Mathematical Critical Thinking Ability of Dyscalculia Students: Analysis of HOTS Problem Solving



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© 2026 Nur Afifah, Ayu Faradillah

Critical thinking (CT) skills in mathematics are essential for solving problems involving High Order Thinking Skills (HOTS), although students with dyscalculia often experience difficulties in this process. This study was conducted to analyze the mathematical CT skills of students with dyscalculia in solving HOTS problems by gender using a qualitative method. This study involved male and female students with dyscalculia. Data were collected through a dyscalculia identification instrument, a HOTS-based CT test, and interviews. The analysis of mathematical CT skills was aligned with four indicators: interpretation, analysis, evaluation, and inference. The findings show differences in students’ mathematical CT skills based on gender. Female students demonstrated competence across all four indicators of CT. The results show V1 (dyscalculia female students) is capable of accurately interpreting problem statements, analyzing relevant information, evaluating appropriate strategies, and drawing correct conclusions. In contrast, V2 (dyscalculia male students) experiences difficulties, particularly in interpreting problems and determining appropriate solution strategies, which in turn affects their overall problem-solving ability. These results suggest that gender may play a role in how students with dyscalculia approach and solve mathematical problems. Therefore, mathematics instruction must consider the unique characteristics of students with dyscalculia as well as gender differences to better support the development of CT skills. The integration of HOTS-based learning activities tailored to students’ needs is highly recommended to create a more inclusive and effective learning environment.

 

Keywords: mathematical critical thinking, dyscalculia, problem solving, higher-order thinking skills, gender.

Afifah, N., Pebrianti, T., Faradillah, A., & Ulfah, S. (2026). Development and validation of mathematical critical thinking test using rasch measurement model. International Journal of Evaluation and Research in Education. https://doi.org/10.33365/jm.v8i1.875

Agusfianuddin, A., Herman, T., & Turmudi, T. (2024). Difficulties in mathematical language and representation among elementary school students when solving word problems. Jurnal Elemen, 10(3), 567–581.

Agusman, A., Purwanto, P., & Rahardi, R. (2025a). An exploration of critical thinking stages of junior high school students in solving contradictory mathematical problems. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 10(3), 200–217.

Agustin, N. D., Sumantri, M. S., & Marini, A. (2024). How can we better comprehend the disposition of elementary school students towards advanced mathematical thinking?. Journal of Education Research and Evaluation, 8(2), 231–239.

Akpur, U. (2020). Critical, reflective, creative thinking and their reflections on academic achievement. Thinking Skills and Creativity, 37, 100683.

Alhazmi, A. A., & Kaufmann, A. (2022). Phenomenological qualitative methods applied to the analysis of cross-cultural experience in novel educational social contexts. Frontiers in psychology, 13, 785134.

Ario, M., Suhendra, Jupri, A., & Nurlaelah, E. (2025). Students’ errors and learning obstacles in solving algebraic word problems: hermeneutic phenomenology. Education Sciences, 15(12), 1674.

Azhari, B., Johar, R., Ramadhani, E., Mailizar, M., & Safrina, K. (2024). Mathematics learning model for children with dyscalculia through special intervention. Jurnal Ilmiah Peuradeun, 12(3), 1155-1184.

Bara, E., Berdica, B., & Bara, G. (2025). The role of critical thinking in enhancing student learning and problem solving for 21st century challenges. International Journal of Social Sciences & Humanities (IJSSH), 10(1), 37-48.

Bartholomew, T. T., Joy, E. E., Kang, E., & Brown, J. (2021). A choir or cacophony? Sample sizes and quality of conveying participants’ voices in phenomenological research. Methodological Innovations, 14(2), 20597991211040063.

Benavides-Varela, S., Callegher, C. Z., Fagiolini, B., Leo, I., Altoè, G., & Lucangeli, D. (2020). Effectiveness of digital-based interventions for children with mathematical learning difficulties: A meta-analysis. Computers & Education, 157, 103953.

Bilhaki, R. R., & Faradillah, A. (2025). Mathematical anxiety and resilience as an influence of mathematical literacy skills. Prisma Sains: Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram, 13(3), 430–448.

