Karina K. R. Hensberry (University of Colorado Boulder, USA), Ariel J. Paul (University of Colorado Boulder, USA), Emily B. Moore (University of Colorado Boulder, USA), Noah S. Podolefsky (University of Colorado Boulder, USA) and Katherine K. Perkins (University of Colorado Boulder, USA)

Copyright: © 2013
|Pages: 21

DOI: 10.4018/978-1-4666-4086-3.ch010

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TopThe use of tools—concrete manipulatives, calculators, measurement devices, computers, etc.—has long been recognized as important in mathematics education, and advances in Computer Technology (CT) position virtual manipulatives and interactive simulations as powerful new tools for teaching and learning mathematics. National Council of Teachers of Mathematics ((NCTM), 2000) Technology Principal asserts that students can learn more mathematics more deeply with the appropriate use of technology because it allows students to shift their focus from computation to reflection, decision making, reasoning, and problem solving. Educational research adds support to NCTM’s call for the use of technology for teaching and learning mathematics. In a meta-analysis of relevant literature, Li and Ma (2010) concluded that CT can positively impact mathematics achievement.

Lei (2010) argues that the *quality* of educational technology—what and how it is used—is more predictive of student outcomes than the *quantity* of technology students interact with. Research supports Lei’s notion that the first aspect of the quality of instruction—the what—is important. Characteristics of CT that impact student achievement include allowing students to experiment and test hypotheses, scaffolding students to avoid common error patterns (Suh, Moyer, & Heo, 2005), providing immediate feedback (Reimer & Moyer, 2005), and presenting information in multiple representational forms (Li & Ma, 2010; Roschelle et al., 2010; Vahey, Lara-Meloy, Moschkovich, & Velazquez, 2010). For example, in a large-scale study examining the impact of an interactive representational technology, Roschelle et al. (2010) found that students in the treatment classes performed equally well on standardized measures of basic mathematical knowledge and significantly better on measures of advanced mathematics than control group students who received “business as usual” instruction.

Regarding the second aspect of the quality of technology—how it is used (Lei, 2010)—Li and Ma (2010) found in their meta-analysis that effect sizes of CT were greatest when combined with instruction that aligned with mathematics reform. Other studies also suggest that instruction aligned with constructivist principles rather than drill and practice is necessary for CT to be effective (e.g., Vahey et al. 2010; Wenglinsky, 2005). For instance, problem solving is a key component of mathematics reform, and the use of CT in a problem-based learning environment was found to support students in developing computation and problem-solving skills (Bottge, Grant, Stephens, & Rueda, 2010). Reform instruction also stresses the use of manipulatives, and virtual manipulatives have been found to be as effective as, and sometimes more than, concrete manipulatives for improving student learning (Burns & Hamm, 2011; Lee & Chen, 2010; Moyer-Packenham & Westenskow, 2012; Moyer-Packenham & Suh, 2011; Reimer & Moyer, 2005; Suh et al., 2005; Yuan, Lee, & Wang, 2010). The immediate feedback provided by virtual manipulatives is important for helping students monitor their own understanding and learning of concepts, and they are easier and faster to use than concrete models or paper and pencil tools (Reimer & Moyer, 2005). Other aspects of reform mathematics teaching found to support students of various backgrounds and ability levels in learning from CT include: ample opportunities for discussion with peers (Vahey et al., 2010; Zahner, Velazquez, Moschkovich, Vahey, & Lara-Meloy, 2012); a focus on meaning and student construction of informal rules before formal introduction of rules and vocabulary (Suh et al., 2005; Vahey et al., 2010; Zahner et al., 2012); and addressing incorrect answers using higher-level moves (Zahner et al., 2012).

