Prospective mathematic teachers’ reflective thinking in solving numeracy problems at the critical reflection stage
DOI:
https://doi.org/10.29408/jel.v10i3.26372Keywords:
critical reflection, numeracy, prior knowledge, reflective thinkingAbstract
The low numeracy skills in Indonesia are one factor affecting the quality of mathematics education, so reflective thinking is needed to improve this ability. This study aims to describe prospective mathematics teachers' reflective thinking process in solving numeracy problems at the critical reflection stage based on prior knowledge. This study used a qualitative, descriptive research methodology. The research participants were 34 prospective mathematics teachers at the State University of Malang, East Java. The instruments used are numeracy tests and interview guidelines. Data analysis includes data reduction, presentation, and conclusion drawing. The findings revealed notable differences in reflective thinking based on prior knowledge levels at the critical reflection stage. Subjects with high prior knowledge tried various solutions, were confident in their answers, and accurately drew conclusions and explained their reasons. Subjects with medium prior knowledge tried different methods but needed more confidence in their results. They could conclude but struggled to explain their reasons. Subjects with low prior knowledge used the same method, needed more confidence, and needed help explaining their reasons despite concluding. These findings imply creating a better training program for prospective mathematics teachers, emphasizing numeracy and reflective thinking growth.
References
Aberdein, A. (2023). Deep disagreement in mathematics. Global Philosophy, 33(1), 17. https://doi.org/10.1007/s10516-023-09653-7
Agustan, S., Juniati, Dwi, & Siswono, T. (2017). Reflective thinking in solving an algebra problem: A case study of field independent-prospective teacher. Journal of Physics: Conference Series, 893(1), 012002. https://doi.org/10.1088/1742-6596/893/1/012002
Aldahmash, A. H. (2021). Mathematics teachers’ reflective thinking: Level of understanding and implementation in their professional practices. PLoS ONE, 16(10), 1–17. https://doi.org/10.1371/journal.pone.0258149
Ali, S. R., & Idris, N. (2013). A model to identify the level of numeracy understanding of primary school pupils: A case study. International Journal of Computer Applications, 67(5), 41–49. https://doi.org/10.5120/11395-6694
Ambarwati, D., & Kurniasih, M. D. (2021). Pengaruh problem based learning berbantuan media youtube terhadap kemampuan literasi numerasi siswa [The effect of problem based learning assisted by youtube media on students’ numeracy literacy skills]. Jurnal Cendekia : Jurnal Pendidikan Matematika, 5(3), 2857–2868. https://doi.org/10.31004/cendekia.v5i3.829
Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9(1), 33–52. https://doi.org/10.1007/s10857-006-9005-9
Annisavitri, R., Sa’dijah, C., Qohar, Abd., Sa’diyah, M., & Anwar, L. (2020). Analysis of mathematical literacy test as a problem-solving ability assessment of junior high school students. AIP Conference Proceedings, 2215(1), 060002. https://doi.org/10.1063/5.0000648
Aquino, H. I., & Ching, D. A. (2022). Effects of reflective learning resource material on achievement of mathematics learning outcome. International Journal of Educational Management and Development Studies, 3(1), 132–148. https://doi.org/10.53378/352866
Ariany, R. L., Widiastuti, T. T., Jauhari, A. L. R., & Fardillah, F. (2021). Classification of student’s mathematical reflective thinking in calculus class. Journal of Physics: Conference Series, 1764(1), 012117. https://doi.org/10.1088/1742-6596/1764/1/012117
Başol, G., & Gencel, İ. E. (2013). Reflective thinking scale: A validity and reliability study. Educational Sciences, 13(2), 941–946. http://files.eric.ed.gov/fulltext/EJ1017318.pdf
Chen, X. (2022). Enhancing motivation to think critically. Journal of Higher Education Research, 3(4), 389–391. https://doi.org/10.32629/jher.v3i4.1019
Choy, S. C., Lee, M. Y., & Sedhu, D. S. (2019). Reflective thinking among teachers: Development and preliminary validation of reflective thinking for teachers questionnaire. Alberta Journal of Educational Research, 65(1), 37–50. https://doi.org/10.55016/ojs/ajer.v65i1.56416
Creswell, J. W. (2015). Penelitian kualitatif & desain riset memilih diantara lima pendekatan [Qualitative inquiry & research design: Choosing among five approaches] (3rd ed.). Pustaka Pelajar.
