Nanda南大9313 RaRbRc
課程目標: 圖形與空間概念發展是幾何與其他數學相關主題的基礎能力之一。本課程主要培養不同學生背景(包括:職前與在職教師、一 般大學生)圖形與空間概念對應到認知科學與數學教育的相關理論與實務。從認知科學和數學教育研究累積的實徵資料,修習 課程的學生瞭解數學教育課程安排、教學活動設計及學生在圖形與空間相關的數學概念發展及迷思概念。 本課程目標包括 R26;瞭解空間能力的在認知科學與數學教育的定義與實徵研究結果 R26;瞭解圖形在認知科學與幾何的研究成果 R26;瞭解兒童空間概念發展的相關理論和主要發展階段 R26;探討圖形與空間概念發展對數學教科書的影響 R26;探討圖形與空間概念發展對數學教學的影響
Course keywords: spatial ability, figure, geometry, mathematics, learning, teaching, neuroscience 課程內容說明: 第一週:空間能力在心理學的定義 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 異同。 Reference:心理學領域對空間能力的定義 (Pellegrino et al., 1984; Yılmaz, 2017) 第二週:空間能力在數學教育的定義 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 的影響為何。 Reference:數學教育領域對空間能力的定義 (Xie et al., 2020) 第三週:空間能力在心理學領域的研究成果(1) 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 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。 Reference: (Lohman, 1993) (Höffler, 2010) 第四週:空間能力在心理學領域的研究成果(2) 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 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。 Reference: (Annett, 1992; Shea et al., 2001)、空間能力和場地獨立的關連性(MacLeod et al., 1986) 第五週:空間能力在數學教育領域的研究成果(1) 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 間的關連性與研究成果。 Reference: (Bishop, 1980; Cheng & Mix, 2014) 第六週:空間能力在數學教育領域的研究成果(2) 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 間的關連性與研究成果。 Reference: (Lean & Clements, 1981) 第七週:空間能力在STEAM領域的研究論述(1) 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 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。 Reference: (Buckley et al., 2018; Lubinski, 2010; Wai et al., 2009) 第八週:空間能力在STEAM領域的研究論述(2) 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 為合適STEM發展的關鍵能力,兩者之間的關連性為何。 Reference: (Buckley et al., 2018; Lubinski, 2010; Wai et al., 2009) 第九週:空間能力對應幾何的認知發展(1) 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 理論。 Reference: (Piaget & Inhelder, 1967; Piaget et al., 1960) 第十週:空間能力對應幾何的認知發展(2) 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 推理類別以及他們與空間能力的關係。 Reference: (Lean & Clements, 1981; Pittalis & Christou, 2010) 第十一週:圖形與幾何學習的關係 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 響學生的幾何認知表現。 Reference: (Hannafin et al., 2008; Hsu et al., 2023) 第十二週:圖形與其他數學內容的關係 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 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。 Reference: (Shah & Hoeffner, 2002) 第十三週:圖形的課程設計(1) 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, 發展對應的課程內容。 Reference: (Gutiérrez et al., 2019; Laborde et al., 2006; Parzysz, 1988) 第十四週:圖形的課程設計(2) 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, 發展對應的教材內容。 Reference: (Dimmel & Herbst, 2015) 第十五週:圖形的教學(1) 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。 Reference: (Alibali et al., 2014; Duval, 2006; Maschietto & Bussi, 2009; Nathan et al., 2021) 第十六週:圖形的教學(2) 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。 Reference: (Brown et al., 2004; Chen & Herbst, 2007; Cheng & Lin, 2007) 評量方式: 一、紙筆評量(20%)─期中考試 二、表現評量(50%)─期中教案、期末教案撰寫及試教 三、上課參與(30%)─出缺席+上課參與討論及發表 本課程將有條件的使用AI進行課程活動及相關作業 參考文獻: Alibali, M. W., Nathan, M. J., Wolfgram, M. S., Church, R. B., Jacobs, S. A., Johnson Martinez, C., & Knuth, E. J. (2014). 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 Annett, M. (1992). Spatial ability in subgroups of left-and right-handers. British Journal of Psychology, 83(4), 493-515. https://doi.org/https://doi.org/10.1111/j.2044-8295.1992.tb02455.x Bishop, A. J. (1980). Spatial abilities and mathematics education—A review. Educational Studies in Mathematics, 11(3), 257-269. https://doi.org/10.1007/BF00697739 Brown, M., Jones, K., Taylor, R., & Hirst, A. (2004). Developing geometrical reasoning. In R. F. M. M. Ian Putt (Ed.), Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA27) (Vol. 1, pp. 127-134). Townsville. Buckley, J., Seery, N., & Canty, D. (2018). A Heuristic framework of Spatial Ability: a Review and Synthesis of Spatial Factor Literature to Support its Translation into STEM Education. Educational Psychology Review, 30(3), 947-972. https://doi.org/10.1007/s10648-018-9432-z Chen, C.-L., & Herbst, P. G. (2007). The interplay among gestures, discourse and diagrams in students' geometrical reasoning. Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Stateline (Lake Tahoe), NV. Cheng, Y.-H., & Lin, F.-L. (2007). The effectiveness and limitation of reading and coloring strategy in learning geometry proof. PME, Cheng, Y.-L., & Mix, K. S. (2014). Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and development, 15(1), 2-11. https://doi.org/10.1080/15248372.2012.725186 Dimmel, K. J., & Herbst, G. P. (2015). The Semiotic Structure of Geometry Diagrams: How Textbook Diagrams Convey Meaning. Journal for Research in Mathematics Education, 46(2), 147-195. https://doi.org/10.5951/jresematheduc.46.2.0147 Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1), 103-131. Gutiérrez, Á., Leder, G. C., Boero, P., Jones, K., & Tzekaki, M. (2019). The Second Handbook of Research on the Psychology of Mathematics Education: The Journey Continues. Brill. https://doi.org/https://doi.org/10.1007/978-94-6300- 561-6 https://doi.org/10.1007/9789463005616_005 Höffler, T. N. (2010). Spatial Ability: Its Influence on Learning with Visualizations—a meta-Analytic Review. Educational Psychology Review, 22(3), 245-269. https://doi.org/10.1007/s10648-010-9126-7 Hannafin, R. D., Truxaw, M. P., Vermillion, J. R., & Liu, Y. (2008). Effects of Spatial Ability and Instructional Program on Geometry Achievement. The Journal of Educational Research, 101(3), 148-157. https://doi.org/10.3200/JOER.101.3.148-157 Hsu, H.-Y., Waisman, I., & Leikin, R. (2023). Influence of field-dependence- independence and symmetry on geometry problem solving: An ERP study International Conference of PME 46, Haifa, Israel. Laborde, C., Kynigos, C., Hollebrands, K., Strässer, R., Gutiérrez, Á., & Boero, P. (2006). Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future. In Teaching and Learning Geometry with Technology (pp. 275-304). Brill. https://doi.org/https://doi.org/10.1163/9789087901127_011 https://doi.org/10.1163/9789087901127 Lean, G., & Clements, M. A. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12(3), 267-299. https://doi.org/10.1007/BF00311060 Lubinski, D. (2010). Spatial ability and STEM: A sleeping giant for talent identification and development. Personality and Individual Differences, 49(4), 344-351. https://doi.org/https://doi.org/10.1016/j.paid.2010.03.022 MacLeod, C. M., Jackson, R. A., & Palmer, J. (1986). On the relation between spatial ability and field dependence. Intelligence, 10(2), 141-151. https://doi.org/https://doi.org/10.1016/0160-2896(86)90011-5 Maschietto, M., & Bussi, M. G. B. (2009). Working with artefacts: Gestures, drawings and speech in the construction of the mathematical meaning of the visual pyramid. Educational Studies in Mathematics, 70, 143-157. Nathan, M. J., Schenck, K. E., Vinsonhaler, R., Michaelis, J. E., Swart, M. I., & Walkington, C. (2021). Embodied geometric reasoning: Dynamic gestures during intuition, insight, and proof. Journal of Educational Psychology, 113(5), 929- 948. https://doi.org/10.1037/edu0000638 Parzysz, B. (1988). "Knowing" vs. "Seeing": Problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19(1), 79-92. Pellegrino, J. W., Alderton, D. L., & Shute, V. J. (1984). Understanding spatial ability. Educational Psychologist, 19(4), 239-253. https://doi.org/10.1080/00461528409529300 Piaget, J., & Inhelder, B. (1967). The child's conception of space. The Norton Library. Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child's conception of geometry (E. A. Lunzer, Trans.). W.W. Norton & Company. Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educational Studies in Mathematics, 75(2), 191-212. https://doi.org/10.1007/s10649-010-9251-8 Shah, P., & Hoeffner, J. (2002). Review of graph comprehension research: Implications for instruction. Educational Psychology Review, 14(1), 47-69. Shea, D. L., Lubinski, D., & Benbow, C. P. (2001). Importance of assessing spatial ability in intellectually talented young adolescents: A 20-year longitudinal study. Journal of Educational Psychology, 93(3), 604-614. https://doi.org/10.1037/0022-0663.93.3.604 Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817-835. https://doi.org/10.1037/a0016127 Xie, F., Zhang, L., Chen, X., & Xin, Z. (2020). Is Spatial Ability Related to Mathematical Ability: a meta-analysis. Educational Psychology Review, 32(1), 113-155. https://doi.org/10.1007/s10648-019-09496-y Yılmaz, H. B. (2017). On the development and measurement of spatial ability. International Electronic Journal of Elementary Education, 1(2), 83-96. https://www.iejee.com/index.php/IEJEE/article/view/279
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數教組的選修課,上課16週。
限碩士班博士班專班
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