運算思維係指運用電腦科學運作的概念，來形塑並解決生活中問題，在STEM 跨領域整合學習中更扮演學科間橋梁的角色。雖然電腦編碼雖然可以做為運算思維的學習框架，但學習者亦應透過其他形式的教學活動，來培養運算思維的底層概念，更靈活地去應用問題解決的技能。
模式辨識是運算思維中的一項重要基礎技能，因此本研究透過數學代數推理結合模式辨識，開發一款破解密碼方程式的行動教育遊戲《Guess My Rule》，並招募60 位20 歲以上的成人參與此研究，其中實驗組、控制組各30 位，以比較有無代數推理鷹架提示的受試者，在《Guess My Rule》遊戲活動的心流、活動焦慮、動機表現，並針對受試者在遊戲中的行為模式進行分析及比較。研究結果顯示，兩組的受試者在《Guess My Rule》遊戲中有良好的心流狀態及動機，且在無聊及焦慮中取得平衡。另一方面，加入代數推理鷹架的實驗組，在心流子維度知行合一，雖高於量表中位數但和量表中位數無呈現顯著關係，而在清楚的回饋向度則略低於控制組，推測學習者可能會因為使用代數推理鷹架提示，獲得的資訊增多，在心流子向度部分受到些微影響。除此之外，研究結果顯示，實驗組遊戲成就和代數推理鷹架的使用次數具顯著負相關，顯示學習成就越低的學習者，鷹架使用次數越高；遊戲成就和心流具顯著正相關，可推測代數推理鷹架的加入，有潛力使得遊戲成就和心理狀態產生關聯。另外，加入代數推理鷹架後，焦慮對心流的影響變得不顯著，推測代數推理鷹架加入，有機會緩解學習者因為焦慮而影響投入的情況。本研究亦針對受試者的遊戲行為進行分析，結果顯示，受試者在遊戲中的答題行為具一定模式，且在提示使用上具有偏好，並會連續使用提示鷹架。

Computational thinking refers to the use of computer science concepts to solve
problems in life. In recent years, computational thinking has become even more
important because of the emphasis on problem solving in STEM cross-curricular
learning. Although coding can be used as a framework for learning computational
thinking, learners should also develop computational thinking concepts through other
types of teaching activities, so that they can apply problem-solving skills more flexibly.
Pattern recognition is one of the important skills in computational thinking.
Therefore, in this study, a mobile educational game "Guess My Rule" was developed.
It combined algebraic reasoning with pattern recognition in the code equation-solving
scenario. 60 adults above age 20 were recruited to participate in this study, divided into 30 participants in the experimental group and 30 in the control group. The study was conducted to compare the flow, activity anxiety, motivation, and behavioral patterns of the participants in the "Guess My Rule" game with and without the algebraic reasoning scaffolding hints. The results of the study showed that the participants in both groups had favorable flow and motivation in this game, and achieved a balance between boredom and anxiety. Furthermore, the flow sub-dimension “action-awareness merging” in the experimental group was above the median but not significantly related to the median. Also, the flow sub-dimension “unambiguous feedback” in the experiment group was slightly lower than in the control group. Additionally, the results showed that game achievement has a correlation with the frequency of uses of scaffolding and the flow, indicating that the lower the academic achievement, the higher the frequency of uses of the algebraic reasoning scaffolding and it can be hypothesized that the addition of the algebraic reasoning scaffolding has the potential to associate game achievement with mental status. In addition, the activity anxiety has become less correlated with the flow with the addition of the algebraic reasoning scaffolding, and it was hypothesized that the addition of the algebraic reasoning scaffolding had the potential to mitigate the impact of anxiety on the engagement of learners. This study also analyzed the game behaviors of the participants, and the results showed that the participants had a certain pattern in question-answering, and they had a preference for the use of hints and would use the hint scaffolding continuously.

吳乃芸。「以海霸桌遊實現實體互動之運算思維課程」。碩士論文，國立成功大
學工程科學系碩士在職專班，2022。https://hdl.handle.net/11296/fw34af。
林巧玲（2021）。六年級代數推理解題表現之研究。國立臺中教育大學數學教育
學系在職專班碩士論文，台中市。 取自
https://hdl.handle.net/11296/h6ye49
洪美雪（2001）。字幕對外語學習成效影響之探究。國立成功大學教育研究所碩
士論文，台南市。 取自https://hdl.handle.net/11296/sx7ca2
孫嘉黛(2020)。運算思維融入高中公民探究與實作課程之行動研究。國立臺灣師
範大學課程與教學研究所碩士論文， 台北市。 取自
https://hdl.handle.net/11296/qjhrpj
Abdullah, A. H., Othman, M. A., Ismail, N., Rahman, S. N. S. A., Mokhtar, M., &
Zaid, N. M. (2019, December 1). Development of Mobile Application for The
Concept of Pattern Recognition in Computational Thinking for Mathematics
Subject. IEEE Xplore. https://doi.org/10.1109/TALE48000.2019.9225910
Adamuz-Povedano, N., Fernández-Ahumada, E., García-Pérez, M. T., & Montejo-
Gámez, J. (2021). Developing Number Sense: An Approach to Initiate
Algebraic Thinking in Primary Education. Mathematics, 9(5), 518.