Damastuti, A. S., Triyanto, T., & Nurhasanah, F. (2023). Reflective thinking students with different adversity quotients in solving mathematics problems. JTAM (Jurnal Teori dan Aplikasi Matematika), 7(4), 1128-1141. https://doi.org/10.31764/jtam.v7i4.16552
Farida, R. N., Qohar, A., & Rahardjo, S. (2021). Analisis kemampuan literasi matematis siswa SMA kelas X dalam menyelesaikan soal tipe PISA konten change and relationship [Analysis of mathematical literacy skills of grade x high school students in solving Pisa type questions on the content of change and relationship]. Jurnal Cendekia: Jurnal Pendidikan Matematika, 5(3), 2802–2815. https://doi.org/10.31004/cendekia.v5i3.972
France, I., Mikite, M., Burgmanis, G., & Namsone, D. (2023). The development of numeracy test using three-dimensional framework to assess numeracy skills in grade 7. ATEE 2022 Annual Conference, 629–641. https://doi.org/10.22364/atee.2022.42
Funny, R. A., Ghofur, M. A., Oktiningrum, W., & Nuraini, N. L. S. (2019). Reflective thinking skills of engineering students in learning statistics. Journal on Mathematics Education, 10(3), 445–458. https://doi.org/10.22342/jme.10.3.9446.445-458
Fyfe, E. R., Rittle-Johnson, B., & DeCaro, M. S. (2012). The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters. Journal of Educational Psychology, 104(4), 1094–1108. https://doi.org/10.1037/a0028389
Ghanizadeh, A. (2017). Validating the persian version of reflective thinking questionnaire and probing iranian university students’ reflective thinking and academic achievement. International Journal of Instruction, 10(3), 209–226. https://doi.org/10.12973/iji.2017.10314a
Gürol. (2011). Determining the reflective thinking skills of pre-service teachers in learning and teaching process. Energy Education Science and Technology Part B-Social and Educational Studies, 3(3), 387–402.
Iswara, H. S., Ahmadi, F., & Ary, D. D. (2022). Numeracy literacy skills of elementary school students through ethnomathematics-based problem solving. Interdisciplinary Social Studies, 2(2), 1604–1616. https://doi.org/10.55324/iss.v2i2.316
Junaedi, Y., & Wahyudin, W. (2020). Improving student’s reflective thinking skills through realistic mathematics education approach. Proceedings of the 4th Asian Education Symposium (AES 2019), 438, 196–202. https://doi.org/10.2991/assehr.k.200513.044
Kember, D., Leung, D. Y. P., Jones, A., Loke, A. Y., McKay, J., Sinclair, K., Tse, H., Webb, C., Yuet Wong, F. K., Wong, M., & Yeung, E. (2000). Development of a questionnaire to measure the level of reflective thinking. Assessment & Evaluation in Higher Education, 25(4), 381–395. https://doi.org/10.1080/713611442
Kholid, M. N., Sa’dijah, C., Hidayanto, E., Permadi, H., & Feby, R. M. (2020). Pupils’ reflective thinking in solving linear equation system problem. Journal for the Mathematics Education and Teaching Practices, 1(1), 19–27. https://dergipark.org.tr/en/download/article-file/1189329
Kholid, M. N., Telasih, S., Pradana, L. N., & Maharani, S. (2021). Reflective thinking of mathematics prospective teachers’ for problem solving. Journal of Physics: Conference Series, 1783(1), 012102. https://doi.org/10.1088/1742-6596/1783/1/012102
Khoshgoftar, Z., & Barkhordari-Sharifabad, M. (2023). Medical students’ reflective capacity and its role in their critical thinking disposition. BMC Medical Education, 23(1), 1–7. https://doi.org/10.1186/s12909-023-04163-x
Klaczynski, P. A. (2014). Heuristics and biases: Interactions among numeracy, ability, and reflectiveness predict normative responding. Frontiers in Psychology, 5(1), 1–15. https://doi.org/10.3389/fpsyg.2014.00665
Linuhung, N., Purwanto, P., Sukoriyanto, S., & Sudirman, S. (2023). How students solve pizza problems: An exploration of students’ mathematical literacy. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(4), 3574–3588. https://doi.org/10.24127/ajpm.v12i4.8997
