A Cross-Sectional Study on the Relationship Between Problem-Solving Ability and Types of Student Errors in Integral Calculus
- 1Universitas Islam Negeri Alauddin Makassar
- 2Universitas Muhammadiyah Makassar
Abstract
Many undergraduate students still experience difficulties in solving integral calculus problems because learning tends to emphasize procedural manipulation rather than conceptual understanding. Previous studies have identified various types of errors in integral calculus; however, limited research has simultaneously examined the relationship between students’ problem-solving ability (PSA) and specific error types based on Newman’s Error Analysis (NEA) in integral calculus contexts. Therefore, this study aimed to analyze students’ PSA, identify the dominant types of errors in solving integral calculus problems, and examine the relationship between PSA and NEA error types. This study employed a cross-sectional descriptive-correlational design involving 74 undergraduate students enrolled in an Integral Calculus course at a university in Indonesia. Data were collected using an integral calculus problem-solving test designed based on Krulik and Rudnick’s problem-solving indicators and analyzed using Newman’s Error Analysis (NEA). Descriptive statistics were used to determine students’ PSA levels and dominant error types, while Spearman’s rho correlation test was applied to examine the relationship between PSA and NEA scores. The findings revealed that students’ PSA generally fell into the moderate category. Transformation error emerged as the most dominant error type, followed by process skill and comprehension errors, while reading and encoding errors were not observed. Transformation errors mainly occurred when students selected inappropriate integration techniques, such as applying substitution instead of integration by parts. Furthermore, the analysis showed a strong negative correlation between PSA and NEA scores , indicating that students with higher problem-solving ability tended to make fewer conceptual and procedural errors. These findings suggest that students’ difficulties in integral calculus are closely related to limitations in conceptual understanding, strategic reasoning, and representation transformation processes. The study contributes to mathematics education research by demonstrating how specific NEA error patterns are associated with students’ levels of problem-solving ability in integral calculus. The findings imply that integral calculus instruction should emphasize conceptual understanding, multiple mathematical representations, and structured problem-solving strategies to reduce dominant transformation and process skill errors. Future research is recommended to explore intervention-based or longitudinal designs to examine how instructional scaffolding and metacognitive training may improve students’ problem-solving performance in calculus learning.
Abstrak
Banyak mahasiswa masih mengalami kesulitan dalam menyelesaikan soal kalkulus integral karena pembelajaran lebih menekankan prosedur dibandingkan pemahaman konseptual. Penelitian sebelumnya telah mengidentifikasi berbagai jenis kesalahan dalam kalkulus integral, tetapi masih terbatas penelitian yang secara simultan mengkaji hubungan antara kemampuan pemecahan masalah (problem-solving ability/PSA) dan jenis kesalahan berdasarkan Newman’s Error Analysis (NEA). Penelitian ini bertujuan menganalisis kemampuan pemecahan masalah mahasiswa, mengidentifikasi jenis kesalahan dominan dalam penyelesaian soal kalkulus integral, serta mengkaji hubungan antara PSA dan jenis kesalahan berdasarkan NEA. Penelitian ini menggunakan desain cross-sectional dengan pendekatan deskriptif-korelasional yang melibatkan 74 mahasiswa pendidikan matematika yang menempuh mata kuliah Kalkulus Integral di salah satu universitas di Indonesia. Data dikumpulkan melalui tes pemecahan masalah kalkulus integral berdasarkan indikator Krulik dan Rudnick, kemudian dianalisis menggunakan Newman’s Error Analysis (NEA). Analisis deskriptif digunakan untuk menentukan tingkat PSA dan jenis kesalahan dominan, sedangkan uji korelasi Spearman’s rho digunakan untuk menguji hubungan antara PSA dan skor NEA. Hasil penelitian menunjukkan bahwa kemampuan pemecahan masalah mahasiswa secara umum berada pada kategori sedang. Transformation error menjadi jenis kesalahan paling dominan, diikuti process skill error dan comprehension error, sedangkan reading error dan encoding error tidak ditemukan. Transformation error terutama terjadi ketika mahasiswa memilih teknik integrasi yang tidak sesuai, seperti menggunakan metode substitusi pada soal yang seharusnya diselesaikan dengan integral parsial. Hasil analisis juga menunjukkan hubungan negatif yang kuat antara PSA dan skor NEA (ρ = -0,787; p < 0,01), yang berarti mahasiswa dengan kemampuan pemecahan masalah lebih tinggi cenderung melakukan lebih sedikit kesalahan. Temuan ini menunjukkan bahwa kesulitan mahasiswa dalam kalkulus integral berkaitan dengan keterbatasan pemahaman konseptual, penalaran strategis, dan kemampuan transformasi representasi matematis. Implikasi penelitian ini menegaskan pentingnya pembelajaran berbasis problem solving, penggunaan multiple representations, dan penguatan pemahaman konseptual untuk mengurangi transformation error dan process skill error. Penelitian selanjutnya disarankan menggunakan desain intervensi atau longitudinal untuk mengkaji efektivitas scaffolding dan pelatihan metakognitif dalam pembelajaran kalkulus integral.
