Scharaschkin Alex
Department of Education, University of Oxford, Oxford, United Kingdom.
AQA Education, London, United Kingdom.
Front Psychol. 2024 Oct 2;15:1399317. doi: 10.3389/fpsyg.2024.1399317. eCollection 2024.
Psychometrics conceptualizes a person's (or , or ), in a cognitive or educational domain, as a latent numerical quantity. Yet both conceptual and empirical studies have shown that the assumption of quantitative structure for such phenomena is unlikely to be tenable. A reason why most applications of psychometrics nevertheless continue to treat them as if they were numerical quantities may be that quantification is thought to be necessary to enable . This is indeed true if one regards the task of measurement as the location of a measurand at a point on the real number line (the viewpoint adopted by, for example, the representational theory of measurement, the realist theory of measurement as the discovery of ratios, and Rasch measurement theory). But this is not the only philosophically respectable way of defining the notion of measurement. This paper suggests that van Fraassen's more expansive view of measurement as, in general, (which could be the real continuum, as in metrological applications in the physical sciences, but could be a different mathematical structure), provides a more appropriate conceptual framework for psychometrics. Taking educational measurement as a case study, it explores what that could look like in practice, drawing on fuzzy logic and mathematical order theory. It suggests that applying this approach to the assessment of intersubjectively constructed phenomena, such as a learner's proficiency in an inherently fuzzily-defined subject area, entails recognizing the theory-dependent nature of valid representations of such phenomena, which need not be conceived of structurally as values of quantities. Finally, some connections are made between this "qualitative mathematical" theorization of educational assessment, and the application of techniques from machine learning and artificial intelligence in this area.
心理测量学将一个人在认知或教育领域的（或 ，或 ）概念化为一个潜在的数值量。然而，概念性研究和实证研究均表明，此类现象的定量结构假设不太可能成立。尽管如此，心理测量学的大多数应用仍继续将它们当作数值量来处理，一个原因可能是，人们认为量化对于实现 是必要的。如果将测量任务视为在实数线上确定一个被测量的位置（例如，测量的表征理论、作为比率发现的测量实在论以及拉施测量理论所采用的观点），那么确实如此。但这并非定义测量概念的唯一一种在哲学上值得尊重的方式。本文认为，范·弗拉森对测量更宽泛的观点，即一般而言 （在物理科学的计量应用中可能是实数连续统，但也可能是不同的数学结构），为心理测量学提供了一个更合适的概念框架。以教育测量为例，本文利用模糊逻辑和数学序理论探讨了这在实践中可能是什么样子。本文表明，将这种方法应用于对主体间建构现象的评估，比如学习者在本质上定义模糊的学科领域的熟练程度，需要认识到此类现象有效表征的理论依赖性，而这些表征不必在结构上被设想为量的值。最后，本文在教育评估的这种“定性数学”理论与机器学习和人工智能技术在该领域的应用之间建立了一些联系。
