Research trends on learning mathematics with the CPA (Concrete-Pictorial-Abstract) approach
DOI:
https://doi.org/10.35194/jp.v13i1.3947Keywords:
CPA, concrete-pictorial-abstract, SLR, systematic literature reviewAbstract
Learning mathematics with the CPA approach has been practiced in Singapore and proven its effectiveness. However, there needs to be a synthesis of previous studies to find research gaps for future research. This article is a preliminary-research for information on the CPA approach and its modifications to mathematical abilities and attitudes. This article is a Systematic Literature Review (SLR) of 39 studies published from 2010 to April 2023 using the Publish or Perish application with the Scopus database. This article aims to find out: (1) Description of mathematics education research trends using the CPA approach in terms of publication year, author, country, level of education, and mathematics content. (2) Application of the CPA approach to the type of mathematical ability and attitude of students. The results showed that research outside the elementary school level needs further investigation. Abstract mathematical concepts require a CPA approach. The CPA approach has a positive effect on students with or without learning disabilities or at risk of failure. Results and suggestions for future research on this topic are provided.
References
AL-salahat, M. M. S. (2022). The effect of using concrete-representational-abstract sequence in Teaching the perimeter of geometric shapes for students with learning disabilities. International Journal of Education in Mathematics, Science and Technology, 10(2), 477–493. https://doi.org/10.46328/ijemst.2291
Amril, L. O., Darhim, & Juandi, D. (2020). The effect experiential learning model based concrete-pictorial-abstract (EL-CPA) on mathematics attitude of deaf students. Journal of Physics: Conference Series, 1657, 1–6. https://doi.org/10.1088/1742-6596/1657/1/012070
Azzumar, F., & Juandi, D. (2023). Concrete-pictorial-abstract approaches to mathematics education: A systematic literature review. Journal of Mathematics and Mathematics Education (JMME), 13(1), 1-11. https://doi.org/10.20961/jmme.v13i1.73962
Bishara, S. (2018). Active and traditional teaching, self-image, and motivation in learning math among pupils with learning disabilities. Cogent Education, 5(1), 1–16. https://doi.org/10.1080/2331186X.2018.1436123
Bouck, E., Park, J., & Nickell, B. (2017). Using the concrete-representational-abstract approach to support students with intellectual disability to solve change-making problems. Research in Developmental Disabilities, 60, 24–36. https://doi.org/10.1016/j.ridd.2016.11.006
Flores, M. M. (2010). Using the concrete-representational-abstract sequence to teach subtraction with regrouping to students at risk for failure. Remedial and Special Education, 31(3), 195–207. https://doi.org/10.1177/0741932508327467
Flores, M. M., & Hinton, V. M. (2019). Improvement in elementary students’ multiplication skills and understanding after learning through the combination of the concrete-representational-abstract sequence and strategic instruction. Education and Treatment of Children, 42(1), 73–99. https://doi.org/10.1353/etc.2019.0004
Flores, M. M., Hinton, V. M., & Burton, M. E. (2016). Teaching problem solving to students receiving tiered interventions using the concrete-representational-abstract sequence and schema-based instruction. Preventing School Failure, 0(0), 1–11.
https://doi.org/10.1080/1045988X.2016.1164117
Flores, M. M., Hinton, V. M., & Meyer, J. M. (2020). Teaching fraction concepts using the concrete-representational-abstract sequence. Remedial and Special Education, 41(3), 165–175. https://doi.org/10.1177/0741932518795477
Flores, M. M., Hinton, V. M., & Taylor, J. J. (2018). CRA fraction intervention for fifth-grade students receiving tier two interventions. Preventing School Failure, 62(3), 198–213. https://doi.org/10.1080/1045988X.2017.1414027
Flores, M. M., Hinton, V., & Strozier, S. D. (2014). Teaching subtraction and multiplication with regrouping using the concrete-representational-abstract sequence and strategic instruction model. Learning Disabilities Research and Practice, 29(2), 75–88. https://doi.org/10.1111/ldrp.12032
Flores, M. M., & Milton, J. H. (2020). Teaching the partial products algorithm using the concrete-representational-abstract sequence. Exceptionality, 28(2), 142–160. https://doi.org/10.1080/09362835.2020.1772070
Flores, M. M., Moore, A. J., & Meyer, J. M. (2020). Teaching the partial products algorithm with the concrete representational abstract sequence and the strategic instruction model. Psychology in the Schools, 57(6), 946–958. https://doi.org/10.1002/pits.22335
Hamilton, R., & Ghatala, E. (1994). Learning and Instruction. McGraw-Hill, Inc.
