Identifying Student Errors Using Newman's Error Analysis in the Teaching Through Problem-Solving (TTP) Approach
Main Article Content
Abstract
This study identifies the specific mathematical errors committed by learners exposed to the Teaching Through Problem-Solving (TTP) approach. While TTP is an active learning method that fosters deep understanding by presenting problems before formal solutions , there is a scarcity of research investigating how student errors manifest within this specific instructional model. Using Newman’s Error Analysis (NEA), the researcher analyzed the written solutions of 32 Grade 7 students at Mindanao State University-Iligan Institute of Technology College of Education-Integrated Developmental School to categorize hurdles into five stages: reading, comprehension, transformation, process skills, and encoding. The findings reveal that Comprehending Error was the most frequent challenge in Problem 1 (34.375%), while Encoding Error emerged as the primary obstacle in Problem 2 (34.375%). These results suggest that while students generally possess strong fundamental literacy, they struggle with moving from literacy to mathematical interpretation and providing narrative closure to their solutions. By pinpointing these exact stages of failure, educators can develop targeted scaffolding and instructional strategies to address the root causes of student difficulties in student-centered environments.
Article Details

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
Acquandoh, E., Zunurain, Z., Kwakye, D. O., & Adornyo, S. R. (2022). Effects of teaching students through problem-solving on students’ academic performance in problem-solving. Jurnal Gantang, 7(2), 121-127. https://doi.org/10.31629/jg.v7i2.5314
Ahdhianto, E., Marsigit, Haryanto, and Nurfauzi, Y. (2020).Improving Fifth-Grade Students' Mathematical Problem-Solving and Critical Thinking Skills Using Problem-Based Learning.Universal Journal of Educational Research 8(5).https://doi.org/10.13189/ujer.2020.080539
Ahzan, Z. N., Simarmata, J. E., & Mone, F. (2022). Using newman error analysis to detect students’ error in solving junior high school mathematics problem. Jurnal Pendidikan MIPA, 23(2), 459-473. https://doi.org/10.23960/jpmipa/v23i2.pp459-473
Alhassora, N., Abu, M., and Abdullah, A. (2017). Newman Error Analysis on Evaluating and Creating Thinking Skills. Serials Publication. Man in India. 97(19): 413-427. https://www.researchgate.net/publication/322062647_NEWMAN_ERROR_ANALYSIS_ON_EVALUATING_AND_CREATING_THINKING_SKILLS
Ali, R., Hukamdad, D., Akhter, A., & Khan, A. (2010). Effect of using problem solving method in teaching mathematics on the achievement of mathematics students. Asian Social Science, 6(2). https://doi.org/10.5539/ass.v6n2p67
Anhalt, C. O., Cortez, R., & Bennett, A. B. (2018). The Emergence of Mathematical Modeling Competencies: An investigation of prospective secondary mathematics teachers. Mathematical Thinking and Learning, 20(3), 202–221. https://doi.org/10.1080/10986065.2018.1474532
Astriani, N., Surya, E., and Syahputra, E. (2017). The Effect of Problem Based Learning to Students’ Mathematical Problem Solving Ability. IJARIIE-ISSN(O)-2395-4396. Vol-3 Issue-2 2017. https://www.researchgate.net/publication/318562413_THE_EFFECT_OF_PROBLEM_BASED_LEARNING_TO_STUDENTS'_MATHEMATICAL_PROBLEM_SOLVING_ABILITY
Bacus, M. R. J. & Guillena, J. B. (2023). Singapore mathematics approach in aiding the modular print distance learning modality in teaching mathematics. International Journal of Trends in Mathematics Education Research, 6(3), 290-297. https://doi.org/10.33122/ijtmer.v6i3.212
Baitokayeva, L. (n.d.). How to develop Grade 7 learners' research skills by using a story-based learning approach in English lessons? Camtree Digital Library. https://hdl.handle.net/20.500.14069/742
Bibi, R., Rauf, M., & Ahmad, N. (2022). Learner’s strategies for heuristic ability in mathematics at the secondary level in Khyber Pakhtunkhwa, Pakistan. Journal of Humanities Social and Management Sciences (Jhsms), 3(2), 76-87. https://doi.org/10.47264/idea.jhsms/3.2.5
Biccard, P. (2024). Productive Struggle in Mathematical Modelling. The Mathematics Enthusiast: Vol. 21 : No. 1 , Article 8. https://doi.org/10.54870/1551-3440.1620
Bjørkvold T, Blikstad-Balas M.(2018). Students as researchers: What and why seventh-grade students choose to write when investigating their own research question. Sci Educ.102(2):304-341. doi: 10.1002/sce.21324. Epub 2017 Dec 19. PMID: 29540938; PMCID: PMC5839246.
