Tracing Students’ Integrative Thinking Development Through Adaptive Integral Worksheets: Evidence from Single-Subject Research



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© 2026 Ina Noviani, Niswa Nagina Lutfiah, Sulistiawati Sulistiawati, Rina Oktaviyanthi

This study aimed to map students’ integrative thinking stages in solving integral problems presented in multiple representations. A Single Subject Research (SSR) using an A–B design was conducted involving three senior high school students categorized as high, moderate, and low ability. The students were selected purposively, and data were collected through task sheets, think-aloud protocols, and written responses across baseline and intervention phases. The intervention used adaptive integral worksheets based on four stages of integrative thinking: Articulate the Models, Examine the Models, Explore the Possibilities, and Assess the Prototypes. Data analysis combined visual plotting and qualitative interpretation. The results showed that moderate- and low-ability students improved significantly, with 100% non-overlapping data (PND), while the high-ability student showed stable performance with minor variations. Qualitative analysis revealed that high-ability students demonstrated advanced articulation but required additional cognitive challenges to sustain focus under time pressure. Meanwhile, moderate-- and low-ability students showed consistent progress across stages, especially when transitioning between representations. This research concludes that adaptive worksheets effectively enhance integrative thinking and support differentiated instructional design tailored to students’ representational reasoning.

 

Keywords: Integrative thinking, Integral problem solving, Multiple representations, Single-subject research, Students’ thinking stages.

Becker, A. (2023). The benefits of single-subject research designs and multi-methodological approaches for neuroscience research. Frontiers in Human Neuroscience, 17, 1190412. https://doi.org/10.3389/FNHUM.2023.1190412

Blair, C., & Ku, S. (2022). A Hierarchical Integrated Model of Self-Regulation. Frontiers in Psychology, 13, 725828. https://doi.org/10.3389/FPSYG.2022.725828

Borji, V., Martínez-Planell, R., & Trigueros, M. (2024). Students’ Understanding of Riemann Sums and Double Integrals: The Case of Task Design in APOS Theory. International Journal of Research in Undergraduate Mathematics Education, 1–29. https://doi.org/10.1007/S40753-024-00250-6

Carvalho, A. R., & Santos, C. (2022). Developing peer mentors’ collaborative and metacognitive skills with a technology-enhanced peer learning program. Computers and Education Open, 3, 100070. https://doi.org/10.1016/J.CAEO.2021.100070

Catagnus, R. M., Garcia, Y. A., & Zhang, D. X. (2023). Single-Subject Design Studies of Mindfulness Interventions for Behavior Change: A Scoping Review and Behavioral Conceptualization. Advances in Neurodevelopmental Disorders, 7(2), 133–164. https://doi.org/10.1007/S41252-022-00294-2

Danday, B. A. (2023). Fostering Critical Thinking Among Pre-service Teachers Through a Multiple Representation-Based Collaborative Pedagogical Approach. 191–217. https://doi.org/10.1007/978-3-031-15959-6_11

Doerr, H. M. ., & Lesh, R. A. . (2003). Foundations of a Models and Modeling Perspective on Mathematics Teaching, Learning, and Problem Solving. 3–33. https://doi.org/10.4324/9781410607713-2

Donaldson, S. I. ., Dubin, Matt., & Csikszentmihalyi, Mihaly. (2025). Flow 2.0 : optimal experience in a complex world : honoring Mihaly Csikszentmihalyi’s legacy. 127.

Dowdy, A., & Jessel, J. (2024). Single Case Research Designs. Research Methods in Special Education, 165–198. https://doi.org/10.4324/9781003526315-10

Farmer, T. W., Bierman, K. L., Hall, C. M., Brooks, D. S., & Lee, D. L. (2021). Tiered Systems of Adaptive Supports and the Individualization of Intervention: Merging Developmental Cascades and Correlated Constraints Perspectives. Journal of Emotional and Behavioral Disorders, 29(1), 3–13. https://doi.org/10.1177/1063426620957651

Gutierrez De Blume, P., Lin, H.-C. K., Drigas, A., Mitsea, E., & Skianis, C. (2023). Meta-Learning: A Nine-Layer Model Based on Metacognition and Smart Technologies. Sustainability 2023, Vol. 15, Page 1668, 15(2), 1668. https://doi.org/10.3390/SU15021668

Heutte, J., Fenouillet, F., Martin-Krumm, C., Gute, G., Raes, A., Gute, D., Bachelet, R., & Csikszentmihalyi, M. (2021). Optimal Experience in Adult Learning: Conception and Validation of the Flow in Education Scale (EduFlow-2). Frontiers in Psychology, 12, 828027. https://doi.org/10.3389/FPSYG.2021.828027

Hochberg, K., Becker, S., Louis, M., Klein, P., & Kuhn, J. (2020). Using Smartphones as Experimental Tools—a Follow-up: Cognitive Effects by Video Analysis and Reduction of Cognitive Load by Multiple Representations. Journal of Science Education and Technology, 29(2), 303–317. https://doi.org/10.1007/S10956-020-09816-W

Hu, L. (2024). Programming and 21st century skill development in K-12 schools: A multidimensional meta-analysis. Journal of Computer Assisted Learning, 40(2), 610–636. https://doi.org/10.1111/JCAL.12904

