課程內容說明：
<br>
<br>第一週：空間能力在心理學的定義
<br>教學說明：簡介空間能力(spatial ability)在心理學的多面向定義，以及這些子構念定義之間的
<br>異同。
<br>Reference：心理學領域對空間能力的定義 (Pellegrino et al., 1984; Y&#305;lmaz, 2017)
<br>
<br>第二週：空間能力在數學教育的定義
<br>教學說明：簡介空間能力在數學教育數學課程發展的主要概念，並探究這些概念對於數學課程形成
<br>的影響為何。
<br>Reference：數學教育領域對空間能力的定義 (Xie et al., 2020)
<br>
<br>第三週：空間能力在心理學領域的研究成果（1）
<br>教學說明：瞭解空間能力在心理學領域的實驗設計及實徵研究成果，用以進一步瞭解不同空間能力
<br>構念對應的研究結果異同，以及這些實徵結果對數學教育的啟發為何。
<br>Reference: (Lohman, 1993) (H&#246;ffler, 2010)
<br>
<br>第四週：空間能力在心理學領域的研究成果（2）
<br>教學說明：瞭解空間能力在心理學領域的實驗設計及實徵研究成果，用以進一步瞭解不同空間能力
<br>構念對應的研究結果異同，以及這些實徵結果對數學教育的啟發為何。
<br>Reference: (Annett, 1992; Shea et al., 2001)、空間能力和場地獨立的關連性(MacLeod 
<br>et al., 1986)
<br>
<br>第五週：空間能力在數學教育領域的研究成果（1）
<br>教學說明：瞭解空間能力在數學教育領域的研究成果，包含空間能力、視覺化、視覺想像等概念之
<br>間的關連性與研究成果。
<br>Reference: (Bishop, 1980; Cheng & Mix, 2014)
<br>
<br>第六週：空間能力在數學教育領域的研究成果（2）
<br>教學說明：瞭解空間能力在數學教育領域的研究成果，包含空間能力、視覺化、視覺想像等概念之
<br>間的關連性與研究成果。
<br>Reference:  (Lean & Clements, 1981)
<br>
<br>第七週：空間能力在STEAM領域的研究論述（1）
<br>教學說明：許多研究指出空間能力在STEAM能力發展上扮演的重要關係。此週文獻主要討論空間能力
<br>為何為STEM素養能力發展的關鍵，兩者之間的關連性又是為何。
<br>Reference: (Buckley et al., 2018; Lubinski, 2010; Wai et al., 2009)
<br>
<br>第八週：空間能力在STEAM領域的研究論述（2）
<br>教學說明：許多研究指出空間能力在STEAM能力發展上扮演的重要關係。此週文獻主要討論空間能力
<br>為合適STEM發展的關鍵能力，兩者之間的關連性為何。
<br>Reference: (Buckley et al., 2018; Lubinski, 2010; Wai et al., 2009)
<br>
<br>第九週：空間能力對應幾何的認知發展（1）
<br>教學說明：空間能力是幾何發展的重要核心能力之一。本週將討論空間能力對應到幾何的認知發展
<br>理論。
<br>Reference: (Piaget & Inhelder, 1967; Piaget et al., 1960)
<br>
<br>第十週：空間能力對應幾何的認知發展（2）
<br>教學說明：本週討論（1）空間能力、視覺心像、和數學（幾何）表現的關係。（2）3D幾何的不同
<br>推理類別以及他們與空間能力的關係。
<br>Reference: (Lean & Clements, 1981; Pittalis & Christou, 2010)
<br>
<br>第十一週：圖形與幾何學習的關係
<br>教學說明：本週探討幾何圖形、空間能力與幾何學習之間的關連性。尤其幾何圖形的視覺化如何影
<br>響學生的幾何認知表現。
<br>Reference: (Hannafin et al., 2008; Hsu et al., 2023)
<br>第十二週：圖形與其他數學內容的關係
<br>教學說明：圖形的理解不單只影響幾何的認知與學習，同時在其他數學內容的學習也扮演相當重要
<br>角色。本週課程討論其他數學內容的圖形理解，以及圖形理解對該數學概念建構的影響。
<br>Reference: (Shah & Hoeffner, 2002)
<br>
<br>第十三週：圖形的課程設計（1）
<br>教學說明：國際學者開始思考從圖形的角度進行課程設計，本週討論不同學者如何以圖形為基礎，
<br>發展對應的課程內容。
<br>Reference: (Guti&#233;rrez et al., 2019; Laborde et al., 2006; Parzysz, 1988)
<br>
<br>第十四週：圖形的課程設計（2）
<br>教學說明：國際學者開始思考從圖形的角度進行課程設計，本週討論不同學者如何以圖形為基礎，
<br>發展對應的教材內容。
<br>Reference: (Dimmel & Herbst, 2015)
<br>
<br>第十五週：圖形的教學（1）
<br>教學說明：本週討論圖形如何影響數學教學（如手勢的使用），並進而成為數學概念建構的關鍵。
<br>Reference: (Alibali et al., 2014; Duval, 2006; Maschietto & Bussi, 2009; Nathan 
<br>et al., 2021)
<br>
<br>第十六週：圖形的教學（2）
<br>教學說明：本週討論圖形如何影響數學教學，並進而成為數學概念建構的關鍵。
<br>Reference: (Brown et al., 2004; Chen & Herbst, 2007; Cheng & Lin, 2007)
<br>
<br>評量方式：
<br>一、紙筆評量(20%)─期中考試
<br>二、表現評量(50%)─期中教案、期末教案撰寫及試教
<br>三、上課參與(30%)─出缺席＋上課參與討論及發表
<br>
<br>本課程將有條件的使用AI進行課程活動及相關作業
<br>
<br>參考文獻：
<br>Alibali, M. W., Nathan, M. J., Wolfgram, M. S., Church, R. B., Jacobs, S. A., 
<br>Johnson Martinez, C., & Knuth, E. J. (2014). How Teachers li<x>nk Ideas in 
<br>Mathematics Instruction Using Speech and Gesture: A Corpus Analysis. Cognition 
