本研究提出以「電腦輔助歸納式發現法」做為國小學童學習數學概念的基本模式，探討學童在非被動接收知識的模式下，藉由電腦輔助進行主動觀察歸納的學習成效與行為，以及班級老師對於此種學習模式的評價與接受度。
所謂「歸納式發現法」的學習模式，是學生透過一系列小心設計的例子，經過類化或比較而發現概念重點，再透過文字鷹架，將所發現之概念重點以文字表達出來的一套發現式學習法。其中例子的設計以「變易理論」為設計原則的主要依據，凸顯目標概念的重要屬性，幫助學生清楚辨識要發現的重點所在。電腦在本研究中扮演的主要角色是透過即時回饋，與學生共同完成符合目標概念的例子以及對於該概念的文字描述。
本研究共有兩個階段。第一階段為系統預試，有五十八名小四學生參與，目的為改善教材設計與系統介面和功能，研究方法為觀察法與系統記錄分析。第二階段則針對預試中得到的資料做修正與改進之後，進一步探討學生同樣在電腦輔助的情況下，使用「歸納式觀察法」學習，與使用坊間教科書常見的「直接教學法」學習的成效差異，以深入了解歸納式發現法對於學習的幫助。此階段參與的學生有五十四名，研究方法為實驗法。
第二階段的研究結果顯示，根據學生前測、立即後測與延遲後測的表現，使用「歸納式觀察法」學習的學生學習效果較佳，對於記憶的保留亦較為長久，且對於基礎程度較差的學生有較大的幫助。以使用時機而言，歸納式發現法更適用於學習較難概念的時候。而問卷與訪談則顯示，無論採用何種模式，學生對於使用電腦學習的上課方式皆相當喜愛及投入，老師亦對於這樣的教學模式給予肯定回應。

This study proposes “computer supported inductive discovery learning” for elementary students learning mathematical concepts. It investigates how elementary students learn mathematics by inductive discovery, instead of learning by being told, in the one-to-one classroom environment. It also explores the class teacher’s perspectives on using such learning model in the teaching practice.
Inductive discovery learning indicates students discover critical concept attributes by generalizing from or comparing among a series of carefully designed examples, and then express their discovery with written language. The example design is based on Variation Theory; that is, the examples emphasize the target concept by separating it from other irrelative things so that students can discern the concept easier. The main function of computers in this study is providing immediate feedbacks to help students complete unfinished examples and concept summary.
There are two phases in this study. The first phase is system preliminary test, aiming on improving the model design as well as system interface and functions. Fifty-eight fourth-graders participated in this phase, and the research methods are observation and system data analysis. The second phase examines how inductive discovery learning can help students learn. That is, under the same computer-supported learning condition, this phase examines how differently students in inductive discovery learning perform from those in common textbook-like learning—directed instruction. Fifty-four third-graders participated in this phase, and the research method is experiment.
The results of the second phase illustrate that students in inductive discover learning not only have better learning performance, but also retain more knowledge after a period of time. Besides, inductive discovery learning helps students with lower initial knowledge level more than those with higher one. As for the cost-effect consideration, it is found that inductive discovery learning is more suitable for difficult concepts. Student questionnaire and interview results show that students like and engage in both kinds computer-supported learning in the second phase, and the involved teachers also give very supportive feedbacks about the idea of providing individual students digital scaffoldings in their classrooms.

英文文獻
Alexander Renkl, Robert K. Atkinson (2003). Structuring the transition from example study to problem solving in cognitive skill acquisition: a cognitive load perspective, Educational Psychologist, 38(1), 15–22.
Alexander Renkl, Robin Stark, Hans Gruber, einz Mandl (1998). Learning from Worked-Out Examples: The Effects of Example Variability and Elicited Self-Explanations, Contemporary Educational Psychology, 23, 90–108.
Allen Leung (2003). Dynamic geometry and the theory of variation, Conference of the International Group for the Psychology of Mathematics Education, 197-205.
