目前已有許多研究指出學習者空間能力與其幾何學科有顯著的正相關，然而大多數量測個體空間能力的方式是以心像旋轉以及空間視覺的測驗量表為主，鮮少探討個體對於感知空間實物大小與距離的能力。雖目前國小課程已將實際量測納入學習活動中，然而礙於傳統教學的限制影響，學習者無法正確的觀察抽象的度量單位與實際大小之間的關係。因此本研究設計一套Ubiquitous Geometry(UG)學習系統，將學習者日常生活常見的物件與其幾何學習內容作結合，並透過行動載具進行實際量測，藉此提升其量測動機與經驗，並強化對於幾何概念的記憶與理解。本研究參與者為某國小五年級三個班級的學生，共計75人，為期五週的實驗期間，三組將進行不同學習方式，以探討不同實驗干預之學習者的學習成效以及其量測估算能力之差異性，並進一步探討實驗組的學習行為與其學習成效間的關聯性。
研究結果表明，在幾何學科測驗中實驗組顯著優於控制組甲、控制組乙；在量測估算能力測驗中實驗組顯著優於控制組乙，此外接受不同學習干預的學習者其量測估算能力與其幾何學習成效皆呈現顯著正相關。實驗組的學習行為分析結果表明，在同儕互評活動中，學習者給予同儕協助(aid)性建議的數量與其學習成效呈現顯著正相關；在同儕競爭的學習活動中，學習者的挑戰次數、挑戰最高分以及觀看挑戰紀錄與其學習成效呈現顯著正相關；學習者實際量測次數與其學習成效和量測估算能力呈現顯著正相關。多數實驗組的學習者皆認為透過實際量測的經驗是能夠有效的提升其對於幾何概念的理解，並且對於其量測估算能力是有幫助的。

Several researchers recently indicated that individual’s spatial ability and learning achievement of geometry have a significant positive correlation. Out of that most of the researchers employed a questionnaire including mental rotation or spatial visualization to test individual’s spatial ability. However, the individual’s ability in perceiving the real object size or the distance to the object has not been thoroughly investigated so far. In this study, we developed the ubiquitous geometry (UG) learning system to support students to learn about geometric concepts, and to enhance their motivation to perform real world measurements. 75 fifth grade students were participated in this study during five weeks, where they were divided into three groups with different learning ways. We investigated the difference of geometry learning achievement and measurement estimation ability among three groups, and further explored the relationship between the learning behavior and learning achievement.
In the geometry test, the results show that experimental group performed better than control groups I and II. The results of measurement estimation test represent that the experimental group performed better than control group II. Moreover, irrespective of the kind of learning way used, students’ geometry learning achievement has a positive correlation with their measurement estimation ability. The results of the learning behavior analysis show that the amount of aid suggestion feedbacks has a positive correlation with learning achievement. In the peer competition, the amount of competition, the highest score of competition and the amount of review competition have positive correlations with learning achievement. The amount of actual measurement has positive correlations with their learning achievement and measurement estimation ability. Finally, most of the participants had a positive attitude towards the UG system and the designed activities, and expressed that the UG system helped them to enhance their measurement ability and knowledge on geometric concepts effectively.

中文部分
1. 王仁癸（2009）。情境教學在國小英語教學的應用。北縣教育，69期，87-91。
2. 吳姈蓉（2004）。行動學習環境下的數學步道及互動解題討論系統之建置與應用。臺灣師範大學工業科技教育學系學位論文，1-158。
3. 李淑芬（2013）。以行動科技結合學生小組成就區分法 (STAD) 融入社會學習領域教學之行動研究。淡江大學教育科技學系碩士在職專班學位論文。
4. 宋千儀（2011）。競爭式學習在實驗策略的合適性探討。臺灣師範大學資訊工程研究所學位論文, 1-140。
5. 林邵珍（2003）。運用 ARCS 動機設計模式之生活科技教學。生活科技教育，36(4)，52-59。
6. 教育部（2003）。國民中小學九年一貫課程綱要。台北，教育部。
7. 曹雅玲、陳鴻綸（2007）。數學步道活動在數學教學之應用。科學教育(302) ，21-37。
8. 張春興（2006）。教育心理學：三化取向的理論與實踐 (修訂版)。臺北：心理。
9. 黃雅琪（2010）。國民小學五年級學童幾何學習表現之研究。國立屏東教育大學數理教育研究所碩士論文，未出版。台灣：屏東。
10. 蕭純如（2009）。網路同儕互評應用於藝術設計領域之研究-以「電腦動畫」課程為例。國立嘉義大學教育科技研究所碩士論文，未出版，嘉義。
11. 韓佳玲（2002）。網路匿名競爭對學習經驗之影響。成功大學教育研究所學位論文, 1-92。
 
英文部分
Baroody, A., & Coslick, R. T. (1998). Fostering children's mathematical power: An investigative approach to K-8 mathematics instruction: Routledge.
