In this Cyberlearning: Transforming Education Exploration project, the PIs investigate how to help middle schoolers simultaneously develop mathematics understanding, mathematics skill, and mathematics disposition. They are taking design-based pedagogical approach, having students practice the math they are learning through architectural design. Their software environment, called "Earthquake Rebuild," sets learners up in a virtual environment where an earthquake has demolished a city, and they must use geometry and arithmetic to make architectural and city planning decisions as they aim to rebuild the city. In this same context software context, the investigators are incorporating means of unobtrusive collection and analysis of performance data, called "stealth assessment," for purposes of both tracking development of understanding and capabilities and providing adaptive learner support. Research addresses practical issues in design of systems that help learners deeply learn content and skills in the context of solving real-world problems and in design of stealth assessments. Research also addresses conceptual issues in mathematics learning, specifically focusing on the ways that informal mathematical conjectures emerge and are transformed into formal mathematics knowledge through concrete application.
Too many middle schoolers fail to develop the kinds of mathematics capabilities they will need to be productive in the workforce and to be engaged citizens. Even more middle schoolers complete middle school without appreciating the connections between mathematics and the real world they live in. The aim of this project is to address both of these issues: to promote deep mathematical understanding and capabilities among middle schoolers and to engage them in "mathematizing" their worlds -- seeing the roles mathematics plays in the natural and built environment around them. To achieve these goals, investigators are designing a software environment that allows students to combine serious play and learning as they use middle-school mathematics to reconstruct a demolished fictional city. The system is being designed to collect data about student understanding in the background (called "stealth assessment") so that as students engage with the system, it can help them use mathematics to rebuild the buildings in the fictional city, more deeply learn the mathematics they are using, and come to appreciate the usefulness of mathematics and mathematical thinking in engaging productively in problem solving and design activities. Investigators will learn more about how to design learning technologies that will help learners learn and appreciate mathematics, how mathematics is learned when students engage more systematically in using math, and how to accomplish the types of stealth assessment needed to personalize learning technologies to the needs of individual students.