Anderson, J.R. (1987). Skill acquisition: Compilation of weak-method problem solutions. Psychological Review, 94, 192-210.
Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. W. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70, 181-214.
B. Rosenshine (1983).Teaching function in instructional programs. Elementary School Journal, 83,335-350.
Baddeley, A. E. (1976).The psychology of memory. New York: Basic Bools.
Bangert-Drowns, R. L., Kulik, J. A., & Kulik, CL. C. (1985). Effectiveness of computer-based education in secondary schools. Journal of Computer-Based Instruction, 12(3), 59-68.
Bielaczyc, K., Pirolli, P., & Brown, A. L. (1995). Training in self-explanation and self-regulation strategies: Investigating the effects of knowledge acquisition activities on problem solving. Cognition and Instruction, 13, 221–252.
Bloom, B., Englehart, M. Furst, E., Hill, W., & Krathwohl, D. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook I: Cognitive domain. New York, Toronto: Longmans, Green.
Bowden, J. & Marton, F. (1998). The university of learning. London: Kogan Page.
Bruner, J. S. (1960). The process of education. New Yourk: Vintage Books.
Bruner, J., Oliver, R., Greenfield, P., et al. (1966). Studies in cognitive growth. New York: Wiley.
Cavin, C. S., Cavin, E. D., & Logowski, J. J. (1981). The effect of computer assisted instruction on the attitudes of college students toward computers and chemistry. Journal of Research in Science Teaching, 18(4), 329-333.
Cavin. C. S., & Lagowski, J. J. (1987). Effects of computer simulated or laboratory experiments and student aptitude on achievement and time in a college general chemistry laboratory course, Journal of Research in Science Teaching, 24(2), 145-160.
Chang, C. Y. (2000). Enhancing tenth graders’ earth science learning through computer-assisted instruction. Journal of Geoscience Education, 48, 81-85.
Chi, M. T. H. (1996). Constructing self-explanations and scaffolded explanations in tutoring. Applied Cognitive Psychology, 10: 33-49.
Chi, M. T. H. (2000). Self-explaining expository texts: The dual process of generating inferences and repairing mental models.
Chi, M. T. H., deLeeuw, N., Chiu, M. & La Vancher, C. (1994). Eliciting self-explanation improves understanding. Cognitive Science, 18, 439–477.
Chi, M. T. H., M. Bassok, M. Lewis, P. Reimann & Glaser, R. (1989). How students study and use examples in learning to solve problems. Cognitive Science, 145-182.
Chi, M., Siler, S., Jeong, H., Yamauchi, T. & Hausmann, R. G. (2001). Learning from human tutoring. Cognitive Science, 25, 471–533.
Chiappetta, E. L., & Russell, J. M. (1982). The relationship among logical thinking, problem solving instruction, and knowledge and application of earth science subject matter. Science Education, 66(1), 85-93.
David Hammer (1997).Discovery learning and discovery teaching. Cognition and Instruction, 15, 482-529.
Dillshaw, F. G., & Bell, S. (1985). Learning outcomes of computer programming instruction for middle-grades students: A pilot study. Paper presented at the National Association for Research in Science Teaching. St. Paul, MN.
Douglas A. Grouws (1992). Handbook of research on mathematics teaching and learning.
Gerald A. Goldin (1990). Epistemology, constructivism, and discovery learning in mathematics. Journal for Research in Mathematics Education, 4, 31-210.
Hermann, G. (1969). Learning by discovery: A critical review studies. Journal of Experimental Education, 38, 58-72.
Hiebert, J., & Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge. Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
Hilgard, E. R. (1957). Introduction to psychology (2nd ed). New York: Harcourt Brace.
Koen Veermans, Ton de Jong & Wouter R. van Joolingen (2000).Promoting self-directed learning in simulation-based discovery learning environments through intelligent support. Interactive Learning Environments, 8, 229–255.
Lloyd P. Rieber, Shyh-Chii Tzeng, Kelly Tribble (2004). Discovery learning, representation, and explanation within a computer-based simulation: finding the right mix. Learning and Instruction 14, 307–323.
