Complex Thinking: How are Students' Mathematical Problem-Solving Skills in Elementary School?
DOI:
https://doi.org/10.51278/bse.v3i3.916Keywords:
Complex Thinking, Mathematical Problem-Solving Skills, Elementary SchoolAbstract
This study aims to see an overview of students' mathematical problem-solving skills in elementary school. This study uses a quantitative approach with a descriptive method. The subjects in this study amounted to 25 grade 5 students in one of the elementary schools in Bandung with details of 10 male and 15 female students. The data collection technique used is a mathematical problem-solving test instrument based on Polya theory on fractional concept material. The data analysis carried out was to calculate descriptive statistics using Microsoft excel and SPSS version 24 to see an overview of mathematical problem-solving skills, categorization of problem-solving scores based on high, medium, and low, and the achievement of students' mathematical problem-solving indicators. From these data, it is then analyzed in depth and linked with relevant theories. The results of this study showed that based on the categorization of student scores, 4 students were in the high category, 15 students were in the medium category, and 6 students were in the low category. The indicator that has a high percentage of students mastered is understanding the problem at 73%, and the lowest indicator at re-checking is 44%. This research can contribute to efforts to create meaningful learning in mathematics by involving complex thinking skills including mathematical problem-solving skills.
Keywords: Complex Thinking, Mathematical Problem-Solving Skills, Elementary School
References
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Çelik, H. C. (2018). The Effects of Activity Based Learners on Sixth Grade Students’ Achievement and Attitudes towards Mathematics Activities. EURASIA Journal of Mathematics, Science and Technology Education, 14(5), 1963-1977.
Clement, J. (2008). Creative Model Construction in Scientists and Students: The Role of Imagery, Analogy, and Mental Simulation. Dordrecht: Pringer Science & Business Media.
Costa, A. L. (1985). Developing of Minds (A Resource Book for Teaching Thinking). Washington DC: ASCD.
Crebert, G,, Patrick, C. J., Cragnolini, V., Smith, C., Worsfold, K., & Webb, F. (2011). Problem Solving Skills Toolkit. 2nd Edition. Tersedia di: http://www.Griffith.Edu.Au./Gihe/ResourcesSupport/Graduate-Attributes
Dinç E., Sezgin-Memnun, D., Lee, E., & Ayd?n, B. (2022). Predicting Non-Routine Mathematical Problem-Solving Anxiety of Ninth Graders. 19th International Conference on Cognition and Exploratory Learning in Digital Age (CELDA 2022), 169-176.
Drake, S. M., & Reid, J. L. (2020). 21st Century Competencies in Light of the History of Integrated Curriculum. Front. Educ, 5, 1-10 https://doi.org/10.3389/feduc.2020.00122
Ekizer, F., & Y?ld?r?m, S. S. (2023). 21st Century Skills and Learning Environments: ELT Students' Perceptions. Educational Research and Reviews, 18(6), 114-128. https://doi.org/10.5897/ERR2023.4332
Eppe, M., Gumbsch, C., Kerzel, M., Nguyen, P. D., Butz, M. V., & Wermter, S. (2022). Intelligent Problem-solving as Integrated Hierarchical Reinforcement Learning. Nature Machine Intelligence, 4(1), 11-20.
Erol, H. (2021). Reflections on the 21st Century Skills into the Curriculum of Social Studies Course. International Journal of Education & Literacy Studies, 9(2), 90-102.
Ersoy, M., & Da?yar, M. (2022). A Mathematical Problem-solving Perception Scale for Secondary School Students: A Validity and Reliability Study. Problems of Education in the 21st Century, 80(5), 693-707. https://doi.org/10.33225/pec/22.80.693
Fauzi, I. (2020). Desain Didaktis Operasi Hitung Penjumlahan dan Pengurangan Pecahan di Kelas 5 Sekolah Dasar. Bandung: Universitas Pendidikan Indonesia
Güven, I., & Alpaslan, B. (2022). Investigation of the Effects of Interdisciplinary Science Activities on 5th Grade Students’ Creative Problem Solving and 21st Century Skills. TOJET: The Turkish Online Journal of Educational Technology, 21(1), 80-96.