Marhami, M., Rohantizani, R., Muhammad, I., Samsidar, S., & Anggraini, I. (2023). Pre-service mathematics teachers’ numeracy in Acehnese culture-based minimum competence assessment. Jurnal Elemen, 9(1), 109–118. https://doi.org/10.29408/jel.v9i1.6765
Mentari, N., Nindiasari, H., & Pamungkas, A. S. (2018). Analisis kemampuan berpikir reflektif siswa SMP berdasarkan gaya belajar [Analysis of reflective thinking ability of junior high school students based on learning style]. Numerical: Jurnal Matematika dan Pendidikan Matematika, 2(1), 31–42. https://doi.org/10.25217/numerical.v2i1.209
Muntazhimah, M. (2021). The relation between prior knowledge and students’ mathematics reflective thinking ability. Journal of Physics: Conference Series, 1731(1), 012043. https://doi.org/10.1088/1742-6596/1731/1/012043
Naitili, C. A. (2024). Implementasi program kampus mengajar angkatan 6 dalam upaya peningkatan kemampuan literasi dan numerasi siswa sekolah dasar [Implementation of the 6th batch teaching campus program to improve literacy and numeracy skills of elementary school students]. HINEF : Jurnal Rumpun Ilmu Pendidikan, 3(1), 160–171. https://doi.org/10.37792/hinef.v3i1.1223
OECD. (2023). PISA 2022 results (Volume 1): The state of learning and equity in education. OECD Publishing.
Pagano, M., & Roselle, L. (2009). Beyond reflection: Refraction and international experiential education. Frontiers: The Interdisciplinary Journal of Study Abroad, 18(1), 217–229. https://doi.org/10.36366/frontiers.v18i1.263
Pambudi, D. S. (2022). Exploration of prospective mathematics teachers’ mathematical connections when solving the integral calculus problems based on prior knowledge. European Journal of Mathematics and Science Education, 3(2), 105–116. https://doi.org/10.12973/ejmse.3.2.105
Pratiwi, R. W. (2021). Analisis kesalahan mahasiswa calon guru matematika dalam menyelesaikan persoalan numerasi [Error analysis of prospective mathematics teacher students in solving numeracy problems]. THEOREMS (THE jOuRnal of mathEMatics), 6(2), 104–121. https://doi.org/10.36665/theorems.v6i2.558
Purnomo, H., Sa’dijah, C., Hidayanto, E., Sisworo, S., Permadi, H., & Anwar, L. (2022). Development of instrument numeracy skills test of Minimum Competency Assessment (MCA) in Indonesia. International Journal of Instruction, 15(3), 635–648. https://doi.org/10.29333/iji.2022.15335a
Rahayu, G., Kurniati, D., Jatmiko, D. D. H., Lestari, N. D. S., & Ambarwati, R. (2022). Analisis kemampuan berpikir kritis siswa SMP dalam memecahkan masalah matematika materi bentuk aljabar ditinjau dari gaya kognitif reflektif dan impulsif [Analysis of critical thinking skills of junior high school students in solving mathematical problems of algebraic form material in terms of reflective and impulsive cognitive styles]. Jurnal Edukasi dan Sains Matematika (JES-MAT), 8(2), 207–216. https://doi.org/10.25134/jes-mat.v8i2.6372
Rakhmawati, Y., & Mustadi, A. (2021). Examining the necessity of reflective module: Literacy numeracy skill of students elementary school. AL-ISHLAH: Jurnal Pendidikan, 13(1), 597–609. https://doi.org/10.35445/alishlah.v13i1.534
Rasyid, M. A. (2017). Profil berpikir reflektif siswa smp dalam pemecahan masalah pecahan ditinjau dari perbedaan gender [Reflective thinking profile of junior high school students in solving fraction problems in terms of gender differences]. Kreano, Jurnal Matematika Kreatif-Inovatif, 8(2), 171–181. https://doi.org/10.15294/kreano.v8i2.9849
Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836–852. https://doi.org/10.1037/a0016026
Rodgers, C. (2002). Defining reflection: Another look at John Dewey and reflective thinking. Teacher College Record, Columbia University, 104(4), 842–866. https://doi.org/10.1177/016146810210400402
