王雪芳、丁境蔚、施淑娟和許天維(2007)。數位個別指導模式成效之比較–以「面積的估算」單元為例(海報發表)。2007年NCS全國計算機會議,臺中市,臺灣。
吳慧珉、鄭俊彥和施淑娟(2015)。認知診斷模式之理論與實務。測驗學刊,62(4),302-328。
李政軒(2016)。無參數加權認知診斷模式。測驗學刊,63(2),133-152。
周文正(1998)。WWW在電腦輔助測試系統之研製。中華民國第七屆電腦輔助教學研討會,高雄市,台灣。
張志吉(2011)。國小三年級學童面積概念結構分析之研究(未出版之碩士論文)。國立臺中教育大學,臺中市。教育部(2018)。十二年國民基本教育課程綱要—數學領域。臺北市:教育部。
陳人豪(2011)。國小高年級學童面積與周長概念之錯誤類型研究(未出版之碩士論文)。國立臺中教育大學,臺中市。陳鉪逸(1996)。我國國小高年級學生平面圖形面積概念的研究。八十五學年度師範院校教育學術論文發表會論文集(2)。國立屏東師範學院。
陳嘉皇(2004)。國小學童面積概念轉化文本之設計與其教學效果之實驗研究(未出版之博士論文)。國立高雄師範大學,高雄市。曾椿惠(2010)。激發式動態呈現對學習成效與認知負荷影響之研究-以一元一次方程式為例(未出版碩士論文)。國立交通大學,新竹市。黃幸美(2009)。整合二維空間幾何與面積概念的課程與教學試驗。科學教育學刊,17(6),509-530。
楊肅健、郭伯臣、林秋斌(2021)。知識結構的電腦化適性診斷測驗數位平臺應用於國小數學補救教學成效之研究。數位學習科技期刊,13(1),23-48。
葉淑慧(2005)。國小面積保留概念電腦測驗發展與實驗教材之研究(未出版之碩士論文)。國立臺南大學,臺南市。蔡春美(1982)。臺東縣山地兒童面積保留與面積測量概念的發展(未出版之碩士論文)。國立臺灣師範大學,臺北市。譚寧君(1994)。高年級面積教材的分析。國民小學數學科新課程概說(高年級),134-165,台北市:教育部。
譚寧君、黃琡懿(2009)。TARIS教學策略融入國小四年級面積教學之研究。科學教育研究與發展季刊,53,43-69。
Alexander, M., Bartlett, J., Truell, A. D., Ouwenga, K. (2001). Testing in a computer technology course: An investigation of equivalency in performance between online and paper and pencil methods. Journal of Career Technical Education, 18, 69-80.
Alsawaier, R. (2017). The effect of gamification on motivation and engagement. International Journal of Information and Learning Technology, 35(1), 56-79.
Artar, A., & Huseynli, B. (2017). Gamification based performance evaluation system a new model suggestion [Conference presentation]. 7th International Conference Leadership, Technology, Innovation and Business Management. Marmaris, Turkey.
Baker, R. (2014). The effect of learning motivation on student’s productive competencies in vocational high school, west Sumatra. International Journal of Asia Social Science, 4(6), 722-723.
Bandura, A. (1994). Self-efficacy. In V. S. Ramachaudran (Ed.), Encyclopedia of human behavior (Vol. 4, pp. 71-81). New York: Academic Press.
Banfield, J., & Wilkerson, B. (2014). Increasing student intrinsic motivation and slef-efficacy through gamification pedagogy. Contemporary Issues in Educational Research, 7(4), 291-298.
Barana, A., Marchisio, M., & Sacchet, M. (2019). Advantages of using automatic formative system for learning mathematics. In: Draaijer S., Joosten-ten Brinke D., Ras E. (eds) Technology Enhanced Assessment. TEA 2018. Communications in Computer and Information Science, vol 1014. Springer, Cham.
Barana, A., Marchisio, M., & Sacchet, M. (2021). Interactive feedback for learning mathematics in a digital learning environment. Education Sciences, 11(6), 279.
Brigham, T. J. (2015). An introduction to gamification: adding game elements for engagement. Medical Reference Services Quarterly, 34(4), 471-480.
Buckley, P. & Doyle, E. (2016). Gamification and student motivation. Interactive Learning Environment, 24(6), 1162-1175.
Buckley, P., & Doyle, E. (2017). Individualising gamification. An investigation of the impact of learning styles and personality traits on the efficacy of gamification using a prediction market. Computers & Education, 106, 43-55.
