近年來，計算建模是 STEM 教育中一個重要的主題。隨著學校中電腦設備的普及，學生可以使用電腦軟體來模擬物理或化學現象， 而不需要實際在實驗室裡搭建設備，這樣可以節省時間和減少實驗器材的消耗，因此有越來越多課程使用計算建模來進行教學。
在前導研究中發現學生偏向參考範例提供的內容，並且無法完全內化教師提供之範例，為了改善學生的學習狀況，對原有的系統進行改進，具體改進包括加入漸進式範例、範例文字說明和任務進度條，希望此種改進能使學生在課程中，更容易獲得計算建模相關的技能與知識。
本研究透過一為期三天的營隊活動課程，使用CoSci 建模平台來輔助學生，並採用漸進式教學的方式引導學生，將複雜的建模過程拆分成各種範例，在課程中傳授給學生，以降低學生學習計算建模的難度。在營隊期間收集35名學生前、後測試卷 內容和建模成品與操作紀錄，並進行分析。本研究欲探討經過此種漸進式教學的學生於計算建模過程中的表現和行為，透過分析前、後測試卷 成績之成對樣本T檢定，評估學生在課程後學習成效；透過分析建模成品成績，探討學生學習計算建模中科學概念的成效；使用滯後序列分析來分析建模行為，探討學生在建模過程的行為序列的有何種模式 。 研究結果顯示經過漸進式教學的學生在計算建模的內容上有更深入的理解，但還是有部分學生無法完成課堂要求，可能需要提供更多幫助給此類學生，更多相關的分析及應用將於文中進行討論 。

In recent years, computational modeling has become an important topic in STEM education. With the widespread availability of computer equipment in schools, students can use computer software to simulate physical or chemical phenomena without the need to physically set up equipment in a laboratory. This saves time and reduces the consumption of experimental materials, leading to an increasing number of courses using computational modeling for teaching purposes.
Preliminary research has found that students tend to rely on the content provided in reference examples and are unable to fully internalize the examples provided by teachers. In order to improve student learning outcomes, the existing system has been enhanced. Specific improvements include the introduction of progressive examples, textual explanations of examples, and task progress indicators. It is hoped that these improvements will make it easier for students to acquire the skills and knowledge related to computational modeling during the course.
This study utilized a three-day camp program and employed the CoSci modeling platform to assist students. The study used a progressive teaching approach, breaking down the complex modeling process into various examples, which were taught to students during the course to reduce the difficulty of learning computational modeling. During the camp, data were collected through pre- and post-tests, as well as modeling artifacts and operation records from 35 students, which were subsequently analyzed.
The aim of this study is to explore the performance and behavior of students who underwent this progressive teaching approach in the process of computational modeling. Student learning outcomes after the course were evaluated through paired sample t-tests on pre- and post-test scores. The effectiveness of students' understanding of scientific concepts in computational modeling was examined through the analysis of modeling artifact scores. Lag sequential analysis was used to analyze modeling behaviors and identify patterns in students' behavioral sequences during the modeling process. The results of the study showed that students who underwent progressive teaching had a deeper understanding of computational modeling. However, some students may still have difficulty meeting the requirements of the course, indicating the need for additional support for these students. Further analysis and applications will be discussed in the paper.

賴柏翰(2021)。學生應用視覺化工程工具進行計算建模之分析。國立中央大學。
周彥丞(2021)。開發觀察鷹架輔助學生使用視覺化程式工具進行計算建模之分析。國立中央大學。
Aksit, O., & Wiebe, E. N. (2020). Exploring force and motion concepts in middle grades using computational modeling: A classroom intervention study. Journal of Science Education and Technology, 29(1), 65-82.
Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of educational research, 70(2), 181-214.
Bakeman, R., & Gottman, J. M. (1997). Observing interaction: An introduction to sequential analysis. Cambridge university press.
Bamberger, Y. M., & Davis, E. A. (2013). Middle-school science students’ scientific modelling performances across content areas and within a learning progression. International Journal of science education, 35(2), 213-238.
Basu, S., Biswas, G., & Kinnebrew, J. S. (2017). Learner modeling for adaptive scaffolding in a computational thinking-based science learning environment. User Modeling and User-Adapted Interaction, 27(1), 5-53.
Benzer, A. I., & Ünal, S. (2021). Models and Modelling in Science Education in Turkey: A Literature Review. Journal of Baltic Science Education, 20(3), 344-359.