https://doi.org/10.3390/math9050518
Agbo, F. J., Oyelere, S. S., Suhonen, J., & Laine, T. H. (2021). Co-design of mini
games for learning computational thinking in an online
environment. Education and Information Technologies.
https://doi.org/10.1007/s10639-021-10515-1
Aho, A. V. (2012). Computation and Computational Thinking. The Computer
Journal, 55(7), 832–835. https://doi.org/10.1093/comjnl/bxs074
Almeda, Ma. V., & Asbell-Clarke, J. (2021). Scaffolding Executive Function in
Game-Based Learning to Improve Productive Persistence and Computational
Thinking in Neurodiverse Learners. HCI in Games: Serious and Immersive
Games, 155–172. https://doi.org/10.1007/978-3-030-77414-1_12
Angeli, C., & Giannakos, M. (2019). Computational thinking education: Issues and
challenges. Computers in Human Behavior, 106185. https://doi.org/10.1016/j.
chb.2019.106185
Australian Curriculum, Assessment, Reporting Authority (ACARA). (2013). Draft
Australian curriculum technologies. Retrieved from
http://consultation.australiancurriculum.edu.au/Static/docs/Technologies
/Draft%20Australian%20Curriculum%20Technologies%20-
72
%20February%202013.pdf
Australian Education Council (2015) National STEM School Education Strategy
2016–2026. Available
at: http://www.scseec.edu.au/site/DefaultSite/filesystem/
documents/National%20STEM%20School%20Education%20Strategy.pdf.
Azevedo, R., & Cromley, J. G. (2004). Does Training on Self-Regulated Learning
Facilitate Students' Learning With Hypermedia? Journal of Educational
Psychology, 96(3), 523–535. https://doi.org/10.1037/0022-0663.96.3.523
Azevedo, R., & Hadwin, A. F. (2005). Scaffolding self-regulated learning and
metacognition – Implications for the design of computer-based
scaffolds. Instructional Science, 33(5/6), 367–379. https://www.jstor.org/
stable/41953688
Basawapatna, A., Repenning, A., & Savignano, M. (2019). The Zones of Proximal
Flow Tutorial. Proceedings of the 50th ACM Technical Symposium on
Computer Science Education. https://doi.org/10.1145/3287324.3287361
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.
https://doi.org/10.1007/s11257-017-9187-0
Barrón-Estrada, M. L., Zatarain-Cabada, R., Romero-Polo, J. A., & Monroy, J. N.
(2021). Patrony: A mobile application for pattern recognition
learning. Education and Information Technologies, 27(1), 1237–1260.
https://doi.org/10.1007/s10639-021-10636-7
Bell, T., & Vahrenhold, J. (2018). CS Unplugged—How Is It Used, and Does It
Work? Progress in Pattern Recognition, Image Analysis, Computer Vision,
and Applications, 497–521. https://doi.org/10.1007/978-3-319-98355-4_29
Bers, M. U., Flannery, L., Kazakoff, E. R., & Sullivan, A. (2014). Computational
thinking and tinkering: Exploration of an early childhood robotics
curriculum. Computers & Education, 72, 145–157.
https://doi.org/10.1016/j.compedu.2013.10.020
Boaler, J., & Selling, S. K. (2017). Psychological Imprisonment or Intellectual
Freedom? A Longitudinal Study of Contrasting School Mathematics
Approaches and Their Impacton Adults' Lives. Journal for Research in
Mathematics Education, 48(1), 78-105.
https://doi.org/10.5951/jresematheduc.48.1.0078
Boyer, K., Buffum, P. S., Culbertson, K., Frankosky, M., Lester, J., Martinez-Arocho,
A., Min, W., Mott, B., Rodriguez, F., & Wiebe, E. (2015). ENGAGE:A gamebased
learning environment for middle school computational
thinking. Proceedings of the 46th ACM Technical Symposium on Computer
Science Education. https://doi.org/10.1145/2676723.2691876
Bråting, K., & Kilhamn, C. (2020). Exploring the intersection of algebraic and
computational thinking. Mathematical Thinking and Learning, 1–16.
https://doi.org/10.1080/10986065.2020.1779012
Buitrago Flórez, F., Casallas, R., Hernández, M., Reyes, A., Restrepo, S., & Danies,
G. (2017). Changing a generation’s way of thinking: Teaching computational
thinking through programming. Review of Educational Research, 87(4), 834-
860. https://doi.org/10.3102/0034654317710096
Bybee, R. W. (2013). The case for STEM education : challenges and opportunities.
National Science Teachers Association.