Chalmers, D., & McAusland, W. D. (2002). Computer Assisted Assessment. Retrieved from: https://www.economicsnetwork.ac.uk/handbook/caa/welcome
Chang, Y. P., Chiu, C. Y., & Tsai, R. C. (2019). Nonparametric CAT for CD in educational setting with small samples. Applied Psychological Measurement, 43(7), 543-561.
Chen, J., & de la Torre, J. (2013). A general cognitive diagnosis model for expert-defined polytomous attributes. Applied Psychological Measurement, 37(6), 419-437.
Chiu, C. Y., & Douglas, J. (2013). A nonparametric approach to cognitive diagnosis by proximity to ideal response patterns. Journal of Classification, 30, 225-230.
Chiu, C. Y., & Kohn, H. F. (2019). Consistency theory for the general nonparametric classification method. Psychometrika, 84, 830-845.
Chiu, C. Y., Sun, & Y., Bian, Y. (2018). Cognitive diagnosis for small educational programs: The general nonparametric classification method. Psychometrika, 83(2), 355-375.
Choi, K. M., Lee, Y. S., & Park, Y. S. (2015). What CDM can tell about what students have learned: An analysis of TIMSS eighth grade mathematics. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1563-1577.
Clement, D. H., Sarama, J. (2004). Engaging young children in mathematics. Lawrence Erlbaum Assiciates, Inc.
Conner, M. C., Mazzocco, M. M. M., Arizona, T. K., Crowe, E. C., Tighe, E. L., Wood, T. S., & Morrison, F. J. (2018). Using assessment to individualize early mathematics instruction. Journal of School Psychology, 66, 97-113.
Conole, G., & Warburton, B. (2005). A review of computer-assisted assessment. Research in Learning Technology, 13(1), 17-31.
Cosgrove, P. J. A. (2016). The effects of gamification on self-efficacy and persistence in virtual world familiarization [Unpublished doctoral dissertation]. University of Missouri-Columbia.
Cross, C. T., Woods, T. A., & Schweingruber, H. (2009). Mathematics Learning in early childhood. National Academies Press.
de la Torre, J. (2009). A cognitive diagnosis model for cognitively based multiple-choice options. Applied Psychological Measurement, 33, 163-183
de la Torre, J., & Minchen, N. (2014). Cognitively diagnostic assessments and the cognitive diagnosis model framework. Psicología Educativa, 89-97.
Deterding, S., Dixon, D., Khaled, R., & Nacke, L. (2011). From game design elements to gamefulness: defining gamification [Conference presentation]. Proceedings of the 15th International Academic MindTrek conference: Envisioning Future Media Environments, Tampere, Finland.
Dichev, C., & Dicheva, D. (2017). Gamifying education: what is known, what is believed and what remains uncertain: a critical review. International Journal of Educational Technology in Higher Education, 14(9).
Effatpanah, F. (2019). Application of cognitive diagnostic models to the listening section of the international English language testing system. International Journal of Language Testing, 9(1).
Erickson, A., Lundell, J., Michela, E., & Pfleger, P. I. (2020). Gamification. In Kimmons & Caskurlu (Ed.), The students’ guide to learning design and research.
Esdal, L. (2016). Our working definition of student achievement and school quality. https://www.educationevolving.org/
Evran, D. (2019). An application of cognitive diagnosis modeling in TIMSS: A comparison of intuitive definitions of Q-matrices. International Journal of Modern Education Studies, 3(1), 4-17.
Filgona, J., & Okoronka, A. U. (2020). Motivation in learning. Asian Journal of Education and Social Studies, 10(4), 16-37.
Fletcher, P., & Collins, M.J. (1987). Computer- administered versus written test- advantages and disadvantage. Journal of Computer in Mathematics and Science Teaching, 6(2),38-43.
Gachkova, M., & Somova, E. (2016). An attempt for gamification of learning in moodle[Conference Presentation]. International Conference on e-Learning, Bratislava, Slovakia.
George, A. C., Robitzsch, A., Kiefer, T., Groß, J., & Ünlü, A. (2016). The R package CDM for cognitive diagnosis models. Journal of Statistical Software, 74(2), 1-24.
Grete J. A., & Green, M. (2000). Improving undergraduate learning with computer-assisted assessment. Journal of Research on Computing in Education, 33(1), 46-54.
Hakulinen, L., Auvinen, T., & Korhonen, A. (2015). The effect of achievement badges on students’ behavior: An empirical study in a university-level computer science course. International Journal of Emerging Technologies in Learning, 10(1), 18-29.
Hamari, J., Koivisto, J., & Sarsa, H. (2014). Does gamification work?—A literature review of empirical studies on gamification[Conference presentation]. 47th Hawaii International Conference on System Science, HA, United States.