Bielik, T., Fonio, E., Feinerman, O., Duncan, R. G., & Levy, S. T. (2021). Working together: Integrating computational modeling approaches to investigate complex phenomena. Journal of Science Education and Technology, 30, 40-57.
Börner, K., & Scharnhorst, A. (2009). Visual conceptualizations and models of science. Journal of Informetrics, 3(3), 161-172.
Caballero, M. D., Kohlmyer, M. A., & Schatz, M. F. (2012). Implementing and assessing computational modeling in introductory mechanics. Physical review special topics-physics education research, 8(2), 020106.
Carey, C. C., & Gougis, R. D. (2017). Simulation modeling of lakes in undergraduate and graduate classrooms increases comprehension of climate change concepts and experience with computational tools. Journal of Science Education and Technology, 26, 1-11.
Chang, C. J., Liu, C. C., Wu, Y. T., Chang, M. H., Chiang, S. F., Chiu, B. C., ... & Chang, C. K. (2016). Students' perceptions on problem solving with collaborative computer simulation. In 24th International Conference on Computers in Education, ICCE 2016 (pp. 166-168). Asia-Pacific Society for Computers in Education.
Chen, S. Y., & Yeh, C. C. (2017). The effects of cognitive styles on the use of hints in academic English: A learning analytics approach. Journal of Educational Technology & Society, 20(2), 251-264.
Chiu, M. H., & Lin, J. W. (2019). Modeling competence in science education. Disciplinary and Interdisciplinary Science Education Research, 1(1), 1-11.
Cisterna, D., Forbes, C. T., & Roy, R. (2019). Model-based teaching and learning about inheritance in third-grade science. International Journal of Science Education, 41(15), 2177-2199.
Clark, D. B., & Sengupta, P. (2020). Reconceptualizing games for integrating computational thinking and science as practice: Collaborative agent-based disciplinarily-integrated games. Interactive Learning Environments, 28(3), 328-346.
Clow, D. (2013). An overview of learning analytics. Teaching in Higher Education, 18(6), 683-695.
Dickes, A. C., Farris, A. V., & Pratim, S. (2020). Sociomathematical Norms for Integrating Coding and Modeling with Elementary Science: A Dialogical Approach. Journal of Science Education and Technology, 29(1), 35-52.
Harrison, A. G., & Treagust, D. F. (2000). A typology of school science models. International journal of science education, 22(9), 1011-1026.
Hutchins, N. M., Biswas, G., Zhang, N., Snyder, C., Lédeczi, Á., & Maróti, M. (2020). Domain-specific modeling languages in computer-based learning environments: A systematic approach to support science learning through computational modeling. International Journal of Artificial Intelligence in Education, 30, 537-580.
Johnson, P. O., & Neyman, J. (1936). Tests of certain linear hypotheses and their application to some educational problems. Statistical research memoirs.
Langbeheim, E., Perl, D., & Yerushalmi, E. (2020). Science teachers’ attitudes towards computational modeling in the context of an inquiry-based learning module. Journal of Science Education and Technology, 29, 785-796.
Leitner, P., Khalil, M., & Ebner, M. (2017). Learning analytics in higher education—a literature review. Learning analytics: Fundaments, applications, and trends: A view of the current state of the art to enhance E-learning, 1-23.
Lin, J. W. (2014). Elementary school teachers’ knowledge of model functions and modeling processes: a comparison of science and non-science majors. International Journal of Science and Mathematics Education, 12, 1197-1220.
Louca, L. T., & Zacharia, Z. C. (2015). Examining learning through modeling in K-6 science education. Journal of Science Education and Technology, 24, 192-215.
Lyon, J. A., Fennell, H. W., & Magana, A. J. (2020). Characterizing students' arguments and explanations of a discipline‐based computational modeling activity. Computer Applications in Engineering Education, 28(4), 837-852.
Miller, J. W., Stromeyer, W. R., & Schwieterman, M. A. (2013). Extensions of the Johnson-Neyman technique to linear models with curvilinear effects: Derivations and analytical tools. Multivariate behavioral research, 48(2), 267-300.
Musaeus, L. H., Tatar, D., & Musaeus, P. (2022). Computational Modelling in High School Biology: A Teaching Intervention. Journal of Biological Education, 1-17.
Namdar, B., & Shen, J. (2015). Modeling-oriented assessment in K-12 science education: A synthesis of research from 1980 to 2013 and new directions. International Journal of Science Education, 37(7), 993-1023.
