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

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.