Braun, V., & Clarke, V. (2021). To saturate or not to saturate? Questioning data saturation as a useful concept for thematic analysis and sample-size rationales. Qualitative research in sport, exercise and health, 13(2), 201–216.

Busetto, L., Wick, W., & Gumbinger, C. (2020). How to use and assess qualitative research methods. Neurological Research and practice, 2(1), 14.

Campbell, R., Goodman-Williams, R., Feeney, H., & Fehler-Cabral, G. (2020). Assessing triangulation across methodologies, methods, and stakeholder groups: The joys, woes, and politics of interpreting convergent and divergent data. American Journal of Evaluation, 41(1), 125–144.

Cárdenas, S. Y., Silva-Pereyra, J., Prieto-Corona, B., Castro-Chavira, S. A., & Fernández, T. (2021). Arithmetic processing in children with dyscalculia: an event-related potential study. PeerJ, 9, e10489.

Cheetham, L. J. (2024). “Because people don’t know what it is, they don’t really know it exists”: a qualitative study of postgraduate medical educators’ perceptions of dyscalculia. BMC Medical Education, 24(1), 896.

Chirove, M., & Ogbonnaya, U. I. (2021). The relationship between grade 11 learners’ procedural and conceptual knowledge of algebra.

Comstock, G., & Grühn, D. (2026). Assessing critical thinking about argumentative essays: the Critical Reasoning and Inference Test (CRIT). Assessment & Evaluation in Higher Education, 1–14.

Crişan, D. R., Tendeiro, J. N., & Meijer, R. R. (2020). On the practical consequences of misfit in Mokken scaling. Applied Psychological Measurement, 44(6), 482–496.

Dabaghi, S., Esmaielzadeh, F., & Rohani, C. (2020). Application of Rasch analysis for development and psychometric properties of adolescents’ quality of life instruments: A systematic review. Adolescent health, medicine and therapeutics, 173–197.

Deonovic, B., Bolsinova, M., Bechger, T., & Maris, G. (2020). A Rasch model and rating system for continuous responses collected in large-scale learning systems. Frontiers in psychology, 11, 500039.

Diana, N., Agustinasari, A., Khatimah, H., Ibnusaputra, M., Adiansha, A. A., & Muslim, M. (2025). HOTS geometry analysis on critical thinking and numeracy skills reviewed learning style and gender. Edumatica: Jurnal Pendidikan Matematika, 15(2), 245–264.

Dotan, D., & Zviran-Ginat, S. (2022). Elementary math in elementary school: The effect of interference on learning the multiplication table. Cognitive Research: Principles and Implications, 7(1), 101.

Draucker, C. B., Rawl, S. M., Vode, E., & Carter-Harris, L. (2020). Integration through connecting in explanatory sequential mixed method studies. Western Journal of Nursing Research, 42(12), 1137–1147.

Fadilla, A. R., Kamid, K., & Rohati, R. (2025). Analyzing the thinking trajectory of students with dyscalculia in solving spatial mathematical problems. Journal of General Education and Humanities, 4(2), 589–604.

Faiziyah, N., & Priyambodho, B. L. (2022). Analisis kemampuan berpikir kritis dalam menyelesaikan soal HOTS ditinjau dari metakognisi siswa [Analysis of critical thinking skills in solving HOTS questions viewed from the perspective of student metacognition]. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 2823-2835.

Faradillah, A., & Fadhilah, Y. H. R. (2021). Mathematical problem-solving on slow learners based on their mathematical resilience. Jurnal Elemen, 7(2), 351–365.

Faradillah, A., & Humaira, T. (2021). Students’ Critical thinking skills on algebraic problems through mathematical resilience. JPI (Jurnal Pendidikan Indonesia), 11(2), 317–327.

Faradillah, A., & Septiana, C. (2022). Mathematical resilience: validity and reliability with rasch model and SPSS in senior high school. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 3545–3555.

