“…With a similar focus on structure, empirical studies have specified skills students need to produce simple proofs in a given area (Gholamazad, Lijedahl, & Zazkis, 2003;Weber, 2006), and have investigated technological environments that can focus students' attention on the axiomatic development of a mathematical theory (Cerulli & Mariotti, 2003). Suggestions and research in keeping with the "natural" route to proof tend to focus on classroom environments in which students and teacher work collaboratively, investigating problems, formulating conjectures, debating the validity of arguments and so forth (Alibert & Thomas, 1991;Blanton & Stylianou, 2003;Rasmussen, Zandieh, King, & Teppo, 2005;Yackel, Rasmussen, & King, 2000).…”