Phil Vahey

Curricular Activity Systems Supporting the Use of Dynamic Representations to Foster Students’ Deep Understanding of Mathematics

A significant body of research has shown the benefits of dynamic representations technologies for learning. Dynamic representations embed mathematical relationships in objects that can be manipulated and illustrated in a concrete way. An example is a position graph that controls the motion of an object or character (e.g., a person running) in a simulated world. Although the technology required to use dynamic representations is now commonplace their use in the classroom is still limited. This chapter describes the notion of a curricular activity system and how it can be used in the design of learning environments that have a wider reach.

Sustainable Use of Dynamic Representational Environments: Toward a District-Wide Adoption of SimCalc-Based Materials

In this chapter, we will discuss pilot research in our multiyear effort aimed at aiding a large, urban school district in the state of Florida to adopt SimCalc MathWorlds® as a sustainable and integral part of middle school mathematics education. Building upon analyses that identify important factors in sustainable use of SimCalc-based materials, we have built local capacity to support the program and designed teacher professional development and district rollout plans to increase the likelihood of sustained use in the district. We have found that our efforts resulted in a replication of prior effectiveness results, as well as strong local support for SimCalc-based materials. These factors have allowed us to steadily increase our presence in the district, and now the district and project team are actively working toward our shared vision of the materials being used by every middle school mathematics teacher in the district. We end with a discussion of next steps and risks associated with our ongoing efforts.