摘要:位移(displacement)是物理學科中的基本概念，也是學童空間概念發展中的重要一環，當然位移概念也是學生學習數理科時不可或缺的基本能力。然而，在傳統的教學或課程中，位移的概念或是對位移的相加或相消的組合概念，通常都是被認為是不証自明的事實，並不需要特別加以講授的。但是，根據皮亞傑的理論和研究，學生的位移或位移的組合概念並非生而知之，而是需要經歷相當長時間的發展才能建立的。此種能力的建立不只是遵守一定發展順序，且其最後所達成階層更是所謂形武操作期的層次。對位栘組合概念的發展的歷程的研究，無疑的可以增進我們對學童空間概念發展的瞭解，並能對未來的相關教材教法的改進有所幫助。 本報告內容包含兩部份：其一是有關位移組合概念的示範式筆測工具的設計；其二是有關採用本測試工具所測得的部份樣本的案例分析。本報告所分析之案例共25份，其中包括國小學生4位，國中學生10位，大學生7位，研究所學生1位，學士後師資學分班學生3位。我們的主要發現有: 1.所設計之紙筆式群測工具，可以相當有效的區分出受測者的位移組合概念的發展階層，並且也能顯現皮亞傑理論中所宣稱的各種概念的特徵。 2.案例的分析顯示，大學生或成人也會對位移或位移的組合問題發生困難，這和皮亞傑所宣稱的發展成熱年齡(10~11歲)有很大的差距。 3.位移組合概念的發展和參考座標系概念的發展有密切的關係，早期的發展是表現互為因果的關係。後期思想操作武的位移組合概念的發展超越參考座標系概念的發展，參考座標系概念的發展只需要具體操作期的能力，思想操作的位移組合概念的發展則需要形式操作期的能力。 4.長度測量的能力和距離概念或距離的組合能力，並不一定是相等的能力。能夠正確測量出甲戊間距離的大小，並不一定知道由甲到戊會相等69由戊到甲；能夠正確測量出所有路段的長度，甚至能夠將測得的結果作四則的運算，也並不一定能夠對實質的位移作正確的組合。 我們認為本研究的結果對於相關教材教法的改進，和進一步有關學生概念發展的研究具有一定的啟示意義。

　　　　　This study included two parts: the first one was to design a group administered paper and pencil diagnostic test for the concept of composition of displacement, and the second to explore the conceptual development of individual cases that were selected from the results of the diagnostic test. Piaget's original clinical interview method for the concept of composition of displacement was used as a guide for designing of the paper and pencil diagnostic test. Twenty-five elementary, high school, and college students were analyzed in this study. The results indicated that the diagnostic tool could effectively classify students's concept of composition of displacement into five developmental levels, and also effectively demonstrated students' conceptual characteristics as described by Piaget. The case analyses indicated that quite a few college students or adults have difficulties with the concept of composition of displacement. This result is contradictory to Piaget's original claim that people develop mature conception of composition of displacement at about ten or eleven years of age. The analysis also indicated that the development of the concept of composition of displacement has the close relation with the development of the concept of reference frame. The early developments of the two concepts were interdependent and parallel, while the later development of the concept of composition of displacement exceeded that of the concept of the reference frame. The final developments of the concept of the reference frame required only concrete operational ability, while that of the concept of composition of displacement required formal operational ability. The ability to measure length with the graded rule did not imply the possession of a correct concept of composition of displacement. Students may be able to measure a distance between two points but did not mean they understood that the distance was equal in both directions. Also the ability to measure the lengths of successive displacement, and make all correct calculations of subtraction and addition, did not mean that the student could do the actual composition.