Boonen, A. J. H., de Koning, B. B., Jolles, J., & Van der Schoot, M. (2016). Word problem solving in contemporary math education: A plea for reading comprehension skills training. Frontiers in Psychology, 7, Article 191. https://doi.org/10.3389/fpsyg.2016.00191
Castillo, D., Carrión, J., Chamba, C., Jiménez-Gaona, Y., Rodríguez-Álvarez, M.J., & Lakshminarayanan, V. (2025). Didactic strategies for conceptual understanding and motivation in university mathematics: a systematic review. Front. Educ. 10:1536470. https://doi.org/10.3389/feduc.2025.1536470
Cuong, L. M., Tien-Trung, N., Ngu, P. N. H., Vangchia, V., Thao, N. P., & Tho, T. T. P. (2025). Mathematics problem-solving research in high school education: Trends and insights from the Scopus database (19832023). European Journal of Science and Mathematics Education. https://doi.org/10.30935/scimath/16038
Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H.-C. (2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6, Article 348. https://doi.org/10.3389/fpsyg.2015.00348
Dubinsky, J. M. & Hamid, A. A. (2024). The neuroscience of active learning and direct instruction. Neuroscience & Biobehavioral Reviews. Volume 163. https://doi.org/10.1016/j.neubiorev.2024.105737
Ekasari, A. & Putra, D. J. (2024). Error Analysis of Learners’ Problem-Solving Abilities in Mathematics Courses: A Newman Error Analysis (NEA) Approach. Journal of science education. 12(1). DOI: http://dx.doi.org/10.17977/jps.v12i12024p044
Eriksson, K., Helenius, O. & Ryve, A. (2019). Using TIMSS items to evaluate the effectiveness of different instructional practices. Instr Sci 47, 1–18. https://doi.org/10.1007/s11251-018-9473-1
Evans, T. & Dietrich, H. (2022). Inquiry-Based Mathematics Education: a call for reform in tertiary education seems unjustified. arXiv. Cornell University. https://doi.org/10.48550/arXiv.2206.12149
Fererde, A. T., Mirhka, A. A., Ayele, M. A., & Arara, A. A. (2024). Enhancing Students’ Conceptual Understanding and Problem-Solving Skills in Learning Trigonometry Through Contextual-Based Mathematical Modeling Instruction. International Journal of Secondary Education. 12(4). https://doi.org/10.11648/j.ijsedu.20241204.15
Gilmore, C., Keeble, S., Richardson, S., & Cragg, L. (2017). The Interaction of Procedural Skill, Conceptual Understanding and Working Memory in Early Mathematics Achievement. Journal of Numerical Cognition, 3(2), Article e5745. https://doi.org/10.5964/jnc.v3i2.51
Hadiyanti, Y. R. & Manurung, M. M. H. (2025). A Qualitative Analysis of Students’’ Errors in Fraction Word Problems Based on Polyas Stages of Problem Solving: Evidence from Papua, Indonesia. Edumatica : Jurnal Pendidikan Matematika. https://doi.org/10.22437/edumatica.v15i2.43746
Haerani, A., Novianingsih, K., & Turmudi, T. (2021). Analysis of Students' Errors in Solving Word Problems Viewed from Mathematical Resilience. Jtam (Jurnal Teori Dan Aplikasi Matematika), 5(1), 246. https://doi.org/10.31764/jtam.v5i1.3928
Hariri, D. D., & Kania, N. (2025). Mapping Critical Thinking Skills through Newman’s Error Analysis in Secondary Students’ Problem-Solving. Jurnal Pendidikan MIPA, 26(3), 1464-1478. https://doi.org/10.23960/jpmipa.v26i3.pp1464-1478
Hasibuan, A. M., Saragih, S., & Amry, Z. (2018). Development of learning materials based on realistic mathematics education to improve problem solving ability and student learning independence. International Electronic Journal of Mathematics Education, 14(1). https://doi.org/10.29333/iejme/4000
Hiroshi, S. & Hiroshi, I. (2025). Teaching through Problem-Solving in Japan: A Study on the Hokkaido University of Education's Attached School. Journal of Hokkaido University of Education. https://doi.org/10.32150/0002000741. https://hokkyodai.repo.nii.ac.jp/record/2000741/files/kyoikurinsyokenkyu_77_17.pdf
Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C. A. (2007). Scaffolding and Achievement in Problem-Based and Inquiry Learning: A Response to Kirschner, Sweller, and Clark (2006) . Educational Psychologist, 42(2), 99–107. https://doi.org/10.1080/00461520701263368
Hourigan, M., Leavy, A.M. Elementary teachers’ experience of engaging with Teaching Through Problem Solving using Lesson Study. Math Ed Res J 35, 901–927 (2022). https://doi.org/10.1007/s13394-022-00418-w
Irianti, N. P., Barr, F. D., Nurasiah, L., & Irsal, N. A. (2024). Error Analysis in Solving Applied Mathematics Problems based on the Newman Procedure. Inteligensi: Jurnal Ilmu Pendidikan, 7(1), 110-117. https://doi.org/10.33366/ilg.v7i1.5883
Johnsen, M.M.W., Sjølie, E. & Johansen, V. (2024). Learning to Collaborate in a Project-based Graduate Course: A Multilevel Study of Student Outcomes. Research Higher Education 65, 439–462. https://doi.org/10.1007/s11162-023-09754-7
Jonsson, B., Norqvist, M., Liljekvist, Y., & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. The Journal of Mathematical Behavior, Volume 36, 20-32, ISSN 0732-3123, https://doi.org/10.1016/j.jmathb.2014.08.003.
Kabael, T. & Baran, A. A. (2023). An investigation of mathematics teachers' conceptions of mathematical literacy related to participation in a web-based pisa course. Bartın Üniversitesi Eğitim Fakültesi Dergisi, 12(2), 315-324. https://doi.org/10.14686/buefad.1053557
Kadijevich, D.M., Stephens, M., Solares-Rojas, A., Guberman, R. (2023). Impacts of TIMSS and PISA on Mathematics Curriculum Reforms. In: Shimizu, Y., Vithal, R. (eds) Mathematics Curriculum Reforms Around the World. New ICMI Study Series. Springer, Cham. https://doi.org/10.1007/978-3-031-13548-4_22
Kaitera, S. & Harmoinen, S. (2022). Developing mathematical problem-solving skills in primary school by using visual representations on heuristics. LUMAT: International Journal on Math, Science and Technology Education, 10(2). https://doi.org/10.31129/lumat.10.2.1696
Legarde, M.A. (2022). Students’ Common Errors in Solving Routine & Non-Routine Problems: A Mixed Method Analysis. International Journal of Multidisciplinary Research and Analysis.5(2). https://doi.org/10.47191/ijmra/v5-i2-42
Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem Solving in Mathematics Education. ICME-13 Topical Surveys. Springer, Cham. https://doi.org/10.1007/978-3-319-40730-2_1
Mardiyana, M. (2017). Errors analysis of problem solving using the Newman stage after applying cooperative learning of TTW type. In AIP Conference Proceedings (Vol. 1913, No. 1). AIP Publishing. https://doi.org/10.1063/1.5016662
Mariawan, I. M. and Parwati, N. N. (2018). Types of junior high school students errors in science problem solving. Journal of Physics Conference Series, 1040, 012039. https://doi.org/10.1088/1742-6596/1040/1/012039
Mora, F. B. & Reyes-Rodriguez, A. (2019). Fostering Middle School Students’ Number Sense through Contextualized Tasks. International Electronic Journal of Elementary Education. https://doi.org/10.26822/iejee.2019155339
Mugabi, T. (2024). Advantages and Disadvantages of Homogenous vs. Heterogenous Groups in Education. HMH Education Company. https://www.hmhco.com/blog/advantages-disadvantages-of-homogeneous-vs-heterogeneous-groups-in-education
Mukminah, M., & Riana, R. (2020). Analisis Kesalahan Newman (Newman Error Analysis-Nea): Perbandingan Ketelitian Antara Siswa Yang Menghafal Dan Tidak Menghafal Alqur’an. JIKAP PGSD: Jurnal Ilmiah Ilmu Kependidikan, 4(1), 46. https://doi.org/10.26858/jkp.v4i1.12045
Mulyana, D., Nurjanah, E., & Lestari, W. D. (2022). The Error Analysis Of Junior High School Students Based On Newman Procedure In Solving Numeration Problems Reviewing From Independent Learning. Venn: Journal of Sustainable Innovation on Education, Mathematics and Natural Sciences, 1(1), 21-30. https://doi.org/10.53696/2964-867X.58
