The van Hiele theory and van Hiele Geometry Test have been extensively used in mathematics assessments across countries. The purpose of this study is to use classical test theory (CTT) and cognitive diagnostic modeling (CDM) frameworks to examine psychometric properties of the van Hiele Geometry Test and to compare how various classification criteria assign van Hiele levels to students. The findings support the hierarchical property of the van Hiele theory and levels. Using conventional and combined criteria to determine mastery of a level, the percentages of students classified into an overall level were relatively high. Although some items had aberrant difficulties and low item discrimination, varied selection of the criteria across levels improved item discrimination power, especially for those items with low item discrimination index (IDI) estimates. Based on the findings, we identify items on the van Hiele Geometry Test that might be revised and we suggest changes to classification criteria to increase the number of students who can be assigned an overall level of geometry thinking according to the theory. As a result, practitioners and researchers may be better positioned to use the van Hiele Geometry Test for classroom assessment.

中文翻译：

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使用CTT和CDM框架检查van Hiele几何测验的心理测验特性和等级分类

van Hiele理论和van Hiele几何测试已在各国的数学评估中广泛使用。这项研究的目的是使用经典测试理论（CTT）和认知诊断建模（CDM）框架来检查van Hiele几何测试的心理测量特性，并比较各种分类标准如何将van Hiele等级分配给学生。这些发现支持了范·海耶尔理论和层次的层级性质。使用常规标准和综合标准来确定对某个水平的掌握程度，分类为总体水平的学生百分比相对较高。尽管有些项目存在异常困难且项目歧视程度较低，但跨级别选择标准的方式可以提高项目歧视能力，特别是对于那些物品识别指数（IDI）估算值较低的物品。根据调查结果，我们确定了范·海勒几何测试中可能需要修订的项目，并建议对分类标准进行更改，以增加根据该理论可被分配总体几何思维水平的学生人数。因此，从业人员和研究人员可能更适合使用van Hiele几何测试进行课堂评估。