<br>and Instruction, 32(1), 65-100. https://doi.org/10.1080/07370008.2013.858161 
<br>Annett, M. (1992). Spatial ability in subgroups of left-and right-handers. 
<br>British Journal of Psychology, 83(4), 493-515. 
<br>https://doi.org/https://doi.org/10.1111/j.2044-8295.1992.tb02455.x 
<br>Bishop, A. J. (1980). Spatial abilities and mathematics education—A review. 
<br>Educational Studies in Mathematics, 11(3), 257-269. 
<br>https://doi.org/10.1007/BF00697739 
<br>Brown, M., Jones, K., Taylor, R., & Hirst, A. (2004). Developing geometrical 
<br>reasoning. In R. F. M. M. Ian Putt (Ed.), Proceedings of the 27th Annual 
<br>Conference of the Mathematics Education Research Group of Australasia (MERGA27) 
<br>(Vol. 1, pp. 127-134). Townsville. 
<br>Buckley, J., Seery, N., & Canty, D. (2018). A Heuristic fr<x>amework of Spatial 
<br>Ability: a Review and Synthesis of Spatial Factor Literature to Support its 
<br>Translation into STEM Education. Educational Psychology Review, 30(3), 947-972. 
<br>https://doi.org/10.1007/s10648-018-9432-z 
<br>Chen, C.-L., & Herbst, P. G. (2007). The interplay among gestures, discourse and 
<br>diagrams in students' geometrical reasoning. Proceedings of the 29th annual 
<br>meeting of the North American Chapter of the International Group for the 
<br>Psychology of Mathematics Education, Stateline (Lake Tahoe), NV.
<br>Cheng, Y.-H., & Lin, F.-L. (2007). The effectiveness and limitation of reading 
<br>and coloring strategy in learning geometry proof. PME, 
<br>Cheng, Y.-L., & Mix, K. S. (2014). Spatial Training Improves Children's 
<br>Mathematics Ability. Journal of Cognition and development, 15(1), 2-11. 
<br>https://doi.org/10.1080/15248372.2012.725186 
<br>Dimmel, K. J., & Herbst, G. P. (2015). The Semiotic Structure of Geometry 
<br>Diagrams: How Textbook Diagrams Convey Meaning. Journal for Research in 
<br>Mathematics Education, 46(2), 147-195. 
<br>https://doi.org/10.5951/jresematheduc.46.2.0147 
<br>Duval, R. (2006). A cognitive analysis of problems of comprehension in a 
<br>learning of mathematics. Educational Studies in Mathematics, 61(1), 103-131. 
<br>Guti&#233;rrez, &#193;., Leder, G. C., Boero, P., Jones, K., & Tzekaki, M. (2019). The 
<br>Second Handbook of Research on the Psychology of Mathematics Education: The 
<br>Journey Continues. Brill. https://doi.org/https://doi.org/10.1007/978-94-6300-
<br>561-6
<br>https://doi.org/10.1007/9789463005616_005 
<br>H&#246;ffler, T. N. (2010). Spatial Ability: Its Influence on Learning with 
<br>Visualizations—a me<x>ta-Analytic Review. Educational Psychology Review, 22(3), 
<br>245-269. https://doi.org/10.1007/s10648-010-9126-7 
<br>Hannafin, R. D., Truxaw, M. P., Vermillion, J. R., & Liu, Y. (2008). Effects of 
<br>Spatial Ability and Instructional Program on Geometry Achievement. The Journal 
<br>of Educational Research, 101(3), 148-157. 
