本研究的主要目的，是針對國中二年級下學期三角幾何課程單元，以「改良式示例版」（簡稱改良組）和「傳統式北北基版」（簡稱傳統組）兩種不同教學方式，在實施五節課，每節課45分鐘之後，在學生學習成就及態度方面比較其優劣性。
由研究者所任教的台北縣某國中二年級6個班級共201人，本研究經由立意抽樣其中3班為改良組（100人），另外3班為傳統組（101人），實驗設計採前測－後測設計的準實驗研究法。並以國二上學期數學科期末總成績，分別將改良組與傳統組各分成高分群（總成績前30名）、低分群（總成績後30名）兩群。為探究改良組與傳統組學生經由兩種不同學習法在三角幾何單元學習成效上的改變，以2×2多因子共變數分析各組學生在前後測之間的差異。研究結果各項資料經統計處理分析與歸納之後，獲得下列結論：
一、針對數學幾何單元，學生數學幾何學習成就：
1-1改良組與傳統組全體學生之學習成就，兩組之間無顯著差異。
1-2改良組與傳統組之低分群學生之學習成就，改良組優於傳統組。
1-3改良組與傳統組之高分群學生之學習成就，改良組優於傳統組。
二、針對數學幾何單元，學生數學幾何學習態度：
2-1改良組與傳統組全體學生之學習態度，改良組優於傳統組。
2-2改良組與傳統組之低分群學生之學習態度，兩組之間無顯著差異。
2-3改良組與傳統組之高分群學生之學習態度，兩組之間無顯著差異。

The main purpose of this study, is his second grades of the second half of the triangular geometric module in order to worked examples of improved version (referred to as the modified group) and traditional-style version-based Taipei-Taipei-Keelung (referred to as the traditional group) of two different teaching methods , in the implementation of five lessons, each lesson 45 minutes after the students achievements and attitudes of their advantages and disadvantages compared.
By researchers in Taipei County to teach in his second grades of a total of six classes of 201 students, the experimental design adopted pre-test & post-test quasi-experimental design study. And Mathematics at the end of the first semester results, respectively, will improve the group and traditional group is divided into well-differentiated, and ill-differentiated groups. To explore the improved group and the traditional group of students learning through two different units in the triangular geometry to study the effectiveness of changes to 2 × 2 ANCOVA students in each group the difference. The results of the data processing by statistical analysis, to obtain the following major findings:

1.Geometric modules for math, geometry math learning achievement of students:
1-1Improved group and traditional group learning achievement of all students, no significant differences between the two groups.
1-2Improved group and the traditional group of students of low academic achievement group, improvement was superior to the traditional group.
1-3Improved group and the traditional group of students of high academic achievement group, improvement was superior to the traditional group.
2.Geometric modules for math, students attitude towards learning mathematics geometry:
2-1Improved group and the traditional group of students learning attitude, improvement was superior to the traditional group.
2-2Improved group and the traditional group of the low group of students learning attitude, there was no significant difference between the two groups.
2-3Improved group and the traditional group of well-differentiated group of students learning attitude, there was no significant difference between the two groups.

第一章	緒論                                                  1
第一節	研究背景與動機                                             1
第二節	研究目的與待答問題                                         5
第三節	名詞釋義                                                   6
第四節	研究範圍與限制                                            10
第二章	文獻探討                                             11
第一節 幾何思考發展層次                                          11
第二節 示例教學法                                                14
第三節 多媒體學習認知理論                                        24
第四節 多媒體教學設計原則                                        28
第三章	研究方法                                             35
第一節 研究流程                                                  35
第二節 研究設計                                                  38
第三節 研究假設                                                  40
第四節 研究對象                                                  41
第五節 研究工具                                                  42
第六節 資料處理與分析                                            45
第四章	研究結果與討論                                       46
第一節	三角幾何學習成就之比較                                    46
第二節	三角幾何學習態度之比較                                    51
第五章	結論與建議                                           56
第一節	結論                                                      56
第二節	建議                                                      58