Jones, S. R. (2013). Understanding the integral: Students’ symbolic forms. The Journal of Mathematical Behavior, 32(2), 122–141. https://doi.org/10.1016/J.JMATHB.2012.12.004

Joo, H., Park, J., & Kim, D. (2021). Visual representation fidelity and self-explanation prompts in multi-representational adaptive learning. Journal of Computer Assisted Learning, 37(4), 1091–1106. https://doi.org/10.1111/JCAL.12548

Kazdin, A. E. (2021). Single-case experimental designs: Characteristics, changes, and challenges. Journal of the Experimental Analysis of Behavior, 115(1), 56–85. https://doi.org/10.1002/JEAB.638

Kemp, A. H., & Fisher, Z. (2023). Application of Single-Case Research Designs in Undergraduate Student Reports: An Example From Wellbeing Science. Teaching of Psychology, 50(1), 86–92. https://doi.org/10.1177/00986283211029929

Kocaöz, O. E., & Yalçın, G. (2022). The effectiveness of Gagne’s model in concept teaching for a student with intellectual disability. Journal of Pedagogical Research, 6(4), 101–110. https://doi.org/10.33902/JPR.202216895

Lanovaz, M. J., & Primiani, R. (2023). Waiting for baseline stability in single-case designs: Is it worth the time and effort? Behavior Research Methods, 55(2), 843–854. https://doi.org/10.3758/S13428-022-01858-9

Levin, J. R., & Ferron, J. M. (2021). Different randomized multiple-baseline models for different situations: A practical guide for single-case intervention researchers. Journal of School Psychology, 86, 169–177. https://doi.org/10.1016/J.JSP.2021.03.003

Li, T., & Zhan, Z. (2022). A Systematic Review on Design Thinking Integrated Learning in K-12 Education. Applied Sciences 2022, Vol. 12, Page 8077, 12(16), 8077. https://doi.org/10.3390/APP12168077

Li, Y., Li, Y., He, X., Fang, J., Zhou, C. Y., & Liu, C. (2025). Learner’s cognitive state recognition based on multimodal physiological signal fusion. Applied Intelligence, 55(2), 1–16. https://doi.org/10.1007/S10489-024-05958-1

Mofield, E. L. (2022). Vertical Differentiation for Gifted, Advanced, and High-Potential Students: 25 Strategies to Stretch Student Thinking. Vertical Differentiation for Gifted, Advanced, and High-Potential Students: 25 Strategies to Stretch Student Thinking, 1–182. https://doi.org/10.4324/9781003293286

Nedaei, M., Radmehr, F., & Drake, M. (2022). Exploring undergraduate engineering students’ mathematical problem-posing: the case of integral-area relationships in integral calculus. Mathematical Thinking and Learning, 24(2), 149–175. https://doi.org/10.1080/10986065.2020.1858516

Noviani, I., Lutfiah, N. N., Sulistiawati, & Oktaviyanthi, R. (2024). Pengembangan lembar kerja integral adaptif untuk integrative thinking (Research Report). Universitas Serang Raya.

Oktaviyanthi, R., & Agus, R. N. (2023). Evaluating graphing quadratic worksheet on visual thinking classification: A confirmatory analysis. Infinity Journal, 12(2), 207–224. https://doi.org/10.22460/INFINITY.V12I2.P207-224

Penfield, R. D., & Giacobbi, Jr., P. R., Jr. (2004). Applying a score confidence interval to Aiken's item content-relevance index. Measurement in physical education and exercise science, 8(4), 213-225. https://doi.org/10.1207/s15327841mpee0804_3

Roberts, J. L., & Inman, T. F. (2023). Strategies for Differentiating Instruction : Best Practices for the Classroom. Strategies for Differentiating Instruction. https://doi.org/10.4324/9781003330561

Sinaga, P., Setiawan, W., & Liana, M. (2022). The impact of electronic interactive teaching materials (EITMs) in e-learning on junior high school students’ critical thinking skills. Thinking Skills and Creativity, 46, 101066. https://doi.org/10.1016/J.TSC.2022.101066

Spoto, A., Nucci, M., Prunetti, E., & Vicovaro, M. (2025). Improving content validity evaluation of assessment instruments through formal content validity analysis. Psychological methods, 30(2), 203. https://psycnet.apa.org/doi/10.1037/met0000545

Turčáni, M., Balogh, Z., & Kohútek, M. (2024). Evaluating computer science students' reading comprehension of educational multimedia-enhanced text using scalable eye-tracking methodology. Smart Learning Environments, 11(1), 1–28. https://doi.org/10.1186/S40561-024-00318-5

Wu, H., & Molnár, G. (2022). Analysing Complex Problem-Solving Strategies from a Cognitive Perspective: The Role of Thinking Skills. Journal of Intelligence, 2022, Vol. 10, Page 46, 10(3), 46. https://doi.org/10.3390/JINTELLIGENCE10030046

Yenioğlu, S., Melekoğlu, M. A., & Yılmaz Yenioğlu, B. (2022). A single-subject case study of twice exceptionality. Gifted Education International, 38(2), 256-272. https://doi.org/10.1177/02614294211064772

Zuidersma, M., Riese, H., Snippe, E., Booij, S. H., Wichers, M., & Bos, E. H. (2020). Single-subject research in psychiatry: Facts and fictions. Frontiers in Psychiatry, 11, 539777. https://doi.org/10.3389/fpsyt.2020.539777

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