Melampaui angka: transformasi pembelajaran pecahan melalui latihan terbimbing berbasis alat peraga pada siswa kelas IV
Abstract
Purpose: This study evaluates the effectiveness of integrating guided discovery methods with mathematical manipulatives to enhance learning outcomes in fraction topics, addressing cognitive barriers caused by the abstract nature of the material and student misconceptions. Design/methodology/approach: A quasi-experimental approach (Nonequivalent Control Group Design) was employed with 60 fifth-grade students in Kuningan Regency. Data were collected via pre-tests and post-tests to measure learning achievements between the experimental and control groups. Findings: Analysis reveals significant improvements in learning outcomes within the experimental group. This integration effectively mitigates early misconceptions through systematic guidance and concrete visualization, bridging the gap between mathematical abstraction and student comprehension. Practical implications: The findings encourage educators to adopt pedagogical innovations that combine guided strategies with physical media to foster dynamic, systematic, and student-centered learning environments in primary education. Originality/value: This study addresses a literature gap by examining the simultaneous integration of guided methods and manipulatives, which were previously studied in isolation within mathematics education contexts.
Purpose: Penelitian ini bertujuan mengevaluasi efektivitas integrasi metode penemuan terbimbing dengan alat peraga matematika dalam meningkatkan hasil belajar materi pecahan, guna mengatasi hambatan kognitif akibat sifat materi yang abstrak dan risiko miskonsepsi pada siswa.Design/methodology/approach: Menggunakan desain kuasi-eksperimen (Nonequivalent Control Group Design) dengan sampel 60 siswa kelas V di Kabupaten Kuningan. Instrumen penelitian berupa pre-test dan post-test untuk mengukur capaian belajar antara kelompok eksperimen dan kontrol. Findings: Hasil analisis menunjukkan peningkatan hasil belajar yang signifikan pada kelompok eksperimen. Integrasi ini secara efektif memitigasi kesalahan konsep dini melalui bimbingan sistematis dan visualisasi konkret yang menjembatani abstraksi matematis dengan pemahaman siswa. Practical implications: Temuan ini merekomendasikan pendidik untuk mengadopsi inovasi pedagogis yang memadukan strategi terbimbing dengan media konkret guna menciptakan lingkungan belajar yang dinamis, sistematis, dan berpusat pada siswa di tingkat sekolah dasar.Originality/value: Studi ini mengisi kesenjangan literatur mengenai penggabungan metode terbimbing dan alat peraga secara simultan yang sebelumnya sering dikaji secara terpisah dalam konteks pembelajaran matematika.
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References
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Crossref
Geiger, V., Gal, I., & Graven, M. (2023). The connections between citizenship education and mathematics education. ZDM – Mathematics Education, 55(5), 923–940. https://doi.org/10.1007/s11858-023-01521-3
Crossref
Grenell, A., Butts, J. R., Levine, S. C., & Fyfe, E. R. (2024). Children's confidence on mathematical equivalence and fraction problems. Journal of Experimental Child Psychology, 246, Artikel 106003. https://doi.org/10.1016/j.jecp.2024.106003
Crossref
Hultdin, U. W., & Norqvist, M. (2024). Students’ reception of two alternative arrangements of mathematical symbols and words: Differences in focus and text navigation. The Journal of Mathematical Behavior, 75, Artikel 101159. https://doi.org/10.1016/j.jmathb.2024.101159
Crossref