參考文獻 
一、中文文獻                                                     60
二、英文文獻                                                     61
附錄
     附錄一：三角幾何單元教學活動設計                                  64
     附錄二：傳統式北北基版教材                                        68
     附錄三：改良式示例版習題解答                                      79
     附錄四：數學幾何學習態度量表                                      81
     附錄五：數學幾何學習成就測驗                                      83
 
圖次
圖2-1機率學中的一個多媒體示例法                                       15
圖2-2多媒體學習認知理論示意圖                                         28
圖3-1實驗變項圖                                                       39






 
表次
表1-1 Van Hiele幾何思考階層原則                                         7
表1-2 示例教學法設計原則                                               7
表1-3 多媒體教學訊息設計原則                                           8
表1-4 動畫加解說的設計原則                                             8
表1-5 插圖加註解的設計原則                                             8
表3-1研究流程                                                         35
表3-2預期完成工作之甘特圖                                             36
表3-3實驗設計模式                                                     38
表4-1傳統組與改良組的全體學生學習成就之比較－敘述統計                 46
表4-2傳統組與改良組的全體學生學習成就之比較－效應檢定                 47
表4-3傳統組與改良組的低分群學生學習成就之比較－敘述統計               48
表4-4傳統組與改良組的低分群學生學習成就之比較－效應檢定               48
表4-5傳統組與改良組的高分群學生學習成就之比較－敘述統計               49
表4-6傳統組與改良組的高分群學生學習成就之比較－效應檢定               49
表4-7傳統組與改良組的全體學生學習態度之比較－敘述統計                 51
表4-8傳統組與改良組的全體學生學習態度之比較－效應檢定                 52
表4-9傳統組與改良組的低分群學生學習態度之比較－敘述統計               53
表4-10傳統組與改良組的低分群學生學習態度之比較－效應檢定              53
表4-11傳統組與改良組的高分群學生學習態度之比較－敘述統計              54
表4-12傳統組與改良組的高分群學生學習態度之比較－效應檢定              54

一、中文文獻
王文科、王智弘(2007)。教育研究法。台北市：五南。
姚文仁(2006)。國中三角形相關概念GSP補救教學之成效研究。未出版之碩士論文，高雄師範大學數學系，高雄市。
洪有情(2007)。國中數學第四冊。台北市：康軒。
張玲粧(2004)。國中數學引導式e-Learning學習模式與學習成效關係之研究。未出版之碩士論文，靜宜大學資訊管理學系研究所，台中市。
教育部(2001)。中小學資訊教育總藍圖。台北市：教育部。
教育部(2003)。國民中小學九年一貫課程綱要數學學習領域。台北市：教育部。
郭昭慧(2004)。國中三角幾何GSP輔助教學之學習成效研究。未出版之碩士論文，義守大學資訊管理學系碩士班，高雄縣。
楊智強(2006)。透過線上家教對國中生數學解題能力及學習態度影響之行動研究。未出版之碩士論文，國立交通大學理學院碩士在職專班網路學習學程，新竹市。