Heyder, A., Weidinger, A. F., Cimpian, A., & Steinmayr, R. (2020). Teachers’ belief that math requires innate ability predicts lower intrinsic motivation among low-achieving students. Learning and Instruction, 65(101220), 1–39. https://doi.org/10.1016/j.learninstruc.2019.101220
Hinton, V., & Flores, M. (2022). Concrete-representational-abstract–integrated as a tier 2 instruction to teach addition. Rural Special Education Quarterly, 41(3), 169–178. https://doi.org/10.1177/87568705221075756
Kaya, S., & Yildiz, N. G. (2023). Using the concrete–representational–abstract sequence to teach math skills to a student with autism spectrum disorder in a general education classroom. International Journal of Developmental Disabilities. https://doi.org/10.1080/20473869.2023.2180539
Kurniawan, H., Budiyono, Sajidan, & Siswandari. (2020). Concrete-pictorial-abstract approach on student’s motivation and problem solving performance in Algebra. Universal Journal of Educational Research, 8(7), 3204–3212. https://doi.org/10.13189/ujer.2020.080749
Mahayukti, G. A., Dianawati, N. P. S., Ardana, I. M., & Suryawan, I. P. P. (2019). The effect of concrete-pictorial-abstract learning strategy on spatial sense ability. Journal of Physics: Conference Series, 1317, 1–9. https://doi.org/10.1088/1742-6596/1317/1/012007
Miller, S. P., & Kaffar, B. J. (2011). Developing Addition with Regrouping Competence among Second Grade Students with Mathematics Difficulties. Investigations in Mathematics Learning, 4(1), 24–49. https://doi.org/10.1080/24727466.2011.11790308
Milton, J. H., Flores, M. M., Hinton, V. M., Dunn, C., & Darch, C. B. (2023). Using the concrete-representational-abstract sequence to teach conceptual understanding of place value, rounding, and expanded Nnotation. Learning Disabilities Research and Practice, 38(1), 15–25. https://doi.org/10.1111/ldrp.12299
Minarni, A., & Napitupulu, E. E. (2017). Developing Instruction Materials Based on Joyful PBL to Improve Students Mathematical Representation Ability. International Education Studies, 10(9), 23–38. https://doi.org/10.5539/ies.v10n9p23
Minarti, E. D., & Wahyudin. (2019). Conceptual understanding and mathematical disposition of college student through Concrete-Representational-Abstract approach (CRA). Journal of Physics: Conference Series, 1157, 1–6. https://doi.org/10.1088/1742-6596/1157/4/042124
Moher, D., Liberati, A., Tetzlaff, J., Altman, D. G., & Group, T. P. (2009). Preferred Reporting Items for Systematic Reviews and Meta-Analyses?: The PRISMA Statement. PLoS Medicine, 6(7), 1–6. https://doi.org/10.1371/journal.pmed.1000097
Peltier, C., & Vannest, K. J. (2018). Using the concrete representational abstract (CRA) instructional framework for mathematics with students with emotional and behavioral disorders. Preventing School Failure, 62(2), 73–82. https://doi.org/10.1080/1045988X.2017.1354809
Pulungan, A. R., & Rakhmawati, F. (2022). Tren Media Pembelajaran Matematika dalam Jurnal Pendidikan Matematika di Seluruh Indonesia. Jurnal Cendekia?: Jurnal Pendidikan Matematika, 6(3), 3443–3458. https://doi.org/10.31004/cendekia.v6i3.1776
Purwadi, I. M. A., Sudiarta, I. G. P., & Supart, I. N. (2019). The effect of concrete-pictorial-abstract strategy toward students’ mathematical conceptual understanding and mathematical representation on fractions. International Journal of Instruction, 12(1), 1113–1126. https://eric.ed.gov/?id=EJ1201375