Ismail, S. A. S., Maat, S. M., & Khalid, F. (2024). 35 years of fraction learning: Integrating systematic review and bibliometric analysis on a global scale. Eurasia Journal of Mathematics, Science and Technology Education, 20(12), em2543. https://doi.org/10.29333/ejmste/15657
Crossref
Jankowska, D. M., Gajda, A., & Karwowski, M. (2019). How children's creative visual imagination and creative thinking relate to their representation of space. International Journal of Science Education, 41(8), 1096–1117. https://doi.org/10.1080/09500693.2019.1594441
Crossref
Jordan, N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45–58. https://doi.org/10.1016/j.jecp.2013.02.001
Crossref
Jukić Matić, L., & Glasnović Gracin, D. (2021). How do teacher guides give support to mathematics teachers? Analysis of a teacher guide and exploration of its use in teachers' practices. Research in Mathematics Education, 23(1), 1–20. https://doi.org/10.1080/14794802.2019.1710554
Crossref
Karim, A., Soebagyo, J., & Edy Purwanto, S. (2021). Stochastic block model reveals maps of in applied mathematics studies using VOSviewer. International Journal of Progressive Mathematics Education, 1(2), 127–142. https://doi.org/10.22236/ijopme.v1i2.6917
Crossref
Lee, V. S., Greene, D. B., Odom, J., Schechter, E., & Slatta, R. W. (2023). What is inquiry-guided learning? In Teaching and learning through inquiry (pp. 3–16). Routledge. https://doi.org/10.4324/9781003447351
Crossref
Luna, M., & Selmer, S. (2021). Examining the responding component of teacher noticing: A case of one teacher’s pedagogical responses to students’ thinking in classroom artifacts. Journal of Teacher Education, 72(5), 579–593. https://doi.org/10.1177/00224871211015980
Crossref
Maffia, A., Manolino, C., & Miragliotta, E. (2025). There is more to algebra than meets the eye: The case of blindness. Educational Studies in Mathematics, 118(1), 63–77. https://doi.org/10.1007/s10649-025-10394-0
Crossref
Mellone, M., Pacelli, T., & Liljedahl, P. (2021). Cultural transposition of a thinking classroom: To conceive possible unthoughts in mathematical problem solving activity. ZDM – Mathematics Education, 53(4), 785–798. https://doi.org/10.1007/s11858-021-01256-z
Crossref
Mudjisusatyo, Y., Darwin, D., & Kisno, K. (2024). Change management in Independent Campus program: Application of the ADKAR model as a change management competency constructor. Cogent Education, 11(1). https://doi.org/10.1080/2331186X.2024.2381892
Crossref
MacLeod, M., & van der Veen, J. T. (2020). Scaffolding interdisciplinary project-based learning: A case study. European Journal of Engineering Education, 45(3), 363–377. https://doi.org/10.1080/03043797.2019.1646210
Crossref
Nabilah, E., Azhar, E., Purwanto, S. E., & Nabilah, E. (2021). Kecemasan siswa dalam menyelesaikan masalah modelling matematika pada praktek kelas virtual. International Journal of Progressive Mathematics Education, 1(1), 41–60. https://doi.org/10.22236/ijopme.v1i1.6595
Crossref
Nuraydin, S., Stricker, J., & Schneider, M. (2022). No transfer effect of a fraction number line game on fraction understanding or fraction arithmetic: A randomized controlled trial. Journal of Experimental Child Psychology, 217, Artikel 105353. https://doi.org/10.1016/j.jecp.2021.105353
Crossref
Nuriadin, I. (2021). Analysis of students mathematical reasoning abilities on number topics. Psychology and Education Journal, 58(1), 4750–4755. https://doi.org/10.17762/pae.v58i1.1634
Crossref
Patston, T. P., Cropley, D. H., Marrone, R. L., & Kaufman, J. C. (2018). Teacher implicit beliefs of creativity: Is there an arts bias? Teaching and Teacher Education, 75, 366–374. https://doi.org/10.1016/j.tate.2018.08.001
Crossref
Pranata, E. (2016). Implementasi model pembelajaran group investigation (GI) berbantuan alat peraga untuk meningkatkan kemampuan pemahaman konsep matematika. JPMI (Jurnal Pendidikan Matematika Indonesia), 1(1), 34–38. https://doi.org/10.26737/jpmi.v1i1.80
