LearnSphere is a web-based data infrastructure designed to transform scientific discovery and innovation in education. It supports learning researchers in addressing a broad range of issues including cognitive, social, and motivational factors in learning, educational content analysis, and educational technology innovation. LearnSphere integrates previously separate educational data and analytic resources developed by participating institutions. The web-based workflow authoring tool, Tigris, allows technical users to contribute sophisticated analytic methods, and learning researchers can adapt and apply those methods using graphical user interfaces, importantly, without additional programming. As part of our use-driven design of LearnSphere, we built a community through workshops and summer schools on educational data mining. Researchers interested in particular student levels or content domains can find student data from elementary through higher-education and across a wide variety of course content such as math, science, computing, and language learning. LearnSphere has facilitated many discoveries about learning, including the importance of active over passive learning activities and the positive association of quality discussion board posts with learning outcomes. LearnSphere also supports research reproducibility, replicability, traceability, and transparency as researchers can share their data and analytic methods along with links to research papers. We demonstrate the capabilities of LearnSphere through a series of case studies that illustrate how analytic components can be combined into research workflow combinations that can be developed and shared. We also show how open web-accessible analytics drive the creation of common formats to streamline repeated analytics and facilitate wider and more flexible dissemination of analytic tool kits.