Putri, H. E., Rahayu, P., Saptini, R. D., & Misnarti. (2016). Keterkaitan Penerapan Pendekatan CPA dan Peningkatan Kemampuan Koneksi Matematis Siswa Sekolah Dasar. Metodik Didaktik, 11(1), 41–49. https://ejournal.upi.edu/index.php/MetodikDidaktik/article/view/3785
Ru?tio?lu, O., & Avc?o?lu, H. (2022). Comparison of the different presentations of Concrete-Representational-Abstract (CRA) sequence to teach functional academic skills for students with developmental retardation. Sustainability, 14(10752), 1–19. https://doi.org/10.3390/su141710752
Saleh, M., Prahmana, R. C. I., Isa, M., & Murni. (2018). Improving the reasoning ability of elementary school student through the Indonesian realistic mathematics education. Journal on Mathematics Education, 9(1), 41–54. https://eric.ed.gov/?id=EJ1173650
Salimi, M., Suhartono, S., Hidayah, R., & Fajari, L. E. W. (2020). Improving mathematics learning of geometry through the concrete-pictorial-Abstract (CPA) approach: Collaborative action research. Journal of Physics: Conference Series, 1663, 1–8. https://doi.org/10.1088/1742-6596/1663/1/012046
Salingay, N. R. R., & Tan, D. A. (2018). Concrete-pictorial-abstract approach on students’ attitude and performance in mathematics. International Journal of Scientific and Technology Research, 7(5), 90–111. https://www.ijstr.org/final-print/may2018/Concrete-pictorial-abstract-Approach-On-Students-Attitude-And-Performance-In-Mathematics.pdf
Shafiee, M. S., & Meng, C. C. (2021). Impact of concrete-pictorial-abstract approach with collaborative lesson research on year four pupils’ proficiency in perimeter. Pertanika Journal of Social Sciences and Humanities, 29(4), 2301–2313. https://doi.org/10.47836/pjssh.29.4.11
Strickland, T. K., & Maccini, P. (2013). The effects of the concrete-representational-abstract integration strategy on the ability of students with learning disabilities to multiply linear expressions within area problems. Remedial and Special Education, 34(3), 142–153. https://doi.org/10.1177/0741932512441712
Umar, U., Hasratuddin, H., & Surya, E. (2022). Pengembangan LKPD Berbasis Model Think Aloud Pair Problem Solving untuk Meningkatkan Kemampuan Pemecahan Masalah Matematis Siswa SD Negeri 067248 Medan. Jurnal Cendekia?: Jurnal Pendidikan Matematika, 6(3), 3402–3416. https://doi.org/10.31004/cendekia.v6i3.1884
Widodo, S. A., & Wahyudin. (2018). Selection of learning media mathematics for junior school students. TOJET: Turkish Online Journal of Educational Technology, 17(1), 154–160. https://eric.ed.gov/?id=EJ1165728
Xiao, Y., & Watson, M. (2019). Guidance on Conducting a Systematic Literature Review. Journal of Planning Education and Research, 39(1), 93–112. https://doi.org/10.1177/0739456X17723971
Yeh, C. Y. C., Cheng, H. N. H., Chen, Z. H., Liao, C. C. Y., & Chan, T. W. (2019). Enhancing achievement and interest in mathematics learning through Math-Island. Research and Practice in Technology Enhanced Learning, 14(5), 1–19. https://doi.org/10.1186/s41039-019-0100-9
Yuliyanto, A., & Turmudi. (2020). Study based on the early mathematical ability of elementary student self-efficacy through the concrete-pictorial-abstract approach. Universal Journal of Educational Research, 8(11), 5901–5912. https://doi.org/10.13189/ujer.2020.082224
