ABSTRACT
This chapter explores effective, research-based mathematics curriculum and instruction for advanced students. It begins with a discussion of the definition of mathematical talent. The impact of the national mathematics standards and their relevance to content for advanced learners are then discussed. Essential characteristics of mathematics curriculum for advanced learners are detailed including the development of higher-level processes akin to those used by mathematicians. Next, connections to the Integrated Curriculum Model are outlined using a model unit from the Project M 3 advanced mathematics curriculum series. Instructional strategies focused on high-level mathematical discussions and writing are then shared to highlight effective pedagogy. Assessment tools follow, including student journaling, portfolios, extended investigations, and projects. Throughout the chapter, numerous examples illustrate important aspects of effective curriculum and instruction to provide clarity and practical applications. The chapter concludes with considerations across all grade levels, including a broadened identification process and equity issues.