Crossref
Pusparini, N. N. (2020). Penggunaan model pembelajaran group investigation dengan metode latihan terbimbing untuk meningkatkan prestasi belajar matematika. Journal of Education Action Research, 4(2), 232–239. https://doi.org/10.23887/jear.v4i2.25018
Crossref
Qirom, M. S., & Juandi, D. (2023). A systematic literature review on the effect of traditional games in mathematics teaching and learning (Scopus database). JIIP – Jurnal Ilmiah Ilmu Pendidikan, 6(9), 7449–7457. https://doi.org/10.54371/jiip.v6i9.2034
Crossref
Quintos, B., Buli, T., Steflitsch, D., & Martin-Beltrán, M. (2025). Lesson study with caregivers as a resource for a culturally sustaining mathematics pedagogy for multilingual learners. Educational Studies in Mathematics. Advance online publication. https://doi.org/10.1007/s10649-025-10407-y
Crossref
Reinhold, F., Hoch, S., Werner, B., Richter-Gebert, J., & Reiss, K. (2020). Learning fractions with and without educational technology: What matters for high-achieving and low-achieving students? Learning and Instruction, 65, Artikel 101264. https://doi.org/10.1016/j.learninstruc.2019.101264
Crossref
Sager, M. T., Sherard, M. K., Walkington, C., Milton, S., & Petrosino, A. J. (2024). Seeing mathematics together: A comparative case study of youths and facilitators collaborating to learn mathematics in informal settings. The Journal of Mathematical Behavior, 75, Artikel 101171. https://doi.org/10.1016/j.jmathb.2024.101171
Crossref
Schindler, M., Simon, A. L., Baumanns, L., & Lilienthal, A. J. (2025). Eye-tracking research in mathematics and statistics education: Recent developments and future trends. A systematic literature review. ZDM – Mathematics Education. Advance online publication. https://doi.org/10.1007/s11858-025-01699-8
Crossref
Serbin, K. S., Bae, Y., & Espinosa, S. (2024). Secondary teachers’ guided reinvention of the definitions of reducible and irreducible elements. The Journal of Mathematical Behavior, 76, Artikel 101188. https://doi.org/10.1016/j.jmathb.2024.101188
Crossref
Setiyani, 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
Crossref
Simamora, R. E., & Ramadhanta, S. A. (2024). Investigating the effects of Realistic Mathematics Education on mathematical creativity through a mixed-methods approach. Indonesian Journal of Science and Mathematics Education, 7(2), 337–360. https://doi.org/10.24042/ijsme.v7i2.21221
Crossref
Tamami, M., Santi, V. M., & Aziz, T. A. (2023). Pengembangan buku ajar matematika dengan pendekatan Contextual Teaching and Learning (CTL) pada materi statistika untuk siswa kelas XI SMK bisnis dan manajemen. International Journal of Progressive Mathematics Education, 3(1), 24–34. https://doi.org/10.22343/ijopme.v3i1.7620
Crossref
Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175. https://doi.org/10.1016/j.tate.2008.08.003
Crossref
Trigueros, M., & Martínez-Planell, R. (2010). Geometrical representations in the learning of two-variable functions. Educational Studies in Mathematics, 73(1), 3–19. https://doi.org/10.1007/s10649-009-9201-5
Crossref
Umi, N., Purna, R., Nugroho, B., Karsoni, & Dinata, B. (2021). Pengembangan video pembelajaran berbasis pemecahan masalah berbantuan Adobe Captivate materi matriks di sekolah kejuruan (SMK) 3 Kota Bumi. International Journal of Progressive Mathematics Education, 1(3), 234–255. https://doi.org/10.22236/ijopme.v1i3.7689
Crossref
Unaenah, E., Suryadi, D., & Turmudi, T. (2024). Epistemological learning obstacles on fractions in elementary school. Jurnal Elemen, 10(1), 1–12. https://doi.org/10.29408/jel.v10i1.18306
Crossref