Farquhar, J., Michels, N., & Robson, J. (2020). Triangulation in industrial qualitative case study research: Widening the scope. Industrial Marketing Management, 87, 160–170.

Fischer, L., Rohm, T., Carstensen, C. H., & Gnambs, T. (2021). Linking of Rasch-scaled tests: Consequences of limited item pools and model misfit. Frontiers in psychology, 12, 633896.

Flake, J. K., & Fried, E. I. (2020). Measurement schmeasurement: Questionable measurement practices and how to avoid them. Advances in methods and practices in psychological science, 3(4), 456–465.

Fridberg, H., Wallin, L., Wallengren, C., Kottorp, A., Forsman, H., & Tistad, M. (2020). Development and evaluation of the measurement properties of a generic questionnaire measuring patient perceptions of person-centred care. BMC Health Services Research, 20(1), 960.

Gökçe, S., & Güner, P. (2024). Pathways from cognitive flexibility to academic achievement: mediating roles of critical thinking disposition and mathematics anxiety. Current Psychology, 43(20), 18192–18206.

Grant, J. G., Siegel, L. S., & D'Angiulli, A. (2020). From schools to scans: A neuroeducational approach to comorbid math and reading disabilities. Frontiers in Public Health, 8, 469.

Harahap, P. A., Dewi, R. A., & Purniati, T. (2025). Analyzing the mathematical critical thinking skills of high school students in arithmetic: a gender differences. Jurnal Pendidikan Progresif, 15(2), 1142–1156.

Hartawan, I. G. N. Y., Pujawan, I. G. N., & Wibawa, N. A. (2026). An exploration of teachers' perspectives on computational thinking in mathematics learning. Indonesian Journal of Educational Development (IJED), 6(4), 1173–1188.

Hennink, M., & Kaiser, B. N. (2022). Sample sizes for saturation in qualitative research: A systematic review of empirical tests. Social science & medicine, 292, 114523.

Hope, D., Kluth, D., Homer, M., Dewar, A., Goddard-Fuller, R., Jaap, A., & Cameron, H. (2025). Exploring the use of Rasch modelling in “common content” items for multi-site and multi-year assessment. Advances in Health Sciences Education, 30(2), 427–438.

Indu, P. V., Vidhukumar, K., Chacko, D., Menon, V., Grover, S., & Gupta, S. (2025). Criterion validity, construct validity, and factor analysis: An introductory overview. Indian Journal of Psychiatry, 67(9), 916–921.

Jacques, Q., Donnan, J., Bishop, L., Howells, R., Gao, Z., & Najafizada, M. (2025). Development of a cannabis health literacy questionnaire: preliminary validation using the Rasch model. BMC Public Health, 25(1), 2539.

Janis, I., Alias, M., Zulkipli, M., & Muhammad-Sukki, F. (2020). Using illustrations to make decisions on the most appropriate qualitative research methodology: The Industry 4.0 scenario. International journal of qualitative methods, 19, 1609406920907247.

Karim, K., & Normaya, N. (2015). Kemampuan berpikir kritis siswa dalam pembelajaran dalam pembelajaran matematika dengan menggunakan model Jucama di sekolah menengah pertama [Students' critical thinking skills in learning mathematics using the Jucama model in junior high schools]. EDU-MAT: Jurnal Pendidikan Matematika, 3(1), 92–104.

Khotimah, S. N., & Wulandari, T. S. H. (2025). Implementation of Problem Based Learning (PBL) Learning Model to Improve Mathematical Critical Thinking Skills and Learning Motivation of Grade 5 Students at UPT SD Negeri Kutorejo 3 Tuban. Indonesian Journal of Education and Mathematical Science, 6(2), 85–90.

Kim, H. (2020). Effects of rating criteria order on the halo effect in L2 writing assessment: a many-facet Rasch measurement analysis. Language Testing in Asia, 10(1), 16.

Klein, E., & Knops, A. (2023). The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia. Journal of Neural Transmission, 130(3), 253–268.

Kohar, A. W., Rahaju, E. B., Fardah, D. K., & Hanifah, U. (2024). Assessing student teachers’ ability in posing mathematical reasoning problems. Center for Educational Policy Studies Journal, 14(2), 9–37.