Sa’dijah, C., Kholid, M. N., Hidayanto, E., & Permadi, H. (2020). Reflective thinking characteristics: A study in the proficient mathematics prospective teachers. Infinity Journal, 9(2), 159–172. https://doi.org/10.22460/infinity.v9i2.p159-172
Saffrina, S., & Baidullah, B. (2024). Student numeracy ability in solving problems on geometry and measurement material. Jurnal Indonesia Sosial Teknologi, 5(5), 2032–2041. https://doi.org/10.59141/jist.v5i5.1075
Saputri, M. D., Pramudya, I., & Slamet, I. (2020). The flexibility of students’ mathematical creative thinking in solving mathematical problems. Proceedings of the 1st International Multidisciplinary Conference on Education, Technology, and Engineering (IMCETE 2019), 410, 121–125. https://doi.org/10.2991/assehr.k.200303.030
Saracoglu, M. (2022). Reflective thinking and inquiry skills as predictors of self-efficacy in teaching mathematics. Problems of Education in the 21st Century, 80(1), 213–231. https://doi.org/10.33225/pec/22.80.213
Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
Sellings, P., Karen, F., & Goriss-Hunter, A. (2018). Developing pre-service teachers: The impact of an embedded framework in literacy and numeracy. Australian Journal of Teacher Education, 43(4), 1–16. https://doi.org/10.14221/ajte.2018v43n4.1
Setiyani, S., Waluya, S. B., Sukestiyarno, Y. L., & Cahyono, A. N. (2022). Mathematical reflective thinking process of prospective elementary teachers review from the disposition in numerical literacy problems. International Journal of Educational Methodology, 8(3), 405–420. https://doi.org/10.12973/ijem.8.3.405
Setiyani, Waluya, S. B., Sukestiyarno, Y. L., & Cahyono, A. N. (2023). Construction of reflective thinking: A field independent student in numerical problems. Journal on Mathematics Education, 15(1), 151–172. https://doi.org/10.22342/jme.v15i1.pp151-172
Simacon, P. D. P., & Veloria, E. V. (2022). Reflective thinking skills and attitude towards problem-solving as mediated by mathematical resilience of the students. Asian Journal of Education and Social Studies, 35, 39–51. https://doi.org/10.9734/ajess/2022/v35i4765
Suharna, H. (2018). Teori berpikir reflektif dalam Menyelesaikan masalah matematika [Reflective thinking theory in solving math problems] (1st ed.). Deepublish.
Syamsuddin, A., Idawati, Haking, H., Tonra, W. S., & Syukriani, A. (2023). Designing worksheets to improve reflective thinking for elementary school students on the solid figure subject. Academic Journal of Interdisciplinary Studies, 12(2), 349-366. https://doi.org/10.36941/ajis-2023-0054
Toraman, Ç., Orakcı, Ş., & Aktan, O. (2020). Analysis of the relationships between mathematics achievement, reflective thinking of problem solving and metacognitive awareness. International Journal of Progressive Education, 16(2), 72–90. https://doi.org/10.29329/ijpe.2020.241.6
Via, Y. (2022). How Are students’ prior knowledge differentiate analytical thinking process in identifying the convergence of real number sequences. Cypriot Journal of Educational Sciences, 17(9), 3289–3302. https://doi.org/10.18844/cjes.v17i9.8013
Via, Y., Tatag, S., & Abadi, A. (2021). The effect of mathematics self-efficacy on numeracy skills of prospective elementary school teachers. Cypriot Journal of Educational Sciences, 16(6), 3405–3417. https://doi.org/10.18844/cjes.v16i6.6590
Wijaya, A. P., Nusantara, T., Sudirman, S., & Hidayanto, E. (2023). How are students’ prior knowledge differentiate analytical thinking process in identifying the convergence of real number sequences? International Journal of Instruction, 16(1), 205–218. https://doi.org/10.29333/iji.2023.16112a
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