Vogt, F., Hauser, B., Stebler, R., Rechsteiner, K., & Urech, C. (2020). Learning through play-pedagogy and learning outcomes in early childhood mathematics. In Innovative approaches in early childhood mathematics (pp. 127–141). Routledge. https://doi.org/10.4324/9780429331244-10
Crossref
Ye, H., Liang, B., Ng, O. L., & Chai, C. S. (2023). Integration of computational thinking in K-12 mathematics education: A systematic review on CT-based mathematics instruction and student learning. International Journal of STEM Education, 10(1), 3. https://doi.org/10.1186/s40594-023-00396-w
Crossref
Zhang, Y., Yang, X., Sun, X., & Kaiser, G. (2023). The reciprocal relationship among Chinese senior secondary students' intrinsic and extrinsic motivation and cognitive engagement in learning mathematics: A three-wave longitudinal study. ZDM – Mathematics Education, 55(2), 399–412. https://doi.org/10.1007/s11858-022-01465-0
Crossref
Crossref
Campbell, A., Craig, T., & Collier-Reed, B. (2020). A framework for using learning theories to inform 'growth mindset' activities. International Journal of Mathematical Education in Science and Technology, 51(1), 26–43. https://doi.org/10.1080/0020739X.2018.1562118
Crossref
Charcape-Echeverría, J. L., Terrones-Marreros, M. A., & Duran-Llaro, K. L. (2023). Impacto de las estrategias lúdicas para mejorar el pensamiento creativo en estudiantes de educación primaria. Revista Arbitrada Interdisciplinaria Koinonía, 8(2), 36–50. https://doi.org/10.35381/r.k.v8i2.2860
Crossref
Ciosek, M., & Samborska, M. (2016). A false belief about fractions-What is its source? The Journal of Mathematical Behavior, 42, 20–32. https://doi.org/10.1016/j.jmathb.2016.02.001
Crossref
Geiger, V., Gal, I., & Graven, M. (2023). The connections between citizenship education and mathematics education. ZDM – Mathematics Education, 55(5), 923–940. https://doi.org/10.1007/s11858-023-01521-3
Crossref
Grenell, A., Butts, J. R., Levine, S. C., & Fyfe, E. R. (2024). Children's confidence on mathematical equivalence and fraction problems. Journal of Experimental Child Psychology, 246, Artikel 106003. https://doi.org/10.1016/j.jecp.2024.106003
Crossref
Hultdin, U. W., & Norqvist, M. (2024). Students’ reception of two alternative arrangements of mathematical symbols and words: Differences in focus and text navigation. The Journal of Mathematical Behavior, 75, Artikel 101159. https://doi.org/10.1016/j.jmathb.2024.101159
Crossref
Ismail, S. A. S., Maat, S. M., & Khalid, F. (2024). 35 years of fraction learning: Integrating systematic review and bibliometric analysis on a global scale. Eurasia Journal of Mathematics, Science and Technology Education, 20(12), em2543. https://doi.org/10.29333/ejmste/15657
Crossref
Jankowska, D. M., Gajda, A., & Karwowski, M. (2019). How children's creative visual imagination and creative thinking relate to their representation of space. International Journal of Science Education, 41(8), 1096–1117. https://doi.org/10.1080/09500693.2019.1594441
Crossref
Jordan, N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45–58. https://doi.org/10.1016/j.jecp.2013.02.001
Crossref
Jukić Matić, L., & Glasnović Gracin, D. (2021). How do teacher guides give support to mathematics teachers? Analysis of a teacher guide and exploration of its use in teachers' practices. Research in Mathematics Education, 23(1), 1–20. https://doi.org/10.1080/14794802.2019.1710554
Crossref
Karim, A., Soebagyo, J., & Edy Purwanto, S. (2021). Stochastic block model reveals maps of in applied mathematics studies using VOSviewer. International Journal of Progressive Mathematics Education, 1(2), 127–142. https://doi.org/10.22236/ijopme.v1i2.6917
Crossref
Lee, V. S., Greene, D. B., Odom, J., Schechter, E., & Slatta, R. W. (2023). What is inquiry-guided learning? In Teaching and learning through inquiry (pp. 3–16). Routledge. https://doi.org/10.4324/9781003447351
