Deep Fractions Learning: A Core Curriculum of Games, Inquiry, and Collaboration

在美国，学生对分数的理解存在着巨大的缺陷。 五年级分数知识预测高中数学成绩，即使在控制 工作记忆、整数知识、智商、阅读能力和人口因素 （Siegler等人，2012年）。因此，解决这一赤字是一个特别重要的领域， 干预有了这个快速通道拨款，深度分数学习，我们建议将 学生学习核心数学课程的方式，使材料更具互动性， 参与，促进对内容的深入学习，并与共同核心保持一致。更 具体而言，我们将开发和评估3-5年级的数字课程， 分数域结合了游戏，协作和查询方法。我们建议 开发一个创新的技术基础设施，将整合Teachley学习游戏， 成功的所有（SFA）合作学习框架，和严格的课程内容。我们将 将研究整合到设计过程中，并与约翰霍普金斯大学合作评估 干预的有效性。 结果。干预措施将鼓励学生取得四个直接成果，即 改进：1）分数的概念理解，2）分数的程序流畅性 操作，3）数学理由，和4）动机。首先，课程将建立两者 概念理解和程序流畅性，提供强大的视觉模型， 有趣的游戏，激励学生练习。协作学习模式与探究 教学方法能提高学生的数学论证能力。最后，我们鼓励这些 在旨在促进参与的激励支持结构内取得成果， 自我效能 提高学生在分数领域的学业成绩和自我效能， 小学数学会促进以后在高中数学中的成功。由于每增加一个 学生在高中完成的数学课程是完成大学学业的两倍多 （阿德尔曼，2006年），干预有可能使一个真实的差异， 学生实现可持续的职业生涯，而不是陷入低薪工作。

There is an enormous deficit in students’ understanding of fractions in the United States. Fifth grade fraction knowledge predicts high school math performance, even when controlling for working memory, whole number knowledge, IQ, reading ability, and demographic factors (Siegler et al., 2012). Therefore, addressing this deficit is a particularly important area for early intervention. With this Fast-Track grant, Deep Fractions Learning , we propose to transform the way in which students learn core math curriculum so that materials are more interactive and engaging, promote deeper learning of content, and are aligned with the Common Core. More specifically, we will develop and evaluate a digital curriculum for grades 3-5 covering the fractions domain that combines games, collaboration, and an inquiry approach. We propose to develop an innovative technology infrastructure that will integrate Teachley learning games, Success for All’s (SFA) cooperative learning framework, and rigorous lesson content. We will integrate research into the design process and work with Johns Hopkins University to evaluate the efficacy of the intervention. Outcomes. The intervention will encourage four direct outcomes for students, namely improved: 1) conceptual understanding of fractions, 2) procedural fluency with fractions operations, 3) mathematical justification, and 4) motivation. First, the curriculum will build both conceptual understanding and procedural fluency, providing strong visual models within engaging games that motivate students to practice. The collaborative learning model and inquiry approach will improve students’ mathematical justification. Finally, we encourage these outcomes within a motivational support structure designed to foster engagement and self-efficacy. Improving students’ academic outcomes and self-efficacy in the area of fractions during elementary school will promote later success in high school mathematics. Since each additional math class students complete in high school more than doubles the odds of college completion (Adelman, 2006), the intervention has the potential to make a real difference in whether students achieve sustainable careers versus being stuck in low-wage jobs.