Komariyah, S., Afifah, D. S. N., Resbiantoro, G. (2018). Analisis Pemahaman Konsep dalam Memecahkan Masalah Matematika ditinjau dari Minat Belajar Siswa. Sosiohumaniora, 4(1), 1-8.
Hidayah, N., Budiman, M. A., & Cahyadi, F. (2020). Analisis Kesulitan Siswa Kelas V Dalam Memecahkan Masalah Matematika Pada Materi Operasi Hitung Pecahan. Thinking Skills and Creativity Journal, 3(1), 46-51.
Indrawati, D., Wahyudi., & Ratu, N. (2014). Peningkatan Kemampuan Pemecahan Masalah Matematika melalui Penerapan Problem Based Learning untuk Siswa Kelas V SD. Satya Widya, 30(1), 17-27.
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Lestiana, H. T., Rejeki, S., & Setyawan, F. (2016). Identifying Students’ Errors on Fractions. Journal of Research and Advances in Mathematics Education, 1(2), 131-139.
Malikha, Z., & Amir, M.F. (2018). Analisis Miskonsepsi Siswa Kelas 5-B MIN Buduran Sidoarjo pada Materi Pecahan ditinjau dari Kemampuan Matematika. Pi: Mathematics Education Journal, 1(2), 75-81. https://doi.org/10.21067/pmej.v1i2.2329.
Moyo, M., & Machaba, F.M. (2021). Grade 9 Learners’ Understanding of Fraction Concepts: Equality of Fractions, Numerator and Denominator. Pythagoras, 42(1), 1-13. https://doi. org/10.4102/pythagoras. v42i1.602
Muslihah, N. N., & Suryaningrat, E. F. (2021). Model Pembelajaran Contextual Teaching and Learning terhadap Kemampuan Pemecahan Masalah Matematis. Plusminus: Jurnal Pendidikan Matematika, 1(3), 553-564.
Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The Natural Number Bias and Magnitude Representation in Fraction Comparison by Expert Mathematicians. Learning and Instruction, 28, 64–72. http://dx.doi.org/10.1016/j.learninstruc.2013.05.003.
Özeren, E. (2023). Predicting Secondary School Students’ 21st-Century Skills Through Their Digital Literacy and Problem-Solving Skills. International Education Studies, 16(2), 61-75. https://doi.org/10.5539/ies.v16n2p61.
Park, J., & Song, J. (2017). The Features of Intuitive Thinking Emerged during Problem Solving Activities about Thermal Phenomena: When Intuitive Thinking Appears and How it is Related to Logical Thinking. Journal of the Korean Association for Research in Science Education, 37(3), 535–549.
Polya, G. (1973). How to Solve IT. A New Aspect of Mathematical Method. Princeton University Press
Schoenfeld, A. H. (1980) Teaching Problem-Solving Skills. The American Mathematical Monthly, 87(10), 794-805. https://doi.org/10.1080/00029890.1980.11995155.
Septiani, U., Fatimah, F., Suswigi, S., Amelia, R., & Hidayat, W. (2019). Analisis Kemampuan Penalaran Matematik Siswa MTs pada Materi Relasi dan Fungsi. Journal on Education, 1(3), 304-307.
Stacey, K. (2005). The Place of Problem Solving in Contemporary Mathematics Curriculum Documents. Journal of Mathematical Behavior, 24, 341-350. https://doi.org/10.1016/j.jmathb.2005.09.004
Suárez-Brito, P., Baena-Rojas, J. J., López-Caudana, E. O., & Glasserman-Morales, L. D. (2022) Academic Literacy as a Component of Complex Thinking in Higher Education: A Scoping Review. European Journal of Contemporary Education, 11(3), 931-945 https://doi.org/10.13187/ejced.2022.3.931.
Sukri, M. (2018). Penerapan Contextual Teaching Learning untuk Meningkatkan Hasil Belajar Siswa dalam Menyelesaikan Soal Cerita Penjumlahan dan Pengurangan Pecahan di Kelas 5 SDN Inpres Balaroa Palu. Jurnal Elektronik Pendidikan Matematika Tadulako, 1(2), 159-169.