Nguyen, H.A., Guo, Y., Stamper, J., McLaren, B.M. (2020). Improving Students’ Problem-Solving Flexibility in Non-routine Mathematics. In: Bittencourt, I., Cukurova, M., Muldner, K., Luckin, R., Millán, E. (eds) Artificial Intelligence in Education. AIED. Lecture Notes in Computer Science(), vol 12164. Springer, Cham. https://doi.org/10.1007/978-3-030-52240-7_74
Nilimaa, J. (2023). New Examination Approach for Real-World Creativity and Problem-Solving Skills in Mathematics. Trends in Higher Education. https://doi.org/10.3390/higheredu2030028
Nisa, K., Nasrullah, A., Hidayat, A., Mahuda, I., & Bhat, I. (2023). Problem-Based Learning in Improving Problem-Solving Ability and Interest in Learning Mathematics: An Empirical Study. International Journal of Mathematics and MathematicsEducation. https://doi.org/10.56855/ijmme.v1i3.725
Noutsara, S., Neunjhem, T., & Chemrutsame, W. (2021). Mistakes in mathematics problems solving based on Newman's error analysis on set materials. Journal La Edusci, 2(1), 20-27. https://doi.org/10.37899/journallaedusci.v2i1.367
O’Dwyer, L. M., Wang, Y., & Shields, K. A. (2015). Teaching for Conceptual Understanding: A Cross National Comparison of the Relationship between Teachers Instructional Practices and Student Achievement in Mathematics. Large-scale Assessments in Education: A SpingerOpen Journal. https://doi.org/10.1186/s40536-014-0011-6
Orosco, M. J., Swanson, H. L., O’Connor, R. E., & Lussier, C. (2011). The Effects of Dynamic Strategic Math on English Language Learners’ Word Problem Solving. The Journal of Special Education, 47(2), 96-107. https://doi.org/10.1177/0022466911416248
Palupi, E. L. W., Sumarto, S. N., & Purbaningrum, M. (2022). Senior high school students’ understanding of mathematical inequality. Jurnal Elemen, 8(1), 201-215. https://doi.org/10.29408/jel.v8i1.4537
Patac, L. P., & Patac Jr., A. V. (2015). An Application of Student Self- Assessment and Newman Error Analysis in Solving Math Problems. Recoletos Multidisciplinary Research Journal, 3(1). https://doi.org/10.32871/rmrj1503.01.17
Payung, Z., Kusumah, Y., Mulyaning, E. C., & Avip, B. (2025). Application of Newmans Error Analysis to Identify Students Errors in Solving Fraction Problems. Journal of innovative mathematics learning. https://doi.org/10.22460/jiml.v8i2.27320
Pongsakdi, N., Kajamies, A., Veermans, K., Lertola, K., Vauras, M., & Lehtinen, E. (2020). What makes mathematical word problem solving challenging? Exploring the roles of word problem characteristics, text comprehension, and arithmetic skills. ZDM Mathematics Education 52, 33–44. https://doi.org/10.1007/s11858-019-01118-9
Prameshti, N. L., Darmawan, P., & Dejarlo, J. O. (2024). Analysis of students' errors in solving statistics problems based on Newman's Error theory: a study on high school students. Polyhedron International Journal in Mathematics Education, 2(2), 56-63.https://doi.org/10.59965/pijme.v2i2.150
Reddington, C. and Canada, R. (2006). How does student participation influence student achievement? New York University. The Steinhardt School of Culture, Education, and Human Development. https://steinhardt.nyu.edu/departments/teaching-and-learning/research/practitioner-action-research/how-does-student
Roorda, G., Vries, S. D., & Smale-Jacobse, A. E. (2024). Using lesson study to help mathematics teachers enhance students problem-solving skills with teaching through problem solving. Frontiers in Education. https://doi.org/10.3389/feduc.2024.1331674
Safrina, Y., Ikhsan, M. H., & Zubainur, C. M. (2022). Improving student geometry problem-solving skills through spatial training. Advances in Social Science, Education and Humanities Research. https://doi.org/10.2991/assehr.k.211229.005
Saleh, K., Yuwono, I., As’ari, A. R., & Sa’dijah, C. (2017). Errors analysis solving problems analogies by Newman procedure using analogical reasoning. International journal of humanities and social sciences, 9(1), 17-26. https://ijhss.net/index.php/ijhss/article/view/253
