Analysis of learning obstacles in grade 1 elementary mathematics using the concrete-pictorial-abstract (CPA) approach

Tanti Listiani; Dhoriva Urwatul Wutsqa; Kuswari Hernawati; Melda Jaya Saragih; Robert Harry Soesanto; Kurniawati Martha; Kurnia Putri Sepdikasari Dirgantoro; Wahyu Setyaningrum; Heri Retnawati

doi:10.31893/multiscience.2026226

Keywords:

learning obstacles

grade 1 elementary mathematics

concrete-pictorial-Abstract (CPA) approach

analysis of learning barriers

Abstract

This study aims to identify and analyze the learning obstacles faced by first-grade elementary school students in mathematics learning using CPA (Concrete-Pictorial-Abstract) approach-based textbooks. The CPA approach is considered effective in helping students understand mathematical concepts gradually, starting from the concrete stage, moving to the pictorial stage, and finally reaching the abstract stage. However, in its implementation, various challenges and difficulties may still be encountered by both students and teachers. This research will be conducted randomly in several Grade 1 classes at Sekolah Lentera Harapan, which are confirmed to be using CPA-approach, namely the Matematika Juara book that adopts the Singapore curriculum. Through qualitative methods and direct observation, this study seeks to gain a deep understanding of the types of learning obstacles experienced by students and to explore the factors that influence the effectiveness of CPA-approach in teaching and learning activities.The expected outcomes of this research include several key aspects. First, documentation of the types of learning obstacles found among students when using CPA-based textbooks. Second, the formulation of more effective teaching strategies to overcome the identified learning obstacles, thereby improving students' understanding of mathematics. Third, a practical guide for teachers on how to optimally implement CPA-based books in Grade 1 classrooms. It is hoped that this study will make a significant contribution to the development of curriculum and mathematics teaching methods, particularly in Grade 1, by promoting more optimal use of the CPA approach.
References
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29. Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). Sage Publications.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to cite

Listiani, T., Wutsqa, D. U., Hernawati, K., Saragih, M. J., Soesanto, R. H., Martha, K., Dirgantoro, K. P. S., Setyaningrum, W., & Retnawati, H. (2025). Analysis of learning obstacles in grade 1 elementary mathematics using the concrete-pictorial-abstract (CPA) approach. Multidisciplinary Science Journal, 8(4), 2026226. https://doi.org/10.31893/multiscience.2026226

[1] Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin & Review, 14(2), 243–248. https://doi.org/10.3758/BF03194059

[2] Babchuk, W. A. (2017). Book Review: Qualitative Research: A Guide to Design and Implementation (4th ed.), by S. B. Merriam and E. J. Tisdell. Adult Education Quarterly, 67(1), 71–73. https://doi.org/10.1177/0741713616671930

[3] Baroody, A. J., & Dowker, A. (2003). The Development of Arithmetic Concepts and Skills: Constructing Adaptive Expertise. Lawrence Erlbaum Associates.

[4] Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27–40. https://doi.org/https://doi.org/10.3316/QRJ0902027

[5] Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa

[6] Brousseau, G. (1997). Theory of Didactical Situations in Mathematics. Kluwer Academic Publishers.

[7] Bruner, J. S. (1996). The culture of education. Harvard University Press.

[8] Cai, J., Kaiser, G., Perry, B., & Wong, N. . (2020). Compendium for early career researchers in mathematics education. Springer.

[9] Clements, D. ., & Sarama, J. (2004). Hypothetical Learning Trajectories: A Special Issue of Mathematical Thinking and Learning (1st ed.). Routledge. https://doi.org/10.4324/9780203063279

[10] Clements, D. H., & Sarama, J. (2009). Learning and Teaching Early Math: The Learning Trajectories Approach. Routledge.

[11] Cobb, Paul, Confrey, Jere, diSessa, Andrea, Lehrer, Richard, & Schauble, Leona. (2003). Design Experiments in Educational Research. Educational Researcher, 32(1), 9–13. https://doi.org/10.3102/0013189X032001009

[12] Creswell, J. W. (2017). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (5th ed.). CA: SAGE Publications.

[13] Denzin, N. K. (1978). The research act: A theoretical introduction to sociological methods (2nd ed.). McGraw-Hill.

[14] Fuson, K. C., Clements, D. H., & Sarama, J. (2015). Making early math education work for all childrenmaking early math education. Phi Delta Kappan, 97(3), 63–68. https://doi.org/10.1177/0031721715614831

[15] Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. SAGE Publications.

[16] Listiani, T., Dirgantoro, K. P. S., Saragih, M. J., & Tamba, K. P. (2019). Analisis Kesalahan Mahasiswa Pendidikan Matematika Dalam Menyelesaikan Soal Geometri Pada Topik Bangun Ruang [Error Analysis of Students in the Mathematics Department in Solving Geometry Problems on the Topic of Solid Figures]. JOHME: Journal of Holistic Mathematics Education, 3(1), 44. https://doi.org/10.19166/johme.v3i1.1708

[17] Listiani, T., & Saragih, M. J. (2022). Hambatan Belajar Mahasiswa dalam Pembelajaran Jarak Jauh pada Mata Kuliah Geometri Analitik. Jurnal Cendekia: Jurnal Pendidikan Matematika, 06(02), 2201–2211.

[18] Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and implementation (4th ed.). Jossey-Bass.

[19] Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). SAGE Publications.

[20] Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175–197. https://doi.org/10.1023/A:1014596316942

[21] NCTM. (2000). Principles and Standar dor School Mathematics. The National Council of Teachers of Mathematics.

[22] Patton, M. Q. (2015a). Qualitative research & evaluation methods: Integrating theory and practice (4th ed.). Sage Publications.

[23] Patton, M. Q. (2015b). Qualitative research & evaluation methods (4th ed.). SAGE Publications.

[24] Piaget, J. (1952). The Child’s Conception of Number. Routledge & Kegan Paul.

[25] Prediger, S., & Hefendehl-Hebeker, L. (2016). On the Relevance of Epistemological Awareness for Classroom Practices of Teachers. Journal Fur Mathematik-Didaktik, 37(1), 239–262. https://doi.org/10.1007/s13138-016-0085-5

[26] Radford, L. (2008). The ethics of being and knowing: Towards a cultural theory of learning. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in Mathematics Education. Sense Publishers.

[27] Suryadi, A. (2021). Diagnosis kesulitan belajar matematika SD. Refika Aditama.

[28] Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and Middle School Mathematics: Teaching Developmentally (9th ed.). Pearson.

[29] Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). Sage Publications.

Abstract

References

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