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

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，我们必须把资源直接投入到这个临界点上：中学数学悬崖。在国际数学测试中，美国四年级到十年级的学生成绩下降幅度最大。该项目旨在解决五年级至八年级的所有146项共同核心州标准（以及所有其他州数学标准），为每个标准提供虚拟现实环境，嵌入一个引人入胜的交互式3-Act数学故事问题。这个项目的理论基础源于生产性失败，即当学生在直接指导之前遇到生产性失败时，他们的表现要好于相反的情况，即首先给予指导。此外，每个模拟器直接将学生的输入与函数输出联系起来，以显示数学是如何工作的，特别是让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，即支持所有科学和工程基础领域的教育，并有可能通过在美国各地学校广泛的商业接受，对美国教育中的一个关键问题产生积极影响。该项目旨在为从五年级到八年级的所有标准提供虚拟现实环境下的模拟，使用一个核心软件平台进行交付，该平台可以在美国各地的教室中普遍使用。这种高风险的技术创新以一种独特的方式嵌入数学内容，即输入导致功能输出，这样学生就可以看到数学是如何实际工作的。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。数学问题有上下文和意义。学生可以直接体验到他们数学能力的结果，而教师则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和错误来解决难题的直接经验之前故意隐瞒教学和信息。这项研究的目的是为了说明，与其他方法相比，数学模拟显示出最高的成就，并且生产性失败是一种可行的学习方式，可以应用于支持高等数学应用和科学发现的所有领域。

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.