Lo, M. L., Pong, W. Y., & Man, C. P. (Eds.) (2005). For each and everyone. Hong Kong: Hong Kong University Press. (Ch.2)
Mark A. McDaneil, Mark S. Schlarger (1990).Discovery learning and transfer of problem-solving skill. Cognition and Instruction, 7, 129-159.
Marton, F. (1981). Phenomenography-describing conceptions of the world around us. Instructional Science, 10, pp. 177-200
Marton, F. & Amy B. M. Tsui (2003). Classroom discourse and the space of learning. Lawrence Erlbaum Assoc Inc.
Marton, F. & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Lawrence Erlbaum Associates.
Marton, F. & Lo Mun Ling (2005). Learning form “The Learning Study”, Biennial Conference of EARLI, 23-27.
Mayer, R. E. & Greeno, J. G. (1972). Structural differences between learning outcomes produced by different instructional methods. Journal of Educational Psychology, 63, 165-173.
Mwangi, W., & Sweller, J. (1998). Learning to solve compare word problems: The effect of example format and generating self-explanations. Cognition and Instruction, 16, 173–199.
R.S. Michalski, J.G. Carbonell, and T.M. Mitchell (1986). Machine learning: An artificial intelligence approach (Vol 2). Los Altos: Morgan Kaufmann.
Reder, L.M., & Anderson, J.R. (1980). A comparison of texts and their summaries: Memorial consequences. Journal of Verbal Learning and Verb41 Behavior, 19, 121-134.
Reder, L.M., Charney, D.H., & Morgan, K.I. (1986). The role of elaborations in learning a skill from an instructional text. Memory % Cognition, 14, 64-78.
Robert J. Marzano, Debra J. Pickering & Jane E. Pollock (2001). Classroom instruction that works. USA: ASCD.
Robert K. Atkinson, Sharon J. Derry, Alexander Renkl, Donald Wortham (2000). Learning from examples: instructional principles form the worked examples research.
Saunders, W., & Shepardson, D. P. (1987). A comparison of concrete and formal science instruction upon science achievement and reasoning ability of sixth grade students. Journal of Research in Science Teaching, 24(1), 39-51.
Shepardson, D. P. (1991). Relationships among problem solving, student interactions, and thinking skills. Paper presented at the Annual Meeting of the National Association of Research in Science Teaching, Lake Geneva, WI.
Silke Schworm, Alexander Renkl (2006). Computer-supported example-based learning: When instructional explanations reduce self-explanations, Computers & Education, 46 ,426–445.
Stein M. K., J. A. Baxter, and G. Leinhardt (1990). Subject matter knowledge and elementary instruction: Acase frome functions and graphing. American Educational Tesearch Journal 27(4):639-663.
Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2, 59–89.
Sweller, J., van Merrie‥nboer, J. J. G., & Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10, 251–296.
Tak-Wai Chan, et at,. (2006). One-to-one technology-enhanced learning: An opportunity for global research collaboration. Research and Practice in Technology Enhanced Learning, 1, 3–29.
Ton de Jong, wouter R. Van Joolingen (1998). Scientific discovery learning with computer simulations of conceptual domains . Interactive Learning Environments. 8, 229–255.
Vygotsky, L. S. (1962). Thought and language. Cambridge, MA : MIT Press.
Worthen, B. R. (1986).Discovery and expository task presentation in elementary mathematics. Journal of Educational Psychology Monographs Supplement, 59.
Xinming Zhu, Herbert A. Simon (1987). Learning from examples and by doing. Cognition and Instruction, 4, 137-166.
Xinming Zhu, Dan Zhu, Yifei Lee, Herbert A. Simon (2003). Cognitive theory to guide curriculum design for learning form examples and by doing, Computers in Mathematics and Science Teaching. 22(4), 285-322.
