PENDESAINAN SOAL PEMODELAN MATEMATIKA UNTUK MEMPROMOSIKAN KEMAMPUAN PROBLEM-POSING SISWA
DOI:
https://doi.org/10.32332/linear.v5i1.8828Kata Kunci:
Pendesainan, Soal Pemodelan, Pengajuan MasalahAbstrak
Problem-posing matematika sangat penting dalam pendidikan matematika, tetapi kurang mendapat perhatian dari siswa, guru, dan peneliti. Rumusan masalah penelitian ini adalah mendesain soal pemodelan matematika untuk mempromosikan kemampuan problem-posing siswa di sekolah dasar yang valid. Penelitian ini menggunakan pendekatan Design Research tipe penelitian pengembangan yang dikembangkan oleh Akker, Gravemeijer, McKenney dan Nieveen. Penelitian pengembangan ini terdiri dari 3 langkah yaitu analisis, desain dan evaluasi. Langkah analisis, analisis siswa, kurikulum, pemodelan matematika dan masalah dunia nyata diimplementasikan. Langkah desain, desain dan produk. Langkah Evaluasi formatif, peneliti menggunakan desain evaluasi formatif yang terdiri dari self-evaluation, one-to-one, expert review, small group, dan field test. Instrumen riset ini adalah soal pemodelan matematika konteks paket ulang tahun. Data dianalisis dengan menggunakan metode analisis deskriptif: (1) walk through, analisis berdasarkan komentar ahli dalam tinjauan ahli untuk mendapatkan soal pemodelan matematika yang valid untuk meningkatkan kemampuan pengajuan masalah siswa; (2) Menganalisis hasil review secara one to one. Riset ini hanya sampai pada one to one. Berdasarkan validasi ahli soal pemodelan sudah baik dan menantang. Siswa berkomentar bahwa soal pemodelan ini menarik dan bagus. Siswa dapat mengajukan soal matematika sekaligus menyelesaikannya dari situasi paket makanan ulang tahun. Sehingga, diperoleh soal pemodelan matematika menggunakan konteks paket ulang tahun yang valid untuk mempromosikan kemampuan problem posing siswa sekolah dasar.
Referensi
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Arikan, E. E., & Ünal, H. (2015). Investigation of problem-solving and problem-posing abilities of seventh-grade students. Educational Sciences: Theory and Practice, 15(5), 1403-1416.
Bataller, A.; Ferrando, I.; Reyes-Torres, A. (2022). Visual Poetry and Real Context Situations in Mathematical Problem Posing and Solving: A Study of the Affective Impact. Mathematics, 10, 1647. https://doi.org/10.3390/math10101647.
Binkley, M., Erstad, O., Herman, J., Raizen, S., Ripley, M., MillerRicci, M., et al. (2012). Defining twenty-first century skills. In P. Griffin, B. McGaw, & E. Care (Eds.), Assessment and teaching of 21st century skills, 17–66). Springer.
Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37-55. https://doi.org/10.1007/s10649-012-9441-7
Bonotto, C., & Santo, L. D. (2015). On the relationship between problem posing, problem solving, and creativity in the primary school. In Singer N. F. (Ed.), Mathematical problem posing (pp. 3-34). Springer. https://doi.org/10.1007/978-1-4614-6258-3_1
Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57-69. https://doi.org/10.1007/s10649-012-9429-3
Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. PNA, 6(4), 135-146. https://doi.org/10.30827/pna.v6i4.6137
Chen, L., Van Dooren, W., Chen, Q., Verschaffel, L. (2011). An Investigation on Chinese Teachers’ Realistic Problem Posing and Problem Solving Ability and Beliefs. International Journal of Science and Mathematics Education, 9, 919-948.
Christidamayani, A. P., & Kristanto, Y. D. (2020). The effects of problem posing learning model on students’ learning achievement and motivation. Indonesian Journal on Learning and Advanced Education, 2(2), 100-108. https://doi.org/10.23917/ijolae.v2i2.9981
Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395-415. https://doi.org/10.1007/s10857-008-9081-0
Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83(1), 87-101. DOI: https://doi.org/10.1007/ s10649-012-9449-z
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Fauzan, A. (2002). Applying Realistic Mathematics Education (RME) in Teaching Geometry in Indonesian Primary Schools. Doctoral dissertation, Enschchede: University of Twente.
Fitriana, L. D., Ekawati, R., & Kovács, Z. (2022). Perspectives on the problem-posing activity by prospective teachers: A cross-national study. Journal on Mathematics Education, 13(1), 2022, 149-172. DOI: http://doi.org/10.22342/jme.v13i1.pp149-172
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Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Dordrecht: Kluwer.