Suryadi, D. (2018). Ontologi dan Epistemologi dalam Penelitian Desain Didaktis (DDR). Bandung: Departemen Pendidikan Matematika UPI.
Suto, I. (2013). 21st Century Skills: Ancient, Ubiquitous, Enigmatic? A Cambridge Assessment Publication, 1-28.
Trilling, B. & Fadel, C. (2009). 21st Century Skills: Learning for Life in Our Times. Francisco: JosseyBass.
Unlu, M., Ertekin, E., & Dilmac, B. (2017). Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching. International Journal of Research in Education and Science, 3(2), 636–636. https://doi.org/10.21890/ijres.328096.
Voogt, J. & Roblin, N. P. (2012): A Comparative Analysis of International Frameworks for 21st Century Competences: Implications for National Curriculum Policies. Journal of Curriculum Studies, 44(3), 299-321. http://dx.doi.org/10.1080/00220272.2012.668938
Wang, Y., & Chiew, V. (2010). On the Cognitive Process of Human Problem Solving. Cognitive Systems Research, 11(1), 81–92. https://doi.org/10.1016/j.cogsys.2008.08.003
Widyastuti, R. T., & Airlanda, G. S. (2021). Efektivitas Model Problem Based Learning terhadap Kemampuan Pemecahan Masalah Matematika Siswa Sekolah Dasar. Jurnal Basicedu, 5(3), 1120-1129. https://doi.org/10.31004/basicedu.v5i3.896
Yapatang, L., & Polyiem, T. (2022). Development of the Mathematical Problem-Solving Ability Using Applied Cooperative Learning and Polya’s Problem-Solving Process for Grade 9 Students. Journal of Education and Learning, 11(3), 40-46. https://doi.org/10.5539/jel.v11n3p40
Aminah, A., & Kurniawati, K. R. A. (2018). Analisis Kesulitan Siswa dalam Menyelesaikan Soal Cerita Matematika Topik Pecahan ditinjau dari Gender. JTAM: Jurnal Teori dan Aplikasi Matematika, 2(2), 118-122. https://doi.org/10.31764/jtam.v2i2.713.
Baykul, Y. (2009). ?lkö?retim Matematik Ö?retimi 6-8. Ankara: Pegem A Yay?nc?l?k
Baena-Rojas, J. J., Ramírez-Montoya, M. S., Mazo-Cuervo. D. M., & López-Caudana. E. O, (2022). Traits of Complex Thinking: A Bibliometric Review of a Disruptive Construct in Education. Journal of Intelligence 10(37), 1-17. https://doi.org/ 10.3390/jintelligence10030037
Business Council of Australia and Australian Chamber of Commenrce and Industry. (2002). Employability Skills For The Future. Canberra: Agps.
Çelik, H. C. (2018). The Effects of Activity Based Learners on Sixth Grade Students’ Achievement and Attitudes towards Mathematics Activities. EURASIA Journal of Mathematics, Science and Technology Education, 14(5), 1963-1977.
Clement, J. (2008). Creative Model Construction in Scientists and Students: The Role of Imagery, Analogy, and Mental Simulation. Dordrecht: Pringer Science & Business Media.
Costa, A. L. (1985). Developing of Minds (A Resource Book for Teaching Thinking). Washington DC: ASCD.
Crebert, G,, Patrick, C. J., Cragnolini, V., Smith, C., Worsfold, K., & Webb, F. (2011). Problem Solving Skills Toolkit. 2nd Edition. Tersedia di: http://www.Griffith.Edu.Au./Gihe/ResourcesSupport/Graduate-Attributes
Dinç E., Sezgin-Memnun, D., Lee, E., & Ayd?n, B. (2022). Predicting Non-Routine Mathematical Problem-Solving Anxiety of Ninth Graders. 19th International Conference on Cognition and Exploratory Learning in Digital Age (CELDA 2022), 169-176.