Cai, J., Lew, H. C., Morris, A., Moyer, J. C., Fong Ng, S., & Schmittau, J. (2005). The
development of studients’ algebraic thinking in earlier grades: Zentralblatt Für
Didaktik Der Mathematik, 37(1), 5–15. https://doi.org/10.1007/bf02655892
Cai, Z., Mao, P., Wang, D., He, J., Chen, X., & Fan, X. (2022). Effects of Scaffolding
in Digital Game-Based Learning on Student’s Achievement: a Three-Level
Meta-analysis. Educational Psychology Review. https://doi.org/10.1007/
s10648-021-09655-0
Chan, S.-W., Looi, C.-K., Ho, W. K., Huang, W., Seow, P., & Wu, L. (2021). Learning
number patterns through computational thinking activities: A Rasch model
analysis. Heliyon, 7(9), e07922. https://doi.org/10.1016/j.heliyon.2021.e07922
Chang, C.-K. (2014). Effects of Using Alice and Scratch in an Introductory
Programming Course for Corrective Instruction. Journal of Educational
Computing Research, 51(2), 185–204. https://doi.org/10.2190/ec.51.2.c
Chen, Y.-C., Hou, H.-T., & Wu, C.-H. (2022). Design and Development of a
Scaffolding-Based Mindtool for Gamified Learning Classrooms. Journal of
Educational Computing Research, https://doi.org/10.1177/07356331 221101081
Choi, J., Lee, Y., & Lee, E. (2016). Puzzle Based Algorithm Learning for Cultivating
Computational Thinking. Wireless Personal Communications, 93(1), 131–145.
https://doi.org/10.1007/s11277-016-3679-9
Chow, S. J., & Yong, B. C. S. (2013). Secondary school students’ motivation and
achievement in combined science. US China Education Review B, 3(4), 213–
228.
Chou, Y.-S., Hou, H.-T., Chang, K.-E., & Su, C.-L. (2021). Designing cognitive-based
game mechanisms for mobile educational games to promote cognitive thinking:
an analysis of flow state and game-based learning behavioral
patterns. Interactive Learning Environments, 1–18.
https://doi.org/10.1080/10494820.2021.1926287
Coleman, T. E., & Money, A. G. (2019). Student-centred digital game–based learning:
a conceptual framework and survey of the state of the art. Higher Education.
https://doi.org/10.1007/s10734-019-00417-0
Csikszentmihalyi, M. (1990). Flow: The Psychology of Optimal Experience. Design
Issues, 8(1), 80. https://doi.org/10.2307/1511458
CSTA (2011). CSTA K–12 computer science standards. The ACM K-12 Education
Task Force. Retrieved from http://www.csta.acm.org/Curriculum/sub/CurrFiles/
CSTA_K-12_CSS.pdf
Cuny, J., Snyder, L., & Wing, J.M. (2010). Demystifying computational thinking for
non-computer scientists. Unpublished manuscript in progress, referenced in
http://www.cs.cmu.edu/~CompThink/resources/TheLinkWing.pd
Delal, H., & Oner, D. (2020). Developing middle school students’ computational
thinking skills using unplugged computing activities. Informatics in Education,
19(1), 1-13. https://doi.org/10.15388/infedu.2020.01
DeOrsey, P., Pooler, C., & Ferrara, M. (2021). Mathematical Zendo: A game of
patterns and logic. Journal of Math Circles, 2(1).
https://digitalcommons.cwu.edu/ mathcirclesjournal/vol2/iss1/2/
Department for Education in England (DOEE) (2013, September 11). National
curriculum in England: Computing programmes of study. Retrieved from
https://www.gov.uk/government/publications/national-curriculum-inenglandcomputing-
programmes-of-study/national-curriculum-in-englandcomputingprogrammes-
of-study
Druckman, D. (1995). The educational effectiveness of interactive games. In D.
Crookall, & K. Arai (Eds.), Simulation and gaming across disciplines and
cultures: ISAGA at a watershed (pp. 178-187). SAGE Publications.
Eisner, E. W., & Elliot, A. (1982). Cognition and Curriculum. Addison-Wesley
Longman Limited.
Eskelinen, M. (2001). The gaming situation. Game studies, 1(1), 68.
http://gamestudies.org/0101/eskelinen/
European Commission. (2014). Digital Agenda for Europe. Retrieved from
https://ec.europa.eu/digital-agenda/en/grand-coalition-digital-jobs.
Eysenck, M. W., & Keane, M. T. (2015). Cognitive Psychology. Psychology Press.
https://doi.org/10.4324/9781315778006
Fagerlund, J., Häkkinen, P., Vesisenaho, M., & Viiri, J. (2020). Computational
thinking in programming with Scratch in primary schools: A systematic
review. Computer Applications in Engineering Education, 29(1).
https://doi.org/10.1002/cae.22255
Fernandez, M. L., & Anhalt, C. O. (2001). Transition Toward Algebra. Mathematics
Teaching in the Middle School, 7(4), 236–241.
https://doi.org/10.5951/mtms.7.4.0236
Fisch, S. M. (2005). Making educational computer games “educational.” Proceeding
of the 2005 Conference on Interaction Design and Children - IDC ’05.