Oh, P. S., & Oh, S. J. (2011). What teachers of science need to know about models: An overview. International Journal of Science Education, 33(8), 1109-1130.
Pardo, A. (2014). Designing learning analytics experiences. Learning analytics: From research to practice, 15-38.
Peng, J., Wang, M., Sampson, D., & van Merriënboer, J. J. (2019). Using a visualisation-based and progressive learning environment as a cognitive tool for learning computer programming. Australasian Journal of Educational Technology, 35(2).
Pierson, A. E., Brady, C. E., & Clark, D. B. (2020). Balancing the environment: Computational models as interactive participants in a STEM classroom. Journal of Science Education and Technology, 29, 101-119.
Pohl, M., Wallner, G., & Kriglstein, S. (2016). Using lag-sequential analysis for understanding interaction sequences in visualizations. International Journal of Human-Computer Studies, 96, 54-66.
Psycharis, S. (2013). Examining the effect of the computational models on learning performance, scientific reasoning, epistemic beliefs and argumentation: An implication for the STEM agenda. Computers & Education, 68, 253-265.
Saari, H., & Viiri, J. (2003). A research‐based teaching sequence for teaching the concept of modelling to seventh‐grade students. International Journal of Science Education, 25(11), 1333-1352.
Schwarz, C. V., Reiser, B. J., Davis, E. A., Kenyon, L., Achér, A., Fortus, D., ... & Krajcik, J. (2009). Developing a learning progression for scientific modeling: Making scientific modeling accessible and meaningful for learners. Journal of Research in Science Teaching: The Official Journal of the National Association for Research in Science Teaching, 46(6), 632-654.
Swaak, J., Van Joolingen, W. R., & De Jong, T. (1998). Supporting simulation-based learning; the effects of model progression and assignments on definitional and intuitive knowledge. Learning and instruction, 8(3), 235-252.
Tlili, A., Wang, H., Gao, B., Shi, Y., Zhiying, N., Looi, C. K., & Huang, R. (2021). Impact of cultural diversity on students’ learning behavioral patterns in open and online courses: A lag sequential analysis approach. Interactive Learning Environments, 1-20.
Treagust, D. F., Chittleborough, G., & Mamiala, T. L. (2002). Students' understanding of the role of scientific models in learning science. International journal of science education, 24(4), 357-368.
Wang, C., Shen, J., & Chao, J. (2022). Integrating computational thinking in STEM education: A literature review. International Journal of Science and Mathematics Education, 20(8), 1949-1972.
Wang, H., Tlili, A., Zhong, X., Cai, Z., & Huang, R. (2021, July). The impact of gender on online learning behavioral patterns: A comparative study based on lag sequential analysis. In 2021 International Conference on Advanced Learning Technologies (ICALT) (pp. 190-194). IEEE.
Weber, J., & Wilhelm, T. (2020). The benefit of computational modelling in physics teaching: a historical overview. European Journal of Physics, 41(3), 034003.
Weintrop, D., & Wilensky, U. (2017). Comparing block-based and text-based programming in high school computer science classrooms. ACM Transactions on Computing Education (TOCE), 18(1), 1-25.
Wells, M., Hestenes, D., & Swackhamer, G. (1995). A modeling method for high school physics instruction. American journal of physics, 63(7), 606-619.
Wilson, A., Watson, C., Thompson, T. L., Drew, V., & Doyle, S. (2017). Learning analytics: Challenges and limitations. Teaching in Higher Education, 22(8), 991-1007.
Windschitl, M., Thompson, J., & Braaten, M. (2008). Beyond the scientific method: Model‐based inquiry as a new paradigm of preference for school science investigations. Science education, 92(5), 941-967.
Yaşar, O., Little, L., Tuzun, R., Rajasethupathy, K., Maliekal, J., & Tahar, M. (2006). Computational math, science, and technology (CMST): a strategy to improve STEM workforce and pedagogy to improve math and science education. In Computational Science–ICCS 2006: 6th International Conference, Reading, UK, May 28-31, 2006. Proceedings, Part II 6 (pp. 169-176). Springer Berlin Heidelberg.
Van Driel, J. H., & Verloop, N. (2002). Experienced teachers' knowledge of teaching and learning of models and modelling in science education. International journal of science education, 24(12), 1255-1272.
Zhang, J. H., Meng, B., Zou, L. C., Zhu, Y., & Hwang, G. J. (2021). Progressive flowchart development scaffolding to improve university students’ computational thinking and programming self-efficacy. Interactive Learning Environments, 1-18.