论文标题
通过降低维度可视化和理解数学中的大规模评估
Visualizing and Understanding Large-Scale Assessments in Mathematics through Dimensionality Reduction
论文作者
论文摘要
在本文中，我们将Logistic PCA（LPCA）应用于减少维度的工具，以可视化模式并表征通过大规模评估测量的给定人群的数学能力的相关性。我们从项目响应理论（IRT）中建立了LPCA，内部产品表示（IPR）和两个Paramenter Logistic模型（2PL）之间参数的等效性。这种等效性提供了三种数据，以查看有助于教育专业人员执行文化解释的数据。特别是，我们分析了从Spaece收集的数据，Spaece是一项数学评估，该数据已在巴西Ceará国的公共教育体系中每年应用。作为主要结果，我们表明，在中学结束时，考生的表现不佳主要是由于他们的残疾在数字意义上引起的。
In this paper, we apply the Logistic PCA (LPCA) as a dimensionality reduction tool for visualizing patterns and characterizing the relevance of mathematics abilities from a given population measured by a large-scale assessment. We establish an equivalence of parameters between LPCA, Inner Product Representation (IPR) and the two paramenter logistic model (2PL) from the Item Response Theory (IRT). This equivalence provides three complemetary ways of looking at data that assists professionals in education to perform in-context interpretations. Particularly, we analyse the data collected from SPAECE, a large-scale assessment in Mathematics that has been applied yearly in the public educational system of the state of Ceará, Brazil. As the main result, we show that the the poor performance of examinees in the end of middle school is primarily caused by their disabilities in number sense.