Bayrak, M. E. (2008). Investigation of effect of visual treatment on elementary school student’s spatial ability and attitude toward spatial ability problems. MIDDLE EAST TECHNICAL UNIVERSITY.
Boud, D., Cohen, R., & Sampson, J. (1999). Peer learning and assessment. Assessment & Evaluation in Higher Education, 24(4), 413-426.
Bright, G., & Hoeffner, K. (1993). Measurement, probability, statistics, and graphing. Research ideas for the classroom: Middle grades mathematics, 78-98.
Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational researcher, 18(1), 32-42.
Burton, D. M. (1985). The history of mathematics: An introduction. AMC, 10, 12.
Chen, C. C., & Huang, T. C. (2012). Learning in a u-Museum: developing a context-aware ubiquitous learning environment. Computers & Education, 59(3), 873–883.
Cheng, Y. L., & Mix, K. S. (2013). Spatial training improves children's mathematics ability. Journal of Cognition and Development(ahead-of-print), 1-10.
Chiou, C. K., Tseng, J. C., Hwang, G. J., & Heller, S. (2010). An adaptive navigation support system for conducting context-aware ubiquitous learning in museums. Computers & Education, 55(2), 834-845.
Chu, H. C., Hwang, G. J., Tsai, C. C., & Tseng, Judy C. R. (2010). A two-tier test approach to developing location-aware mobile learning system for natural science course. Computers & Education, 55, 1618-1627.
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning.
Corno, L., & Rohrkemper, M. (1985). The intrinsic motivation to learn in classrooms. Research on motivation in education, 2, 53-90.
Curtis, M., Luchini, K., Bobrowsky, W., Quintana, C., & Soloway, E. (2002). Handheld use in K-12: A descriptive account. Paper presented at the Wireless and Mobile Technologies in Education, 2002. Proceedings. IEEE International Workshop on.
Davis, F. D. (1989). Perceived usefulness, perceived ease of use, and user acceptance of information technology. MIS quarterly, 319-340.
Davis, G. A., & Rimm, S. B. (1989). Education of the gifted and talented: Prentice-Hall, Inc.
Falchikov, N. (1995). Peer feedback marking: developing peer assessment. Programmed Learning, 32(2), 175-187.
Fallows, S., & Chandramohan, B. (2001). Multiple approaches to assessment: reflections on use of tutor, peer and self-assessment. Teaching in Higher Education, 6(2), 229-246.
Gardner, H. (1993). Multiple intelligences: The theory in practice: Basic books.
Garrett, A. W., & Davis Jr, O. (2003). A time of uncertainty and change: School mathematics from World War II until the new math. A history of school mathematics, 1, 493-520.
Graf, S. (2008). Adaptivity and personalization in ubiquitous learning systems HCI and Usability for Education and Work (pp. 331-338): Springer.
Guay, R. B., & McDaniel, E. D. (1977). The relationship between mathematics achievement and spatial abilities among elementary school children. Journal for Research in Mathematics Education, 211-215.
Habibi, M. (2012). The Role of intuitive and Life-related Activities in Improving Teaching of Geometry in Primary School. Journal of American Science, 8(6).
Hannafin, R. D., Truxaw, M. P., Vermillion, J. R., & Liu, Y. (2008). Effects of spatial ability and instructional program on geometry achievement. The Journal of Educational Research, 101(3), 148-157.
Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities? Mathematical Thinking and Learning, 5(4), 259-280.
Holmes, J., Adams, J. W., & Hamilton, C. J. (2008). The relationship between visuospatial sketchpad capacity and children's mathematical skills. European Journal of Cognitive Psychology, 20(2), 272-289.
Huang, S. H., Wu, T. T., Chen, H. R., Yang, P. C., & Huang, Y. M. (2012). Mathematics Assisted Instruction System of M/U-Learning Environment. Paper presented at the Wireless, Mobile and Ubiquitous Technology in Education (WMUTE), 2012 IEEE Seventh International Conference on.
Hwang, G. J. (2006). Criteria and Strategies of Ubiquitous Learning. Proceedings of the IEEE InternationalConference on Sensor Networks, Ubiquitous, and Trustworthy Computing (vol. 2, pp.72-77). IEEE Computer Society: Washington, DC, USA.
Hwang, G. J., Tsai, C. C., Chu, H. C., & Kinshuk Chen, C. Y. (2012). A context-aware ubiquitous learning approach to conducting scientific inquiry activities in a science park. Australasian Journal of Educational Technology, 28(5), 931–947.