https://doi.org/10.1145/1109540.1109548
Francisco, J. M., & Hähkiöniemi, M. (2011). STUDENTS’ WAYS OF REASONING
ABOUT NONLINEAR FUNCTIONS IN GUESS-MY-RULE
GAMES. International Journal of Science and Mathematics Education, 10(5),
1001–1021. https://doi.org/10.1007/s10763-011-9310-3
Fu, K.-S. (1982). Pattern recognition for automatic visual inspection. Robot
Vision. https://doi.org/10.1117/12.933606
Gadanidis, G., Cendros, R., Floyd, L., & Namukasa, I. (2017). Computational
Thinking in Mathematics Teacher Education. Contemporary Issues in
Technology and Teacher Education, 17(4), 458–477.
https://www.learntechlib.org/p/173103/
Google for Education (2010). Exploring computational thinking Retrieved from
www.google.com/edu/resources/programs/exploring-computationalthinking/
index.html#!home
Google.(2015). Exploring Computational Thinking. Retrieved from https://
www.google.com/edu/resources/programs/exploring-computationalthinking/
Gowers, T., Barrow-Green, J., & Leader, I. (Eds.). (2008). The Princeton companion
to mathematics. Princeton University Press.
Graesser, A. C., Wiemer-Hastings, K., Wiemer-Hastings, P., & Kreuz, R. (1999).
AutoTutor: A simulation of a human tutor. Cognitive Systems Research, 1(1),
35–51. https://doi.org/10.1016/s1389-0417(99)00005-4
Grover, S., & Pea, R. (2013). Computational thinking in K–12: A review of the state
of the field. Educational researcher, 42(1), 38-43.
https://doi.org/10.3102/0013189x12463051
Grizioti, M., & Kynigos, C. (2021). Code the mime: A 3D programmable charades
game for computational thinking in MaLT2. British Journal of Educational
Technology, 52(3), 1004–1023. https://doi.org/10.1111/bjet.13085
Hannafin, M., Land, S., & Oliver, K. (2013). Open learning environments:
Foundations, methods, and models. Instructional-Design Theories and
Models: A New Paradigm of Instructional Theory, 115–140.
https://doi.org/10.4324/ 9781410603784-12
Heeffer, Albrecht. (2010). “From the second unknown to the symbolic equation”. In
Heeffer A. & Van Dyck, M. (eds) Philosophical Aspects of Symbolical
Reasoning in Early Modern Mathematics (pp.57-101), College Publications.
Hilliard, J., Kear, K., Donelan, H., & Heaney, C. (2020). Students’ experiences of
anxiety in an assessed, online, collaborative project. Computers &
Education, 143, 103675. https://doi.org/10.1016/j.compedu.2019.103675
Hogle, J. G. (1996). Considering Games as Cognitive Tools: In Search of
Effectiv. ERIC. https://eric.ed.gov/?id=ED425737
Hooshyar, D., Pedaste, M., Yang, Y., Malva, L., Hwang, G.-J., Wang, M., Lim, H., &
Delev, D. (2021). From gaming to computational thinking: An adaptive
educational computer game-based learning approach. Journal of Educational
Computing Research, 59(3), 383-409.
https://doi.org/10.1177/0735633120965919
Hou, H.-T., & Li, M.-C. (2014). Evaluating multiple aspects of a digital educational
problem-solving-based adventure game. Computers in Human Behavior, 30,
29–38. https://doi.org/10.1016/j.chb.2013.07.052
Hou, H. T. (2015). Integrating cluster and sequential analysis to explore learners’ flow
and behavioral patterns in a simulation game with situated-learning context for
science courses: A video-based process exploration. Computers in human
behavior, 48, 424-435.
Hou, H. T. & Keng, S. H. (2021) A Dual-scaffolding framework integrating peerscaffolding
and cognitive-scaffolding for an augmented reality-based
educational board game: An analysis of learners’ collective flow state and
collaborative learning behavioral patterns, Journal of Educational Computing
Research. 59(3), 547-573. https://doi.org/10.1177/0735633120969409
Hou, H.-T., Fang, Y.-S., & Tang, J. T. (2021). Designing an alternate reality board game
with augmented reality and multi-dimensional scaffolding for promoting spatial
and logical ability. Interactive Learning Environments, 1–21.
https://doi.org/10.1080/10494820.2021.1961810
Hou, HT., Wu, CS. & Wu, CH. (2022).Evaluation of a mobile-based scaffolding board
game developed by scaffolding-based game editor: analysis of learners’
performance, anxiety and behavior patterns. J. Comput. Educ.
https://doi.org/10.1007/s40692-022-00231-1
Hsieh, Y.-H., Lin, Y.-C., & Hou, H.-T. (2013). Exploring the role of flow experience,
learning performance and potential behavior clusters in elementary students’
game-based learning. Interactive Learning Environments, 24(1), 178–193.
https://doi.org/10.1080/10494820.2013.834827
Hsu, T.-C., Chang, S.-C., & Hung, Y.-T. (2018). How to learn and how to teach
computational thinking: Suggestions based on a review of the
literature. Computers & Education, 126, 296–310. https://doi.org/ 10.1016/
j.compedu.2018.07.004
Jackson, S. L., Stratford, S. J., Krajcik, J., & Soloway, E. (1994). Making Dynamic
Modeling Accessible to Precollege Science Students. Interactive Learning
Environments, 4(3), 233–257. https://doi.org/10.1080/1049482940040305
Jaipal-Jamani, K., & Angeli, C. (2017). Effect of robotics on elementary preservice
teachers’ self-efficacy, science learning, and computational thinking. Journal
of science education and technology, 26(2), 175-192.