Zhang, S., Yu, S., Xiao, J., Liu, Y., & Jiang, T. (2022). The effects of concrete-representational-abstract sequence instruction on fractions for chinese elementary students with mathematics learning disabilities. International Journal of Science and Mathematics Education, 20(7), 1481–1498. https://doi.org/10.1007/s10763-021-10215-9
Amril, L. O., Darhim, & Juandi, D. (2020). The effect experiential learning model based concrete-pictorial-abstract (EL-CPA) on mathematics attitude of deaf students. Journal of Physics: Conference Series, 1657, 1–6. https://doi.org/10.1088/1742-6596/1657/1/012070
Azzumar, F., & Juandi, D. (2023). Concrete-pictorial-abstract approaches to mathematics education: A systematic literature review. Journal of Mathematics and Mathematics Education (JMME), 13(1), 1-11. https://doi.org/10.20961/jmme.v13i1.73962
Bishara, S. (2018). Active and traditional teaching, self-image, and motivation in learning math among pupils with learning disabilities. Cogent Education, 5(1), 1–16. https://doi.org/10.1080/2331186X.2018.1436123
Bouck, E., Park, J., & Nickell, B. (2017). Using the concrete-representational-abstract approach to support students with intellectual disability to solve change-making problems. Research in Developmental Disabilities, 60, 24–36. https://doi.org/10.1016/j.ridd.2016.11.006
Flores, M. M. (2010). Using the concrete-representational-abstract sequence to teach subtraction with regrouping to students at risk for failure. Remedial and Special Education, 31(3), 195–207. https://doi.org/10.1177/0741932508327467
Flores, M. M., & Hinton, V. M. (2019). Improvement in elementary students’ multiplication skills and understanding after learning through the combination of the concrete-representational-abstract sequence and strategic instruction. Education and Treatment of Children, 42(1), 73–99. https://doi.org/10.1353/etc.2019.0004
Flores, M. M., Hinton, V. M., & Burton, M. E. (2016). Teaching problem solving to students receiving tiered interventions using the concrete-representational-abstract sequence and schema-based instruction. Preventing School Failure, 0(0), 1–11.
https://doi.org/10.1080/1045988X.2016.1164117
Flores, M. M., Hinton, V. M., & Meyer, J. M. (2020). Teaching fraction concepts using the concrete-representational-abstract sequence. Remedial and Special Education, 41(3), 165–175. https://doi.org/10.1177/0741932518795477
Flores, M. M., Hinton, V. M., & Taylor, J. J. (2018). CRA fraction intervention for fifth-grade students receiving tier two interventions. Preventing School Failure, 62(3), 198–213. https://doi.org/10.1080/1045988X.2017.1414027
Flores, M. M., Hinton, V., & Strozier, S. D. (2014). Teaching subtraction and multiplication with regrouping using the concrete-representational-abstract sequence and strategic instruction model. Learning Disabilities Research and Practice, 29(2), 75–88. https://doi.org/10.1111/ldrp.12032
Flores, M. M., & Milton, J. H. (2020). Teaching the partial products algorithm using the concrete-representational-abstract sequence. Exceptionality, 28(2), 142–160. https://doi.org/10.1080/09362835.2020.1772070
Flores, M. M., Moore, A. J., & Meyer, J. M. (2020). Teaching the partial products algorithm with the concrete representational abstract sequence and the strategic instruction model. Psychology in the Schools, 57(6), 946–958. https://doi.org/10.1002/pits.22335
Hamilton, R., & Ghatala, E. (1994). Learning and Instruction. McGraw-Hill, Inc.
