Profiles of Conceptual, Procedural, and Technical Errors in Solving Pictogram Problems among Elementary School Students

Ageng Triyono; Teguh Wibowo; Dyan Murdiasih

doi:10.30998/s8vjy228

Authors

Ageng Triyono Universitas Muhammadiyah Purworejo Author
Teguh Wibowo Author
Dyan Murdiasih Author

DOI:

https://doi.org/10.30998/s8vjy228

Keywords:

Conceptual errors, procedural errors, technical errors, pictograms, statistics, Kastolan theory

Abstract

The ability to comprehend pictogram material is a critical foundation for developing students’ data interpretation skills from early education; however, students’ mastery of this topic remains low and is rarely analyzed systematically. This study aims to analyze the profile of conceptual, procedural, and technical errors made by fourth-grade elementary students in solving pictogram problems, based on Kastolan’s theory. A descriptive qualitative approach was employed, involving 11 students from a public elementary school in Purworejo Regency who had participated in statistics lessons on pictograms as outlined in the Merdeka Curriculum. Data were collected through validated pictogram tests and in-depth interviews with students who made errors. Data analysis was conducted thematically by triangulating test results and interview data to identify error patterns and root causes. The findings indicate that students’ errors were dominated by technical errors (43%), followed by procedural (29%) and conceptual errors (28%). Technical errors mainly involved miscalculations and incorrect mathematical notation, conceptual errors pertained to misunderstanding icons as representations of data units, while procedural errors arose from unsystematic problem-solving steps and insufficient attention to task instructions. The main contributing factors were weak foundations in visual statistics concepts and limited practice in mathematical visual communication. This study highlights the urgency of strengthening instructional strategies that integrate conceptual, procedural, and technical aspects, as well as the need for diagnostic assessment and targeted remediation based on error type. These findings provide practical contributions for teachers and curriculum developers in building robust statistical literacy at the elementary level.

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Author Biographies

Teguh Wibowo

Mathematics Education
Dyan Murdiasih

Primary school teachers

References

(BSKAP), B. S. K. dan A. P. (2022). Capaian Pembelajaran Mata Pelajaran Matematika Fase A-F. Kementerian Pendidikan Dasar dan Menengah Republik Indonesia. https://kurikulum.kemdikbud.go.id/file/cp/dasmen/10. CP Matematika.pdf

Anuniwat, D., & Ningtyas, Y. D. W. K. (2024). Intended Statistics Curriculum at the Elementary Level: Thailand vs. Indonesia. Journal of Instructional Mathematics, 5(2), 108–120. https://doi.org/10.37640/jim.v5i2.2131

Arteaga, P., Díaz-Levicoy, D., & Batanero, C. (2020). Chilean Primary School Children’s Understanding of Statistical Graphs. Acta Scientiae, 22(5), 2–24. https://doi.org/10.17648/acta.scientiae.5884

Astari, E., & Marsigit. (2019). Mathematical connections process for elementary school students in problem solving of statistics. Journal of Physics: Conference Series, 1280(4). https://doi.org/10.1088/1742-6596/1280/4/042008

Bawadi, S., Novaliyosi, N., Pujiastuti, H., Yuhana, Y., & Hendrayana, A. (2023). Implementation of Teacher and Student Independent Curriculum in Mathematics Learning: Systematic Literature Review. JIIP - Jurnal Ilmiah Ilmu Pendidikan, 6(1), 602–609. https://doi.org/10.54371/jiip.v6i1.1292

Benecke, K., & Kaiser, G. (2023). Teachers’ approaches to handling student errors in mathematics classes. Asian Journal for Mathematics Education, 2(2), 161–182. https://doi.org/10.1177/27527263231184642

Bestari, A. M., Rani, A. N. M., & Gusmarini. (2024). Analysis Error Student in Solving Problem Logarithm Based on the Kastolan Procedure. Journal of Research on Mathematics Instruction (JRMI), 5(1), 1–9. https://doi.org/10.33578/jrmi.v5i1.85

Clawson, T. H., Leafman, J., Nehrenz, G. M., & Kimmer, S. (2012). Using Pictograms for Communication. Military Medicine, 177(3), 291–295. https://doi.org/10.7205/MILMED-D-11-00279

Delastri, L., & Lolang, E. (2023). Students ’ Conceptual Error and Procedural Error in Solving Algebraic Problems. Multicultural Education, 9(1), 18–24. https://doi.org/10.5281/zenodo.7508092

Dwita, A., & Retnawati, H. (2022). Students’ errors in solving mathematical problems. AIP Conference Proceedings, 2575(December), 040007. https://doi.org/10.1063/5.0107794