Hassan, L., Rantalainen, J., Xi, N., Pirkkalainen, H., & Hamari, J. (2020). The relationship between player types and gamification feature preferences [Conference presentation]. GamiFIN Conference 2020, Levi, Finland.
Hewson, C. M., & Charlton, J. (2018). An investigation of the validity of course-based online assessment methods: the role of computer-related attitudes and assessment mode preferences. Journal of Computer Assisted Learning, 35(5).
Howse, T. D., & Howse, M. E. (2015). Linking the Van Hiele Theory to Instruction. Teaching Children Mathematics, 21(5), 305-313.
Huang, Y. M., Huang, Y. M., Liu, C. H., & Tsai, C. C. (2013). Applying social tagging to manage cognitive load in a Web 2.0 self-learning environment. Interactive Learning Environments, 21(3), 273-289.
Jong, T. (2010). Cognitive load theory, educational research, and instructional design: Some food for thought. Instructional Science, 38(2), 105-134.
Karimi, K., & Nickpayam, J. (2017). Gamification from the viewpoint of motivational theory. Italian Journal of Science & Engineering,1(1),34-42.
Khaddage, F., Lattemann, C., & Acosta-Diaz, R. (2014). Mobile gamification in education engage, educate and entertain via gamified mobile apps [Conference presentation]. Society for Information Technology & Teacher Education International Conference, Chesapeake, VA, United States.
Kiryakova, G., Angelova, N., & Yordanova, L. (2014). Gamification in education. American Society of Business and Behavioral Sciences, 21(1), 32-39.
Kotwal, M. (2020). Top features to look for in an online assessment software. https://technologycounter.com/blog/best-features-of-online-assessment-software
Lee, J., & Hammer, J. (2011). Gamification in education: What, how, why bother? Academic Exchange Quarterly,15(2), 1-5.
Lee, Y. W., & Sawaki, Y. (2009). Cognitive diagnosis approaches to language assessment: An overview. Language Assessment Quarterly, 6(3), 172-189
Lingard, M. (2005). Introduction computer-assisted assessment: considerations for the new practitioner. Investigations in University Teaching and Learning, 2(2), 69-75.
Lister, M. C. (2015). Gamification: The effect on student motivation and performance at the post-secondary level. Issue and Trends in Educational Technology, 3(2).
Liu, H. Y., You, X. F., Wang, W. Y., Ding, S. L., & Chang, H. H. (2013). The development of computerized adaptive testing with cognitive diagnosis for an English achievement test in China. Journal of Classification, 30, 152-172.
Liu, Z. F., & Lin, C. H. (2010). The survey study of mathematics motivation strategies for learning questionnaire(MMSLQ) for 10-12 Taiwanese students. The Turkish Online Journal of Educational Technology, 9(2), 221-233.
Lukashenko, R., & Anohina, A. (2009). Knowledge assessment system: an overview. Scientific Journal of Riga Technical University Computer Science, 38(38), 25-36.
Mahoney, P., Macfarlane, S., & Ajjawi, R. (2019). A qualitative synthesis of video feedback in higher education. Teaching in Higher Education, 24(2), 157-179.
Manizade, A., & Mason, M. M. (2014). Developing the area of a trapezoid. Journal of Mathematics Teacher Education, 107(7), 509-514.
Martin, W. G., & Strutchens, M. E. (2000). Geometry and measurement, In E. A. Silver & P. A. Kenney (Eds.), Results from the seventh mathematics assessment of the national assessment of educational progress, 193-234, Reston, VA: NCTM.
Mohamad, S. N. M., Sazali, N. S. S., & Salleh, M. A. M. (2018). Gamification approach in education to increase learning engagement. International Journal of Humanities, Arts and Social Science, 4(1), 22-32.
Nand, K., Baghaei, N., Casey, J., Barmada, B., Mehdipour, F., & Liang, H. N. (2019). Engaging children with educational content via Gamification. Smart Learn. Environ, 6(6).
Nikolova, M. (2012). Characteristic and forms of the assessment of knowledge. Mathematics, Nauchni Trudove Narusenskiya, 6.2, 93-98.
Novo, A., & Calixto, J. A. (2009). Academic achievement and/or educational attainment – the role of teacher librarians in students’ future: main findings of a research in Porttugal [Conference presentation]. 38th IASL Annual Conference, Abano Terme, Padua, Italia.
Nugroho, R. A., Kusumawati, N. S., & Ambarwati, O. C. (2018). Student perception on the use of computer based test. IOP Conference Series: Materials Science and Engineering, 306.