Heyder, A., Weidinger, A. F., Cimpian, A., & Steinmayr, R. (2020). Teachers’ belief that math requires innate ability predicts lower intrinsic motivation among low-achieving students. Learning and Instruction, 65(101220), 1–39. https://doi.org/10.1016/j.learninstruc.2019.101220
Hinton, V., & Flores, M. (2022). Concrete-representational-abstract–integrated as a tier 2 instruction to teach addition. Rural Special Education Quarterly, 41(3), 169–178. https://doi.org/10.1177/87568705221075756
Kaya, S., & Yildiz, N. G. (2023). Using the concrete–representational–abstract sequence to teach math skills to a student with autism spectrum disorder in a general education classroom. International Journal of Developmental Disabilities. https://doi.org/10.1080/20473869.2023.2180539
Kurniawan, H., Budiyono, Sajidan, & Siswandari. (2020). Concrete-pictorial-abstract approach on student’s motivation and problem solving performance in Algebra. Universal Journal of Educational Research, 8(7), 3204–3212. https://doi.org/10.13189/ujer.2020.080749
Mahayukti, G. A., Dianawati, N. P. S., Ardana, I. M., & Suryawan, I. P. P. (2019). The effect of concrete-pictorial-abstract learning strategy on spatial sense ability. Journal of Physics: Conference Series, 1317, 1–9. https://doi.org/10.1088/1742-6596/1317/1/012007
Miller, S. P., & Kaffar, B. J. (2011). Developing Addition with Regrouping Competence among Second Grade Students with Mathematics Difficulties. Investigations in Mathematics Learning, 4(1), 24–49. https://doi.org/10.1080/24727466.2011.11790308
Milton, J. H., Flores, M. M., Hinton, V. M., Dunn, C., & Darch, C. B. (2023). Using the concrete-representational-abstract sequence to teach conceptual understanding of place value, rounding, and expanded Nnotation. Learning Disabilities Research and Practice, 38(1), 15–25. https://doi.org/10.1111/ldrp.12299
Minarni, A., & Napitupulu, E. E. (2017). Developing Instruction Materials Based on Joyful PBL to Improve Students Mathematical Representation Ability. International Education Studies, 10(9), 23–38. https://doi.org/10.5539/ies.v10n9p23
Minarti, E. D., & Wahyudin. (2019). Conceptual understanding and mathematical disposition of college student through Concrete-Representational-Abstract approach (CRA). Journal of Physics: Conference Series, 1157, 1–6. https://doi.org/10.1088/1742-6596/1157/4/042124
Moher, D., Liberati, A., Tetzlaff, J., Altman, D. G., & Group, T. P. (2009). Preferred Reporting Items for Systematic Reviews and Meta-Analyses?: The PRISMA Statement. PLoS Medicine, 6(7), 1–6. https://doi.org/10.1371/journal.pmed.1000097
Peltier, C., & Vannest, K. J. (2018). Using the concrete representational abstract (CRA) instructional framework for mathematics with students with emotional and behavioral disorders. Preventing School Failure, 62(2), 73–82. https://doi.org/10.1080/1045988X.2017.1354809
Pulungan, A. R., & Rakhmawati, F. (2022). Tren Media Pembelajaran Matematika dalam Jurnal Pendidikan Matematika di Seluruh Indonesia. Jurnal Cendekia?: Jurnal Pendidikan Matematika, 6(3), 3443–3458. https://doi.org/10.31004/cendekia.v6i3.1776
Purwadi, I. M. A., Sudiarta, I. G. P., & Supart, I. N. (2019). The effect of concrete-pictorial-abstract strategy toward students’ mathematical conceptual understanding and mathematical representation on fractions. International Journal of Instruction, 12(1), 1113–1126. https://eric.ed.gov/?id=EJ1201375
Putri, H. E., Rahayu, P., Saptini, R. D., & Misnarti. (2016). Keterkaitan Penerapan Pendekatan CPA dan Peningkatan Kemampuan Koneksi Matematis Siswa Sekolah Dasar. Metodik Didaktik, 11(1), 41–49. https://ejournal.upi.edu/index.php/MetodikDidaktik/article/view/3785