Hartmann, L. M., Krawitz, J., & Schukajlow, S. (2021). Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems? ZDM Math. Educ., 53, 919–935.
Hartmann, L. M., Krawitz, J., & Schukajlow, S. (2023). Posing and Solving Modelling Problems—Extending the Modelling Process from a Problem Posing Perspective. Journal für Mathematik-Didaktik, DOI: https://doi.org/10.1007/s13138-023-00223-3
Hasanah, N., Hayashi, Y., & Hirashima, T. (2017). Investigation of learning environment for arithmetic word problems by problem posing as sentence integration in Indonesian language. Journal of Physics: Conference Series, 812(012060), 1-6. https://doi.org/10.1088/1742-6596/812/1/012060
Hersh, R., & John-Steiner, V. (2017). The origin of insight in mathematics. In R. Leikin & B. Sriraman (Eds.), Creativity and giftedness: Interdisciplinary perspectives from mathematics and beyond (pp. 135–146). Springer.
Jupri, A., & Drivers, P. (2016). Student Difficulties in Mathematizing Word Problem in Algebra. Eurasia Journal of Mathematics, Sciences, and Technology Education, 12(9), 2481 - 2502.
Kadir, K., Kodirun, Cahyono, E., Hadi, A. L., Sani, A., & Jafar. (2020). The ability of prospective teachers to pose contextual word problem about fractions addition. Journal of Physics: Conference Series, 1581(012025), 1-9. https://doi.org/10.1088/1742-6596/1581/1/012025
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Klein, S., & Leikin, R. (2020). Opening mathematical problems for posing open mathematical tasks: What do teachers do and feel? Educational Studies in Mathematics, 105, 349–365
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Lee, S.Y. (2020). Research Status of Mathematical Problem Posing in Mathematics Education Journals. International Journal of Science and Mathematics Education, https://doi.org/10.1007/s10763-020-10128-z.
Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424.
Leung, S. S. (2013). Teachers implementing mathematical problem posing in the classroom: Challenges and strategies. Educational Studies in Mathematics, 83(1), 103-116. https://doi.org/10.1007/s10649-012-9436-4
Lowrie, T. (2002). Young children posing problems: the influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal, 14(2), 87-98.
Maaß, K., Doorman, M., Jonker, V., & Wijers, M. (2019). Promoting active citizenship in mathematics teaching. ZDM–mathematics Education, 51, 991–1003.
Masriyah, M., Kurniasari, K., & Palupi, E. L. W. (2018). Characteristics of pre-service teachers’ performance in problem posing. Journal of Physics: Conference Series, 1088(012115), 1-5. https://doi.org/10.1088/1742-6596/1088/1/012115
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Passarella, S. (2021b). Mathematics Teachers’ Inclusion of Modelling and Problem Posing in their Mathematics Lessons: an Exploratory Questionnaire. European Journal of Science and Mathematics Education, 9(2), 4356. https://doi.org/10.30935/scimath/10773
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Arikan, E. E., & Ünal, H. (2015). Investigation of problem-solving and problem-posing abilities of seventh-grade students. Educational Sciences: Theory and Practice, 15(5), 1403-1416.
Bataller, A.; Ferrando, I.; Reyes-Torres, A. (2022). Visual Poetry and Real Context Situations in Mathematical Problem Posing and Solving: A Study of the Affective Impact. Mathematics, 10, 1647. https://doi.org/10.3390/math10101647.
Binkley, M., Erstad, O., Herman, J., Raizen, S., Ripley, M., MillerRicci, M., et al. (2012). Defining twenty-first century skills. In P. Griffin, B. McGaw, & E. Care (Eds.), Assessment and teaching of 21st century skills, 17–66). Springer.
Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37-55. https://doi.org/10.1007/s10649-012-9441-7
Bonotto, C., & Santo, L. D. (2015). On the relationship between problem posing, problem solving, and creativity in the primary school. In Singer N. F. (Ed.), Mathematical problem posing (pp. 3-34). Springer. https://doi.org/10.1007/978-1-4614-6258-3_1
Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57-69. https://doi.org/10.1007/s10649-012-9429-3
Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. PNA, 6(4), 135-146. https://doi.org/10.30827/pna.v6i4.6137
Chen, L., Van Dooren, W., Chen, Q., Verschaffel, L. (2011). An Investigation on Chinese Teachers’ Realistic Problem Posing and Problem Solving Ability and Beliefs. International Journal of Science and Mathematics Education, 9, 919-948.