https://doi.org/10.1007/s10956-016-9663-z
Jumaat, N. F., & Tasir, Z. (2014, April 1). Instructional Scaffolding in Online
Learning Environment: A Meta-analysis. IEEE Xplore.
https://doi.org/10.1109/LaTi CE.2014.22
Jun Zhang, L. (2001). Exploring variability in language anxiety: two groups of PRC
students learning ESL in Singapore. RELC Journal, 32(1), 73–91.
https://doi.org/10.1177/003368820103200105
Kale, U., & Yuan, J. (2020). Still a New Kid on the Block? Computational Thinking
as Problem Solving in Code.org. Journal of Educational Computing Research,
073563312097205. https://doi.org/10.1177/0735633120972050
Karaahmetoğlu, K., & Korkmaz, Ö. (2019). The effect of project-based arduino
educational robot applications on students’ computational thinking skills and
their perception of Basic Stem skill levels. Participatory Educational
Research, 6(2), 1–14. https://doi.org/10.17275/per.19.8.6.2
Kazimoglu, C., Kiernan, M., Bacon, L., & MacKinnon, L. (2011). Understanding
Computational Thinking before Programming. International Journal of Game-
Based Learning, 1(3), 30–52. https://doi.org/10.4018/ijgbl.2011070103
Keller, J. M. (1987). Development and use of the ARCS model of instructional
design. Journal of Instructional Development, 10(3), 2–10.
https://doi.org/10.1007/bf02905780
Kerrigan, J. (2018). Active Learning Strategies for the Mathematics
Classroom. College Teaching, 66(1), 35–36.
https://doi.org/10.1080/87567555. 2017. 1399335
Kiili, K. (2005). Digital game-based learning: Towards an experiential gaming
model. The Internet and Higher Education, 8(1), 13–24.
https://doi.org/10.1016/j.iheduc.2004.12.001
Kiili, K. (2006). Evaluations of an Experiential Gaming Model. Human Technology:
An Interdisciplinary Journal on Humans in ICT Environments.
https://jyx.jyu.fi/handle/123456789/20195
Kite, V., Park, S., & Wiebe, E. (2021). The Code-Centric Nature of Computational
Thinking Education: A Review of Trends and Issues in Computational
Thinking Education Research. SAGE Open, 11(2),
https://doi.org/10.1177/21582440211016418
Kotini, I., & Tzelepi, S. (2014). A Gamification-Based Framework for Developing
Learning Activities of Computational Thinking. Gamification in Education and
Business, 219–252. https://doi.org/10.1007/978-3-319-10208-5_12
Krouska, A., Troussas, C., & Sgouropoulou, C. (2021). Mobile game-based learning
as a solution in COVID-19 era: Modeling the pedagogical affordance and
student interactions. Education and Information Technologies, 1–13.
https://doi.org/10.1007/s10639-021-10672-3
Land, S.M., Greene, B.A. Project-based learning with the world wide web: A
qualitative study of resource integration. ETR&D 48, 45–66 (2000).
https://doi.org/10.1007/BF02313485
Langer, J. A. (1983). Instructional scaffolding: Reading and writing as natural
language activities. Language Arts, 60(2), 168-175.
https://www.jstor.org/stable/41961447#metadata_info_tab_contents
Lee, I., Martin, F., Denner, J., Coulter, B., Allan, W., Erickson, J., Malyn-Smith, J., & Werner, L. (2011). Computational thinking for youth in practice. ACM
Inroads, 2(1), 32. https://doi.org/10.1145/1929887.1929902
Lee, L.-K., Cheung, T.-K., Ho, L.-T., Yiu, W.-H., & Wu, N.-I. (2019). Learning
Computational Thinking Through Gamification and Collaborative
Learning. Blended Learning: Educational Innovation for Personalized
Learning, 339–349. https://doi.org/10.1007/978-3-030-21562-0_28
Leifheit, L. (2021). The Role of Self-Concept and Motivation Within the
“Computational Thinking” Approach to Early Computer Science Education.
Deutsche Nationalbibliothek. http://d-nb.info/1231790725
Liao, C. H., Chiang, C.-T., Chen, I-Chuan., & Parker, K. R. (2022). Exploring the
relationship between computational thinking and learning satisfaction for non-
STEM college students. International Journal of Educational Technology in
Higher Education, 19(1). https://doi.org/10.1186/s41239-022-00347-5
Ling, M. K. D., & Loh, S. C. (2021). Relationships between cognitive pattern
recognition and specific mathematical domains in mathematics
education. International Journal of Mathematical Education in Science and
Technology, 1–21. https://doi.org/10.1080/0020739x.2021.1949059
Liu, J., Sun, J., & Wang, S. (2006). Pattern Recognition: An overview. IJCSNS
International Journal of Computer Science and Network Security, 6(6).