Ru?tio?lu, O., & Avc?o?lu, H. (2022). Comparison of the different presentations of Concrete-Representational-Abstract (CRA) sequence to teach functional academic skills for students with developmental retardation. Sustainability, 14(10752), 1–19. https://doi.org/10.3390/su141710752
Saleh, M., Prahmana, R. C. I., Isa, M., & Murni. (2018). Improving the reasoning ability of elementary school student through the Indonesian realistic mathematics education. Journal on Mathematics Education, 9(1), 41–54. https://eric.ed.gov/?id=EJ1173650
Salimi, M., Suhartono, S., Hidayah, R., & Fajari, L. E. W. (2020). Improving mathematics learning of geometry through the concrete-pictorial-Abstract (CPA) approach: Collaborative action research. Journal of Physics: Conference Series, 1663, 1–8. https://doi.org/10.1088/1742-6596/1663/1/012046
Salingay, N. R. R., & Tan, D. A. (2018). Concrete-pictorial-abstract approach on students’ attitude and performance in mathematics. International Journal of Scientific and Technology Research, 7(5), 90–111. https://www.ijstr.org/final-print/may2018/Concrete-pictorial-abstract-Approach-On-Students-Attitude-And-Performance-In-Mathematics.pdf
Shafiee, M. S., & Meng, C. C. (2021). Impact of concrete-pictorial-abstract approach with collaborative lesson research on year four pupils’ proficiency in perimeter. Pertanika Journal of Social Sciences and Humanities, 29(4), 2301–2313. https://doi.org/10.47836/pjssh.29.4.11
Strickland, T. K., & Maccini, P. (2013). The effects of the concrete-representational-abstract integration strategy on the ability of students with learning disabilities to multiply linear expressions within area problems. Remedial and Special Education, 34(3), 142–153. https://doi.org/10.1177/0741932512441712
Umar, U., Hasratuddin, H., & Surya, E. (2022). Pengembangan LKPD Berbasis Model Think Aloud Pair Problem Solving untuk Meningkatkan Kemampuan Pemecahan Masalah Matematis Siswa SD Negeri 067248 Medan. Jurnal Cendekia?: Jurnal Pendidikan Matematika, 6(3), 3402–3416. https://doi.org/10.31004/cendekia.v6i3.1884
Widodo, S. A., & Wahyudin. (2018). Selection of learning media mathematics for junior school students. TOJET: Turkish Online Journal of Educational Technology, 17(1), 154–160. https://eric.ed.gov/?id=EJ1165728
Xiao, Y., & Watson, M. (2019). Guidance on Conducting a Systematic Literature Review. Journal of Planning Education and Research, 39(1), 93–112. https://doi.org/10.1177/0739456X17723971
Yeh, C. Y. C., Cheng, H. N. H., Chen, Z. H., Liao, C. C. Y., & Chan, T. W. (2019). Enhancing achievement and interest in mathematics learning through Math-Island. Research and Practice in Technology Enhanced Learning, 14(5), 1–19. https://doi.org/10.1186/s41039-019-0100-9
Yuliyanto, A., & Turmudi. (2020). Study based on the early mathematical ability of elementary student self-efficacy through the concrete-pictorial-abstract approach. Universal Journal of Educational Research, 8(11), 5901–5912. https://doi.org/10.13189/ujer.2020.082224
Zhang, S., Yu, S., Xiao, J., Liu, Y., & Jiang, T. (2022). The effects of concrete-representational-abstract sequence instruction on fractions for chinese elementary students with mathematics learning disabilities. International Journal of Science and Mathematics Education, 20(7), 1481–1498. https://doi.org/10.1007/s10763-021-10215-9
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2024-06-30
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