Crossref
Luna, M., & Selmer, S. (2021). Examining the responding component of teacher noticing: A case of one teacher’s pedagogical responses to students’ thinking in classroom artifacts. Journal of Teacher Education, 72(5), 579–593. https://doi.org/10.1177/00224871211015980
Crossref
Maffia, A., Manolino, C., & Miragliotta, E. (2025). There is more to algebra than meets the eye: The case of blindness. Educational Studies in Mathematics, 118(1), 63–77. https://doi.org/10.1007/s10649-025-10394-0
Crossref
Mellone, M., Pacelli, T., & Liljedahl, P. (2021). Cultural transposition of a thinking classroom: To conceive possible unthoughts in mathematical problem solving activity. ZDM – Mathematics Education, 53(4), 785–798. https://doi.org/10.1007/s11858-021-01256-z
Crossref
Mudjisusatyo, Y., Darwin, D., & Kisno, K. (2024). Change management in Independent Campus program: Application of the ADKAR model as a change management competency constructor. Cogent Education, 11(1). https://doi.org/10.1080/2331186X.2024.2381892
Crossref
MacLeod, M., & van der Veen, J. T. (2020). Scaffolding interdisciplinary project-based learning: A case study. European Journal of Engineering Education, 45(3), 363–377. https://doi.org/10.1080/03043797.2019.1646210
Crossref
Nabilah, E., Azhar, E., Purwanto, S. E., & Nabilah, E. (2021). Kecemasan siswa dalam menyelesaikan masalah modelling matematika pada praktek kelas virtual. International Journal of Progressive Mathematics Education, 1(1), 41–60. https://doi.org/10.22236/ijopme.v1i1.6595
Crossref
Nuraydin, S., Stricker, J., & Schneider, M. (2022). No transfer effect of a fraction number line game on fraction understanding or fraction arithmetic: A randomized controlled trial. Journal of Experimental Child Psychology, 217, Artikel 105353. https://doi.org/10.1016/j.jecp.2021.105353
Crossref
Nuriadin, I. (2021). Analysis of students mathematical reasoning abilities on number topics. Psychology and Education Journal, 58(1), 4750–4755. https://doi.org/10.17762/pae.v58i1.1634
Crossref
Patston, T. P., Cropley, D. H., Marrone, R. L., & Kaufman, J. C. (2018). Teacher implicit beliefs of creativity: Is there an arts bias? Teaching and Teacher Education, 75, 366–374. https://doi.org/10.1016/j.tate.2018.08.001
Crossref
Pranata, E. (2016). Implementasi model pembelajaran group investigation (GI) berbantuan alat peraga untuk meningkatkan kemampuan pemahaman konsep matematika. JPMI (Jurnal Pendidikan Matematika Indonesia), 1(1), 34–38. https://doi.org/10.26737/jpmi.v1i1.80
Crossref
Pusparini, N. N. (2020). Penggunaan model pembelajaran group investigation dengan metode latihan terbimbing untuk meningkatkan prestasi belajar matematika. Journal of Education Action Research, 4(2), 232–239. https://doi.org/10.23887/jear.v4i2.25018
Crossref
Qirom, M. S., & Juandi, D. (2023). A systematic literature review on the effect of traditional games in mathematics teaching and learning (Scopus database). JIIP – Jurnal Ilmiah Ilmu Pendidikan, 6(9), 7449–7457. https://doi.org/10.54371/jiip.v6i9.2034
Crossref
Quintos, B., Buli, T., Steflitsch, D., & Martin-Beltrán, M. (2025). Lesson study with caregivers as a resource for a culturally sustaining mathematics pedagogy for multilingual learners. Educational Studies in Mathematics. Advance online publication. https://doi.org/10.1007/s10649-025-10407-y
Crossref
Reinhold, F., Hoch, S., Werner, B., Richter-Gebert, J., & Reiss, K. (2020). Learning fractions with and without educational technology: What matters for high-achieving and low-achieving students? Learning and Instruction, 65, Artikel 101264. https://doi.org/10.1016/j.learninstruc.2019.101264
