(3), 471-486. https://doi.org/10.1007/s10649-021-10046-z

Krefting, L. (1991). Rigor in qualitative research: The assessment of trustworthiness. The American journal of occupational therapy, 45(3), 214-222. https://doi.org/10.5014/ajot.45.3.214

Ladecký, M., Pultarová, I., Zeman, J., & Vondřejc, J. (2019). Reference material preconditioning for FFT-based solvers. PAMM, 19(1), e201900283. https://doi.org/10.1002/pamm.201900283

Lee, J., Lee, Y., Gong, S., Bae, J., & Choi, M. (2016). A meta-analysis of the effects of non-traditional teaching methods on the critical thinking abilities of nursing students. BMC Medical Education, 16(1), 240. https://doi.org/10.1186/s12909-016-0761-7

Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255-276. https://doi.org/10.1007/s10649-007-9104-2

Lukman, L., Wahyudin, W., Suryadi, D., Dasari, D., & Prabawanto, S. (2022). Studying student statistical literacy in statistics lectures on higher education using grounded theory approach. Infinity Journal, 11(1), 163-176. https://doi.org/10.22460/infinity.v11i1.p163-176

Maulida, A. S., Wahyudin, W., Turmudi, T., & Nurlaelah, E. (2024). Differences in the influence of self-regulated learning levels on enhancing students’ mathematical reasoning abilities. DWIJA CENDEKIA: Jurnal Riset Pedagogik, 8(2), 221-231. https://doi.org/10.20961/jdc.v8i2.89291

Maulida, A. S., Wahyudin, W., Turmudi, T., & Nurlaelah, E. (2024). The effect of experiential learning and directed instructions assisted by augmented reality on students' self-regulated learning. Infinity Journal, 13(2), 553-568. https://doi.org/10.22460/infinity.v13i2.p553-568

Miatun, A., & Muntazhimah, M. (2018). The effect of discovery learning and problem-based learning on middle school students’ self-regulated learning. Journal of Physics: Conference Series, 948(1), 012021. https://doi.org/10.1088/1742-6596/948/1/012021

Navarro-López, E. M., & Licéaga-Castro, E. (2010). Combining passivity and classical frequency-domain methods: An insight into decentralised control. Applied Mathematics and Computation, 215(12), 4426-4438. https://doi.org/10.1016/j.amc.2010.01.012

Nuraziza, N. E., Susanto, S., Suwito, A., Trapsilasiwi, D., & Ambarwati, R. (2022). Analysis of student’s mathematical reasoning in terms of learning independence during distance learning. Journal of Education and Learning Mathematics Research (JELMaR), 3(1), 22-32.

Öztürk, M., & Sarikaya, İ. (2021). The relationship between the mathematical reasoning skills and video game addiction of Turkish middle schools students: A serial mediator model. Thinking Skills and Creativity, 40, 100843. https://doi.org/10.1016/j.tsc.2021.100843

Palengka, I., Juniati, D., & Abadi, A. (2022). Mathematical reasoning of prospective mathematics teachers in solving problems based on working memory capacity differences. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2193. https://doi.org/10.29333/ejmste/12670

Palinussa, A. L., Molle, J. S., & Gaspersz, M. (2021). Realistic mathematics education: Mathematical reasoning and communication skills in rural contexts. International Journal of Evaluation and Research in Education, 10(2), 522-534. https://doi.org/10.11591/ijere.v10i2.20640

Pape, S. J., Zimmerman, B. J., & Pajares, F. (2002). This Issue. Theory Into Practice, 41(2), 62-63. https://doi.org/10.1207/s15430421tip4102_1

Pertiwi, C. M., Rohaeti, E. E., & Hidayat, W. (2021). The students' mathematical problem-solving abilities, self-regulated learning, and VBA Microsoft Word in new normal: A development of teaching materials. Infinity Journal, 10(1), 17-30. https://doi.org/10.22460/infinity.v10i1.p17-30

Rahayuningsih, S., Hasbi, M., Mulyati, M., & Nurhusain, M. (2021). The effect of self-regulated learning on students’ problem-solving abilities. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(2), 927-939. https://doi.org/10.24127/ajpm.v10i2.3538

Rohaeti, E. E., Nurjaman, A., Sari, I. P., Bernard, M., & Hidayat, W. (2019). Developing didactic design in triangle and rectangular toward students mathematical creative thinking through Visual Basic for PowerPoint. Journal of Physics: Conference Series, 1157(4), 042068. https://doi.org/10.1088/1742-6596/1157/4/042068

Sari, V. T. A., & Hidayat, W. (2019). The students’ mathematical critical and creative thinking ability in double-loop problem solving learning. Journal of Physics: Conference Series, 1315(1), 012024. https://doi.org/10.1088/1742-6596/1315/1/012024

Schoenfeld, A. H. (2014). Mathematical problem solving. Academic Press.

Siregar, H. M., Solfitri, T., & Siregar, S. N. (2021). The relationship between perceptions of online learning and self-regulation of mathematics education students. Jurnal Didaktik Matematika, 8(2), 208-221. https://doi.org/10.24815/jdm.v8i2.21882

Sudirman, M., Fatimah, S., & Jupri, A. (2017). Improving problem solving skill and self regulated learning of senior high school students through scientific approach using quantum learning strategy. International Journal of Science and Applied Science: Conference Series, 2(1), 249-255.

Sudirman, S., García-García, J., Rodríguez-Nieto, C. A., & Son, A. L. (2024). Exploring junior high school students' geometry self-efficacy in solving 3D geometry problems through 5E instructional model intervention: A grounded theory study. Infinity Journal, 13(1), 215-232. https://doi.org/10.22460/infinity.v13i1.p215-232

Talib, C. A., Aliyu, F., Malik, A. M. b. A., & Siang, K. H. (2019). Enhancing students' reasoning skills in engineering and technology through game-based learning. International Journal of Emerging Technologies in Learning, 14(24), 69-80. https://doi.org/10.3991/ijet.v14i24.12117

Ukobizaba, F., Ndihokubwayo, K., Mukuka, A., & Uwamahoro, J. (2021). From what makes students dislike mathematics towards its effective teaching practices. Bolema - Mathematics Education Bulletin, 35(70), 1200-1216. https://doi.org/10.1590/1980-4415v35n70a30

Van Gog, T., Kester, L., & Paas, F. (2011). Effects of concurrent monitoring on cognitive load and performance as a function of task complexity. Applied Cognitive Psychology, 25(4), 584-587. https://doi.org/10.1002/acp.1726

Xiao, S., Yao, K., & Wang, T. (2019). The relationships of self-regulated learning and academic achievement in university students. In Forum on Psychological Health Education and Counselling for School Students (PHECSS2018), (Vol. 60, pp. 01003). https://doi.org/10.1051/shsconf/20196001003

Yandari, I. A. V., Nindiasari, H., Khaerunnisa, E., Pamungkas, A. S., Karso, K., & Nurjanah, N. (2018). Self-regulated learning in designing explorative learning tools among mathematics pre-service teachers through explorative module. In Global Conference on Teaching, Assessment, and Learning in Education (GC-TALE 2017), (Vol. 42, pp. 00106). https://doi.org/10.1051/shsconf/20184200106

Zimmerman, B. J. (2002). Becoming a self-regulated learner: An overview. Theory Into Practice, 41(2), 64-70. https://doi.org/10.1207/s15430421tip4102_2

Zimmerman, B. J., & Schunk, D. H. (2013). Self-regulated learning and academic achievement: Theoretical perspectives. Routledge. https://doi.org/10.4324/9781410601032