EAGER: Illuminating Learning by Splitting: A Learning Analytics Approach to Fraction Game Data Analysis

在我们这个日益科技化的社会，数学素养是一项关键的需求。分数已被确定为一个关键的理解领域，无论是为了在代数上取得成功，还是为了获得更高水平的数学。该项目使用学习分析和教育数据挖掘方法来研究小学生如何在折射中学习，这是一款旨在使用分裂模型教授分数的在线游戏。该项目使用了分数理解前后测试的数据和3000名三年级学生的游戏记录数据来检验以下问题：1)分裂是学习分数的有效方法吗？2)学生如何通过分裂学习？3)学生通过分裂学习有没有共同的途径？4)不同学习者有没有最优的学习途径？分裂是一个著名的分数学习理论，专家们非常赞同。然而，无论是用当前的定性方法还是定量方法，上述研究问题都很少能超越该领域目前的理解水平。通过使用聚类分析、关联规则挖掘和预测分析等数据挖掘方法，该项目提供了大量关于学生通过拆分学习的见解，包括：对非结构化学习环境中表现出的学习概况进行分类，常见错误和判断模式，学习中探索的价值或成本，以及不同学生(如预试得分较低的学生)通过学习的最佳途径。项目工作人员通过传统和新渠道分享方法和结果，以最大限度地影响现场和政策。除了会议和期刊出版物外，首席研究员还在几个背景下工作，在这些背景下，这项工作是该领域发展对学习的理解的新方法的典范。此外，这些背景中的许多都与首席州立学校官员的共享学习合作等努力有关，导致这些调查结果和产品很有可能迅速影响全国各地的大量学校。

Mathematical literacy is a critical need in our increasingly technological society. Fractions have been identified as a key area of understanding, both for success in Algebra and for access to higher-level mathematics. The project uses learning analytics and educational data mining methods to examine how elementary students learn in Refraction, an online game designed to teach fractions using the splitting model. The project uses the data from a pre- and posttest of fraction understanding and log data from 3000 third-grade students' gameplay to examine the following questions:1) Is splitting an effective way to learn fractions?2) How do students learn by splitting?3) Are there common pathways students follow as they learn by splitting?4) Are there optimal pathways for diverse learners?Splitting is a well-known theory of fraction learning and has significant expert buy in. However, few of the research questions above can be advanced past the field's present level of understanding with either current qualitative or quantitative methods. By using data mining methods such as cluster analysis, association rule mining, and predictive analysis, the project provides numerous insights about student learning through splitting, including: classification of learning profiles exhibited in unstructured learning environments, common mistakes and sense-making patterns, the value or cost of exploration in learning, and the best path through learning for different students (such as those who score low on a pre-test).The project staff shares the methods and results through traditional and novel outlets for maximum impact on the field and on policy. In addition to conferences and journal publications, the principal investigator is working in several contexts in which this work is an exemplar of new ways the field can develop understanding of learning. In addition, many of these contexts have connections to efforts such as the Chief State School Officers' Shared Learning Collaborative, leading to a high probability that the findings and products can quickly impact large numbers of schools across the country.