Organisation for Economic Co-Operation and Development. (2013), Education at a Glance 2013. OECD Publishing. https://doi.org/10.1787/2076264x
Parhizgar, S. (2012). Testing and technology: Past, present and future. Theory and Practice in Language Studies, 2(1), 174-178.
Park, S., & Kim, S. (2021). Leaderboard design principles to enhance learning and motivation in a gamified educational environment: Development study. JMIR Serious Games, 9(2):e14746.
Paulsen, J., & Valdivia, D. S. (2021). Examining cognitive diagnostic modeling in classroom assessment conditions. The Journal of Experimental Education.
Pelling, N. (2011). The (short) prehistory of “gamification” … Funding Startups (& other impossibilities).
Pezzino, M. (2018). Online assessment, adaptive feedback and the importance of visual learning for students. The advantages, with a few caveats, of using MapleTA. International Review of Economics Education, 28, 11-28.
Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child's conception of geometry. Basic Books.
Piaget, J., Inhelder, B., Langdon, F. J., & Lunzer, J. L. (1967). The Child’s Conception of Space. W.W. Norton & Company, Inc.
Rajani, N. B., Mastellos, N. & Filippos, T. F. (2021). Impact of gamification on the self-efficacy and motivation to quit smokers: observation study of two gamified smoking cessation mobile apps. JMIR Serious Games, 9(2):e27290.
Ravand, H., & Robitzsch, A. (2018). Cognitive diagnostic model of best choice: a study of reading comprehension. An International Journal of Experimental Educational Psychology, 38(10), 1255-1277.
Rejeki, S., & Putri, R. I. I. (2018). Models to support students’ understanding of measuring area of circles. Journal of Physics: Conference Series, 948.
Rojas, M. O., Chiluiza, K., & Valcke, M. (2017). Gamification in computer programming: effects on learning, engagement, self-efficacy and intrinsic motivation [Conference presentation]. The 11th european conference on games based learning. England
Rosenshine, B., & Stevens, R. J. (1986). Teaching functions. In M. C. Wittrock (Ed.), Handbook of Research on Teaching (3rd ed., pp. 376-391). New York: Macmillan.
Ross, J., & Lancastle, S. (2019) Increasing student engagement with formative assessment through the application of screen cast video feedback – a case in engineering, Edulearn19 Proceedings, 3962-3971.
Sandrone, S., & Carlson, C. (2021). Gamification and game-based education in neurology and neuroscience: Application, challenge and opportunities. Brain Disorders, 1.
Satsangi, R., & Bouck, E. C. (2015). Using virtual manipulative instruction to teach the concepts of area and perimeter to secondary students with learning disabilities. Learning Disability Quarterly, 38(3), 174-186.
Shaban, A., Pearson, E., & Chang, V. (2021). Evaluation of user experience, cognitive load, and training performance of a gamified cognitive training application for children with learning disabilities. Frontiers in Computer Science, 6(3):617056.
Shaw, L. F., Specht, M., van Rosmalen, P., & Bryan, J. B. (2020). Do badges affect intrinsic motivation in introductory programming students? Simulation & Gaming, 51(1), 33-54.
Sigman, D., & Mancuso, M. (2017). Designing a comprehensive assessment system. San Francisco, CA: WestEd.
Siozos, P., Palaigeorgiou, G., & Triantafyllakos, G. (2009). Computer based testing using “digital ink”: participatory design of a tablet PC based assessment application for secondary education. Computer & Education, 52(4), 811-819.
Sisman, G. T., & Aksu, M. (2016). A study on sixth grade students’ misconceptions and errors in spatial measurement: length, area and volume. International Journal on Science and Mathematics Education, 14(7), 1293-1319.
Spanellis, A., Dorfler, V., & Macbryde, J. (2016). Gamification and innovation: a mutually beneficial union [Conference presentation]. 30th Annual Conference of the British Academy of Management. Newcastle upon tyne, UK.
Stefanie, S. E. (1998). A Piagetian perspective on singing development. Musikpsychologie, 13, 108-125.
Stephens, D., Bull, J., & Wade, W. (1998). Computer-assisted assessment: suggested guidelines for an institutional strategy. Assessment & Evaluation in Higher Education, 23(3), 283-294.
Su, C. H., & Cheng, C. H. (2014). A Mobile gamification learning system for improving the learning motivation and achievements. Journal of Computer Assisted Learning, 31(3), 268-286.
Tatsuoka, K. K. (1990). Toward an integration of item-response theory and cognitive error diagnosis. In N. Frederiksen, R. Glaser, A. Lesgold, & M. Safto (Eds.), Monitoring skills and knowledge acquisition (pp. 453–488). Hillsdale: Lawrence Erlbaum Associates.