Sambo, T. F. & Makgakga, T. P. (2024). Applying Problem Solving Approach in Teaching Addition and Subtraction Word Problems in Diverse Grade 3 Classrooms. Research in Social Sciences and Technology, 9(1), 31-46. https://doi.org/10.46303/ressat.2024.1
Schulz, A. (2024). Assessing student teachers’ procedural fluency and strategic competence in operating and mathematizing with natural and rational numbers. J Math Teacher Educ 27, 981–1008. https://doi.org/10.1007/s10857-023-09590-7
Setiawan, H., Handican, R., & Rurisman, R. (2023). Revolutionizing math education: unleashing the potential of web-based learning media for enhanced mathematical problem solving skills. JDIME : Journal of Development and Innovation in Mathematics Education, 1(2), 01-11. https://doi.org/10.32939/jdime.v1i2.2978
Sionicio, J. And Barbacena, L. (2021). Effects of Teaching through Problem-Solving(TtPS) on Students’ Metacognition and Academic Performance. BU R&D Journal. 24(2): 66-76. https://doi.org/10.47789/burdj.mbtcbbgs.20212402.06
Siskawati, E., Zaenuri, & Wardono. (2021). Analysis of students’ error in solving math problem-solving problem based on Newman Error Analysis (NEA). In Journal of Physics: Conference Series (Vol. 1918, No. 4, p. 042108). IOP Publishing. https://doi.org/10.1088/1742-6596/1918/4/042108
Ofori, E. and Johnson, A. (2025). Empowering Students in Online Learning: The Benefits of Student-Chosen Groups vs. Instructor-Assigned Groups. OLC Accelerate 2025. Accelerating Online Learning Worldwide. https://olc.secure-platform.com/accelerate2025/gallery/rounds/82045/details/22300
Omer, S.M., Evers, K., Wang, CY., & Chen, S. (2025). Technology-enhanced mathematics learning: review of the interactions between technological attributes and aspects of mathematics education from 2013 to 2022. Humanit Soc Sci Commun 12, 1079. https://doi.org/10.1057/s41599-025-05475-7
Susanti, E. (2025). Enhancing Problem-Solving Skills in Elementary Students Through Realistic Mathematics Education. SCIENCE : Jurnal Inovasi Pendidikan Matematika dan IPA. https://doi.org/10.51878/science.v5i1.4344
Syafri, F. S., Isran, D., & Nurhikma, _. (2021). The relationship between mathematical problem-solving ability, mathematical connection ability, and ability to read the qur’an. Advances in Social Science, Education and Humanities Research. https://doi.org/10.2991/assehr.k.210227.033
Syawali, D. S., & Mulyawati, I. (2024). Analysis of Students' Errors in Solving Plane Geometry Word Problems Based on Newman's Error Analysis (NEA) Method. Prima: Jurnal Pendidikan Matematika, 8(2), 374. https://doi.org/10.31000/prima.v8i2.11199
Takahashi, A., Lewis, C. and Perry, R. (2013). A US lesson study network to spread teaching through problem solving. International Journal for Lesson and Learning Studies, Vol. 2 No. 3, pp. 237-255. https://doi.org/10.1108/IJLLS-05-2013-0029
Triliana, T., & Asih, E. C. M. (2019). Analysis of students’ errors in solving probability based on Newman’s error analysis. Journal of Physics: Conference Series, 1211, 012061. https://doi.org/10.1088/1742-6596/1211/1/012061
Utami, A. D. (2016). Tipe Kesalahan Mahasiswa Dalam Menyelesaikan Soal-soal Geometri Berdasar Newman's Error Analysis (NEA). JIPM (Jurnal Ilmiah Pendidikan Matematika), 4(2), 85. https://doi.org/10.25273/jipm.v4i2.842
Vidad, D. C., & Quimbo, M. A. T.. (2021). Students’ Problem-solving Difficulties and Coping Strategies in Mathematics: A Model-Building Study. International Journal of Learning, Teaching and Educational Research. https://doi.org/10.26803/ijlter.20.9.9
Weimer, M. (2011). 10 Benefits of Getting Students to Participate in Classroom Discussions. Faculty Focus. https://www.facultyfocus.com/articles/teaching-and-learning/10-benefits-of-getting-students-to-participate-in-classroom-discussions/
Zhu, H. (2023). Transforming Mathematics Education: Fostering Critical Thinkers. Advances in Social Science, Education, and Humanities Research. https://doi.org/10.2991/978-2-38476-158-6_16