 
中文文獻
艾如昀（1994）。國小學生處理小數的歷程與困難。國立中正大學心理研究所碩士論文。
周筱亭（1990）。電子計算器對於國民小學小數運算學習之影響(I)。臺灣省國民學校教師研習會。
林右姍（2007）。國小兒童分數概念之探討。國立屏東教育大學教育心理與輔導學系碩士論文。
林清山（1987）。教學的心理學基礎。台北：台灣書店。
祁永華、謝錫金、岑紹基（2005）。變易理論與學習空間。香港：香港大學出版社。
邱貴發（1992）。電腦輔助教學成效探討。視聽教育雙月刊, 33(4), 11-18。
洪榮昭（1992）。電腦輔助教學之設計原理與應用。台北：師大書苑。
張平東（1993）。國小數學教材教法新論。台北：五南圖書出版公司。
張春興（2005）。教育心理學。台北：東華書局。
張英傑、周菊美（2005）。中小學數學科教材教法卅John A. Van De Walle著。台北：五南圖書出版公司。
張添洲（2002）。教材教法－發展與革新。台北：五南圖書出版公司。
張臺隆（2004）。中部地區國民小學校長資訊素養與實施資訊科技融入教學情形之研究。台中師範學院國民教育研究所碩士論文。
教育部（2003）。國民教育階段九年一貫課程綱要細目，教育部。
莊大慶（2007）。國小學同等值分數概念發展之研究。國立屏東教育大學教育心理與輔導學系碩士論文。
許桂敏（1994）。電腦輔助教學與傳統教學在微積分學習效果上之比較研究。國科會研究報告，NSC82-0111-S011-011A。
部編版（2008）。國民小學數學五至八冊。
郭孟儒（2002）。國小五年級學童小數迷思概念及其成因之研究。國立屏東師範學院數理教育研究所碩士論文。
陳文利（2001）。國小四年級學童小數迷思概念之研究。國立屏東師範學院數理教育研究所碩士論文。
陳明宏、呂玉琴（2005）。國小四年級學童分數概念之診斷教學研究。國立臺北教育大學學報，第18卷第2期（94年9月）1～32
陳慧佳（2005）。網路即時互動系統應用在國小教學之個案研究–以等值分數單元為例。國立屏東師範學院數理教育研究所碩士論文。
湯錦雲（2002）。國小五年級學童分數概念與運算錯誤類型之研究。國立屏東師範學院數理教育研究所碩士論文。
黃憲銘（2006）以格子謎題遊戲式輔助小學數學技巧熟練之數位學習設計與實作。國立交通大學理學院網路學習學程碩士論文。
黃寶彰（2003）。六、七年級學童數學學習困難部分之研究。國立屏東師範學院數理教育研究所碩士論文。
楊坤堂（2007）。數學學習障礙。台北：五南圖書出版公司。
董家莒、張俊彥（1999）。以「問題解決」為策略之電腦輔助教學學習成效：以土石流單元為例。中華民國第十五屆科學教育學術研討會手冊，133。
劉曼麗（2001）。國小學童的小數知識研究。屏東師院學報, 14, 823-858。
劉曼麗（2002）。台灣地區國小學童小數概念研究(II)：國小學童「小數與小數運算」概念之調查研究。九十年度行政院國家科學委員會專題研究計劃成果報告，國科會科學教育發展處。（NSC90-2521-S-153-003）。
劉曼麗（2005）。小數診斷教學研究。科學教育學刊（Chinese Journal of Science Education）。13, 29-52。
鄭谷苑、郭俊賢（2004）。學習原理：心智、經驗與學校卅John D. Bransford et at., 著。台北：遠流。
翰林文教事業(2008)。國民小學數學第七冊。
翰林文教事業(2008)。國民小學數學第五冊。
賴慧玲（2002）。教學模式卅Mary Alice Gunter, Thomas H. Estes　＆ Jan Schwab 著。台北：五南圖書出版公司。
霍秉坤（2004）。教學方法與設計。香港：商業印書館。
簡茂發和劉湘川（1993）。八十一學年度國民教育階段學生基本學習成就評量國小組試題編製及抽測結果報告。國立臺中師範學院。