二、英文文獻
Atkinson, R. K. (2002). Optimizing learning from examples using animated pedagogical agents. Journal of Educational Psychology, 94(2), 416. 
Atkinson, R. K. , Catrambone, R. & Merrill, M. M. (2003). Aiding transfer in statistics: Examining the use of conceptually oriented equations and elaborations during subgoal learning. Journal of Educational Psychology, 95(4), 762-773. 
Atkinson, R. K. & Derry, S. J. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181. 
Atkinson, R. K. , Renkl, A. & Merrill, m. M. (2003). Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked-out steps. Journal of Educational Psychology, 95(4), 774-783. 
Catrambone, R. (1995). Aiding subgoal learning: Effects on transfer. Journal of Educational Psychology, 87(1), 5. 
Catrambone, R. (1996). Generalizing solution procedures learned from examples. Journal of Experimental Psychology / Learning, Memory & Cognition, 22(4), 1020. 
Catrambone, R. (1998). The subgoal learning model: Creating better examples so that students can solve novel problems. Journal of Experimental Psychology / General, 127(4), 355. 
Catrambone, R. & Holyoak, K. (1985). The role of schemas in analogical problem solving. 
Chi, M. T. H. , Bassok, M. & Pittsburgh Univ, P. A. L. R. & Development, C. (1988). Learning from examples via self-explanations. Technical report no. 11. 
Gerjets, P. & Scheiter, K. (2003). Goal configurations and processing strategies as moderators between instructional design and cognitive load: Evidence from hypertext-based instruction. Educational Psychologist, 38(1), 33-41. 
Gerjets, P. , Scheiter, K. & Catrambone, R. (2004). Designing instructional examples to reduce intrinsic cognitive load: Molar versus modular presentation of solution procedures. Instructional Science: An International Journal of Learning and Cognition, 32, 33-58. 
Gerjets, P. , Scheiter, K. & Schuh, J. (2008). Information comparisons in example-based hypermedia environments: Supporting learners with processing prompts and an interactive comparison tool. Educational Technology Research & Development, 56(1), 73-92. 
Jeung, H. -J. & Chandler, P. (1997). The role of visual indicators in dual sensory mode instruction. Educational Psychology, 17(3), 329. 
Kalyuga, S. , Chandler, P. , Sweller, J. & Tuovinen, J. (2001). When problem solving is superior to studying worked examples. Journal of Educational Psychology, 93(3), 579. 
LeFevre, J. -A. & Dixon, P. (1986). Do written instructions need examples?. Cognition & Instruction, 3(1), 1. 
Mayer, R. E. & Moreno, R. (2003). Nine ways to reduce cognitive load in multimedia learning. Educational Psychologist, 38(1), 43-52. 
Mayer, R. E. (2001). Multimedia learning. New York: Cambridge University Press. 
Mayer, R. E. (Ed. ). (2005). The Cambridge handbook of multimedia learning. New York: Cambridge University Press. 
Mwangi, W. & Sweller, J. (1998). Learning to solve compare word problems: The effect of example format and generating self-explanations. Cognition & Instruction, 16(2), 173. 
Najjar, L. J. (1997) . A framework for learning from media: The effects of materials, tasks, and tests on performance (GIT-GVU-97-21). Atlanta, GA: Georgia Institute of Technology, Graphics, Visualization and Usability Center. Also available World Wide Web: http://www.cc.gatech.edu/gvu/reports.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
Paas, F. , Renkl, A. & Sweller, J. (2003). Cognitive load theory and instructional design: Recent developments. Educational Psychologist, 38(1), 1-4. 
Quilici, J. L. & Mayer, R. E. (2002). Teaching students to recognize structural similarities between statistics word problems. Applied Cognitive Psychology, 16(3), 325-341. 
Recker, M. M. & Pirolli, P. (1995). Modeling individual differences in students' learning strategies. Journal of the Learning Sciences, 4(1), 1. 
Renkl, A. (1997). Learning from worked-out examples: A study on individual differences. Cognitive Science, 21(1), 1. 
Renkl, A. & Atkinson, R. K. (2002). Learning from examples: Fostering self-explanations in computer-based learning environments. Interactive Learning Environments, 10(2), 105-119. 
Renkl, A. , Atkinson, R. K. , Maier, U. H. & Staley, R. (2002). From example study to problem solving: Smooth transitions help learning. Journal of Experimental Education, 70(4), 293. 
Renkl, A. , Stark, R. , Gruber, H. & Mandl, H. (1998). Learning from worked-out examples: The effects of example variability and elicited self-explanations. Contemporary Educational Psychology, 23(1), 90. 
Schank, R. , Berman, T. R. , & Macpherson, K. A. (1999). Learning by doing. In C. M. Reigeluth, Instructional design theories and models(Mahwah, NJ: Erlbaum. ), Vol. Ⅱ,pp. 161-181. 
Sweller, J. (1990). Cognitive processes and instruction procedures. Australian Journal of Education, 34(2), 125-130. 
Sweller, J. & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition & Instruction, 2(1), 59. 
Tarmizi, R. A. & Sweller, J. (1988). Guidance during mathematical problem solving. Journal of Educational Psychology, 80(4), 424-436. 
Ward, M. & Sweller, J. (1990). Structuring effective worked examples. Cognition & Instruction, 7(1), 1.