https://www.utm.mx/~jjf/rp/RPA1.pdf
Lodi, M., Martini, S. Computational Thinking, Between Papert and Wing. Sci &
Educ 30, 883–908 (2021). https://doi.org/10.1007/s11191-021-00202-5
Lu, J. J., & Fletcher, G. H. L. (2009). Thinking about computational
thinking. Proceedings of the 40th ACM Technical Symposium on Computer
Science Education - SIGCSE ’09. https://doi.org/10.1145/1508865.1508959
Lye, S. Y., & Koh, J. H. L. (2014). Review on teaching and learning of computational
thinking through programming: What is next for K-12? Computers in Human
Behavior, 41, 51–61. https://doi.org/10.1016/j.chb.2014.09.012
Ma, H., Zhao, M., Wang, H., Wan, X., Cavanaugh, T. W., & Liu, J. (2021). Promoting
pupils’ computational thinking skills and self-efficacy: a problem-solving
instructional approach. Educational Technology Research and Development.
https://doi.org/10.1007/s11423-021-10016-5
Ma, J., Zhang, Y., Bin, H., Wang, K., Liu, J., & Gao, H. (2022). The Development of
Students’ Computational Thinking Practices in AI Course Using the Game-
Based Learning: A Case Study. IEEE Xplore. https://doi.org/ 10.1109/
ISET55194.2022.00065
Madariaga, L., Allendes, C., Nussbaum, M., Barrios, G., & Acevedo, N. (2023).
Offline and online user experience of gamified robotics for introducing
computational thinking: Comparing engagement, game mechanics and coding
motivation. Computers & Education, 193, 104664. https://doi.org/10.1016
/j.compedu.2022.104664
Maloney, E. A., & Beilock, S. L. (2012). Math anxiety: who has it, why it develops,
and how to guard against it. Trends in Cognitive Sciences, 16(8), 404–406.
https://doi.org/10.1016/j.tics.2012.06.008
Mariani, L. (1997). Teacher support and teacher challenge in promoting learner
autonomy. Perspectives: A Journal of TESOL Italy, XXIII (2). Retrieved from
http://www. learningpaths. org/papers/papersupport. htm.
Medeiros, R. P., Ramalho, G. L., & Falcao, T. P. (2019). A Systematic Literature
Review on Teaching and Learning Introductory Programming in Higher
Education. IEEE Transactions on Education, 62(2), 77–90.
https://doi.org/10.1109/te.2018.2864133
Menon, D., Viéville, T., & Romero, M. (2019). Computational thinking development
and assessment through tabletop escape games. International Journal of Serious
Games, 6(4), 3–18. https://doi.org/10.17083/ijsg.v6i4.319
Moreno-Armella, L., Hegedus, S. J., & Kaput, J. J. (2008). From static to dynamic
mathematics: historical and representational perspectives. Educational Studies
in Mathematics, 68(2), 99–111. https://doi.org/10.1007/s10649-008-9116-6
Moyer-Packenham, P. S., Lommatsch, C. W., Litster, K., Ashby, J., Bullock, E. K.,
Roxburgh, A. L., Shumway, J. F., Speed, E., Covington, B., Hartmann, C.,
Clarke-Midura, J., Skaria, J., Westenskow, A., MacDonald, B., Symanzik, J., &
Jordan, K. (2019). How design features in digital math games support learning
and mathematics connections. Computers in Human Behavior, 91, 316–332.
https://doi.org/10.1016/j.chb.2018.09.036
Muliyati, D., Sumardani, D., Siswoyo, S., Bakri, F., Permana, H., Handoko, E., &
Sari, N. L. K. (2022). Development and evaluation of granular simulation for
integrating computational thinking into computational physics courses.
Education and Information Technologies, 27(2), 2585-2612.
https://doi.org/10.1007/s10639-021-10724-8
Nakamura, T., & Kawasaki, T. (2019, December 1). Computer Science Unplugged for
Developing Computational Thinking and Mathematical Thinking. IEEE Xplore.
https://doi.org/10.1109/IJCIME49369.2019.00108
Nicholson, S. (2018). Creating Engaging Escape Rooms for the
Classroom. Childhood Education, 94(1), 44–49.
https://doi.org/10.1080/00094056.2018.1420363
Pérez, A. (2018). A framework for computational thinking dispositions in
mathematics education. Journal for Research in Mathematics Education,
49(4), 424-461. https://doi.org/10.5951/jresematheduc.49.4.0424
Peifer, C., & Zipp, G. (2019). All at once? The effects of multitasking behavior on
flow and subjective performance. European Journal of Work and
Organizational Psychology, 28(5), 682–690.
https://doi.org/10.1080/1359432x.2019.1647168
Pires, F., Maquine Lima, F. M., Melo, R., Serique Bernardo, J. R., & de Freitas, R.
