摘要 本研究旨在根據van Hiele 幾何理論，提供一個測驗編製歷程之個例，並修 正Fuys, Geddes, & Tischler（1988）所提出之 van Hiele 立體幾何思考層次之行為 描述，編製一套符合van Hiele 立體幾何思考層次之工具。 本研究之預試樣本為臺中市某國小四至六年級學生，每年級各兩班共6 班計 183 位學生，以研究者所自編之「吳 馬 李氏van Hiele 立體幾何思考層次測驗」 （WLVHSGL）為 工具，探討本份測驗之信度、效度，並初探預試樣本在van Hiele 立體幾何思考層次分布情形。 本研究的結論如下： 一、本研究呈現了一個測驗編製歷程之個例，研究群從 2005 年 5 月開始編製此 份問卷，至 2005 年 12 月共修正九次。本測驗的共 74 題選擇題，其中層次 一佔22 題，層次二佔41 題，層次三佔 11 題。 二、本研究針對Fuys 等人（1988）提出van Hiele 平面幾何層次的行為描述，修 正後，提出了van Hiele 立體幾何思考層次的行為描述。 三、本測驗的信度 alpha 值為 0.9210（ p < 0. 0 1 ），效標關聯效度為 0.718 （ p < 0. 0 1 ）。 四、研究結果顯示，在183 人中，最多人分布在層次二，百分比為39.3％，不同 年級之學童在van Hiele 立體幾何思考層次的表現，四年級的學童多分布在 層次一，百分比為 45.2％，五年級的學童多分布在層次二，百分比為 44.2 ％，六年級的學童多分布在層次二，百分比為 52.2％，及層次三，百分比為 45.0％。表示臺中市地區的學童在 van Hiele 立體幾何思考層次的表現是有 階層性的，年級較低的其立體幾何思考層次就較低，這有與van Hiele 的論 點相吻合。

Abstract This research was undertaken to develop the van Hiele test of the solid geometry for elementary school students. The content presented were partial results of the project funded by the National Science Council of the Executive Yuan (Project No.: NSC 94 2521 S 142003). The instrument used in this project was “WuMaLi’s van Hiele Solid Geometry Test” (WMLVHSGT) was used as the measurement instrument in order to investigate the concept of solid geometry shape. In order to test the validity and the reliability, the participates of this research were grades 4 to 6 pupils in the central region of Taiwan, with one class selected from each grades 4 to 6, for a total of 6 classes (183 pupils) selected from one primary schools. This research has the following findings: 1. There are five van Hiele levels. In this study, the WMLVHSGT was developed to measure the students at the first three van Hiele levels (visual, descriptive, and theoretical level). This test was revised 9 times during May to December, 2005. 2. The pretest students random selected from two counties. The statistics data, after analyzing by SPSS 10.0 for windows, we got alpha reliability 0.92 ( p < 0. 01 ), which showed the reliability of this tool is quite high. 3. The WMLVHSGT not only invites experts to examine but also take reference to “Wu’s van Hiele geometric thinking level test” (Wu, 2000) and get the validity of the test. The correlation coefficient is 0.718, which showed the validity of this test is quite high. 4. There are 74 questions in total. There are 22 questions for the first van Hiele level, 41 questions for the second van Hiele level, and 11questions for the third van Hiele level.