Drake, S. M., & Reid, J. L. (2020). 21st Century Competencies in Light of the History of Integrated Curriculum. Front. Educ, 5, 1-10 https://doi.org/10.3389/feduc.2020.00122
Ekizer, F., & Y?ld?r?m, S. S. (2023). 21st Century Skills and Learning Environments: ELT Students' Perceptions. Educational Research and Reviews, 18(6), 114-128. https://doi.org/10.5897/ERR2023.4332
Eppe, M., Gumbsch, C., Kerzel, M., Nguyen, P. D., Butz, M. V., & Wermter, S. (2022). Intelligent Problem-solving as Integrated Hierarchical Reinforcement Learning. Nature Machine Intelligence, 4(1), 11-20.
Erol, H. (2021). Reflections on the 21st Century Skills into the Curriculum of Social Studies Course. International Journal of Education & Literacy Studies, 9(2), 90-102.
Ersoy, M., & Da?yar, M. (2022). A Mathematical Problem-solving Perception Scale for Secondary School Students: A Validity and Reliability Study. Problems of Education in the 21st Century, 80(5), 693-707. https://doi.org/10.33225/pec/22.80.693
Fauzi, I. (2020). Desain Didaktis Operasi Hitung Penjumlahan dan Pengurangan Pecahan di Kelas 5 Sekolah Dasar. Bandung: Universitas Pendidikan Indonesia
Güven, I., & Alpaslan, B. (2022). Investigation of the Effects of Interdisciplinary Science Activities on 5th Grade Students’ Creative Problem Solving and 21st Century Skills. TOJET: The Turkish Online Journal of Educational Technology, 21(1), 80-96.
Komariyah, S., Afifah, D. S. N., Resbiantoro, G. (2018). Analisis Pemahaman Konsep dalam Memecahkan Masalah Matematika ditinjau dari Minat Belajar Siswa. Sosiohumaniora, 4(1), 1-8.
Hidayah, N., Budiman, M. A., & Cahyadi, F. (2020). Analisis Kesulitan Siswa Kelas V Dalam Memecahkan Masalah Matematika Pada Materi Operasi Hitung Pecahan. Thinking Skills and Creativity Journal, 3(1), 46-51.
Indrawati, D., Wahyudi., & Ratu, N. (2014). Peningkatan Kemampuan Pemecahan Masalah Matematika melalui Penerapan Problem Based Learning untuk Siswa Kelas V SD. Satya Widya, 30(1), 17-27.
Kaufman JK (2013). 21 Ways to 21st Century Skills: Why Students Need Them and Ideas for Practical Implementation. Kappa Delta Pi Record, 49(2), 78-83.
Kemendikbud. (2013). Materi Pelatihan Guru Implementasi Kurikulum 2013. Jakarta: Kemendibud.
Lestiana, H. T., Rejeki, S., & Setyawan, F. (2016). Identifying Students’ Errors on Fractions. Journal of Research and Advances in Mathematics Education, 1(2), 131-139.
Malikha, Z., & Amir, M.F. (2018). Analisis Miskonsepsi Siswa Kelas 5-B MIN Buduran Sidoarjo pada Materi Pecahan ditinjau dari Kemampuan Matematika. Pi: Mathematics Education Journal, 1(2), 75-81. https://doi.org/10.21067/pmej.v1i2.2329.
Moyo, M., & Machaba, F.M. (2021). Grade 9 Learners’ Understanding of Fraction Concepts: Equality of Fractions, Numerator and Denominator. Pythagoras, 42(1), 1-13. https://doi. org/10.4102/pythagoras. v42i1.602
Muslihah, N. N., & Suryaningrat, E. F. (2021). Model Pembelajaran Contextual Teaching and Learning terhadap Kemampuan Pemecahan Masalah Matematis. Plusminus: Jurnal Pendidikan Matematika, 1(3), 553-564.
Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The Natural Number Bias and Magnitude Representation in Fraction Comparison by Expert Mathematicians. Learning and Instruction, 28, 64–72. http://dx.doi.org/10.1016/j.learninstruc.2013.05.003.
