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Mekong Delta Natural Science Conference
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Pham, V. B., Bui, P. U., & Nguyen, T. T. L. (2025). Designing and evaluating a scale of mathematical problem-solving ability of grade 6 students on the content "Fracrational value of a number". Dong Thap University Journal of Science, 14(04S), 254-268. https://doi.org/10.52714/dthu.14.04S.2025.1585
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Designing and evaluating a scale of mathematical problem-solving ability of grade 6 students on the content "Fracrational value of a number"
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Abstract
Developing competencies, including mathematical problem-solving ones, is an inevitable trend in education. Assessing students' competencies accurately will be an important basis for proposing appropriate teaching methods as well as evaluating the effectiveness of those methods. This study designed a rubric for assessing written tests on mathematical problem-solving competencies. Through the assessment of 66 teachers and experiments on 132 students, the study proposed a good rubric for assessment, and also made recommendations for designing similar rubrics in the future.
Keywords
assessment, mathematical problem-solving, grade 6, competencies, rubric
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
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Bùi, A. K., Võ, T. T. P, Đỗ, T. P. T, & Bùi, P. T. H. (2023). Giáo trình Đánh giá kết quả học tập Toán và Khoa học tự nhiên. NXB Đại học Cần Thơ.
Cahyadi, M. R., Maryanto, B. P. A., Syaifuddin, M., & Darmayanti, R. (2023). Development of Essay Test Assessment Rubric for Polya Theory-Based Mathematical Problem-Solving. JNPM (Jurnal Nasional Pendidikan Matematika), 7(1), 167. https://doi.org/10.33603/jnpm.v7i1.7724
Charles, R. I., Lester, F., & O’Daffer, P. G. (2008). How to evaluate progress in problem solving (8. print). The National Council of Teachers of Mathematics.
Choirudin, C., Degeng, I. N. S., Kuswandi, D., Purnomo, P., & Maba, A. P. (2022). Career readiness among low-income Muslim students. International Journal of Evaluation and Research in Education (IJERE), 11(3), 1400. https://doi.org/10.11591/ijere.v11i3.22727
Cohen, L., Manion, L., & Morrison, K. (2017). Research Methods in Education. Routledge. https://doi.org/10.4324/9781315456539
Darmayanti, R., Sugianto, R., & Muhammad, Y. (2022). Analysis of Students’ Adaptive Reasoning Ability in Solving HOTS Problems Arithmetic Sequences and Series in Terms of Learning Style. Numerical: Jurnal Matematika Dan Pendidikan Matematika, 73–90. https://doi.org/10.25217/numerical.v6i1.2340
Darmayanti, R., Syaifuddin, M., Rizki, N., Sugianto, R., & Hasanah, N. (2022). High school students’ mathematical representation ability: Evaluation of disposition based on mastery learning assessment model (MLAM). Journal of Advanced Sciences and Mathematics Education, 2(1), 1–15. https://doi.org/10.58524/jasme.v2i1.93
Dawson, P. (2017). Assessment rubrics: towards clearer and more replicable design, research and practice. Assessment & Evaluation in Higher Education, 42(3), 347–360. https://doi.org/10.1080/02602938.2015.1111294
DeVellis, R. F. (2017). Scale development: theory and applications (Fourth edition). SAGE.
