In the real world of research mathematics, mathematicians do not know in advance if their assertions are true or false. Extending the Frontiers of Mathematics: Inquiries into proof and argumentation requires students to develop a mature process that will serve them throughout their professional careers, either inside or outside of mathematics. Its inquiry-based approach to the foundations of mathematics promotes exploring proofs and other advanced mathematical ideas through these features:
- Puzzles and patterns introduce the pedagogy. These precursors to proofs generate creativity and imagination that the author builds on later
- Prove and extend or disprove and salvage, a consistent format of the text, provides a framework for approaching problems and creating mathematical proofs
- Mathematical challenges are presented which build upon each other, motivate analytical skills, and foster interesting discussion
