How some research mathematicians and statisticians use proof in undergraduate mathematics

When does an argument use a generic example?

“…Hanna (2000) asserts that the role of proof in K12 education is to explain why a statement is true. Others have noted that proving can be used to help learners understand a definition (Yopp, 2011). We agree with the field (e.g., Leron & Zaslavsky, 2013) that generic example arguments can have value in their own right, but it would be problematic to use an argument's pedagogical utility as a criterion for judging whether it uses a generic example.…”

“…There are many reasons for engaging in argument and proving activities, other than generating formal proofs that have been identified in the literature (e.g., Yopp, 2011). Our goal is not to assume any research or teaching purpose for judging arguments or engaging students in argument construction, and our framework reflects this.…”

Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathematics classrooms

“…Although others are reported in the literature (e.g., aesthetic, intellectual challenge, learning new methods), this set (shown in Fig. 1) is well documented, appears consistently, and is recognized as highly influential (e.g., Mejía-Ramos & Inglis, 2009;Weber, 2010a;Yopp, 2011).…”

“…(For a recent comprehensive review, see Yopp (2011).) We focus on a subset of purposes of proof in the mathematician community offered by de Villiers (1999).…”

“…It should be noted that this set of purposes was developed in relation to the work of research mathematicians as professional mathematicians and not their work as instructors of undergraduate or graduate mathematics, which has been the focus of some more recent literature (e.g., Weber, 2010b;Yopp, 2011). de Villiers and Hanna both use the term proof in their work.…”