Carr et al. (2009) link the 5E (interactive) model to three stages of mathematics instruction: introduce, investigate, and summarize. As its name implies, this model is based on a recursive cycle of five cognitive stages in inquiry-based learning: (a) engage, (b) explore, (c) explain, (d) elaborate, and (e) evaluate. Teachers have a multi-faceted role in this model. As a facilitator, the teacher nurtures creative thinking, problem-solving, interaction, communication, and discovery. As a model, the teacher initiates thinking processes, inspires positive attitudes toward learning, motivates, and demonstrates skill-building techniques. Finally, as a guide, the teacher helps to bridge language gaps and foster individuality, collaboration, and personal growth. The teacher flows in and out of these various roles within each lesson.
Carr, John, Catherine Caroll, Sarah Cremer, Mardi Gale, and Rachel Languoff. 2009. Making Mathematics Accessible to English Learners: A Guidebook for Teachers. San Francisco, CA: WestEd.