本研究旨在探討國中數學教師在幾何教學中使用教學手勢的方式與其對學生學習的影響，聚焦於幾何單元中教學手勢如何促進學生的概念建構與問題解決。研究者針對以下三個問題分析：(1)台灣教師在進行範例教學時會使用哪些教學手勢？(2)教師在解題歷程三階段中使用的教學手勢是否存在差異？(3)不同教師於相同範例教學中使用的教學手勢是否有所差異？(4)不同性別、不同年資教師於相同範例教學時，使用之教學手勢是否有差異?
本研究採用質性觀察之分析方法，以八年級平行四邊形單元為研究範圍，透過錄影觀察教師教學中使用的手勢，並詳細記錄教師手勢的使用情況。依據 Hui-Yu Hsu（2021）的教學手勢分類框架，分析不同類型手勢在解題三階段（佈題、圖形操作、算式證明）的分佈與作用。研究發現教師手勢類型中，教師常使用指向、標示與切割等手勢，這些手勢在幾何圖形的視覺化與空間關係的講解中發揮重要功效。解題階段的手勢差異中，圖形操作階段手勢次數最高，且具體使用手勢在引導學生觀察與推理中顯示了顯著效果；算式證明階段的動態手勢則幫助學生理清證明邏輯。教師手勢風格的差異性上，不同教師在手勢使用頻率與種類上存在差異，這些差異對於學生的學習參與度和理解效果有直接影響。
研究結論指出，教師的教學手勢是在幾何教學中不可或卻的輔助工具，教師如果能適當運用即能夠有效降低學生的認知負荷，能夠增強學生對於幾何抽象概念的視覺化，並在幾何推理過程中能有效的搭起學生的鷹架，研究結果進一步強調，教學手勢對幾何學習具有關鍵的作用，特別是在學生需要理解抽象概念或是解題歷程中的算式證明推理過程方面，未來建議教師在專業發展中納入手勢教學的訓練，並且在數學教學設計中融入更多具體化的手勢，結合教具或動態教學工具，以進一步提升學生在幾何學習的效果。

This study aims to explore how junior high school mathematics teachers use instructional gestures in geometry teaching and their impact on students' learning, focusing on how teaching gestures in geometry units promote students' conceptual construction and problem-solving. The study analyzes the following three questions: (1) What Ds of instructional gestures do Taiwanese teachers use during example teaching? (2) Are there differences in the use of instructional gestures across the three stages of problem-solving? (3) Do different teachers employ varying instructional gestures during the same example teaching? (4) Are there differences in the instructional gestures used by teachers of different genders and years of experience when teaching the same example?
The study adopts qualitative observation and analysis methods, focusing on the parallelogram unit for eighth-grade students. Through video observations of teachers' use of gestures during lessons, detailed records were kept. Based on Hui-Yu Hsu's (2021) framework for categorizing instructional gestures, the study analyzed the distribution and roles of different Ds of gestures in the three problem-solving stages (problem presentation, graphical operations, and formula proof). The findings revealed that teachers frequently used gestures such as pointing, highlighting, and cutting. These gestures played a significant role in explaining the visualization and spatial relationships of geometric figures. Regarding differences in gestures across the problem-solving stages, the graphical operations stage showed the highest frequency of gesture use. Specific gestures demonstrated remarkable effectiveness in guiding students' observations and reasoning. During the formula proof stage, dynamic gestures helped students clarify the logical sequence of proofs.On the variation in teachers' gesture styles, the frequency and Ds of gestures used by different teachers varied significantly, directly influencing students' engagement and comprehension.
The study concludes that instructional gestures are indispensable tools in geometry teaching. When teachers appropriately use gestures, they can effectively reduce students' cognitive load, enhance the visualization of abstract geometric concepts, and provide scaffolding for students during geometric reasoning processes. The results further emphasize the critical role of teaching gestures in geometry learning, especially in helping students understand abstract concepts or navigate the reasoning processes in formula proofs.Future recommendations suggest incorporating gesture training into teachers' professional development and integrating more concrete gestures in mathematics teaching design. Combining these with teaching aids or dynamic teaching tools can further improve students' learning outcomes in geometry.

中文部分：
朱亮.(2008).初中生幾何學習困難原因初探.云南教育(中學教師)(06).
吳毓瑩,呂金燮,&吳昭容.(2009).重讀幾何思維的階層論:載體理論的啟示.科學教育學刊,17(2),157-177.
李加祿.(2019).初中學生幾何學習的困因及其對策. 初中數學教與學(24).
周海霞.(2015).初二學生幾何學習困難的成因及對策. 數學之友(06).
林勇吉.(2021).數學與肢體運動: 應用 [體現認知] 於數學教學. 臺灣數學教師, 42(1),17-28.
林若桓.(2018).繪本融入八年級學習障礙學生學習幾何作圖之個案研究 東海大學]. 臺灣博碩士論文知識加值系統.台中市. https://hdl.handle.net/11296/r646kg
教育部.(2018).十二年國民基本教育課程綱要國民中小學暨普通型高級中等學校數學領域。.臺北市：教育部。.
教育部.(2023).十二年國民基本教育課程綱要之數學領綱最新修正版。.臺北市：教育部。.
