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Focus on The Correctness of Results: Factors Contributing to Invisible Thinking Processes in High-Resilience Mathematical Students
Abstract
The cognitive process of thinking plays a pivotal role in understanding one's surroundings and effectively solving problems. This research endeavors to delve into the intricate factors contributing to the concealment of thinking processes in writing among students with high mathematical resilience. Employing a qualitative approach, specifically adopting a case study research design, the study concentrates on the students enrolled at SMPI Al-Lailiyah Sumenep. The comprehensive dataset is derived from the results of numeracy-type tests and interviews conducted with the student. The outcomes of this research shed light on a persistent challenge observed during the problem-solving phase among students exhibiting high mathematical resilience. A predominant tendency is noted, wherein these students habitually prioritize the correctness of final results over conveying the step-by-step reasoning behind their solutions. Several causative factors contribute to this phenomenon. First, the students’ established approach to problem-solving, emphasizing the end result, impedes the transparent expression of their cognitive processes in writing. Additionally, past experiences related to the types of questions posed, the depth of their understanding of mathematical concepts, a lack of feedback from teachers, and the absence of visible thinking routines in written assignments during the learning process collectively contribute to the challenge.
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Al-Abdullatif, A. M., & Alsaeed, M. S. (2019). Evaluating visible learning: Mathematics teachers’ practices in technology-enhanced classrooms. Cogent education, 6(1), 1686798. https://doi.org/10.1080/2331186X.2019.1686798
Albay, E. M., & Eisma, D. V. (2021). Performance task assessment supported by the design thinking process: Results from a true experimental research. Social Sciences & Humanities Open, 3(1), 100116. https://doi.org/10.1016/j.ssaho.2021.100116
Alexander, P. A., Zhao, H., & Sun, Y. (2020). Spontaneous focusing on what and why? What children’s imprecise responses reveal about their mathematical thinking and relational reasoning. Mathematical Thinking and Learning, 22(4), 332–350. https://doi.org/10.1080/10986065.2020.1818471
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. https://doi.org/10.1016/j.tate.2022.103736
As’ari, A. R., Kurniati, D., & Subanji, S. (2019). Teachers expectation of students’ thinking processes in written works: A survey of teachers’ readiness in making thinking visible. Journal on Mathematics Education, 10(3), 409–424. https://doi.org/10.22342/jme.10.3.7978.409-424
Attami, D., Budiyono, B., & Indriati, D. (2020). The mathematical problem-solving ability of junior high school students based on their mathematical resilience. Journal of Physics: Conference Series, 1469(1), 012152. https://doi.org/10.1088/1742-6596/1469/1/012152
Brooks, C., Burton, R., van der Kleij, F., Ablaza, C., Carroll, A., Hattie, J., & Neill, S. (2021). Teachers activating learners: The effects of a student-centred feedback approach on writing achievement. Teaching and Teacher Education, 105, 103387. https://doi.org/10.1016/j.tate.2021.103387
Burgess, S., Hauberg, D. S., Rangvid, B. S., & Sievertsen, H. H. (2022). The importance of external assessments: High school math and gender gaps in STEM degrees. Economics of Education Review, 88, 102267. https://doi.org/10.1016/j.econedurev.2022.102267
Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches. Thousand Oaks, CA: Sage Publication.
Czocher, J. A. (2016). Introducing modeling transition diagrams as a tool to connect mathematical modeling to mathematical thinking. Mathematical Thinking and Learning, 18(2), 77–106. https://doi.org/10.1080/10986065.2016.1148530
de Vries, J. A., Dimosthenous, A., Schildkamp, K., & Visscher, A. J. (2022). The impact on student achievement of an assessment for learning teacher professional development program. Studies in Educational Evaluation, 74, 101184. https://doi.org/10.1016/j.stueduc.2022.101184
Fatimah, A. E., & Fitriani, F. (2021). Analisis kemampuan berpikir kritis matematis ditinjau dari resiliensi matematis mahasiswa pendidikan teknik informatika dan komputer. Journal of Didactic Mathematics, 2(2), 94–100. https://doi.org/10.34007/jdm.v2i2.871
Ferrini-Mundy, J. (2000). Principles and standards for school mathematics: A guide for mathematicians. Notices of the American Mathematical Society, 47(8), 868–876.
