title: Routines for Reasoning: Fostering the Mathematical Practices in All Students
author:  Grace Kelemanik 
description: "This book is a must read for every K-12 teacher serious about shifting the nature of learning mathematics in the next decade." --<strong>Timothy D. Kanold, Former Director of Mathematics and Science, and School Superintendent, Adlai E. Stevenson HSD 125 </strong><br /><br />"This book honors the art of teaching and the brilliance of students thinking. It will help teachers think a lot harder about what the mathematical practices mean...This book should be on every mathematics teacher's bookshelf." --<strong>Elham Kazemi, Geda and Phil Condit Professor in Mathematics Education, University of Washington; coauthor of <em>Intentional Talk</em></strong><br /><br />"The instructional routines outlined will help teachers all over the world create opportunities to surface and extend student thinking to support developing mathematical communities in their classrooms. I highly recommend this book to anyone who wants to learn how to implement inquiry-oriented mathematics instruction that works." --<strong>David Wees, formative assessment specialist in mathematics, New Visions for Public Schools, New York City</strong>
zlib_text: First published 1977
  Ha awAuucKOM JMWKe
  ©  English translation, Mir Publishers, 1978
  
  CONTENTS
  Foreword
  1. What Is Proof?
  2. Why Is Proof a Necessity?
  3. What Should Be Meant by a Proof?
  4. What Propositions May Be Accepted Without Proof?
  
  FOREWORD
  One fine day at the very start of a school year I happened 
  to overhear two young girls chatting. They exchanged views on 
  lessons, teachers, girl-friends, made remarks about new subjects. 
  The elder was very much puzzled by lessons in geometry.
  “Funny/1 she said, “the teacher enters the classroom, draws 
  two equal triangles on the blackboard and next wastes the whole 
  lesson proving to us that they are equal. I've no idea what's that 
  for." “And how are you going to answer the lesson?" asked the 
  younger. “Fll learn from the textbook 
  although it's going to be 
  a hard task trying to remember where every letter goes.
  The same evening I heard that girl diligently studying geometry 
  sitting at the window: “To prove the point let’s superpose 
  t