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.

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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.