Christidamayani, A. P., & Kristanto, Y. D. (2020). The effects of problem posing learning model on students’ learning achievement and motivation. Indonesian Journal on Learning and Advanced Education, 2(2), 100-108. https://doi.org/10.23917/ijolae.v2i2.9981
Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395-415. https://doi.org/10.1007/s10857-008-9081-0
Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83(1), 87-101. DOI: https://doi.org/10.1007/ s10649-012-9449-z
Ellerton, N.F., Singer, F.M., & Cai, J. (2015). Problem Posing in Mathematics: Reflecting on the Past, Energizing the Present, and Foreshadowing the Future. In: Singer, F.M., Ellerton, N.F., Cai, J. (Eds.), Mathematical Problem Posing. Research in Mathematics Education. New York: Springer.
Fauzan, A. (2002). Applying Realistic Mathematics Education (RME) in Teaching Geometry in Indonesian Primary Schools. Doctoral dissertation, Enschchede: University of Twente.
Fitriana, L. D., Ekawati, R., & Kovács, Z. (2022). Perspectives on the problem-posing activity by prospective teachers: A cross-national study. Journal on Mathematics Education, 13(1), 2022, 149-172. DOI: http://doi.org/10.22342/jme.v13i1.pp149-172
Freudenthal, H. (1973). Mathematics as an Educational Task. Reidel. https://doi.org/10.1007/978-94010-2903-2.
Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Dordrecht: Kluwer.
Hartmann, L. M., Krawitz, J., & Schukajlow, S. (2021). Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems? ZDM Math. Educ., 53, 919–935.
Hartmann, L. M., Krawitz, J., & Schukajlow, S. (2023). Posing and Solving Modelling Problems—Extending the Modelling Process from a Problem Posing Perspective. Journal für Mathematik-Didaktik, DOI: https://doi.org/10.1007/s13138-023-00223-3
Hasanah, N., Hayashi, Y., & Hirashima, T. (2017). Investigation of learning environment for arithmetic word problems by problem posing as sentence integration in Indonesian language. Journal of Physics: Conference Series, 812(012060), 1-6. https://doi.org/10.1088/1742-6596/812/1/012060
Hersh, R., & John-Steiner, V. (2017). The origin of insight in mathematics. In R. Leikin & B. Sriraman (Eds.), Creativity and giftedness: Interdisciplinary perspectives from mathematics and beyond (pp. 135–146). Springer.
Jupri, A., & Drivers, P. (2016). Student Difficulties in Mathematizing Word Problem in Algebra. Eurasia Journal of Mathematics, Sciences, and Technology Education, 12(9), 2481 - 2502.
Kadir, K., Kodirun, Cahyono, E., Hadi, A. L., Sani, A., & Jafar. (2020). The ability of prospective teachers to pose contextual word problem about fractions addition. Journal of Physics: Conference Series, 1581(012025), 1-9. https://doi.org/10.1088/1742-6596/1581/1/012025
Kemendikbud RI. (2018). Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 37/2018 [Regulation of the Minister of Education and Culture of the Republic of Indonesia Number 37/2018]. Retrieved from https://jdih.kemdikbud.go.id.
Kerekes, J., Diglio, M., & King, K. P. (2009). How can teachers enable students to pose and solve problems using contexts within and outside mathematics? International Forum of Teaching and Studies, 5(2), 5-10.
Kilpatrick, J. (1987). Problem Formulating: Where do good problems come from. In Schoenfeld A. H. (Ed.), Cognitive sciences and mathematics education (pp. 123-147). Routledge. https://doi.org/10.4324/9780203062685
Klein, S., & Leikin, R. (2020). Opening mathematical problems for posing open mathematical tasks: What do teachers do and feel? Educational Studies in Mathematics, 105, 349–365
Kuipers, J. C. (2011). Education. In Frederick W. H., & Worden R. L. (Eds.), Indonesia: A Country Study (pp. 150-155). Federal Research Division.
Leavy, A., & Hourigan, M. (2021). Balancing competing demands: Enhancing the mathematical problem posing skills of prospective teachers through a mathematical letter writing initiative. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-021-09490-8
Lee, S.Y. (2020). Research Status of Mathematical Problem Posing in Mathematics Education Journals. International Journal of Science and Mathematics Education, https://doi.org/10.1007/s10763-020-10128-z.
Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424.
Leung, S. S. (2013). Teachers implementing mathematical problem posing in the classroom: Challenges and strategies. Educational Studies in Mathematics, 83(1), 103-116. https://doi.org/10.1007/s10649-012-9436-4
Lowrie, T. (2002). Young children posing problems: the influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal, 14(2), 87-98.
Maaß, K., Doorman, M., Jonker, V., & Wijers, M. (2019). Promoting active citizenship in mathematics teaching. ZDM–mathematics Education, 51, 991–1003.
