Supporting Teachers’ Instrumental Genesis with Dynamic Mathematical Software

This chapter addresses the need to prepare and support teachers of mathematics in order that they will be able to co-construct with their students classroom environments in which the Standards for Mathematical Practice as well as the content standards (CCSSM, 2010) are implemented fruitfully. Specifically, the chapter describes and illustrates design elements of learning environments with potential to positively impact pre- and in-service teachers’ knowledge of mathematics, facility with technology, and beliefs about how mathematics may be learned. The practice of using appropriate tools strategically is highlighted; however, each of the practice standards is integral to a classroom environment which supports mathematical proficiency (National Research Council, 2001). This chapter examines and illustrates the explicit and intentional instructional design features of using provocative tasks, dynamic technology scaffolding, and sustained intellectual press, which together interact in classrooms to promote the mathematical practices and habits of mind explicated in the CCSSM.