Forsström, S. E. (2019). Role of teachers in students’ mathematics learning processes based on robotics integration. Learning, Culture and Social Interaction, 21, 378–389. https://doi.org/10.1016/j.lcsi.2019.04.005
Fraser, S., Beswick, K., & Crowley, S. (2019). Making tacit knowledge visible: Uncovering the knowledge of science and mathematics teachers. Teaching and Teacher Education, 86, 102907. https://doi.org/10.1016/j.tate.2019.102907
Glenn, D. E., Demir-Lira, Ö. E., Gibson, D. J., Congdon, E. L., & Levine, S. C. (2018). Resilience in mathematics after early brain injury: The roles of parental input and early plasticity. Developmental Cognitive Neuroscience, 30, 304–313. https://doi.org/10.1016/j.dcn.2017.07.005
Gulkilik, H., Moyer-Packenham, P. S., Ugurlu, H. H., & Yuruk, N. (2020). Characterizing the growth of one student’s mathematical understanding in a multi-representational learning environment. Journal of Mathematical Behavior, 58, 100756. https://doi.org/10.1016/j.jmathb.2020.100756
Hanney, R. (2018). Problem topology: Using cartography to explore problem solving in student-led group projects. International Journal of Research and Method in Education, 41(4), 411–432. https://doi.org/10.1080/1743727X.2017.1421165
Hull, T. H., Balka, D. S., & Miles, Ruth, H. (2011). Visible thinking in the K-8 mathematics classroom. Newbury Park, CA: Corwin Press Inc.
Hwang, G. J., Wang, S. Y., & Lai, C. L. (2021). Effects of a social regulation-based online learning framework on students’ learning achievements and behaviors in mathematics. Computers and Education, 160, 104031. https://doi.org/10.1016/j.compedu.2020.104031
Johnston-Wilder, & Lee, C. (2010, September 1-4). Developing mathematical resilience. Paper presented at the BERA Annual Conference 2010, University of Warwick, Coventry, England. Retrieved from https://oro.open.ac.uk/24261/2/3C23606C.pdf
Kim, J. Y., & Lim, K. Y. (2019). Promoting learning in online, ill-structured problem solving: The effects of scaffolding type and metacognition level. Computers and Education, 138, 116–129. https://doi.org/10.1016/j.compedu.2019.05.001
Kline, L. S. (2008). Documentation panel: The “making learning visible” project. Journal of Early Childhood Teacher Education, 29(1), 70–80. https://doi.org/10.1080/10901020701878685
Komala, E. (2018). Mathematical resilience mahasiswa pada mata kuliah Struktur Aljabar I menggunakan pendekatan explisit instruction integrasi peer instruction. Mosharafa: Jurnal Pendidikan Matematika, 6(3), 357–364. https://doi.org/10.31980/mosharafa.v6i3.324
Kooken, J., Welsh, M. E., McCoach, D. B., Johnston-Wilder, S., & Lee, C. (2016). Development and validation of the mathematical resilience scale. Measurement and Evaluation in Counseling and Development, 49(3), 217–242. https://doi.org/10.1177/0748175615596782
Kurnia, H. I., Royani, Y., Hendiana, H., & Nurfauziah, P. (2018). Analisis kemampuan komunikasi matematik siswa SMP ditinjau dari resiliensi matematik. Jurnal Pembelajaran Matematika Inovatif, 1(5), 933–940. https://journal.ikipsiliwangi.ac.id/index.php/jpmi/article/view/1597/288
Lee, G., & Simpkins, S. D. (2021). Ability self-concepts and parental support may protect adolescents when they experience low support from their math teachers. Journal of Adolescence, 88, 48–57. https://doi.org/10.1016/j.adolescence.2021.01.008
Legesse, M., Luneta, K., & Ejigu, T. (2020). Analyzing the effects of mathematical discourse-based instruction on eleventh-grade students’ procedural and conceptual understanding of probability and statistics. Studies in Educational Evaluation, 67, 100918. https://doi.org/10.1016/j.stueduc.2020.100918
Li, Q., Gu, Q., & He, W. (2019). Resilience of Chinese teachers: Why perceived work conditions and relational trust matter. Measurement, 17(3), 143–159. https://doi.org/10.1080/15366367.2019.1588593
Lim, N. G. (2022). Developing high-level thinking. In N. G. Lim, Clash of the mind and heart: Parents' Playbook for helping youths succeed (pp. 125–143). Singapore: World Scientific Publishing. https://doi.org/10.1142/9789811252617_0009
Lutovac, S. (2019). Pre-service mathematics teachers’ narrated failure: Stories of resilience. International Journal of Educational Research, 98, 237–244. https://doi.org/10.1016/j.ijer.2019.09.006
Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). London, England: Pearson Education.
