Guiding principles for teaching mathematics via reasoning and proving

International audienceAgainst the backdrop of policy documents and educational researchers' vision of proof as an essential component of teaching mathematics across content areas and grade levels, teaching of reasoning and proof in mathematics classrooms remains an elusive goal. Teachers and the type of teaching they enact in classrooms are crucial for achieving this goal. This theoretical paper builds on the concept of proof-based teaching and suggest a set of guiding principles for what we call teaching mathematics via reasoning and proving. These principles were developed as a part of a multi-year design based project, and implemented in an undergraduate course Mathematical Reasoning and Proving for Secondary Teachers. We illustrate these principles using examples from proof-oriented lessons plan developed by prospective secondary teachers