我國學生水平面及空間概念成長之研究

　　　　　本研究包括三個主要部份:一是探討紙筆式群測法和皮亞傑式個別面診法對學童水平面概念發展的診斷效果的差異性；二是利用紙筆式群測法對我國中小學校之學童進行縱向性的大樣本測試，以瞭解我國學童的水平面概念或空間概念的成長情形；三是探討我國學生水平面概念或空間概念發展的性別差異情形及其發生的起始年齡。 本研究証實採用水平面概念的紙筆式群測法雖然可以觀察到皮亞傑所宣稱的各種概念模式，但是紙筆式群測法對概念階層的鑑別能力則不如個別面診方法的好。在原來皮亞傑理論的七個發展階層中紙筆式群測法只能判別四個階層。困難的原因有二：一是因為群測法無法對個別的受測者在適當的時機提供觀察操作或對話的機會；二是對低層次孩童表現的困難，我們無法判別是因為技巧的問題或是概念的問題。紙筆式群測法所診斷出的高層次水平面正確概念階層的表現有非常高的穩定性，但低層次概念階層的穩定性表現則較差。 本研究針對六仟餘位中小學生水平面概念的測試結果顯示，我國孩童的空間概念的成長可以概略的區分為四個階段：約六歲以前學前幼兒時期的拓樸空間概念至幾何空間概念發展期；女生約六歲至十歲，男生約六歲至八歲的區域性幾何空間概念或區域性參考座標系概念的發展期；然後是女生約從十歲至十五歲，男生約從八歲至十五歲的整體性幾何空間概念或整體性參考座標概念的發展期；最後是約在十五至十六歲以後的成長停滯期。 我們發現男女性別差異在七至八歲時期即已顯示在較低概念階層的發展上，而在九至十歲以後開始顯示在較高概念階層的發展上，然後隨年齡之增長而逐漸擴大。當女生在十四至十五歲時，她們的發展程度只相當於男生在十二至十三歲時的發展程度。 水平面概念的發展的最高階層只相當於認知成長的具體操作期，又水平面概念的發展程度代表空間概念的發展程度，因此本研究之結果對中小學教材教法的改革應具有重要之參考價值。
　　　　　This study includes three main parts: (a) to investigate the difference between the paper and pencil group test and the clinical interview method for the diagnosis of water-level concept; (b) to understand the developmental trend of the water-level concept or spatial concept of the Chinese students; (c) to understand the sex difference of the development of the water-level concept or spatial concept of the Chinese students and their beginning ages. Our study has shown that the paper and pencil group test can elicit most of the conceptual models of the water level problem as claimed by the Piaget's theory, however the paper and pencil group test can only differentiate four of the seven developmental stages of the water level problem as originally claimed by Piaget. The reasons for this difficulty are two: the first is that the paper and pencil group test can not provide the subjects with appropriate hand on manipulations and observations of the set-ups, and/or the test lacks the instantaneous conversations between the tester and testee; secondly, it is difficult to judge the difficulties of performances of the very young students as due to their lack of skill or due to their weakness of conceptual development. We also noted that the high level performance of the water-level concept in the paper and pencil group demonstrat3ed a very stable characteristics, while that of the low level performance is relatively low. Based on the results of the tests to about six thousand elementary and secondarily students, we can see four main periods of developments: before the age of six, or the pre-school or kindergarten period, is the period for the development of topological to geometrical spatial concept; from about the age of six to ten for the female students, and from about the age of six to eight for male students are the periods for the development of local spatial concept or local reference system concept; then from about the age of ten to fifteen for female students and eight to fifteen for the male students are the period for the development of global spatial concept or global reference system concept; and finally from about the age of fifteen or sixteen on for both sexes there show a slow down development for the spatial ability. The sex difference for the development of spatial concept show up as early as the age of seven or eight for the low level spatial concept, and at about the age of nine or ten for the high level spatial concept, and the difference increases gradually thereafter. The development of the female students at the age of fourteen or fifteen is only equivalent to the development of the male students at about the age of twelve or thirteen.