<br>https://doi.org/10.3200/JOER.101.3.148-157 
<br>Hsu, H.-Y., Waisman, I., & Leikin, R. (2023). Influence of field-dependence-
<br>independence and symmetry on geometry problem solving: An ERP study 
<br>International Conference of PME 46, Haifa, Israel. 
<br>Laborde, C., Kynigos, C., Hollebrands, K., Str&#228;sser, R., Guti&#233;rrez, &#193;., & Boero, 
<br>P. (2006). Handbook of Research on the Psychology of Mathematics Education: 
<br>Past, Present and Future. In Teaching and Learning Geometry with Technology (pp. 
<br>275-304). Brill. https://doi.org/https://doi.org/10.1163/9789087901127_011
<br>https://doi.org/10.1163/9789087901127 
<br>Lean, G., & Clements, M. A. (1981). Spatial ability, visual imagery, and 
<br>mathematical performance. Educational Studies in Mathematics, 12(3), 267-299. 
<br>https://doi.org/10.1007/BF00311060 
<br>Lubinski, D. (2010). Spatial ability and STEM: A sleeping giant for talent 
<br>identification and development. Personality and Individual Differences, 49(4), 
<br>344-351. https://doi.org/https://doi.org/10.1016/j.paid.2010.03.022 
<br>MacLeod, C. M., Jackson, R. A., & Palmer, J. (1986). On the relation between 
<br>spatial ability and field dependence. Intelligence, 10(2), 141-151. 
<br>https://doi.org/https://doi.org/10.1016/0160-2896(86)90011-5 
<br>Maschietto, M., & Bussi, M. G. B. (2009). Working with artefacts: Gestures, 
<br>drawings and speech in the construction of the mathematical meaning of the 
<br>visual pyramid. Educational Studies in Mathematics, 70, 143-157. 
<br>Nathan, M. J., Schenck, K. E., Vinsonhaler, R., Michaelis, J. E., Swart, M. I., 
<br>& Walkington, C. (2021). Embodied geometric reasoning: Dynamic gestures during 
<br>intuition, insight, and proof. Journal of Educational Psychology, 113(5), 929-
<br>948. https://doi.org/10.1037/edu0000638 
<br>Parzysz, B. (1988). "Knowing" vs. "Seeing":  Problems of the plane 
<br>representation of space geometry figures. Educational Studies in Mathematics, 
<br>19(1), 79-92. 
<br>Pellegrino, J. W., Alderton, D. L., & Shute, V. J. (1984). Understanding spatial 
<br>ability. Educational Psychologist, 19(4), 239-253. 
<br>https://doi.org/10.1080/00461528409529300 
<br>Piaget, J., & Inhelder, B. (1967). The child's conception of space. The Norton 
<br>Library. 
<br>Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child's conception of 
<br>geometry (E. A. Lunzer, Trans.). W.W. Norton & Company. 
<br>Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking 
<br>and their relation with spatial ability. Educational Studies in Mathematics, 
<br>75(2), 191-212. https://doi.org/10.1007/s10649-010-9251-8 
<br>Shah, P., & Hoeffner, J. (2002). Review of graph comprehension research: 
<br>Implications for instruction. Educational Psychology Review, 14(1), 47-69. 
<br>Shea, D. L., Lubinski, D., & Benbow, C. P. (2001). Importance of assessing 
<br>spatial ability in intellectually talented young adolescents: A 20-year 
<br>longitudinal study. Journal of Educational Psychology, 93(3), 604-614. 
<br>https://doi.org/10.1037/0022-0663.93.3.604 
<br>Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: 
<br>Aligning over 50 years of cumulative psychological knowledge solidifies its 
<br>importance. Journal of Educational Psychology, 101(4), 817-835. 
<br>https://doi.org/10.1037/a0016127 
<br>Xie, F., Zhang, L., Chen, X., & Xin, Z. (2020). Is Spatial Ability Related to 
<br>Mathematical Ability: a me<x>ta-analysis. Educational Psychology Review, 32(1), 
<br>113-155. https://doi.org/10.1007/s10648-019-09496-y 
<br>Y&#305;lmaz, H. B. (2017). On the development and measurement of spatial ability. 
<br>International Electronic Journal of Elementary Education, 1(2), 83-96. 
<br>https://www.iejee.com/index.php/IEJEE/article/view/279 
<br>
<br>
<br>