Crossref
Sager, M. T., Sherard, M. K., Walkington, C., Milton, S., & Petrosino, A. J. (2024). Seeing mathematics together: A comparative case study of youths and facilitators collaborating to learn mathematics in informal settings. The Journal of Mathematical Behavior, 75, Artikel 101171. https://doi.org/10.1016/j.jmathb.2024.101171
Crossref
Schindler, M., Simon, A. L., Baumanns, L., & Lilienthal, A. J. (2025). Eye-tracking research in mathematics and statistics education: Recent developments and future trends. A systematic literature review. ZDM – Mathematics Education. Advance online publication. https://doi.org/10.1007/s11858-025-01699-8
Crossref
Serbin, K. S., Bae, Y., & Espinosa, S. (2024). Secondary teachers’ guided reinvention of the definitions of reducible and irreducible elements. The Journal of Mathematical Behavior, 76, Artikel 101188. https://doi.org/10.1016/j.jmathb.2024.101188
Crossref
Setiyani, 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
Crossref
Simamora, R. E., & Ramadhanta, S. A. (2024). Investigating the effects of Realistic Mathematics Education on mathematical creativity through a mixed-methods approach. Indonesian Journal of Science and Mathematics Education, 7(2), 337–360. https://doi.org/10.24042/ijsme.v7i2.21221
Crossref
Tamami, M., Santi, V. M., & Aziz, T. A. (2023). Pengembangan buku ajar matematika dengan pendekatan Contextual Teaching and Learning (CTL) pada materi statistika untuk siswa kelas XI SMK bisnis dan manajemen. International Journal of Progressive Mathematics Education, 3(1), 24–34. https://doi.org/10.22343/ijopme.v3i1.7620
Crossref
Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175. https://doi.org/10.1016/j.tate.2008.08.003
Crossref
Trigueros, M., & Martínez-Planell, R. (2010). Geometrical representations in the learning of two-variable functions. Educational Studies in Mathematics, 73(1), 3–19. https://doi.org/10.1007/s10649-009-9201-5
Crossref
Umi, N., Purna, R., Nugroho, B., Karsoni, & Dinata, B. (2021). Pengembangan video pembelajaran berbasis pemecahan masalah berbantuan Adobe Captivate materi matriks di sekolah kejuruan (SMK) 3 Kota Bumi. International Journal of Progressive Mathematics Education, 1(3), 234–255. https://doi.org/10.22236/ijopme.v1i3.7689
Crossref
Unaenah, E., Suryadi, D., & Turmudi, T. (2024). Epistemological learning obstacles on fractions in elementary school. Jurnal Elemen, 10(1), 1–12. https://doi.org/10.29408/jel.v10i1.18306
Crossref
Vogt, F., Hauser, B., Stebler, R., Rechsteiner, K., & Urech, C. (2020). Learning through play-pedagogy and learning outcomes in early childhood mathematics. In Innovative approaches in early childhood mathematics (pp. 127–141). Routledge. https://doi.org/10.4324/9780429331244-10
Crossref
Ye, H., Liang, B., Ng, O. L., & Chai, C. S. (2023). Integration of computational thinking in K-12 mathematics education: A systematic review on CT-based mathematics instruction and student learning. International Journal of STEM Education, 10(1), 3. https://doi.org/10.1186/s40594-023-00396-w
Crossref
Zhang, Y., Yang, X., Sun, X., & Kaiser, G. (2023). The reciprocal relationship among Chinese senior secondary students' intrinsic and extrinsic motivation and cognitive engagement in learning mathematics: A three-wave longitudinal study. ZDM – Mathematics Education, 55(2), 399–412. https://doi.org/10.1007/s11858-022-01465-0
Crossref
Authors
Supriadi, E., Sessu , A., & Prihandhika, A. (2025). Melampaui angka: transformasi pembelajaran pecahan melalui latihan terbimbing berbasis alat peraga pada siswa kelas IV. International Journal of Progressive Mathematics Education, 5(1), 161–174. https://doi.org/10.22236/ijopme.v5i1.19384
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