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Editorial Advisory Board

Table of Contents

Foreword

James W. Wilson

Preface

Drew Polly

Chapter 1

Core Math Tools: Supporting Equitable Implementation of the Common Core State Standards for Mathematics
(pages 1-22)

Christian Hirsch, Brin Keller, Nicole Fonger, Alden Edson

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Chapter 2

Supporting Mathematical Communication through Technology
(pages 23-37)

Chandra Hawley Orrill, Drew Polly

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Chapter 3

Michelle Rutherford

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Chapter 5

Fostering Mathematical Competence through Technology-Enhanced Interactive Environments
(pages 53-77)

Azita Manouchehriazi, Jennifer Czocher, Ravi Somayajulu, Yating Liu, Pingping Zhang, Jenna Tague

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Chapter 6

Using Technology to Engage Students with the Standards for Mathematical Practice: The Case of DGS
(pages 78-101)

Milan Sherman

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Chapter 7

Lisa Ames, Heejung An, Sandra Alon

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Chapter 8

Integrating Digital Technologies for Spatial Reasoning: Using Google SketchUp to Model the Real World
(pages 110-127)

D. Craig Schroeder, Carl W. Lee

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Chapter 9

Design and Implementation of Computational Modeling for Learning Mathematical Concepts
(pages 128-146)

Shelby P. Morge, Mahnaz Moallem, Chris Gordon, Gene Tagliarini, Sridhar Narayan

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Chapter 10

PhET Interactive Simulations: New Tools to Achieve Common Core Mathematics Standards
(pages 147-167)

Karina K. R. Hensberry, Ariel J. Paul, Emily B. Moore, Noah S. Podolefsky, Katherine K. Perkins

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Chapter 11

Do Technologies Support the Implementation of the Common Core State Standards in Mathematics of High School Probability and Statistics?
(pages 168-183)

Woong Lim, Dong-Gook Kim

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Chapter 12

Sketchpad®, TinkerPlots®, and Fathom®: Using Dynamic Geometry® Software Tools Strategically
(pages 184-199)

Karen Greenhaus

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Chapter 13

Solving Equations is All about Balance: Using Virtual Manipulatives in the Middle School Classroom
(pages 201-214)

Robin Magruder, Margaret Mohr-Schroeder

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Chapter 14

Two Classroom Portraits Demonstrating the Interplay of Secondary Mathematics Teachers’ TPACK on their Integration of the Mathematical Practices
(pages 215-227)

Jessica Taylor Ivy, Dana Pomykal Franz

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Chapter 15

Supporting Pattern Exploration and Algebraic Reasoning through the Use of Spreadsheets
(pages 228-233)

Ayhan Kursat Erbas, Sarah Ledford, Chandra Hawley Orrill, Drew Polly

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Chapter 16

Common Core Standards for Mathematical Practice and TPACK: An Integrated Approach to Instruction
(pages 234-249)

Jayme Linton, David Stegall

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Chapter 17

Supporting the Common Core State Standards in Mathematics through Mathematics Journals
(pages 250-262)

Christie Martin, Drew Polly

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Chapter 18

The Impact of Investigations and the Interactive Whiteboard on Students’ Mathematical Practice in Investigations Classrooms
(pages 263-279)

Linda Boland

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Chapter 19

LessonSketch: An Environment for Teachers to Examine Mathematical Practice and Learn about its Standards
(pages 281-294)

Patricio Herbst, Wendy Aaron, Vu Minh Chieu

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Chapter 20

Sandra Madden

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Chapter 21

A Framework for Developing Robust Online Professional Development Materials to Support Teacher Practice under the Common Core
(pages 319-331)

Theodore Kopcha, Keri Duncan Valentine

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Chapter 22

The Use of Digital Resources to Support Elementary School Teachers’ Implementation of the Common Core State Standards
(pages 332-338)

Amy Jensen Lehew, Drew Polly

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Chapter 23

Christine Browning, Alden Edson, Diane Rogers

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Chapter 24

TPACK Pathways that Facilitate CCSS Implementation for Secondary Mathematics Teacher Candidates
(pages 353-369)

Nathan Borchelt, Axelle Faughn, Kathy Jaqua, Kate Best

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Chapter 25

Using the iPad to Develop Preservice Teachers’ Understanding of the Common Core State Standards for Mathematical Practice
(pages 370-386)

Mary Grassetti, Silvy Brookby

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About the Contributors

Index