Gunawardena, E. (2010). A rubric to self-assess and peer-assess mathematical problem solving tasks of college students. Acta Didactica Napocensia, 3(1), 75–88. https://eric.ed.gov/?id=EJ1056109
Hoa, A. T., & Dương, P. V. (2024). Vận dụng mô hình 5E trong dạy học chủ đề “Đạo hàm cấp hai” (Toán 11) theo hướng phát triển năng lực giải quyết vấn đề toán học cho học sinh. Tạp chí Giáo dục, 24(20), 30–35. https://tcgd.tapchigiaoduc.edu.vn/index.php/tapchi/article/view/2496
Hung, J. C., & Wang, C.-C. (2021). Exploring the website object layout of responsive web design: results of eye tracking evaluations. The Journal of Supercomputing, 77(1), 343–365. https://doi.org/10.1007/s11227-020-03283-1
Jonan, Y. R. (2020). Pengembangan Rubrik Penskoran pada Asesmen Otentik untuk Materi Volume dan Luas Balok. Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, 4(2), 275. https://doi.org/10.31331/medivesveteran.v4i2.1174
Lamm, K., Lamm, A., & Edgar, D. (2020). Scale Development and Validation: Methodology and Recommendations. Journal of International Agricultural and Extension Education, 27(2), 24–35. https://doi.org/10.5191/jiaee.2020.27224
Leacock, T., & Nesbit, J. (2007). A Framework for Evaluating the Quality of Multimedia Learning Resources. Educational Technology and Society, 10, 44–59. https://www.sfu.ca/~jcnesbit/articles/LeacockNesbit2007.pdf
Nguyễn, H. H., Hoa, A. T., Lê, H. V., & Trịnh, T. L. M. (2023). Phát triển năng lực giải quyết vấn đề toán học cho học sinh lớp 10 khi dạy học chủ đề các hệ thức lượng trong tam giác. Tạp chí Khoa học Trường Đại học Hồng Đức, 63, 39–52. https://vjol.info.vn/index.php/DHHD/article/view/87358
Nguyễn, T. T. T. (2025). Một số biện pháp phát triển năng lực tư duy và lập luận toán học cho học sinh trong dạy học chủ đề “Phân số” (Toán 6). Tạp chí Giáo dục, 25(2), 36–40. https://tcgd.tapchigiaoduc.edu.vn/index.php/tapchi/article/view/2912
Nurhaifa, I., Hamdu, G., & Suryana, Y. (2020). Rubrik Penilaian Kinerja pada Pembelajaran STEM Berbasis Keterampilan 4C. Indonesian Journal of Primary Education, 4(1), 101–110. https://doi.org/10.17509/ijpe.v4i1.24742
Nurtanto, M., Kholifah, N., Masek, A., Sudira, P., & Samsudin, A. (2021). Crucial problems in arranged the lesson plan of vocational teacher. International Journal of Evaluation and Research in Education (IJERE), 10(1), 345. https://doi.org/10.11591/ijere.v10i1.20604
Otgonbaatar, K. (2021). Effectiveness of anchoring vignettes in re-evaluating self-rated social and emotional skills in mathematics. International Journal of Evaluation and Research in Education (IJERE), 10(1), 237. https://doi.org/10.11591/ijere.v10i1.20716
Özer, B., Duran, V., & Tekke, M. (2020). Training of trainers: An action-based research for improving the pedagogical skills of academicians. International Journal of Evaluation and Research in Education (IJERE), 9(3), 704. https://doi.org/10.11591/ijere.v9i3.20327
Palinussa, A. L., Molle, J. S., & Gaspersz, M. (2021). Realistic mathematics education: Mathematical reasoning and communication skills in rural contexts. International Journal of Evaluation and Research in Education (IJERE), 10(2), 522. https://doi.org/10.11591/ijere.v10i2.20640
Phan, A. T. (2014). Đánh giá năng lực giải quyết vấn đề của học sinh trong dạy học toán lớp 11 Trung học phổ thông [Doctor Dissertation]. Trường Đại học Vinh.
Rezaei, A. R., & Lovorn, M. (2010). Reliability and validity of rubrics for assessment through writing. Assessing Writing, 15(1), 18–39. https://doi.org/10.1016/j.asw.2010.01.003
Salazar-Torres, J., Rincón Leal, O., & Vergel Ortega, M. (2021). The rubric as an assessment tool for solving problem situations in the physics and mathematics teaching context. Journal of Physics: Conference Series, 1981(1), 012018. https://doi.org/10.1088/1742-6596/1981/1/012018
Suwarno, S., & Aeni, C. (2021). PENTINGNYA RUBRIK PENILAIAN DALAM PENGUKURAN KEJUJURAN PESERTA DIDIK. Edukasi: Jurnal Pendidikan, 19(1), 161. https://doi.org/10.31571/edukasi.v19i1.2364
The Jamovi Project. (2024). jamovi (2.6). [Computer software] Retrieved from https://www.jamovi.org.
Trần, T. Á. (2008). Một số nguyên tắc điều tra xã hội học. Tạp chí Khoa học Trường Đại học Cần Thơ, 9, 18–27. https://ctujsvn.ctu.edu.vn/index.php/ctujsvn/article/view/533
Võ, X. M., & Tô, Q. L. (2023). Phát triển năng lực giải quyết vấn đề toán học cho học sinh lớp 10 qua dạy học giải bài tập phương trình quy về phương trình bậc hai. Tạp chí Khoa học Trường Đại học Đồng Tháp, 12(6), 3–11. https://doi.org/10.52714/dthu.12.6.2023.1110
Wu, M. L. (2003). The Application of Item Response Theory to Measure Problem-solving Proficiencies [Doctor Dissertation]. The University of Melbourne.