Masriyah, M., Kurniasari, K., & Palupi, E. L. W. (2018). Characteristics of pre-service teachers’ performance in problem posing. Journal of Physics: Conference Series, 1088(012115), 1-5. https://doi.org/10.1088/1742-6596/1088/1/012115
Mukminin, A., Habibi, A., Prasojo, L. D., Idi, A., & Hamidah, A. (2019). Curriculum reform in Indonesia: Moving from an exclusive to inclusive curriculum. Center for Educational Policy Studies Journal, 9(2), 53–72. https://doi.org/10.26529/cepsj.543
National Council of Teachers of Mathematics (2020). Principle and Standard for School Mathematics. Reston: Va, NCTM.
Nedaei, M., Radmehr, F., & Drake, M. (2019). Exploring engineering undergraduate students’ attitudes toward mathematical problem posing. Journal of Professional Issues in Engineering Education and Practice, 145(4), 4019009
Palm, T. (2006). Word problems as simulations of real-world situations: a proposed framework. For the Learning of Mathematics, 26(1), 42-47
Papadopoulos, I., Patsiala, N., Baumanns, L., & Rott, B. (2021). Multiple approaches to problem posing: Theoretical considerations regarding its definition, conceptualisation, and implementation. Center for Educational Policy Studies Journal, 1–22. https://doi.org/10.26529/cepsj.878
Passarella, S. (2021a). Emergent modelling to introduce the distributivity property of multiplication: a design research study in a primary school. International Journal of Mathematical Education in Science and Technology, https://doi.org/10.1080/0020739X.2021.1910869
Passarella, S. (2021b). Mathematics Teachers’ Inclusion of Modelling and Problem Posing in their Mathematics Lessons: an Exploratory Questionnaire. European Journal of Science and Mathematics Education, 9(2), 4356. https://doi.org/10.30935/scimath/10773
Passarella, S. (2022). Real Contexts in Problem-Posing: An Exploratory Study of Students’ Creativity. International Journal of Innovation in Science and Mathematics Education, 30(1), 15-29.
Permendikbudristekdik RI. (2022). Standar Kompetensi Lulusan Pada Pendidikan Anak Usia Dini, Jenjang Pendidikan Dasar, Dan Jenjang Pendidikan Menengah. Jakarta: Kemendikbud.
Radmehr, F. & Vos, P. (2020). Issues and challenges of 21st century assessment in mathematics education. In L. Leite, E. Oldham, A. S. Afonso, F. Viseu, L. Dourado, H. Martinho (Eds.), Science and mathematics education for 21st century citizens: challenges and ways forward (pp. 437‒462). New York: Nova Science Publishers.
Riyanto, B. (2022). Kepraktisan Soal Pemodelan Matematika menggunakan konteks biaya parkir. Jurnal Santiaji Pendidikan, 12(1), 53 - 65.
Riyanto, B. (2021a). Designing Mathematical Modeling Tasks for Learning Mathematics. Atlantis Press. 2nd National Conference on Mathematics Education 2021 (NaCoME 2021), Advance in Social Scinece, Education and Humanities Research, Volume 656.
Riyanto, B. (2021b). Pendesainan Pembelajaran Pemodelan Matematika Matematika untuk Pembelajaran Berkualitas pada Masa Pandemi Codid-19. Prosiding Seminar Nasional PGRI Provinsi Sumatera Selatan dan Universitas PGRI Palembang 2 Nopember 2021, 131 - 139.
Riyanto, B. (2021c). Developing mathematical modeling tasks using parking fee for learning mathematics. Journal of Mathematics and Mathematics Education, 11(2), 40 - 49.
Riyanto, B. (2020). Pendesainan Pembelajaran Pemodelan Matematika Sekolah Menengah Atas. Doctoral Dissertation. Palembang: Universitas Sriwijaya.
Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55, 68–78. https://doi.org/10.1037//0003-066x.55.1.68
Schoenherr, J. (2024). Personalizing real-world problems: Posing own problems increases self-efficacy expectations, intrinsic value, attainment value, and utility value. Br J Educ Psychol. 2024, 00:1–18. DOI: 10.1111/bjep.12653
Stoyanova E., & Ellerton N. F. (1996). A framework for research into students’ problem posing in school mathematics, In P. C. Clarkson (Ed.), Technology in mathematics education (pp. 518–525), Mathematics Education Research Group of Australasia: The University of Melbourne.
Tessmer, M. (1993). Planning and Conducting Formative Evaluation. Philadelphia: Kogan Page.
Ulger, T. K., Bozkurt, I., & Altun, M. (2022). International Electronic Journal of Mathematics Education, 17(3), em0687
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