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研究生：	鐘敏綺 Chung, Min-Chi
論文名稱：	以擴增實境表徵學習數學分數概念對學生學習理解之影響 The Effects of learning through Augmented Reality Representations on Students’ Understanding of Fraction
指導教授：	王健華 Wang, Chien-Hwa
學位類別：	碩士 Master
系所名稱：	圖文傳播學系 Department of Graphic Arts and Communications
論文出版年：	2019
畢業學年度：	107
語文別：	英文
論文頁數：	71
中文關鍵詞：	數位學習、表徵、擴增實境、分數學習
英文關鍵詞：	e-learning, representations, augmented reality, fraction learning
DOI URL：	http://doi.org/10.6345/THE.NTNU.DGAC.006.2019.F05
論文種類：	學術論文
相關次數：	點閱：158 下載：32
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表徵（Representations）常見於STEM教學當中，教師在教學中常以圖示、操作物等表徵，將學生難以理解的抽象概念予以具體化。然而，應用表徵進行學習，學生並非能自然而然習得其對應的抽象概念，甚至應用至真實情境當中。此外，大多數低先備知識學生，因無法掌握所學數學概念與生活間之關聯，導致缺乏學習數學的動機，甚至也傾向只注意表徵表層資訊，而無法更深入注意到關鍵資訊。本研究提出以擴增實境技術所創造的表徵 (AR Representations)，將數學概念以不同於常見具體或抽象的方式呈現，導引學生從真實情境中出發注意關鍵表徵資訊，來解決以上之問題。為檢測此教具之教學效果，本研究採用準實驗法，並有來自北台灣共101位國小三年級學生參與本次實驗。學生的前後測試卷分數為學生理解之量化數據，高低先備知識則以前測分數進行區別，同時亦採集質性的訪談資料。研究結果顯示，實驗組學生在使用擴增實境表徵學習後，高低先備知識學生之後測成績並不顯著。總結而言，藉由擴增實境表徵學習，低先備知識學生之理解與高先備知識學生之間的差異呈現彌平的趨勢。此外，透過質化訪談討論，更發現這一群學生比起其他組別能將所學應用至更多元的例子中。本研究亦根據結論，提出教育意涵及未來研究建議。

Representations are widely used in science, technology, engineering, mathematics (STEM) fields. Teachers often make use of representations, such as pictures, manipulatives, to demonstrate abstract concepts, which students find hard to understand, in more concrete and tangible ways. However, it is not automatically that students can pick up the target abstract concepts with those representations. Moreover, learning with pictures in textbooks, students have difficulty in translating from pictures to real-life situations. Nevertheless, most low prior knowledge students are lack of learning motivation in face with the mathematics concepts because they are not able to relate what they learned with their own real-life situations, and vice versa; also tend to pay attention to the task-irrelevant information. With the technique of augmented reality, the present study proposed “AR Representations” instructions, which are different from the well-used concrete or abstract concepts. By redirecting students’ attention to the most relevant information, the instructions aimed to solve the above problems. Thus, quasi-experiments were performed to verify the effectiveness of AR Representations instructions. 101 3rd-grade elementary students in northern Taiwan have participated. Pretest and posttest scores were collected as quantitative data of understanding. Levels of prior knowledge were also derived from pretest scores. Results of this study showed there was no significant difference on students’ understanding between high and low level of prior knowledge after learning with AR Representations. In conclusion, With the aid of AR representations, (1) low prior knowledge students’ understanding would equate with the higher ones’, and (2) low prior knowledge students could identify more novel examples other than textbooks provide. Pedagogical implications and future research are also discussed.

Chinese Abstract   1
Abstract   2
Table of Content    3
List of Tables    6
List of Figures   7

CHAPTER ONE INTRODUCTION    8
1 Background    8
1.1 Representations in STEM education    8
1.2 Students’ learning difficulty in mathematics    9
1.3 The effectiveness of AR in mathematics education    9
2 Research purposes and questions    10
2.1 Assumption of solution to the problems    10
2.2 The process of validating the assumption    11
3 Limitations    13
4 Definition of terms    13
4.1 AR Representations    13
4.2 Prior Knowledge    13
4.3 Understanding    13

CHAPTER TWO LITERATURE REVIEW    14
1 Learning mediated with representations    14
1.1 The effectiveness of representations    14
1.2 The mechanism of linking representations    15
1.3 External and internal representations    17
2 Prior Knowledge    18
2.1 The impact of prior knowledge on students’ learning mediated with representations    18
2.2 The role of prior knowledge in multimedia intervention    19
3 Understanding    19
3.1 Procedural and conceptual understanding    19
3.2 The impacts of attention on understanding in learning    20
4 Learning with AR instruments    20
4.1 The benefits of mixed reality    20
4.2 AR applications in math    22
5 Learning Fractions    24
5.1 Common difficulties in learning fraction    24
5.2 Fraction teaching applications    24
5.3 Learning fractions mediated with representations    25
6 Summary    25

CHAPTER THREE RESEARCH METHOD    27
1 Research Framework    27
2 Participants    28
3 Instruments    29
3.1 Fraction Understanding Test    29
3.2 Interview Questions    31
4 Instructional Design for AR Representations    31
4.1 Design principles    31
4.2 Development of AR Representations    33
5 Procedure    37
6 Data analysis    39

CHAPTER FOUR RESULTS AND DISCUSSION    40
1 Results    40
1.1 RQ1: Overall, do instruction treatments (picture/ AR) affect students’ understanding?    40
1.2 RQ2: Is there a significant difference between learning with pictures and AR representations on students’ understanding?    41
1.3 RQ3: Is there a significant difference between high and low prior knowledge on students’ understanding?    43
1.4 RQ4: Whether the level of prior knowledge has an interaction effect with representations on students’ understanding?    43
1.5 RQ A1: Is there a significant difference between high and low prior knowledge on understanding in picture representation group?    43
1.6 RQ A2: Is there a significant difference between high and low prior knowledge on understanding in AR representation group?    45
1.7 Interview data    46
2 Discussion    47
2.1 Multiple representations facilitated by AR Representations    47
2.2 "Concrete-Pictorial-Abstract" sequences of AR Representations    48
2.3 High and low level of prior knowledge students’ perception to AR Representations    49
2.4 Enhancement of analogical thinking with personal experiences    51

CHAPTER FIVE CONCLUSION AND SUGGESTIONS    52
1 Conclusion    52
1.1 With the aid of AR Representations, low prior knowledge students’ understanding would equate with the higher ones’    52
1.2 With the aid of AR representations, low prior knowledge students could identify more novel examples other than textbooks provide    53
2 Contributions of the study    53
2.1 Creation of real-life representations by integrating CPA transition and AR technique    53
2.2 Non-3D mathematics AR overlay    54
3 Limitations of the study    54
4 Suggestions for Future Research    55
4.1 The applicable scope of non-3D AR Representations    55
4.2 Discovery learning with AR Representations    55
4.3 Graphical analogical thinking    56

REFERENCES    57
APPENDICES    64
Appendix A: Understanding pretest    64
Appendix B: Understanding posttest    67
Appendix C: Pictures treatment instructions    70
                                

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