Educational assessments, specifically standardized and normalized exams, owe most of their foundations to psychological test theory in psychometrics. While the theoretical assumptions of these practices are widespread and relatively uncontroversial in the testing community, there are at least two that are philosophically and mathematically suspect and have troubling implications in education. Assumption 1 is that repeated assessment measures that are calculated into an arithmetic mean are thought to represent some real stable, quantitative psychological trait or ability plus some error. Assumption 2 is that aggregated, group-level educational data collected from assessments can then be interpreted to make inferences about a given individual person over time without explicit justification. It is argued that the former assumption cannot be taken for granted; it is also argued that, while it is typically attributed to 20th century thought, the assumption in a rigorous form can be traced back at least to the 1830s via an unattractive Platonistic statistical thesis offered by one of the founders of the social sciences—Belgian mathematician Adolphe Quetelet (1796–1874). While contemporary research has moved away from using his work directly, it is demonstrated that cognitive psychology is still facing the preservation of assumption 1, which is becoming increasingly challenged by current paradigms that pitch human cognition as a dynamical, complex system. However, how to deal with assumption 1 and whether it is broadly justified is left as an open question. It is then argued that assumption 2 is only justified by assessments having ergodic properties, which is a criterion rarely met in education; specifically, some forms of normalized standardized exams are intrinsically non-ergodic and should be thought of as invalid assessments for saying much about individual students and their capability. The article closes with a call for the introduction of dynamical mathematics into educational assessment at a conceptual level (e.g., through Bayesian networks), the critical analysis of several key psychological testing assumptions, and the introduction of dynamical language into philosophical discourse. Each of these prima facie distinct areas ought to inform each other more closely in educational studies.

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关于教育评估理论：对阿道夫·奎特莱、柏拉图主义和遍历性的高级讨论

教育评估，特别是标准化和规范化考试，其大部分基础都归功于心理测量学中的心理测试理论。虽然这些实践的理论假设在测试社区中广泛存在且相对没有争议，但至少有两个在哲学和数学上是可疑的，并且对教育产生了令人不安的影响。假设 1 是计算成算术平均值的重复评估措施被认为代表了一些真正稳定的、数量化的心理特征或能力加上一些错误。假设 2 是从评估中收集的聚合的、群体级别的教育数据可以被解释为随着时间的推移对给定的个人做出推断，而无需明确的理由。有人认为，不能认为前一种假设是理所当然的。也有人认为，虽然它通常归因于 20 世纪的思想，但这种严格形式的假设至少可以追溯到 1830 年代，通过社会科学的创始人之一——比利时数学家提出的柏拉图主义统计论文没有吸引力阿道夫·奎特莱 (1796–1874)。虽然当代研究已经不再直接使用他的作品，但事实证明，认知心理学仍然面临着保留假设 1 的问题，而当前的范式将人类认知视为一个动态的复杂系统，这正日益受到挑战。然而，如何处理假设 1 以及它是否具有广泛的合理性仍然是一个悬而未决的问题。然后有人认为，假设 2 只能通过具有遍历特性的评估来证明，这是教育中很少达到的标准；具体而言，某些形式的标准化考试本质上是非遍历性的，应被视为无效评估，因为它对个别学生及其能力进行了过多评价。文章最后呼吁在概念层面（例如通过贝叶斯网络）将动态数学引入教育评估，对几个关键的心理测试假设进行批判性分析，并将动态语言引入哲学话语中。在教育研究中，这些表面上不同的领域中的每一个都应该更密切地相互交流。某些形式的标准化考试本质上是非遍历性的，应该被视为无效的评估，因为它对个别学生及其能力的评价过多。文章最后呼吁在概念层面（例如通过贝叶斯网络）将动态数学引入教育评估，对几个关键的心理测试假设进行批判性分析，并将动态语言引入哲学话语中。在教育研究中，这些表面上不同的领域中的每一个都应该更密切地相互交流。某些形式的标准化考试本质上是非遍历性的，应该被视为无效的评估，因为它对个别学生及其能力的评价过多。文章最后呼吁在概念层面（例如通过贝叶斯网络）将动态数学引入教育评估，对几个关键的心理测试假设进行批判性分析，并将动态语言引入哲学话语中。在教育研究中，这些表面上不同的领域中的每一个都应该更密切地相互交流。文章最后呼吁在概念层面（例如通过贝叶斯网络）将动态数学引入教育评估，对几个关键的心理测试假设进行批判性分析，并将动态语言引入哲学话语中。在教育研究中，这些表面上不同的领域中的每一个都应该更密切地相互交流。文章最后呼吁在概念层面（例如通过贝叶斯网络）将动态数学引入教育评估，对几个关键的心理测试假设进行批判性分析，并将动态语言引入哲学话语中。在教育研究中，这些表面上不同的领域中的每一个都应该更密切地相互联系。