Köhler, C., Robitzsch, A., & Hartig, J. (2020). A bias-corrected RMSD item fit statistic: An evaluation and comparison to alternatives. Journal of Educational and Behavioral Statistics, 45(3), 251–273.

Kohn, J., Rauscher, L., Kucian, K., Käser, T., Wyschkon, A., Esser, G., & von Aster, M. (2020). Efficacy of a computer-based learning program in children with developmental dyscalculia. What influences individual responsiveness?. Frontiers in psychology, 11, 505087.

Kusmaharti, D., Yustitia, V., Faizah, H., Rohimah, S. M., & Faridah, L. (2025). Critical Thinking Processes in Numeracy Tasks among Primary School Students with High Mathematics Anxiety. Tadris: Jurnal Keguruan dan Ilmu Tarbiyah, 10(2), 571-582.

Lena, M. S., & Nikolov, M. (2025). The roles of teachers and contextual and motivational factors in young learners’ motivation: a structural equation modelling (SEM) approach. Education Sciences, 15(10), 1388.

Lim, W. M. (2025). What is qualitative research? An overview and guidelines. Australasian Marketing Journal, 33(2), 199–229.

Love, B., Vetere, A., & Davis, P. (2020). Should interpretative phenomenological analysis (IPA) be used with focus groups? Navigating the bumpy road of “iterative loops,” idiographic journeys, and “phenomenological bridges”. International Journal of Qualitative Methods, 19, 1609406920921600.

Marnı, S., Alıman, M., & Harsıatı, T. (2020). Students’ critical thinking skills based on gender and knowledge group. Journal of Turkish Science Education, 17(4), 544–560.

Martins, L. G., & Martinho, M. H. (2021). Estratégias, dificuldades e comunicação escrita na resolução de um problema matemático. Bolema: Boletim de Educação Matemática (70), 903–936.

May, J., Redding, E., Whatley, S., Łucznik, K., Clements, L., Weber, R., ... & Reed, S. (2020). Enhancing creativity by training metacognitive skills in mental imagery. Thinking Skills and creativity, 38, 100739.

Mitani, H. (2021). Test score gaps in higher order thinking skills: Exploring instructional practices to improve the skills and narrow the gaps. AERA Open, 7, 23328584211016470.

Mohammed, S. G. A., Kadah, S. M. S., Khattab, A. N., & ElNeshwey, H. M. (2024). Exploring the relationship between dyscalculia and working memory in Egyptian children. The Egyptian Journal of Otolaryngology, 40(1), 163.

Mokkink, L. B., Boers, M., Van Der Vleuten, C. P. M., Bouter, L. M., Alonso, J., Patrick, D. L., ... & Terwee, C. B. (2020). COSMIN Risk of Bias tool to assess the quality of studies on reliability or measurement error of outcome measurement instruments: a Delphi study. BMC Medical Research Methodology, 20(1), 293.

Mokkink, L. B., Herbelet, S., Tuinman, P. R., & Terwee, C. B. (2025). Content validity: judging the relevance, comprehensiveness, and comprehensibility of an outcome measurement instrument–a COSMIN perspective. Journal of Clinical Epidemiology, 185, 111879.

Muharani, D. R., & Sucipto, L. (2023). The effect of self-efficacy and math anxiety on students’ non-routine mathematics problem solving ability. IJECA International Journal of Education & Curriculum Application.

Muhtarom, M., Shodiqin, A., & Astriani, N. (2020). Exploring senior high school student's abilities in mathematical problem posing. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 69–79.

Nurmaliza, N., Dahlia, A., Nufus, H., & Nurdin, E. (2022). Analysis of mathematical critical thinking ability viewed from habits of mind. Jurnal Pendidikan MIPA, 23(3), 904–917.

Onoshakpokaiye, O. E., & Eyetan, V. (2026). Exploring anxiety levels in mathematics and gender dispositions among students in secondary school. Indonesian Journal of Education and Mathematical Science, 7(1), 17–28.

