Strategically Fostering Dynamic Interactive Environments

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in mathematical reasoning" (NCTM 2014, p. 78). With these tools come novel forms of mathematical representations. The National Council of Teachers of Mathematics confirms the dichotomy by defining representation as referring "both to process and to product--in other words, to the act of capturing a mathematical concept or relationship in some form and to the form itself" (NCTM 2000, p. 67). Thus, by working with external rep representations, students access, assimilate, accommodate, and build internal representations. With advances in technology, the forms and capabilities of external representations are opening new windows both to do and to study mathematics so that students' internal representations will evolve. The intent of this article is to provide teachers with a more nuanced explanation of the role technology plays in helping students mediate between external and internal representations of linear functions. Teachers may (re)consider the questions that they might ask when creating an activity using technology or engaging in formative assessment during an activity using technology. In this article, the author first shares an activity in which students use TI-Nspire to study linear functions. Then she shares some of the major results of a study that she completed and its implications for the teaching and learning environment.