Introduction to Reasoning and Proof: Grades 3-5 (Math Process Standards Series)

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NCTM's Process Standards were designed to support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every elementary teacher the opportunity to explore each one of the standards in depth. And with language and examples that don't require prior math training to understand, the series offers friendly, reassuring advice to any teacher preparing to embrace the Process Standards.

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Overview


NCTM's Process Standards were designed to support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every elementary teacher the opportunity to explore each one of the standards in depth. And with language and examples that don't require prior math training to understand, the series offers friendly, reassuring advice to any teacher preparing to embrace the Process Standards.

In Introduction to Reasoning and Proof, Karren Shultz-Ferrell, Brenda Hammond, and Josepha Roblesfamiliarize you with ways to help students explore their reasoning and support their mathematical thinking. They offer an array of entry points for understanding, planning, and teaching, including strategies that help students develop strong mathematical reasoning and construct solid justifications for their thinking. Full of activities that are modifiable for immediate use with students of all levels and written by veteran teachers for teachers of every level of experience, Introduction to Reasoning and Proof highlights the importance of encouraging children to describe their reasoning about mathematical activities, while also recommending ways to question students about their conclusions and their thought processes in ways that help support classroom-wide learning.

Best of all, like all the titles in the Math Process Standards Series, Introduction to Reasoning and Proof comes with two powerful tools to help you get started and plan well: a CD-ROM with activities customizable to match your lessons and a correlation guide that helps you match mathematical content with the processes it utilizes.

If your students could benefit from more opportunities to explain their reasoning about math concepts. Or if you're simply looking for new ways to work the reasoning and proof standards into your curriculum, read, dog-ear, and teach with Introduction to Reasoning and Proof. And if you'd like to learn about any of NCTM's process standards, or if you're looking for new, classroom-tested ways to address them in your math teaching, look no further than Heinemann's Math Process Standards Series. You'll find them explained in the most understandable and practical way: from one teacher to another.

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Product Details

Meet the Author

Susan O'Connell is the coauthor of Putting the Practices Into Action, Mastering the Basic Math Facts in Addition and Subtraction, and Mastering the Basic Math Facts in Multiplication and Division. She served as editor of Heinemann's popular Math Process Standards series and was the author of its Introduction to Problem Solving and Introduction to Communication books. Sue also wrote the bestselling Now I Get It (Heinemann 2005). Sue O'Connell has years of experience as a classroom teacher, instructional specialist, district school improvement specialist, and university PDS coordinator. She is a nationally known speaker and education consultant, providing math professional development for schools and districts across the country.

Karren Shultz-Ferrell is coauthor of Introduction to Reasoning and Proof (Grades PreK - 2, 3 - 5, and 6 - 8), part of Heinemann's Math Process Standards Series. She is an elementary mathematics instructional specialist for Montgomery County Public Schools in Maryland and former classroom teacher. A board representative for the Maryland Council of Teachers of Mathematics, Karren consults with school systems and presents at state, regional, and national conferences.

Brenda Hammond is a coauthor of Introduction to Reasoning and Proof (Grades PreK - 2 and 3 - 5), part of Heinemann's Math Process Standards Series. A staff development teacher in Montgomery County, Maryland, she has taught for more than thirty years at the elementary and university levels. She has been a presenter at national conferences, a mathematics consultant, and the author of First Word Problems (2003). Brenda is a recipient the Presidential Award for Excellence in Mathematics Teaching.

Josepha Robles is a coauthor of Introduction to Reasoning and Proof (Grades PreK - 2 and 3 - 5), part of Heinemann's Math Process Standards Series. She has taught for more than twenty-five years in public and private schools. She is a math content coach in Montgomery County, Maryland, a math consultant in the private sector, and a published author who has presented at NCTM national, regional and state conferences.

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Table of Contents


Foreword     viii
Acknowledgments     x
NCTM Process Standards and Expectations     xi
Introduction: The Reasoning and Proof Standard     1
Why Focus on Reasoning and Proof?     1
What Is the Reasoning and Proof Standard?     2
Developing Skills and Attitudes     2
How This Book Will Help You     3
Questions for Discussion     5
Creating a Learning Environment That Promotes Reasoning and Proof     6
Our Attitude Toward Mathematics     6
A Safe, Supportive, and Respectful Classroom     7
Engaging and Challenging Mathematics     8
Questioning     13
Additional Factors That Promote Reasoning     15
Discourse     15
Recording Sheets     16
Writing     16
Wait Time     17
Probing Questions     17
Group Work     18
Models, Manipulatives, and Technological Tools     15
Reflecting on Problem Solving and Reasoning     18
High Standards and Expectations     19
Final Thoughts     19
Questions for Discussion     19
Reasoning in Grades 3 Through 5     21
WhatCan You Expect of Students?     21
Types of Reasoning     22
Inductive Reasoning     23
Deductive Reasoning     26
Additional Tools That Support Students' Reasoning Skills     39
Final Thoughts     39
Questions for Discussion     40
Is It Always True? Making Conjectures     41
The Role of Conjectures in Reasoning and Proof     41
How Can You Help Your Students Make Conjectures?     43
Making Conjectures About Important Mathematical Ideas and Relationships     47
What Questions Help Students to Think About Conjectures?     48
Final Thoughts     50
Questions for Discussion     51
Developing and Evaluating Mathematical Arguments     52
The Role of Mathematical Arguments in Reasoning and Proof     52
How Can You Help Your Students Create Justifications?     53
Questioning That Promotes the Development of Mathematical Arguments     53
Helping Students Develop and Evaluate Mathematical Arguments     54
Final Thoughts     63
Questions for Discussion     64
How the Process Standards Support Reasoning and Proof     65
Problem Solving     65
Communication      69
Representation     76
Connections     78
Final Thoughts     81
Questions for Discussion     82
Assessing Students' Reasoning     83
Why Assess Students' Reasoning?     83
How to Assess Students' Reasoning     84
Student Discussions     85
Partner or Small-Group Work     86
Written Responses     88
Representations     88
Diagnostic Interviews     88
Additional Ways to Assess Students' Reasoning     90
Development of Students' Reasoning Skills     92
Assessing Students' Reasoning with Rubrics     93
Final Thoughts     94
Questions for Discussion     95
Reasoning and Proof Across the Content Standards     96
Number and Operations     97
Lesson: Factors of Even and Odd Numbers (Allyssia's Work)     99
Algebra     104
Lesson: A = A     108
Geometry     111
Lesson: Geometric Sorting Rules     111
Lesson: Pentominoes     116
Measurement     119
Lesson: Frozen Fruit Salad     120
Data Analysis and Probability      123
Lesson: Spinner Activity     124
Final Thoughts     126
Questions for Discussion     127
Conclusion     129
Resources to Support Teachers     132
Additional Resources for Reasoning and Proof     132
Text Resources     132
Web Resources     133
Staff Development Training Videos     134
References     135
About the CD-ROM     137
Why Are the Activities on a CD?     137
Editing a Problem to Motivate and Engage Students     137
Personalizing Tasks or Capitalizing on Students' Interests     137
Editing a Problem to Differentiate Instruction     139
Creating Shortened or Tiered Tasks     139
Modifying Readability of Tasks     140
Modifying Data     141
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