Özeren, E. (2023). Predicting Secondary School Students’ 21st-Century Skills Through Their Digital Literacy and Problem-Solving Skills. International Education Studies, 16(2), 61-75. https://doi.org/10.5539/ies.v16n2p61.
Park, J., & Song, J. (2017). The Features of Intuitive Thinking Emerged during Problem Solving Activities about Thermal Phenomena: When Intuitive Thinking Appears and How it is Related to Logical Thinking. Journal of the Korean Association for Research in Science Education, 37(3), 535–549.
Polya, G. (1973). How to Solve IT. A New Aspect of Mathematical Method. Princeton University Press
Schoenfeld, A. H. (1980) Teaching Problem-Solving Skills. The American Mathematical Monthly, 87(10), 794-805. https://doi.org/10.1080/00029890.1980.11995155.
Septiani, U., Fatimah, F., Suswigi, S., Amelia, R., & Hidayat, W. (2019). Analisis Kemampuan Penalaran Matematik Siswa MTs pada Materi Relasi dan Fungsi. Journal on Education, 1(3), 304-307.
Stacey, K. (2005). The Place of Problem Solving in Contemporary Mathematics Curriculum Documents. Journal of Mathematical Behavior, 24, 341-350. https://doi.org/10.1016/j.jmathb.2005.09.004
Suárez-Brito, P., Baena-Rojas, J. J., López-Caudana, E. O., & Glasserman-Morales, L. D. (2022) Academic Literacy as a Component of Complex Thinking in Higher Education: A Scoping Review. European Journal of Contemporary Education, 11(3), 931-945 https://doi.org/10.13187/ejced.2022.3.931.
Sukri, M. (2018). Penerapan Contextual Teaching Learning untuk Meningkatkan Hasil Belajar Siswa dalam Menyelesaikan Soal Cerita Penjumlahan dan Pengurangan Pecahan di Kelas 5 SDN Inpres Balaroa Palu. Jurnal Elektronik Pendidikan Matematika Tadulako, 1(2), 159-169.
Suryadi, D. (2018). Ontologi dan Epistemologi dalam Penelitian Desain Didaktis (DDR). Bandung: Departemen Pendidikan Matematika UPI.
Suto, I. (2013). 21st Century Skills: Ancient, Ubiquitous, Enigmatic? A Cambridge Assessment Publication, 1-28.
Trilling, B. & Fadel, C. (2009). 21st Century Skills: Learning for Life in Our Times. Francisco: JosseyBass.
Unlu, M., Ertekin, E., & Dilmac, B. (2017). Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching. International Journal of Research in Education and Science, 3(2), 636–636. https://doi.org/10.21890/ijres.328096.
Voogt, J. & Roblin, N. P. (2012): A Comparative Analysis of International Frameworks for 21st Century Competences: Implications for National Curriculum Policies. Journal of Curriculum Studies, 44(3), 299-321. http://dx.doi.org/10.1080/00220272.2012.668938
Wang, Y., & Chiew, V. (2010). On the Cognitive Process of Human Problem Solving. Cognitive Systems Research, 11(1), 81–92. https://doi.org/10.1016/j.cogsys.2008.08.003
Widyastuti, R. T., & Airlanda, G. S. (2021). Efektivitas Model Problem Based Learning terhadap Kemampuan Pemecahan Masalah Matematika Siswa Sekolah Dasar. Jurnal Basicedu, 5(3), 1120-1129. https://doi.org/10.31004/basicedu.v5i3.896
Yapatang, L., & Polyiem, T. (2022). Development of the Mathematical Problem-Solving Ability Using Applied Cooperative Learning and Polya’s Problem-Solving Process for Grade 9 Students. Journal of Education and Learning, 11(3), 40-46. https://doi.org/10.5539/jel.v11n3p40
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Published
2023-11-20
How to Cite
Fauzi, I., Rakhmat, C., & Budiman, N. (2023). Complex Thinking: How are Students’ Mathematical Problem-Solving Skills in Elementary School?. Bulletin of Science Education, 3(3), 228–240. https://doi.org/10.51278/bse.v3i3.916
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