Padgett, R. N., & Morgan, G. B. (2020). Using the eRm package for Rasch modeling. Measurement: Interdisciplinary Research and Perspectives, 18(3), 163–176.

Papini, N., Kang, M., Ryu, S., Griese, E., Wingert, T., & Herrmann, S. (2021). Rasch calibration of the 25-item Connor-Davidson resilience scale. Journal of Health Psychology, 26(11), 1976-1987.

Park, E. Y. (2019). Rasch analysis of the disability acceptance scale for individuals with cerebral palsy. Frontiers in Neurology, 10, 1260.

Parsazadeh, N., Cheng, P. Y., Wu, T. T., & Huang, Y. M. (2021). Integrating computational thinking concept into digital storytelling to improve learners’ motivation and performance. Journal of Educational Computing Research, 59(3), 470–495.

Peters, L., de Beeck, H. O., & De Smedt, B. (2020). Cognitive correlates of dyslexia, dyscalculia and comorbid dyslexia/dyscalculia: Effects of numerical magnitude processing and phonological processing. Research in Developmental Disabilities, 107, 103806.

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, 52(1), 33-44.

Powell, S. R., Berry, K. A., & Benz, S. A. (2020). Analyzing the word-problem performance and strategies of students experiencing mathematics difficulty. The Journal of Mathematical Behavior, 58, 100759.

Putra, B. Y. G., Yaniawati, P., Fitri, N., Sharif, S., Supianti, I. I., & Mudrikah, A. (2025). Analyzing student errors in PISA “Change and Relationship” tasks using the AVAEM framework. Infinity Journal, 14(4), 1105–1128.

Putri, I. I., Rahmat, A., Riandi, R., & Riza, L. S. (2024). Assessing undergraduate cognitive system thinking instruments in genetics lectures: a rasch model analysis. AL-ISHLAH: Jurnal Pendidikan, 16(3), 3924–3937.

Rahayuningsih, S., Sirajuddin, S., & Nasrun, N. (2021). Cognitive flexibility: exploring students’ problem-solving in elementary school mathematics learning. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 59-70.

Ramírez-Uclés, I. M., & Ramírez-Uclés, R. (2020). Gender differences in visuospatial abilities and complex mathematical problem solving. Frontiers in psychology, 11, 191.

Reigosa-Crespo, V., Castro-Cañizares, D., Estévez-Pérez, N., Santos, E., Torres, R., Mosquera, R., ... & Valdés-Sosa, M. (2020). Numerical skills and dyscalculia. From basic research to practice in Cuba (Habilidades numéricas y discalculia: de la investigación básica a la práctica en Cuba). Studies in Psychology, 41(2), 373–403.

Reinhold, F., Hofer, S., Berkowitz, M., Strohmaier, A., Scheuerer, S., Loch, F., ... & Reiss, K. (2020). The role of spatial, verbal, numerical, and general reasoning abilities in complex word problem solving for young female and male adults. Mathematics Education Research Journal, 32(2), 189–211.

Ricco, R. B., Koshino, H., Sierra, A. N., Bonsel, J., Monteza, J. V., & Owens, D. N. (2021). Individual differences in analytical thinking and complexity of inference in conditional reasoning. Thinking & Reasoning, 27(3), 319–349.

Rodríguez-Rojas, M. P., Ramírez-Segura, A. M., Valenzuela-Mora, P., Dampuré, J., & Riveros Munévar, F. (2024). Critical thinking evaluation scale: Design and validation in a Colombian population. Sage Open, 14(4), 21582440241297418.

Roorda, G., de Vries, S., & Smale-Jacobse, A. E. (2024, January). Using lesson study to help mathematics teachers enhance students’ problem-solving skills with teaching through problem solving. In Frontiers in Education (Vol. 9, p. 1331674). Frontiers Media SA.

Rubenstein, L. D., Callan, G. L., Neumeister, K. S., & Ridgley, L. M. (2020). Finding the problem: How students approach problem identification. Thinking Skills and Creativity, 35, 100635.

