In the teaching of math-fact automaticity, most classroom teachers are unaware of research-based practices such as the use of a controlled response time, the scaffolded teaching of individual math facts, the limiting of exposure to new math facts, the separation of math facts with common operands, and even the definition of automaticity. As a…

Reasoning Mind products are used by over 100,000 students a year and have shown positive outcomes. In this design case we focus on implementation: how Reasoning Mind's approach evolved to tackle the challenge of achieving consistently high-quality implementations with many different schools, teachers, and students. Key insights include the…

Educators are being encouraged to shift their instructional paradigm from teacher-centered to learner-centered through the use of technology. For online courses, legacy learning management products originally designed to support and deliver teacher-centered instruction may represent a constraint to implementing the learner-centered paradigm. Yet,…

Technological advances afford teacher educators, designers, and researchers the opportunity to use videos as an instructional tool to help parents, caregivers, teachers, and other adults support young children's mathematical development. We created five Magic Math Minute videos to highlight examples of young children's mathematical thinking and to…

In this design case, we describe our first attempt to create a virtual mathematics tutoring program for students with learning disabilities. We describe in detail how the design was motivated by the pandemic which forced schools into remote learning, how a university and school collaborated on the design, the rationale for our design decisions,…

This design case describes the development of the Invention Coach, an intelligent exploratory learning environment (ELE) for the constructivist activity of Invention. The Invention Coach scaffolds students as they invent mathematical formulas to describe contrasting cases. In this paper, we detail our process and rationale for three key design…

Historically, what people can learn is co-determined by the "representational infrastructure" for knowledge building. When Latin was the required medium of knowledge building, few could engage in scholarly activities; without the change to the vernacular, nearly universal access to higher education would not be possible. The highly…