Hwang, G. J., Tsai, C. C., & Yang, Stephen. J. H (2008). Criteria, strategies and research issues of context-aware ubiquitous learning. Journal of Educational Technology & Society, 11(2), 81–91.
Hwang, G. J., Wu, T. T., & Chen, Y. J. (2007). Ubiquitous computing technologies in education. Journal of Distance Education Technology, 5 (4), 1-4.
Hwang, W.Y., Chen, H.S.L., Shadiev, R., Huang, R.Y.M. & Chen, C.Y. (2012). Improving English as a foreign language writing in elementary schools using mobile devices in familiar situational contexts. Computer Assisted Language Learning, 1-20. DOI:10.1080/09588221.2012.733711
Hwang, W. Y., & Hu, S. S. (2013). Analysis of peer learning behaviors using multiple representations in virtual reality and their impacts on geometry problem solving. Computers & Education, 62, 308-319.
Ibáñez, M. B., García, J. J., Galán, S., Maroto, D., Morillo, D., & Kloos, C. D. (2011). Design and Implementation of a 3D Multi-User Virtual World for Language Learning. Journal of Educational Technology & Society, 14(4).
Jones, G., Taylor, A., & Broadwell, B. (2009). Estimating linear size and scale: Body rulers. International Journal of Science Education, 31(11), 1495-1509.
Jones, M. G., Gardner, G. E., Taylor, A. R., Forrester, J. H., & Andre, T. (2012). Students' accuracy of measurement estimation: Context, units, and logical thinking. School Science and Mathematics, 112(3), 171-178.
Kaufman, J. H., & Schunn, C. D. (2011). Students’ perceptions about peer assessment for writing: their origin and impact on revision work. Instructional Science, 39(3), 387-406.
Kelch, K. (2011). CURRICULUM DEVELOPMENT IN ENGLISH LANGUAGE TEACHING: INNOVATIONS AND CHALLENGES FOR THE ASIAN CONTEXT. International Journal of Organizational Innovation, 3(3).
Keller, J. M. (1983). Motivational design of instruction. Instructional design theories and models: An overview of their current status, 1, 383-434.
Keller, J. M. (1984). The use of the ARCS model of motivation in teacher training. Aspects of educational technology, 17, 140-145.
Keller, J. M. (1987a). Development and use of the ARCS model of instructional design. Journal of instructional development, 10(3), 2-10.
Keller, J. M. (1987b). Strategies for stimulating the motivation to learn. Performance & Instruction, 26(8), 1-7.
Kelley, T. L. (1928). Crossroads in the mind of man: A study of differentiable mental abilities: Stanford university press.
Kohn, A. (1987). The case against competition.
Kulik, J. A., & Kulik, C. L. C. (1988). Timing of feedback and verbal learning. Review of Educational Research, 58(1), 79-97.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation: Cambridge university press.
Lesh, R., & Lamon, S. J. (1992). Assessment of Authentic Performance in School Mathematics. AAAS Press Series on Assessment and Evaluation: ERIC.
Lin, H. C. K., Chen, M. C., & Chang, C. K. (2013). Assessing the effectiveness of learning solid geometry by using an augmented reality-assisted learning system. Interactive Learning Environments(ahead-of-print), 1-12.
Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child development, 1479-1498.
Liu, T. Y., Tan, T. H., & Chu, Y. L. (2009). Outdoor Natural Science Learning with an RFID-Supported Immersive Ubiquitous Learning Environment. Educational Technology & Society, 12(4), 161-175.
Lo, J., & Hyland, F. (2007). Enhancing students’ engagement and motivation in writing: The case of primary students in Hong Kong. Journal of Second Language Writing, 16(4), 219-237.
Lohman, D. F., Pellegrino, J. W., Alderton, D. L., & Regian, J. (1987). Dimensions and components of individual differences in spatial abilities Intelligence and cognition: Contemporary frames of reference (pp. 253-312): Springer.
Malone, Thomas W, & Lepper, Mark R. (1987). Making learning fun: A taxonomy of intrinsic motivations for learning. Aptitude, learning, and instruction, 3, 223-253.
Marja. (1998). Realistic Mathematics Education as work in progress. Theory into practice in Mathematics Education. Kristiansand, Norway: Faculty of Mathematics and Sciences.
Mathematics., N. C. o. T. o. (1989). Curriculum and evaluation standards for school mathematics: Natl Council of Teachers of.
Moir, A., & Jessel, D. (1989). Brain sex: The real difference between men and women (Vol. 149): Mandarin London.
Napier, E. (1981). Competition in the Classroom. Kappa Delta Pi Record, 18(1), 18-23.
Nilges, L., & Usnick, V. (2000). The role of spatial ability in physical education and mathematics. Journal of Physical Education, Recreation & Dance, 71(6), 29-33.
