Introduction to Representation: Grades 3-5 (Math Process Standards Series)

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.

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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 Representation, Bonnie Ennis and Kimberly Witeck share ways to help students use algorithms, graphs, manipulatives, diagrams, and other written and pictorial forms to express math ideas. They offer an array of entry points for understanding, planning, and teaching, including strategies that help students internalize manipulatives and other models of mathematical thinking so that they can begin documenting their mathematical processes. 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 Representation highlights the importance of encouraging children to demonstrate their mathematical thinking techniques through a variety of mathematical means, while also recommending ways to implement representation-based teaching without rewriting your curriculum.

Best of all, like all the titles in the Math Process Standards Series, Introduction to Representation 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 you need to better understand how students represent their thinking. Or if you're simply looking for new ways to work the representation standard into your curriculum, read, dog-ear, and teach with Introduction to Representation. 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.

Bonnie Ennis is coauthor of Introduction to Representation (Grades K - 2 and 3 - 5), part of Heinemann's Math Process Standards Series. A math teacher for twenty-three years, she is currently the coordinator for math instruction in the Wicomico County Public Schools. She is also an adjunct instructor at Salisbury University and a member of the Board of Directors for both the Maryland Council of Supervisors of Mathematics and the Maryland Council of Teachers of Mathematics.

Kimberly Witeck is coauthor of Introduction to Representation (Grades PreK - 2 and 3 - 5), part of Heinemann's Math Process Standards Series. A former elementary teacher and peer instructional coach, she is a Title I Math Teacher in Fairfax County Public Schools in Virginia. She conducts parent education workshops and professional staff development, presenting at workshops and conferences. She lives in Arlington, Virginia, with her husband and two children.

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Table of Contents


Foreword     xi
Acknowledgments     xiii
NCTM Process Standards and Expectations     xv
Introduction to the Representation Standard     1
How Representations Support Learning     11
The Value of Understanding How to Represent Math ideas     11
Organizing Information     11
Venn Diagrams     16
Recording Ideas or Observations     21
Communicate, Communicate, Communicate     23
Using Representations to Model a Process or Concept     25
The Role of the Teacher     26
Questions for Discussion     26
Using Manipulatives to Model and Illustrate Key Math Concepts     28
Modeling Ideas with Manipulatives     28
Building Understanding Through the Use of Manipulatives     32
Moving from the Concrete to the Abstract     35
Manipulatives and Student Learning Styles     36
Manipulatives Can Influence Understanding     38
Manipulatives and Technology     38
The Role of the Teacher     41
Questions for Discussion     42
Using Pictures and Diagrams to Represent Mathematical Thinking     43
Moving from Manipulatives to Pictures: Why Transition?     44
What Does a Picture Tell You About the Student's Thinking?     44
Can You Really Teach Fractions so They Will Remember? Absolutely!     49
The Role of the Teacher     56
Questions for Discussion     57
Using Numbers and Symbols to Represent Mathematical Ideas     58
Moving from Pictures to Equations     58
It's All About Timing     59
The Role of Alternative Algorithms     63
Using Equations to Solve Problems and Visualize Ideas     67
The Role of the Teacher     69
Questions for Discussion     71
Using Tables and Graphs to Record, Organize, and Communicate Ideas     72
It's Not Just About Bar Graphs Anymore!     72
Why Graph?     72
From Real Graphs to Pictographs     73
Line Plots or Line Graphs     75
Try Working Backward     77
Stem-and-Leaf Plots     78
Histograms     80
Circle Graphs     80
Teacher     83
Questions for Discussion     84
Assessing Students' Representations     85
Why Assess?     85
Assessing Representation     86
Observations     87
Interviews and Conferences     88
Performance-Based Tasks     89
Portfolios-Collections of Student Work     91
Assessment Equity     92
Feedback     92
Questions for Discussion     93
Representation Across the Content Standards     94
Number and Operations     95
Algebra     99
Geometry     103
Measurement     107
Data Analysis: Statistics and Probability     111
Conclusion     114
Questions for Discussion     115
Conclusion: Accepting the Challenge     117
Resources for Teachers     125
References     129
About the CD-ROM     1317
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