Engel, J. (2019). Statistical Literacy and Society: What Is Civic Statistics? Actas Del Tercer Congreso Internacional Virtual de Educación Estadística, 39(1), 1–12. https://www.ugr.es/~fqm126/civeest/ponencias/engel.pdf

Farokhah, L., Herman, T., & Jupri, A. (2019). Students’ ability of mathematical representation on statistics topic in elementary school. Journal of Physics: Conference Series, 1157(3), 032110. https://doi.org/10.1088/1742-6596/1157/3/032110

Fitri, A., Herman, T., Sa’ud, U. S., Suparman, T., Rahman, & DS, Y. N. (2024). Analysis of the Implementation of the Independent Curriculum in Mathematics Subjects in Elementary Schools (Vol. 1, Issue 20, pp. 906–915). Atlantis Press SARL. https://doi.org/10.2991/978-2-38476-118-0_103

Fitriyaningsih, A., Sugita, G., Anggraini, A., & Murdiana, I. N. (2024). Analysis of Errors in Solving Story Questions on Algebraic Operations Based Kastolan Theory Students SMP Negeri 6 Palu. Numerical: Jurnal Matematika Dan Pendidikan Matematika, 8(1), 230–237. https://doi.org/10.25217/numerical.v8i1.4489

Franklin, C., & Bargagliotti, A. (2020). Introducing GAISE II: A Guideline for Precollege Statistics and Data Science Education. Harvard Data Science Review, 2(4), 1–9. https://doi.org/10.1162/99608f92.246107bb

Habibie, Z. R., Kartono, K., Kartono, W., & Kharisudin, I. (2023). Analysis of Student Statistical literacy Using Test Questions integrated with Indonesian Education Issues as a form of Contextual approach. Polyhedron International Journal in Mathematics Education, 1(2), 86–93. https://doi.org/10.59965/pijme.v1i2.48

Hasanah, R., Yuanita, P., Saragih, S., & Roza, Y. (2023). 10.47435/jtmt.v4i02.1975 Analysis Of Student Errors On Algebraic Form Material Based On Kastolan. JTMT: Journal Tadris Matematika, 4(02), 190–196. https://doi.org/10.47435/jtmt.v4i02.1975

Kartini, & Alawiyah, T. (2023). Students’ Errors in Solving Matrix Multiplication Problems Based on Kastolan Theory. Mosharafa: Jurnal Pendidikan Matematika, 12(1), 181–190. https://doi.org/10.31980/mosharafa.v12i1.766

Kastolan. (1992). Identifikasi Jenis-Jenis Kesalahan Menyelesaikan Soal-Soal Matematika yang Dilakukan Siswa Kelas 2 Program A1 SMA Negeri Sekotamadya. Malang: IKIP Malang.

Khoiroh, M., Nahdliya, N., Anggraini, D. D., Umah, U., & Asriningsih, T. M. (2023). Analysis of Creativity Among Elementary School Children in Solving Two-Dimensional Shape Problems in Grade V. International Journal of Research Publication and Reviews, 4(3), 1679–1684. https://doi.org/10.55248/gengpi.2023.32720

Legesse, M., Luneta, K., & Ejigu, T. (2020). Analyzing the effects of mathematical discourse-based instruction on eleventh-grade students’ procedural and conceptual understanding of probability and statistics. Studies in Educational Evaluation, 67(January), 100918. https://doi.org/10.1016/j.stueduc.2020.100918

Londono, D., & Alsina, A. (2023). Statistical knowledge of primary school children: An overview of study approaches. International Electronic Journal of Mathematics Education, 18(2), em0733. https://doi.org/10.29333/iejme/12984

Lubis, S. W., Fitriani, F., Lubis, A. M., Siregar, Y. A., & Samoh, S. (2024). Analysis of Errors in Students’ Mathematical Communication Skills Based on Kastolan Stages at Ban Eyoh School, Thailand. Kreano, Jurnal Matematika Kreatif-Inovatif, 15(2), 363–374. https://doi.org/10.15294/m8cymg05

Nahdi, D. S., & Jatisunda, M. G. (2020). Conceptual Understanding and Procedural Knowledge: A Case Study on Learning Mathematics of Fractional Material in Elementary School. Journal of Physics: Conference Series, 1477(4). https://doi.org/10.1088/1742-6596/1477/4/042037

Nur, I. R. D., Yulian, V. N., & Laelasari, L. (2021). An analysis of Elementary School Students Errors in Solving Statistics Problems in Online Learning during a Pandemic Period. SJME (Supremum Journal of Mathematics Education), 5(2), 207–214. https://doi.org/10.35706/sjme.v5i2.5302

Pomalato, S. W. D., Ili, L., Ningsi, B. A., Fadhilaturrahmi, F., Hasibuan, A. T., & Primayana, K. H. (2020). Student Error Analysis in Solving Mathematical Problems. Universal Journal of Educational Research, 8(11), 5183–5187. https://doi.org/10.13189/ujer.2020.081118