Tatsuoka, K. K. (2009). Cognitive assessment: An introduction to the rule space method. Routledge.
Tossavainen, T., Suomalainen, H., & Makalainen, T. (2017). Student teacaher’s concept definition of area and their understanding about two-dimensionality of area. International Journal of Mathematical Education in Science and Technology, 48(4), 520-532.
Toth, A., & Tovolgyi, S. (2016). The introduction of gamification: A review paper about the applied gamification in the smartphone applications [Conference presentation]. 2016 7th IEEE International Conference on Cognitive Infocommunications. Worclaw, Poland.
Trends in International Mathematics and Science Study. (2019). International results in mathematics and science. Chestnut Hills, MA:TIMSS.
Tseng, S. C., & Tsai, C. C. (2010). Taiwan college students’ self-efficacy and motivation of learning in online peer assessment environments. The Internet and Higher Education, 13(3), 164-169.
Turan, Z., Avinc, Z., Kara, K., & Goktas, Y. (2016). Gamification and education: achievements, cognitive loads, and views of students, International Journal of Emerging Technologies in Learning, 11(7), 64-69.
University of Leicester. (1999). What is Computer Assisted Assessment? Retrieved from: http://www2.le.ac.uk/Members/rjm1/talent/book/c3p2.html – 01.10.2008
van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.
Wafa, M. N., Hussaini, S. A. M., & Pazhman, J. (2020). Evaluation of students’ mathematical ability in Afghanistan’s schools using cognitive diagnosis models, EURASIA Journal of Mathematics, Science and Technology Education, 16(6), em1849.
Wang, L. C., & Chen, M. P. (2010). The effects of game strategy and preference‐matching on flow experience and programming performance in game‐based learning. Innovations in Education and Teaching International, 47(1), 39-52.
Wang, S. L., & Hwang, G. J. (2012). The role of collective efficacy, cognitive quality, and task cohesion in computer-supported collaborative learning(CSCL). Computer & Education, 58(2), 679-687.
Wang, S., Douglas, J. (2015). Consistency of nonparametric classification in cognitive diagnosis, Psychometirka, 80(1), 85-100.
Wanner, S. C. A. (2019). Mitigating misconceptions of preservice teachers: the relationship between area and parameter. Ohio Journal of School Mathematics, 82, 36-44.
Way, J. (2011). The development of spatial and geometric thinking: the importance of instruction. https://nrich.maths.org/2487
Welbers, K., Konijn, E. A., Burgers, C., de Vaate, A. B., Eden, A., & Brugman, B. C. (2019). Gamification as a tool for engaging student learning: A field experiment with a gamified app. E-Learning and Digital Media, 16(2), 92-109.
Wilson, M., & Sloane, K. (2000). From principle to practice: An embedded assessment system. Applied Measurement Education, 13(2), 181-208.
Winarti, D., Amin, S. M., Lukito, A., & Galen, F.H.J. van (2012). Learning the concept of area and perimeter by exploring their relation. Journal on Mathematics Education, 3(1), 41-54.
Wu, H. M. (2019). Online individualized tutor for improving mathematics learning: a cognitive diagnostic model approach. Educational Psychology, 39(10), 1218-1232.
Wu, Y. L. (2016). Gamification design: A comparison of four m-learning courses. Innovations in Education and Teaching International, 55(4), 470-478
Xu, X., & von Davier, M. (2006). Cognitive diagnosis for NAEP proficiency data (ETS Research Rep. No. RR-06-08). Princeton, NJ: Educational Testing Service.
Yamaguchi, K., Okada, K. (2018). Comparison among cognitive diagnostic models for the TIMSS 2007 four grade mathematics assessment. PLoS ONE, 13(2).
Yusuf, M. (2011). The impact of self-efficacy, achievement motivation, and self-regulated learning strategies on students’ academic achievement. Procedia Social and Behavioral Science, 15, 2623-2626.
Zaharin, F. Z., Karim, N. S. A,, Adenan, N. H., Junus, N. W. M., Tarmizi, R. A., Hamid, N. Z. A., & Latib, L. A. (2021). Gamification in Mathematics: Students’ Perceptions in Learning Perimeter and Area. Jurnal Pendidikan Sains Dan Matematik Malaysia, 11, 72-80.
Zhang, J., Lu, J., Yang, J., Zhang, Z., & Sun, S. (2021). Exploring multiple strategic problem solving behaviors in educational psychology research by using mixture cognitive diagnosis model. Frontiers in Psychology, 3.
Zichermann, G., & Cunningham, C. (2011). Gamification by design: implementing game mechanics in web and mobile apps. Sebastopol, CA: O’Reilly Media.