Zulfa, H., Saputro, D. R. S., & Riyadi. (2019). Students’ difficulties in mathematics learning with artisan character type in HOTS trigonometry test. Journal of Physics: Conference Series, 1321(2), 022104. https://doi.org/10.1088/1742-6596/1321/2/022104
Asmana, A. T. (2018). PENGEMBANGAN RUBRIK ANALITIK UNTUK ASESMEN KOMUNIKASI MATEMATIKA TERTULIS DALAM PEMECAHAN MASALAH MATEMATIKA. Jurnal Pembelajaran Matematika, 5(1). https://jurnal.uns.ac.id/jpm/article/view/26028
Bộ Giáo dục và Đào tạo. (2018). Chương trình giáo dục phổ thông môn Toán.
Bryman, A. (2016). Social research methods (Fifth Edition). Oxford University Press.
Bùi, A. K., Võ, T. T. P, Đỗ, T. P. T, & Bùi, P. T. H. (2023). Giáo trình Đánh giá kết quả học tập Toán và Khoa học tự nhiên. NXB Đại học Cần Thơ.
Cahyadi, M. R., Maryanto, B. P. A., Syaifuddin, M., & Darmayanti, R. (2023). Development of Essay Test Assessment Rubric for Polya Theory-Based Mathematical Problem-Solving. JNPM (Jurnal Nasional Pendidikan Matematika), 7(1), 167. https://doi.org/10.33603/jnpm.v7i1.7724
Charles, R. I., Lester, F., & O’Daffer, P. G. (2008). How to evaluate progress in problem solving (8. print). The National Council of Teachers of Mathematics.
Choirudin, C., Degeng, I. N. S., Kuswandi, D., Purnomo, P., & Maba, A. P. (2022). Career readiness among low-income Muslim students. International Journal of Evaluation and Research in Education (IJERE), 11(3), 1400. https://doi.org/10.11591/ijere.v11i3.22727
Cohen, L., Manion, L., & Morrison, K. (2017). Research Methods in Education. Routledge. https://doi.org/10.4324/9781315456539
Darmayanti, R., Sugianto, R., & Muhammad, Y. (2022). Analysis of Students’ Adaptive Reasoning Ability in Solving HOTS Problems Arithmetic Sequences and Series in Terms of Learning Style. Numerical: Jurnal Matematika Dan Pendidikan Matematika, 73–90. https://doi.org/10.25217/numerical.v6i1.2340
Darmayanti, R., Syaifuddin, M., Rizki, N., Sugianto, R., & Hasanah, N. (2022). High school students’ mathematical representation ability: Evaluation of disposition based on mastery learning assessment model (MLAM). Journal of Advanced Sciences and Mathematics Education, 2(1), 1–15. https://doi.org/10.58524/jasme.v2i1.93
Dawson, P. (2017). Assessment rubrics: towards clearer and more replicable design, research and practice. Assessment & Evaluation in Higher Education, 42(3), 347–360. https://doi.org/10.1080/02602938.2015.1111294
DeVellis, R. F. (2017). Scale development: theory and applications (Fourth edition). SAGE.
Gunawardena, E. (2010). A rubric to self-assess and peer-assess mathematical problem solving tasks of college students. Acta Didactica Napocensia, 3(1), 75–88. https://eric.ed.gov/?id=EJ1056109
Hoa, A. T., & Dương, P. V. (2024). Vận dụng mô hình 5E trong dạy học chủ đề “Đạo hàm cấp hai” (Toán 11) theo hướng phát triển năng lực giải quyết vấn đề toán học cho học sinh. Tạp chí Giáo dục, 24(20), 30–35. https://tcgd.tapchigiaoduc.edu.vn/index.php/tapchi/article/view/2496
Hung, J. C., & Wang, C.-C. (2021). Exploring the website object layout of responsive web design: results of eye tracking evaluations. The Journal of Supercomputing, 77(1), 343–365. https://doi.org/10.1007/s11227-020-03283-1
Jonan, Y. R. (2020). Pengembangan Rubrik Penskoran pada Asesmen Otentik untuk Materi Volume dan Luas Balok. Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, 4(2), 275. https://doi.org/10.31331/medivesveteran.v4i2.1174
Lamm, K., Lamm, A., & Edgar, D. (2020). Scale Development and Validation: Methodology and Recommendations. Journal of International Agricultural and Extension Education, 27(2), 24–35. https://doi.org/10.5191/jiaee.2020.27224
