SBIR Phase II: Productive Failure in Math Simulations: Where Data Input is Directly Linked to Functional Output

SBIR 第二阶段：数学模拟中的生产性失败：数据输入直接与功能输出相关联

• 批准号: 1738444
• 负责人: James Laidlaw
• 金额: $ 75万
• 依托单位: MidSchoolMath, LLC
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-15 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1738444&HistoricalAwards=false
• 关键词: SBIR; Phase; II; Productive; Failure

This SBIR Phase II project was initiated as a direct result of extensive research into the US math crisis and the complexity of the problem. As a nation, we must invest resources directly into the breaking point: the mid school math cliff. The US shows the greatest decline worldwide from 4th to 10th grade on International tests in math. This project is designed to address all 146 Common Core State Standards (and all other state math standards) from 5th to 8th grade, providing a virtual reality context for each standard, embedded in an engaging, interactive 3-Act math story problem. The theoretical foundation of the project stems from Productive Failure, the concept that students perform better when they encounter productive failure prior to direct instruction in contrast to the reverse, where instruction is given first. Additionally, each simulator directly links student input to functional output to show how the math works, specifically allowing students to persist in exploring solutions. This project supports the NSF mission to support education for all fields fundamental to science and engineering, and holds the potential to positively impact a critical problem in U.S. education through broad commercial acceptance in schools throughout the US. This project is designed to provide simulations in a virtual reality context for all standards from 5th to 8th grade, using a core software platform for delivery that can be ubiquitously used in classrooms throughout the United States. This high-risk technical innovation uniquely embeds math content in such a way that input leads to functional output such that students can see how the math actually works. Students watch the outcomes of their solutions, both the successes and the failures so they can try again. Math problems have context and meaning. Students experience the direct results of their mathematical abilities, while teachers have the ability to deploy specific problems and receive real-time metrics to further respond and support student comprehension. Underlying the advanced classroom technology is the pedagogical framework based on Productive Failure and the intentional withholding of instruction and information prior to direct experience with grappling with a difficult problem with trial and error repetition. The goal of the research is to illustrate that math simulations show the highest achievement in comparison to other methodologies and that Productive Failure is a viable tenant of learning that can be applied to all fields supporting higher math applications and scientific discovery.

这个SBIR第二阶段项目的启动是对美国数学危机和问题复杂性进行广泛研究的直接结果。作为一个国家，我们必须将资源直接投入到临界点：中学数学悬崖。美国在国际数学测试中从4年级到10年级的下降幅度最大。该项目旨在解决从5年级到8年级的所有146个共同核心国家标准（以及所有其他国家数学标准），为每个标准提供虚拟现实背景，嵌入一个引人入胜的互动式3幕数学故事问题。该项目的理论基础源于生产性失败，即学生在直接教学之前遇到生产性失败时表现得更好，而不是相反，首先进行教学。此外，每个模拟器都直接将学生输入与函数输出联系起来，以显示数学是如何工作的，特别是允许学生坚持探索解决方案。该项目支持美国国家科学基金会的使命，支持科学和工程基础的所有领域的教育，并通过在美国各地的学校广泛的商业接受，具有积极影响美国教育中的一个关键问题的潜力。该项目旨在为5至8年级的所有标准提供虚拟现实环境中的模拟，使用可在美国各地教室中普遍使用的核心软件平台进行交付。这种高风险的技术创新独特地嵌入了数学内容，输入导致功能输出，这样学生就可以看到数学实际上是如何工作的。学生们观察他们解决方案的结果，包括成功和失败，这样他们就可以再试一次。数学问题有语境和意义。学生体验他们的数学能力的直接结果，而教师有能力部署特定的问题，并接收实时指标，以进一步响应和支持学生的理解。先进的课堂技术的基础是基于生产性失败的教学框架，以及在通过反复试验解决难题的直接经验之前故意保留教学和信息。该研究的目的是说明数学模拟与其他方法相比取得了最高成就，并且生产性失败是一种可行的学习租户，可以应用于支持高等数学应用和科学发现的所有领域。