(2019). Gamification and Engagement: Development of Computational
Thinking and the Implications in Mathematical Learning. 2019 IEEE 19th
International Conference on Advanced Learning Technologies (ICALT).
https://doi.org/10.1109/icalt.2019.00112
Pulimood, S. M., Pearson, K., & Bates, D. C. (2016). A Study on the Impact of
Multidisciplinary Collaboration on Computational Thinking. Proceedings of
the 47th ACM Technical Symposium on Computing Science Education.
https://doi.org/10.1145/2839509.2844636
Reinhold, F., Hoch, S., Werner, B., Richter-Gebert, J., & Reiss, K. (2020). Learning
fractions with and without educational technology: What matters for highachieving
and low-achieving students? Learning and Instruction, 65, 101264.
https://doi.org/10.1016/j.learninstruc.2019.101264
Reiser, B. J. (2002). Why Scaffolding Should Sometimes Make Tasks
More. Computer Support for Collaborative Learning: Foundations for a
CSCL Community: Proceedings of CSCL 2002 Boulder, Colorado, USA
January 7-11, 2002, 255.
Reiser, B. J. (2004). Scaffolding Complex Learning: The Mechanisms of Structuring
and Problematizing Student Work. Journal of the Learning Sciences, 13(3),
273–304. https://doi.org/10.1207/s15327809jls1303_2
Rheinberg, F., & Engeser, S. (2018). Intrinsic Motivation and Flow. Motivation and
Action, 579–622. https://doi.org/10.1007/978-3-319-65094-4_14
Richardson, F. C., & Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale:
Psychometric data. Journal of Counseling Psychology, 19(6), 551–
554. https://doi.org/10.1037/h0033456
Rivera, F. (2013). Teaching and Learning Patterns in School Mathematics. Springer
Netherlands. https://doi.org/10.1007/978-94-007-2712-0
Rodríguez del Rey, Y. A., Cawanga Cambinda, I. N., Deco, C., Bender, C., Avello‐
Martínez, R., & Villalba‐Condori, K. O. (2020). Developing computational
thinking with a module of solved problems. Computer Applications in
Engineering Education, 29(3), 506–516. https://doi.org/10.1002/cae.22214
Prensky, M. (2001). Digital Natives, Digital Immigrants Part 2: Do They Really Think
Differently? On the Horizon, 9(6), 1–6. https://doi.org/10.1108/
10748120110424843
Saleem, A. N., Noori, N. M., & Ozdamli, F. (2021). Gamification Applications in Elearning:
A Literature Review. Technology, Knowledge and Learning.
https://doi.org/10.1007/s10758-020-09487-x
Santos-Trigo, M., Barrera-Mora, F., & Camacho-Machín, M. (2021). Teachers’ Use of
Technology Affordances to Contextualize and Dynamically Enrich and Extend
Mathematical Problem-Solving Strategies. Mathematics, 9(8), 793.
https://doi.org/10.3390/math9080793
Sarid, O, Anson, O, Yaari, A, Margalith, M. (2004). Academic stress, immunological
reaction, and academic performance among students of nursing and
physiotherapy. Research in Nursing & Health, 27(5), 370–377.
https://doi.org/10.1002/nur.20028
Scantamburlo, T. (2014). Philosophical aspects in pattern recognition
research. Dspace.unive.it. http://dspace.unive.it/handle/10579/4639
Schifter, D., Monk, S., Russell, S. J., & Bastable, V. (2017). Early algebra: What does
understanding the laws of arithmetic mean in the elementary grades? In
Algebra in the early grades (pp. 413-448). Routledge.
Selby, C., Woollard, J., Selby, C., & Woollard, J. (2013). Computational thinking: the
developing definition. Eprints.soton.ac.uk. https://eprints.soton.ac.uk/356481
Settle, A. (2011). Computational thinking in a game design course. Proceedings of the
2011 Conference on Information Technology Education - SIGITE ’11.
https://doi.org/10.1145/2047594.2047612
Shin, N., Bowers, J., Krajcik, J., & Damelin, D. (2021). Promoting computational
thinking through project-based learning. Disciplinary and Interdisciplinary
Science Education Research, 3(1). https://doi.org/10.1186/s43031-021-00033-
y
Shugen, W. (2002). Framework of pattern recognition model based on the cognitive
psychology. Geo-spatial Information Science, 5(2), 74-78.
https://doi.org/10.1007/bf02833890
Shute, V. J., Sun, C., & Asbell-Clarke, J. (2017). Demystifying computational
thinking. Educational Research Review, 22, 142–158.
https://doi.org/10.1016/j.edurev.2017.09.003
Siagian, M. D., Suwanto, S., & Siregar, R. (2021). The relationship of students’ prior
knowledge and emotional intelligence to mathematical connection
ability. Jurnal Riset Pendidikan Matematika, 8(1), 61–72.
https://doi.org/10.21831/jrpm.v8i1.39182
Simons, K. D., & Klein, J. D. (2006). The Impact of Scaffolding and Student
Achievement Levels in a Problem-based Learning Environment. Instructional
Science, 35(1), 41–72. https://doi.org/10.1007/s11251-006-9002-5
Sinclair, N., Watson, A., Zazkis, R., & Mason, J. (2011). The structuring of personal
example spaces. The Journal of Mathematical Behavior, 30(4), 291–303.