Möhring, W., Ribner, A. D., Segerer, R., Libertus, M. E., Kahl, T., Troesch, L. M., & Grob, A. (2021). Developmental trajectories of children’s spatial skills: Influencing variables and associations with later mathematical thinking. Learning and Instruction, 75, 101515. https://doi.org/10.1016/j.learninstruc.2021.101515
Musich, S., Wang, S. S., Schaeffer, J. A., Kraemer, S., Wicker, E., & Yeh, C. S. (2022). The association of increasing resilience with positive health outcomes among older adults. Geriatric Nursing, 44, 97–104. https://doi.org/10.1016/j.gerinurse.2022.01.007
Novitasari, M., Sutama, Narimo, S., Fathoni, A., Rahmawati, L., & Widyasari, C. (2020). Habituation of digital literacy and critical thinking in mathematics in elementary school. International Journal of Scientific and Technology Research, 9(3), 3395–3399. https://doi.org/10.31004/basicedu.v6i4.3173
Perry, M., Bates, M. S., Cimpian, J. R., Beilstein, S. O., & Moran, C. (2022). Impacting teachers’ reflection on elementary mathematics classroom videos in online asynchronous professional learning contexts. Teaching and Teacher Education: Leadership and Professional Development, 1, 100003. https://doi.org/10.1016/j.tatelp.2022.100003
Pitts, C., Anderson, R., & Haney, M. (2018). Measures of instruction for creative engagement: Making metacognition, modeling and creative thinking visible. Learning Environments Research, 21(1), 43–59. https://doi.org/10.1007/s10984-017-9238-9
Pusat Asesmen dan Pembelajaran. (2020). Desain pengembangan soal AKM. Jakarta, Indonesia: Badan Penelitian dan Pengembangan dan Perbukuan Kementerian Pendidikan dan Kebudayaan.
Rahmatiya, R., & Miatun, A. (2020). Analisis kemampuan pemecahan masalah matematis ditinjau dari resiliensi matematis siswa SMP. Teorema: Teori dan Riset Matematika, 5(2), 187–202. https://doi.org/10.25157/teorema.v5i2.3619
Ritchhart, R., & Perkins, D. (2008). Making thinking visible. Educational Leadership, 65(5), 57–61. https://doi.org/10.3115/1599600.1599641
Rosen, Y., & Tager, M. (2014). Making student thinking visible through a concept map in computer-based assessment of critical thinking. Journal of Educational Computing Research, 50(2), 249–270. https://doi.org/10.2190/EC.50.2.f
Røykenes, K. (2016). “My math and me”: Nursing students’ previous experiences in learning mathematics. Nurse Education in Practice, 16(1), 1–7. https://doi.org/10.1016/j.nepr.2015.05.009
Salmon, A. (2016). How visible thinking enhances children’s learning. Lincoln, NE: Exchange Press, Inc.
Sheppard, M. E., & Wieman, R. (2020). What do teachers need? Math and special education teacher educators’ perceptions of essential teacher knowledge and experience. Journal of Mathematical Behavior, 59, 100798. https://doi.org/10.1016/j.jmathb.2020.100798
Stylianides, A. J., & Stylianides, G. J. (2022). Introducing students and prospective teachers to the notion of proof in mathematics. Journal of Mathematical Behavior, 66, 100957. https://doi.org/10.1016/j.jmathb.2022.100957
Sugiyono, S. (2016). Metode penelitian kuntitatif, kualitatif dan R&D. Bandung, Indonesia: Alfabeta.
Supriadi, D., Mardiyana, M. & Subanti, S. (2015). Analisis proses berpikir siswa dalam memecahkan masalah matematika berdasarkan langkah Polya ditinjau dari kecerdasan emosional siswa kelas VIII SMP Al Azhar Syifa Budi tahun pelajaran 2013/2014. Jurnal Elektronik Pembelajaran Matematika, 3(2), 204–214.
van Dooren, W., de Bock, D., Vleugels, K., & Verschaffel, L. (2010). Just answering . . . or thinking? Contrasting pupils’ solutions and classifications of missing-value word problems. Mathematical Thinking and Learning, 12(1), 20–35. https://doi.org/10.1080/10986060903465806
van Garderen, D., Lannin, J. K., & Kamuru, J. (2020). Intertwining special education and mathematics education perspectives to design an intervention to improve student understanding of symbolic numerical magnitude. Journal of Mathematical Behavior, 59, 100782. https://doi.org/10.1016/j.jmathb.2020.100782
Wardhani, W. A., Subanji, S., & Dwiyana, D. (2016). Proses berpikir siswa berdasarkan kerangka kerja Mason. Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan, 1(3), 297–313. https://doi.org/10.17977/jp.v1i3.6152
Wright, P., Carvalho, T., & Fejzo, A. (2022). Visible mathematics pedagogy: A model for transforming classroom practice. Educational Action Research, 30(2), 168–191. https://doi.org/10.1080/09650792.2020.1850497
Yeager, D. S., & Dweck, C. S. (2012). Mindsets that promote resilience: When students believe that personal characteristics can be developed. Educational Psychologist, 47(4), 302–314. https://doi.org/10.1080/00461520.2012.722805
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