Purwati, I., Murtiyasa, B., Sumardi, S., Kontesa, D. A., & Hakim, L. (2022). Analysis of learning difficulties of mathematics statistics materials in class v elementary school students. Math Didactic: Jurnal Pendidikan Matematika, 8(3), 272–280. https://doi.org/10.33654/math.v8i3.1929

Rafi, I., & Heri, R. (2023). How do Indonesia and New Zealand facilitate their students in learning statistics? A comparative study on the intended mathematics curriculum. Materials of International Practical Internet Conference Challenges of Science, November, 251–258. https://doi.org/10.31643/2023.32

Rahmawati, N. K., Triyono, A., Kusuma, A. P., & Putri, I. N. (2024). Types and Factors of Student Difficulty Solving Algebra Problems Based on Polya Stages. Logaritma : Jurnal Ilmu-Ilmu Pendidikan Dan Sains, 12(02), 231–250. https://doi.org/10.24952/logaritma.v12i2.13397

Rong, L., & Mononen, R. (2022). Error analysis of students with mathematics learning difficulties in Tibet. Asian Journal for Mathematics Education, 1(1), 52–65. https://doi.org/10.1177/27527263221089357

Roswahyuliani, L., Putra, H. D., Widiartini, A., & Hendriana, H. (2023). Analysis of elementary school students’ mathematical communication ability on statistics. JIML: Journal of Innovative Mathematics, 6(4), 248–261. https://doi.org/10.22460/jiml.v6i4.p18254

Rukminingsih, Adnan, G., & Latief, M. A. (2020). Metode Penelitian Pendidikan: Penelitian Kuantitatif, Penelitian Kualitatif, Penelitian Tindakan Kelas (E. Munastiwi & H. Ard (eds.); Pertama). Erhaka Utama.

Rushton, S. J. (2018). Teaching and learning mathematics through error analysis. Fields Mathematics Education Journal, 3(1), 4. https://doi.org/10.1186/s40928-018-0009-y

Schoen, R. C., Rhoads, C., Perez, A., Jacobbe, T., & Li, L. (2025). Improving the teaching and learning of statistics. Learning and Instruction, 95(August 2024), 102018. https://doi.org/10.1016/j.learninstruc.2024.102018

Shamsuddin, M., Mahlan, S. B., Alias, F. A., Hamat, M., & Mohamed, S. A. (2021). Analysis of Student Error in Statistical Subject: A Case Study for Online Learning. International Journal of Academic Research in Progressive Education and Development, 10(3), 82–93. https://doi.org/10.6007/ijarped/v10-i3/10714

Sidiq, U., & Choiri, M. (2019). Metode Penelitian Kualitatif di Bidang Pendidikan (A. Mujahidin (ed.); Pertama). CV. Nata Karya.

Smith, V. C. (2018). The effects of structured mathematical discourse on mathematics comprehension and classroom participation (Ph.D. Thesis) [Trevencaa Nazarene University]. https://www.proquest.com/docview/2108693948

Sonia, A., Suanto, E., Kartini, & Maimunah. (2023). Analyzing Students Errors Based On Kastolan Theory In Solving AKM-Numeration Type Questions In Geometry Domain. AXIOM: Jurnal Pendidikan Dan Matematika, 12(1), 34–35. https://doi.org/10.30821/axiom.v12i1.15549

VanLehn, K., Burkhardt, H., Cheema, S., Kang, S., Pead, D., Schoenfeld, A., & Wetzel, J. (2021). Can an orchestration system increase collaborative, productive struggle in teaching-by-eliciting classrooms? Interactive Learning Environments, 29(6), 987–1005. https://doi.org/10.1080/10494820.2019.1616567

Veloo, A., Krishnasamy, H. N., & Wan Abdullah, W. S. (2015). Types of student errors in mathematical symbols, graphs and problem-solving. Asian Social Science, 11(15), 324–334. https://doi.org/10.5539/ass.v11n15p324

Walls, J. W. (2021). Elementary Teacher Beliefs of Mathematics Discourse During Whole Class Discussions. A dissertation submitted to the Graduate Faculty of Auburn University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.

Webb, N. M., Franke, M. L., Ing, M., Turrou, A. C., Johnson, N. C., & Zimmerman, J. (2019). Teacher practices that promote productive dialogue and learning in mathematics classrooms. International Journal of Educational Research, 97(July), 176–186. https://doi.org/10.1016/j.ijer.2017.07.009

Wild, C. J., Utts, J. M., & Horton, N. J. (2018). What Is Statistics? In International Handbook of Research in Statistics Education (pp. 5–36). https://doi.org/10.1007/978-3-319-66195-7_1