https://doi.org/10.1016/j.jmathb.2011.04.001
Soni, A., & Kumari, S. (2015). The Role of Parental Math Anxiety and Math Attitude
in Their Children’s Math Achievement. International Journal of Science and
Mathematics Education, 15(2), 331–347. https://doi.org/10.1007/s10763-015-
9687-5
Sırakaya, M., Alsancak Sırakaya, D., & Korkmaz, Ö. (2020). The Impact of STEM
Attitude and Thinking Style on Computational Thinking Determined via
Structural Equation Modeling. Journal of Science Education and
Technology, 29(4), 561–572. https://doi.org/10.1007/s10956-020-09836-6
Sáez-López, J.-M., Román-González, M., & Vázquez-Cano, E. (2016). Visual
programming languages integrated across the curriculum in elementary
school: A two year case study using “Scratch” in five schools. Computers &
Education, 97, 129–141. https://doi.org/10.1016/j.compedu.2016.03.003
Sáez-López, J.-M., Sevillano-García, M.-L., & Vazquez-Cano, E. (2019). The effect
of programming on primary school students’ mathematical and scientific
understanding: educational use of mBot. Educational Technology Research
and Development, 67(6), 1405–1425. https://doi.org/10.1007/s11423-019-
09648-5
Steen, B. (1988). Body Composition and Aging. Nutrition Reviews, 46(2), 45–51.
https://doi.org/10.1111/j.1753-4887.1988.tb05386.x
Sun, C.-T., Wang, D.-Y., & Chan, H.-L. (2011). How digital scaffolds in games direct
problem-solving behaviors. Computers & Education, 57(3), 2118–2125.
https://doi.org/10.1016/j.compedu.2011.05.022
Sun, L., Hu, L., & Zhou, D. (2021). Improving 7th-graders’ computational thinking
skills through unplugged programming activities: A study on the influence of
multiple factors. Thinking Skills and Creativity, 42, 100926.
https://doi.org/10.1016/j.tsc.2021.100926
Sung, W., Ahn, J., & Black, J. B. (2017). Introducing Computational Thinking to
Young Learners: Practicing Computational Perspectives Through Embodiment
in Mathematics Education. Technology, Knowledge and Learning, 22(3), 443–
463. https://doi.org/10.1007/s10758-017-9328-x
Tanenbaum, C., Gray, T., Lee, K., Williams, M., & Upton, R. (2016). STEM 2026: A
vision for innovation in STEM education. US Department of Education,
Washington, DC. From https://www.voced.edu.au/content/ngv:75381
Tang, X., Yin, Y., Lin, Q., Hadad, R., & Zhai, X. (2020). Assessing computational
thinking: A systematic review of empirical studies. Computers &
Education, 148, 103798. https://doi.org/10.1016/j.compedu.2019.103798
Theodoridis, S. (2003). Konstantinos koutroumbas pattern recognition. In Beijing:
Mechanical (pp. 163-205). Industrial Press.
Vygotsky, L. S. (1978). Mind in society : The development of higher psychological
processes. Cambridge, MA: Harvard University Press
Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., & Wilensky, U.
(2015). Defining Computational Thinking for Mathematics and Science
Classrooms. Journal of Science Education and Technology, 25(1), 127–147.
https://doi.org/10.1007/s10956-015-9581-5
Widya, Rifandi, R., & Laila Rahmi, Y. (2019). STEM education to fulfil the 21st
century demand: a literature review. Journal of Physics: Conference
Series, 1317, 012208. https://doi.org/10.1088/1742-6596/1317/1/012208
Windsor, W. (2010). Algebraic Thinking: A Problem Solving Approach. In ERIC.
Mathematics Education Research Group of Australasia.
https://eric.ed.gov/?id=ED521033
Wing, J. M. (2006). Computational thinking. Communications of the ACM, 49(3), 33.
https://doi.org/10.1145/1118178.1118215
Wing, J. M. (2011). Research notebook: Computational thinking—What and why. The
Link Magazine, 6, 20-23.
Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problemsolving.
Child Psychology & Psychiatry & Allied Disciplines, 17(2), 89–
100. https://doi.org/10.1111/j.1469-7610.1976.tb00381.x
Yadav, A., Mayfield, C., Zhou, N., Hambrusch, S., & Korb, J. T. (2014). Computational
Thinking in Elementary and Secondary Teacher Education. ACM Transactions
on Computing Education, 14(1), 1–16. https://doi.org/10.1145/2576872
Caeli, E. N., & Yadav, A. (2020). Unplugged Approaches to Computational Thinking:
a Historical Perspective. TechTrends. https://doi.org/10.1007/s11528-019-
00410-5
Yang, Y., Yuan, K., Feng, X., Li, X., & van Aalst, J. (2022). Fostering low‐achieving
students’ productive disciplinary engagement through knowledge‐building
inquiry and reflective assessment. British Journal of Educational Technology.
https://doi.org/10.1111/bjet.13267
Yen, W.-C., & Lin, H.-H. (2020). Investigating the effect of flow experience on learning
performance and entrepreneurial self-efficacy in a business simulation systems
context. Interactive Learning Environments, 1–16. https://doi.org/10.1080/
10494820.2020.1734624