Saga, M., Rkhaila, A., Ounine, K., & Oubaha, D. (2022). Developmental dyscalculia: The progress of cognitive modeling in the field of numerical cognition deficits for children. Applied Neuropsychology: Child, 11(4), 904–914.

Salisa, R. D., & Meiliasari, M. (2023). A literature review on dyscalculia: What dyscalculia is, its characteristics, and difficulties students face in mathematics class. Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika, 5(1), 82–94.

Schreiber, I., & Ashkenazi, H. (2024). The impact of various teaching methods on the knowledge of students of different genders: The case of mathematics word problems abstract. Heliyon, 10(16).

Schukajlow, S., Rakoczy, K., & Pekrun, R. (2023). Emotions and motivation in mathematics education: Where we are today and where we need to go. ZDM–Mathematics Education, 55(2), 249–267.

Shreeves, M., Gugerty, L., & Moore, D. (2020). Individual differences in strategy use and performance during fault diagnosis. Cognitive Research: Principles and Implications, 5(1), 49.

Simanjuntak, D. A., Makmuri, M., & Rahayu, W. (2021). Problem-based learning: Its effect on higher-order mathematical thinking skills in terms of student's initial abilities and mathematical beliefs. Al-Jabar: Jurnal Pendidikan Matematika, 12(2), 457–466.

Stoet, G., & Geary, D. C. (2020). Gender differences in the pathways to higher education. Proceedings of the National Academy of Sciences, 117(25), 14073–14076.

Strohmaier, A. R., Schons, C., Knabbe, A., Vogel, M., Saado, K., & Obersteiner, A. (2025). The relation between text comprehension and computation in mathematical word-problem solving. Learning and Instruction, 101, 102235.

Suherman, S., & Vidákovich, T. (2022). Assessment of mathematical creative thinking: A systematic review. Thinking Skills and Creativity, 44, 101019.

Sukarelawan, M. I., Puspitasari, A. D., Sulisworo, D., Kuswanto, H., & Jumadi, J. (2022). A shift in the conceptual understanding of physics students through the wright map. Jurnal Pendidikan dan Pengajaran, 55(1), 127–141.

Sumarna, N., & Rahmawati, I. (2024). Pengembangan kemampuan berpikir kritis dan literasi matematika: penerapan desain instruksional pengintegrasian PBL dan ClassPoint [Developing critical thinking skills and mathematical literacy: implementing integrated PBL and classpoint instructional design]. PYTHAGORAS: Jurnal Matematika dan Pendidikan Matematika, 19(2), 153–164.

Suseelan, M., Chew, C. M., & Chin, H. (2023). Higher-order thinking word problem-solving errors made by low-performing pupils: Comparative case study across school types in Malaysia. Current Psychology, 42(25), 21449–21461.

Syaidi, A., & Murti, R. C. (2024). Optimizing critical thinking skills of fourth grade students through inquiry-based learning: elementary school mathematics. Jurnal Pendidikan MIPA, 25(2), 752-764.

Tomaszewski, L. E., Zarestky, J., & Gonzalez, E. (2020). Planning qualitative research: Design and decision making for new researchers. International journal of qualitative methods, 19, 1609406920967174.

Uto, M. (2021). Accuracy of performance-test linking based on a many-facet Rasch model. Behavior Research Methods, 53(4), 1440–1454.

van Dijke-Droogers, M., Drijvers, P., & Bakker, A. (2022). Introducing statistical inference: Design of a theoretically and empirically based learning trajectory. International Journal of Science and Mathematics Education, 20(8), 1743-1766.

Wahab, A., Kusuma, Y. S., Juandi, D., Turmudi, T., Buhaerah, B., & Syaiful, S. (2024). Understanding students’ struggles in solving mathematical problems: a systematic literature review using polya’s framework. Jurnal Pendidikan Progresif, 14(3), 1728-1753.

Ye, J., Lai, X., & Wong, G. K. W. (2022). A multigroup structural equation modeling analysis of students’ perception, motivation, and performance in computational thinking. Frontiers in Psychology, 13, 989066.

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