本研究旨在分析臺灣中部地區高年級學生在van Hiele 幾何推理層次的分布情形，以「吳-馬-陳氏幾何推理層次測驗」為研究工具，研究對象為臺灣中部地區2009 年第二學期在學的國小學生五年級的學生328 人及六年級的學生413人，全部樣本大小為741 人。得到研究結果摘述如下：A 縣和B 市的學生均是分布在創造性層次的學生最多，其次分布在批判性層次。縣市與層次兩變項有相關，且B 市在幾何推理層次的表現優於A 縣，顯示在van Hiele 幾何推理層次中，兩縣市的學生有著明顯的城鄉差異，這也代表著教育水平越高的縣市，越多學生達到較高層次，再次顯示教學和引導能提升學童的幾何思考概念，這點與van Hiele 的理論相吻合。五年級和六年級的學生均是分布在創造性層次的學生最多，其次分布在批判性層次。五年級、六年級的學生在van Hiele 幾何推理的發展可能比van Hiele 立體幾何概念的發展、van Hiele 平面幾何概念在三角形部份的發展以及van Hiele平面幾何概念在四邊形部份的發展都高一個層次。年級與層次兩變項沒有相關，顯示其年級愈高，分布在較高層次的人數並沒有明顯增多。男學生和女學生均是分布在創造性層次的學生最多，其次分布在批判性層次。性別對層次兩變項沒有顯著差異。

The purpose of this study is to discuss the distributions of the van Hielegeometrical reasoning levels of 5th and 6th graders. This study uses “Wu-Ma-Chen’svan Hiele Geometric Reasoning Test” (GRT) as the research tool, choosing 741 fifthandsixth-grade students in Central Taiwan as the subjects. The GRT was developedby the authors in 2010.Using the Chi-Square Test to analyze the data, the conclusions were drawn asfollows:(1) Most of A county’s and B city’s students are in the creative level. In the vanHiele geometrical reasoning level, scores of students from B City are better than thosefrom A County.(2) Most of fifth- and sixth-grade students are in the creative level, but thenumber of students is not obviously higher in the higher grade.(3) Most of male and female students are in the creative level, but in the vanHiele geometrical reasoning level, the scores of those students in the different gendersare not obviously different.