Leacock, T., & Nesbit, J. (2007). A Framework for Evaluating the Quality of Multimedia Learning Resources. Educational Technology and Society, 10, 44–59. https://www.sfu.ca/~jcnesbit/articles/LeacockNesbit2007.pdf
Nguyễn, H. H., Hoa, A. T., Lê, H. V., & Trịnh, T. L. M. (2023). Phát triển năng lực giải quyết vấn đề toán học cho học sinh lớp 10 khi dạy học chủ đề các hệ thức lượng trong tam giác. Tạp chí Khoa học Trường Đại học Hồng Đức, 63, 39–52. https://vjol.info.vn/index.php/DHHD/article/view/87358
Nguyễn, T. T. T. (2025). Một số biện pháp phát triển năng lực tư duy và lập luận toán học cho học sinh trong dạy học chủ đề “Phân số” (Toán 6). Tạp chí Giáo dục, 25(2), 36–40. https://tcgd.tapchigiaoduc.edu.vn/index.php/tapchi/article/view/2912
Nurhaifa, I., Hamdu, G., & Suryana, Y. (2020). Rubrik Penilaian Kinerja pada Pembelajaran STEM Berbasis Keterampilan 4C. Indonesian Journal of Primary Education, 4(1), 101–110. https://doi.org/10.17509/ijpe.v4i1.24742
Nurtanto, M., Kholifah, N., Masek, A., Sudira, P., & Samsudin, A. (2021). Crucial problems in arranged the lesson plan of vocational teacher. International Journal of Evaluation and Research in Education (IJERE), 10(1), 345. https://doi.org/10.11591/ijere.v10i1.20604
Otgonbaatar, K. (2021). Effectiveness of anchoring vignettes in re-evaluating self-rated social and emotional skills in mathematics. International Journal of Evaluation and Research in Education (IJERE), 10(1), 237. https://doi.org/10.11591/ijere.v10i1.20716
Özer, B., Duran, V., & Tekke, M. (2020). Training of trainers: An action-based research for improving the pedagogical skills of academicians. International Journal of Evaluation and Research in Education (IJERE), 9(3), 704. https://doi.org/10.11591/ijere.v9i3.20327
Palinussa, A. L., Molle, J. S., & Gaspersz, M. (2021). Realistic mathematics education: Mathematical reasoning and communication skills in rural contexts. International Journal of Evaluation and Research in Education (IJERE), 10(2), 522. https://doi.org/10.11591/ijere.v10i2.20640
Phan, A. T. (2014). Đánh giá năng lực giải quyết vấn đề của học sinh trong dạy học toán lớp 11 Trung học phổ thông [Doctor Dissertation]. Trường Đại học Vinh.
Rezaei, A. R., & Lovorn, M. (2010). Reliability and validity of rubrics for assessment through writing. Assessing Writing, 15(1), 18–39. https://doi.org/10.1016/j.asw.2010.01.003
Salazar-Torres, J., Rincón Leal, O., & Vergel Ortega, M. (2021). The rubric as an assessment tool for solving problem situations in the physics and mathematics teaching context. Journal of Physics: Conference Series, 1981(1), 012018. https://doi.org/10.1088/1742-6596/1981/1/012018
Suwarno, S., & Aeni, C. (2021). PENTINGNYA RUBRIK PENILAIAN DALAM PENGUKURAN KEJUJURAN PESERTA DIDIK. Edukasi: Jurnal Pendidikan, 19(1), 161. https://doi.org/10.31571/edukasi.v19i1.2364
The Jamovi Project. (2024). jamovi (2.6). [Computer software] Retrieved from https://www.jamovi.org.
Trần, T. Á. (2008). Một số nguyên tắc điều tra xã hội học. Tạp chí Khoa học Trường Đại học Cần Thơ, 9, 18–27. https://ctujsvn.ctu.edu.vn/index.php/ctujsvn/article/view/533
Võ, X. M., & Tô, Q. L. (2023). Phát triển năng lực giải quyết vấn đề toán học cho học sinh lớp 10 qua dạy học giải bài tập phương trình quy về phương trình bậc hai. Tạp chí Khoa học Trường Đại học Đồng Tháp, 12(6), 3–11. https://doi.org/10.52714/dthu.12.6.2023.1110
Wu, M. L. (2003). The Application of Item Response Theory to Measure Problem-solving Proficiencies [Doctor Dissertation]. The University of Melbourne.
Zulfa, H., Saputro, D. R. S., & Riyadi. (2019). Students’ difficulties in mathematics learning with artisan character type in HOTS trigonometry test. Journal of Physics: Conference Series, 1321(2), 022104. https://doi.org/10.1088/1742-6596/1321/2/022104
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