Ogata, H., Akamatsu, R., & Yano, Y. (2005). Computer supported ubiquitous learning environment for vocabulary learning using RFID tags Technology Enhanced Learning (pp. 121-130): Springer.
Peng, H., Chuang, P. Y., Hwang, G. J., Chu, H. C., Wu, T. T., & Huang, S. X. (2009). Ubiquitous Performance-support System as Mindtool: A Case Study of Instructional Decision Making and Learning Assistant. Journal of Educational Technology & Society, 12(1).
Pepitone, E. A. (1985). Children in cooperation and competition Learning to cooperate, cooperating to learn (pp. 17-65): Springer.
Philpot, T. A., Hall, R. H., Hubing, N., & Flori, R. E. (2005). Using games to teach statics calculation procedures: Application and assessment. Computer Applications in Engineering Education, 13(3), 222-232.
Pintrich, P. R., & De Groot, E. V. (1990). Motivational and self-regulated learning components of classroom academic performance. Journal of educational psychology, 82(1), 33.
Pownell, D., & Bailey, G. D. (2001). Getting a Handle on Handhelds: What To Consider before You Introduce Handheld Computers in Your Schools. American School Board Journal, 188(6), 18-21, 48.
Regueras, L. M., Verdú, E., Verdú, M. J., Pérez, M. Á., de Castro, J. P., & Muñoz, M. F. (2008). Motivating students through on-line competition: An analysis of satisfaction and learning styles Advances in Web Based Learning-ICWL 2008 (pp. 167-177): Springer.
Roberts, M. L., & Wortzel, L. H. (1979). NEW LIFE-STYLE DETERMINANTS OF WOMEN'S FOOD SHOPPING BEHAVIOR. Journal of Marketing, 43(3).
Rowan, T. E. (1990). Implementing the Standards: Spatial Sense. The Geometry Standards in K-8 Mathematics. Arithmetic Teacher, 37(6), 24-28.
Schon, D. A. (1987). Educating the reflective practitioner: Jossey-Bass San Francisco.
Shih, S. C., Kuo, B. C., & Liu, Y. L. (2012). Adaptively Ubiquitous Learning in Campus Math Path. Educational Technology & Society, 15(2), 298-308.
Shih, W. C., Tseng, S. S., Yang, C. C., Lin, C. Y., & Liang, T. (2012). A Folksonomy-based Guidance Mechanism for Context-aware Ubiquitous Learning: A Case Study of Chinese Scenic Poetry Appreciation Activities. Journal of Educational Technology & Society, 15(1).
Shin, S. C., Kuo, B. C., & Liu, Y. L. (2012). Adaptively Ubiquitous Learning in Campus Math Path. Journal of Educational Technology & Society, 15(2).
Sowder, J. T. (1992). Estimation and number sense.
Stahl, R. J. (1992). From" academic strangers" to successful members of a cooperative learning group: An inside-the-learner perspective. Cooperative Learning in Social Studies Classroom, An Introduction to Social Study, 8-15.
Suchman, L. A. (1987). Plans and situated actions: the problem of human-machine communication: Cambridge university press.
Tan, T. H., Lin, M. S., Chu, Y. L., & Liu, T. Y. (2012). Educational Affordances of a Ubiquitous Learning Environment in a Natural Science Course. Journal of Educational Technology & Society, 15(2).
Tartre, L. A. (1990). Spatial orientation skill and mathematical problem solving. Journal for Research in Mathematics Education, 216-229.
Thom, R. (2002). Measurement? It's Fun! Didn't You Guess? Australian Primary Mathematics Classroom, 7(2), 26.
Topping, K. (1998). Peer assessment between students in colleges and universities. Review of Educational Research, 68(3), 249-276.
Towler, L., & Broadfoot, P. (1992). Self‐assessment in the Primary School. Educational Review, 44(2), 137-151.
Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M., Wray, J., & Rigelman, N. R. M. (2007). Elementary and middle school mathematics: Teaching developmentally.
Wen, J. R., Cheng, K. M., Chen, C. P., & Hsieh, Y. H. (2013). A study on the application of ubiquitous learning environment to english learning in elementary schools. Universal Journal of Education and General Studies, 2(2), 53-65.
Yahya, S., Ahmad, E. A., & Jalil, K. A. (2010). The definition and characteristics of ubiquitous learning: A discussion. International Journal of Education & Development using Information & Communication Technology, 6(1).
Yang, W. S., Cheng, H. C., & Dia, J. B. (2008). A location-aware recommender system for mobile shopping environments. Expert Systems with Applications, 34(1), 437-445.
Yu, F. Y., Chang, L. J., Liu, Y. H., & Chan, T. W. (2002). Learning preferences towards computerised competitive modes. Journal of Computer Assisted Learning, 18(3), 341-350.