連宥鈞,&吳昭容.(2020).手勢融入範例對低能力學生運算與幾何學習的影響. . Taiwan Journal of Mathematics Education, 7(2), 45-70. https://doi.org/10.6278/tjme.202010_7(2).003
英文部分：
Alibali, M. W., Heath, D. C., & Myers, H. J. (2001). Effects of Visibility between Speaker and Listener on Gesture Production: Some Gestures Are Meant to Be Seen. Journal of Memory and Language, 44(2), 169-188. https://doi.org/10.1006/jmla.2000.2752
Alibali, M. W., Kita, S., & Young, A. J. (2000). Gesture and the process of speech production: We think, therefore we gesture. Language and Cognitive Processes, 15(6), 593-613. https://doi.org/10.1080/016909600750040571
Alibali, M. W., & Nathan, M. J. (2012). Embodiment in Mathematics Teaching and Learning: Evidence From Learners' and Teachers' Gestures. Journal of the Learning Sciences, 21(2), 247-286. https://doi.org/10.1080/10508406.2011.611446
Alibali, M. W., Nathan, M. J., Boncoddo, R., & Pier, E. (2019). Managing common ground in the classroom: teachers use gestures to support students’ contributions to classroom discourse. Zdm, 51(2), 347-360. https://doi.org/10.1007/s11858-019-01043-x
Alibali, M. W., Nathan, M. J., Wolfgram, M. S., Church, R. B., Jacobs, S. A., Johnson Martinez, C., & Knuth, E. J. (2013). How Teachers Link Ideas in Mathematics Instruction Using Speech and Gesture: A Corpus Analysis. Cognition and Instruction, 32(1), 65-100. https://doi.org/10.1080/07370008.2013.858161
Chawla, P., & Krauss, R. M. (1994). Gesture and speech in spontaneous and rehearsed narratives. . 580-601.
Chris, C. (1994). Paradigms regained: towards a historical sociology of the textbook. Journal of Curriculum Studies, 26(1), 1-29. https://doi.org/10.1080/0022027940260101
Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processings. Exploiting mental imagery with computers in mathematics education,
Duval, R. (1998). Geometry from a cognitive point of view. Perspectives on the Teaching of Geometry for the 21st Century, 37-52.
Duval, R. (2006). A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics. Educational Studies in Mathematics, 61(1-2), 103-131. https://doi.org/10.1007/s10649-006-0400-z
Duval, R. (2007). Cognitive functioning and the understanding of mathematical processes of proof. In Theorems in school (pp. 135-161). Brill.
Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education: development status and directions. Zdm, 45(5), 633-646. https://doi.org/10.1007/s11858-013-0539-x
Flevares, L. M., & Perry, M. (2001). How many do you see? The use of nonspoken representations in first-grade mathematics lessons. Journal of Educational Psychology, 93(2), 330-345. https://doi.org/10.1037/0022-0663.93.2.330
Flevares, L. M., & Perry, M. (2001). How many do you see? The use of nonspoken representations in first-grade mathematics lessons. Journal of Educational Psychology, 93(2), 330-345. https://doi.org/10.1037/0022-0663.93.2.330
Glenberg, A. M., & Robertson, D. A. (1999). Indexical understanding of instructions. Discourse processes, 28(1), 1-26.
Gerwing, J., & Bavelas, J. (2004). Linguistic influences on gesture’s form. Gesture, 4(2), 157-195.
Hiele, P. M. v. (1986). Structure and insight: A theory of mathematics education. (No Title).
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for research in mathematics education, 28(5), 524-549.
Healy, L., & Hoyles, C. (1998). Justifying and proving in school mathematics. Summary of the results from a survey of the proof conceptions of students in the UK. London: Institute of Education.
Hsu, H.-Y. (2007). Geometric calculations are more than just the application of procedural knowledge. Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education,
Hsu, H.-Y., & Silver, E. A. (2014). Cognitive complexity of mathematics instructional tasks in a Taiwanese classroom: An examination of task sources. Journal for research in mathematics education, 45(4), 460-496.
Hsu, H.-Y. (2021). How teachers scaffold students in visualizing diagram for understanding geometric problem solving. Paper presented in The 14th International Congress on Mathematical Education. ICME: Shanghai, China.
Karadag, Z., & McDougall, D. (2011). GeoGebra as a cognitive tool: Where cognitive theories and technology meet. In Model-Centered Learning (pp. 169-181). Brill.
Koedinger, K. R., & Anderson, J. R. (1990). Theoretical and empirical motivations for the design of ANGLE: A new geometry learning environment. Working notes of the 1990 AAAI Spring Symposia on Knowledge-Based Environments for Learning and Teaching, Stanford University, March,
Levy, E. T., & McNeill, D. (1992). Speech, gesture, and discourse. Discourse processes, 15(3), 277-301.
Magone, M. E., Cai, J., Silver, E. A., & Wang, N. (1994). Validating the cognitive complexity and content quality of a mathematics performance assessment. International Journal of Educational Research, 21(3), 317-340.
McNeil, N. M., Alibali, M. W., & Evans, J. L. (2000). The role of gesture in children's comprehension of spoken language: Now they need it, now they don't. Journal of Nonverbal Behavior, 24, 131-150.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development.
Stevanoni, E., & Salmon, K. (2005). Giving Memory a Hand: Instructing Children to Gesture Enhances their Event Recall. Journal of Nonverbal Behavior, 29(4), 217-233. https://doi.org/10.1007/s10919-005-7721-y
Valverde, G. A. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Springer Science & Business Media.