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BibTeX
@article{suharti2026crosssectional,
title = {{A Cross-Sectional Study on the Relationship Between Problem-Solving Ability and Types of Student Errors in Integral Calculus}},
author = {Suharti and Puji Qur’ani Al Haq and Nasrun},
journal = {Kreano: Jurnal Matematika Kreatif-Inovatif},
year = {2026},
month = jun,
doi = {10.15294/kreano.v17i1.48041},
url = {https://doi.org/10.15294/kreano.v17i1.48041},
note = {CC BY-SA},
}
RIS
TY - JOUR
TI - A Cross-Sectional Study on the Relationship Between Problem-Solving Ability and Types of Student Errors in Integral Calculus
AU - Suharti
AU - Puji Qur’ani Al Haq
AU - Nasrun
PY - 2026
DA - 2026/06/01
JO - Kreano: Jurnal Matematika Kreatif-Inovatif
DO - 10.15294/kreano.v17i1.48041
UR - https://doi.org/10.15294/kreano.v17i1.48041
AB - Many undergraduate students still experience difficulties in solving integral calculus problems because learning tends to emphasize procedural manipulation rather than conceptual understanding. Previous studies have identified various types of errors in integral calculus; however, limited research has simultaneously examined the relationship between students’ problem-solving ability (PSA) and specific error types based on Newman’s Error Analysis (NEA) in integral calculus contexts. Therefore, this study aimed to analyze students’ PSA, identify the dominant types of errors in solving integral calculus problems, and examine the relationship between PSA and NEA error types. This study employed a cross-sectional descriptive-correlational design involving 74 undergraduate students enrolled in an Integral Calculus course at a university in Indonesia. Data were collected using an integral calculus problem-solving test designed based on Krulik and Rudnick’s problem-solving indicators and analyzed using Newman’s Error Analysis (NEA). Descriptive statistics were used to determine students’ PSA levels and dominant error types, while Spearman’s rho correlation test was applied to examine the relationship between PSA and NEA scores. The findings revealed that students’ PSA generally fell into the moderate category. Transformation error emerged as the most dominant error type, followed by process skill and comprehension errors, while reading and encoding errors were not observed. Transformation errors mainly occurred when students selected inappropriate integration techniques, such as applying substitution instead of integration by parts. Furthermore, the analysis showed a strong negative correlation between PSA and NEA scores , indicating that students with higher problem-solving ability tended to make fewer conceptual and procedural errors. These findings suggest that students’ difficulties in integral calculus are closely related to limitations in conceptual understanding, strategic reasoning, and representation transformation processes. The study contributes to mathematics education research by demonstrating how specific NEA error patterns are associated with students’ levels of problem-solving ability in integral calculus. The findings imply that integral calculus instruction should emphasize conceptual understanding, multiple mathematical representations, and structured problem-solving strategies to reduce dominant transformation and process skill errors. Future research is recommended to explore intervention-based or longitudinal designs to examine how instructional scaffolding and metacognitive training may improve students’ problem-solving performance in calculus learning. Abstrak Banyak mahasiswa masih mengalami kesulitan dalam menyelesaikan soal kalkulus integral karena pembelajaran lebih menekankan prosedur dibandingkan pemahaman konseptual. Penelitian sebelumnya telah mengidentifikasi berbagai jenis kesalahan dalam kalkulus integral, tetapi masih terbatas penelitian yang secara simultan mengkaji hubungan antara kemampuan pemecahan masalah (problem-solving ability/PSA) dan jenis kesalahan berdasarkan Newman’s Error Analysis (NEA). Penelitian ini bertujuan menganalisis kemampuan pemecahan masalah mahasiswa, mengidentifikasi jenis kesalahan dominan dalam penyelesaian soal kalkulus integral, serta mengkaji hubungan antara PSA dan jenis kesalahan berdasarkan NEA. Penelitian ini menggunakan desain cross-sectional dengan pendekatan deskriptif-korelasional yang melibatkan 74 mahasiswa pendidikan matematika yang menempuh mata kuliah Kalkulus Integral di salah satu universitas di Indonesia. Data dikumpulkan melalui tes pemecahan masalah kalkulus integral berdasarkan indikator Krulik dan Rudnick, kemudian dianalisis menggunakan Newman’s Error Analysis (NEA). Analisis deskriptif digunakan untuk menentukan tingkat PSA dan jenis kesalahan dominan, sedangkan uji korelasi Spearman’s rho digunakan untuk menguji hubungan antara PSA dan skor NEA. Hasil penelitian menunjukkan bahwa kemampuan pemecahan masalah mahasiswa secara umum berada pada kategori sedang. Transformation error menjadi jenis kesalahan paling dominan, diikuti process skill error dan comprehension error, sedangkan reading error dan encoding error tidak ditemukan. Transformation error terutama terjadi ketika mahasiswa memilih teknik integrasi yang tidak sesuai, seperti menggunakan metode substitusi pada soal yang seharusnya diselesaikan dengan integral parsial. Hasil analisis juga menunjukkan hubungan negatif yang kuat antara PSA dan skor NEA (ρ = -0,787; p < 0,01), yang berarti mahasiswa dengan kemampuan pemecahan masalah lebih tinggi cenderung melakukan lebih sedikit kesalahan. Temuan ini menunjukkan bahwa kesulitan mahasiswa dalam kalkulus integral berkaitan dengan keterbatasan pemahaman konseptual, penalaran strategis, dan kemampuan transformasi representasi matematis. Implikasi penelitian ini menegaskan pentingnya pembelajaran berbasis problem solving, penggunaan multiple representations, dan penguatan pemahaman konseptual untuk mengurangi transformation error dan process skill error. Penelitian selanjutnya disarankan menggunakan desain intervensi atau longitudinal untuk mengkaji efektivitas scaffolding dan pelatihan metakognitif dalam pembelajaran kalkulus integral.
SN - 2086-2334
SN - 2442-4218
ER -