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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
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
