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里，数学素养是一项至关重要的需求。分数已经被认为是理解的一个关键领域，无论是在代数上的成功还是在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refaction中学习，refaction是一款旨在使用分裂模型教授分数的在线游戏。该项目使用分数理解的前后测试数据，以及3000名三年级学生游戏玩法的日志数据来检验以下问题：1)分割是学习分数的有效方法吗？2)学生如何通过分裂学习？3)学生在分裂学习时是否有共同的途径？4)是否存在适合不同学习者的最佳途径？分割是一种众所周知的分数学习理论，并得到了许多专家的认可。然而，上面的研究问题很少能够超越当前定性或定量方法对该领域的理解水平。通过使用数据挖掘方法，如聚类分析、关联规则挖掘和预测分析，该项目提供了许多关于学生通过分裂学习的见解，包括：在非结构化学习环境中展示的学习概况的分类、常见错误和意义构建模式、学习探索的价值或成本，以及不同学生（例如那些在预测试中得分较低的学生）的最佳学习路径。项目工作人员通过传统和新颖的渠道分享方法和结果，以期对实地和政策产生最大影响。除了会议和期刊出版物之外，首席研究员还在几个环境中工作，在这些环境中，这项工作是该领域发展对学习理解的新方法的典范。此外，许多这些背景都与诸如首席州立学校官员共享学习协作等努力有关，这使得研究结果和产品很有可能迅速影响到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.