PhET Interactive Simulations: New Tools to Achieve Common Core Mathematics Standards

PhET Interactive Simulations: New Tools to Achieve Common Core Mathematics Standards

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)
DOI: 10.4018/978-1-4666-4086-3.ch010
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This chapter focuses on the design and use of interactive simulations as a powerful tool for learning mathematics. Since 2002, the PhET Interactive Simulations project at the University of Colorado Boulder ( has been developing and studying the use of interactive simulations in teaching and learning STEM. While the project’s initial work focused on science learning, the project now includes a significant effort in mathematics learning. In this chapter, the authors describe the PhET project, including theoretical perspective, design goals, and research-based simulation design principles. They demonstrate how these design principles are applied to simulations, describe how they support achievement of the Common Core State Standards for Mathematics (CCSSM), and provide supporting evidence from individual student interviews. Finally, the authors discuss various approaches to using these simulations in class and provide guidance on leveraging their capabilities to support knowledge construction in mathematics in a uniquely engaging and effective way.
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The 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
James W. Wilson
Drew Polly
Chapter 1
Christian Hirsch, Brin Keller, Nicole Fonger, Alden Edson
Core Math Tools is an open-source suite of Java-based software tools that include general purpose tools—a spreadsheet, a computer algebra system... Sample PDF
Core Math Tools: Supporting Equitable Implementation of the Common Core State Standards for Mathematics
Chapter 2
Chandra Hawley Orrill, Drew Polly
Technology has the potential to support the creation and use of mathematical representations for exploring, reasoning about, and modeling... Sample PDF
Supporting Mathematical Communication through Technology
Chapter 3
Michelle Rutherford
Teachers and educators transitioning to the Common Core State Standards face a significant challenge of creating new lessons and resources, as well... Sample PDF
Implementing Common Core State Standards using Digital Curriculum
Chapter 4
P. Mark Taylor
In the implementation of the Common Core State Standards, teacher educators have an unprecedented opportunity. Both preservice and inservice... Sample PDF
A Framework for TPACK Action Research
Chapter 5
Azita Manouchehriazi, Jennifer Czocher, Ravi Somayajulu, Yating Liu, Pingping Zhang, Jenna Tague
In this longitudinal research project, the authors traced the impact of a mathematics enrichment program on a group of approximately 80 middle and... Sample PDF
Fostering Mathematical Competence through Technology-Enhanced Interactive Environments
Chapter 6
Milan Sherman
This chapter discusses how the use of Dynamic Geometry Software (DGS) can be used to support students’ engagement with the Standards for... Sample PDF
Using Technology to Engage Students with the Standards for Mathematical Practice: The Case of DGS
Chapter 7
Lisa Ames, Heejung An, Sandra Alon
The Common Core State Mathematics Standards (CCSSM) recommend that technology should be integrated into teaching and learning Mathematics. This... Sample PDF
The Incorporation of Geometer’s Sketchpad in a High School Geometry Curriculum
Chapter 8
D. Craig Schroeder, Carl W. Lee
The Common Core State Standards for Mathematics include mathematical practices for modeling and also references to the appropriate use of... Sample PDF
Integrating Digital Technologies for Spatial Reasoning: Using Google SketchUp to Model the Real World
Chapter 9
Shelby P. Morge, Mahnaz Moallem, Chris Gordon, Gene Tagliarini, Sridhar Narayan
The Common Core State Standards (CCSS) call for a change in the way mathematics is taught. The mathematical practices outlined by the CCSS call for... Sample PDF
Design and Implementation of Computational Modeling for Learning Mathematical Concepts
Chapter 10
Karina K. R. Hensberry, Ariel J. Paul, Emily B. Moore, Noah S. Podolefsky, Katherine K. Perkins
This chapter focuses on the design and use of interactive simulations as a powerful tool for learning mathematics. Since 2002, the PhET Interactive... Sample PDF
PhET Interactive Simulations: New Tools to Achieve Common Core Mathematics Standards
Chapter 11
Woong Lim, Dong-Gook Kim
This chapter reviews the roles of technology in statistics education and introduces technologies available for classroom use. A few concrete... Sample PDF
Do Technologies Support the Implementation of the Common Core State Standards in Mathematics of High School Probability and Statistics?
Chapter 12
Karen Greenhaus
The Common Core State Standards for Mathematics (CCSSM) include overarching Standards for Mathematical Practice that cite dynamic geometry® software... Sample PDF
Sketchpad®, TinkerPlots®, and Fathom®: Using Dynamic Geometry® Software Tools Strategically
Chapter 13
Robin Magruder, Margaret Mohr-Schroeder
Virtual manipulatives provide benefits to students as they encounter the Common Core State Standards for Mathematics content and practice standards.... Sample PDF
Solving Equations is All about Balance: Using Virtual Manipulatives in the Middle School Classroom
Chapter 14
Jessica Taylor Ivy, Dana Pomykal Franz
This chapter examines the practices and beliefs of two secondary mathematics teachers with similar demographic backgrounds. The influence of their... Sample PDF
Two Classroom Portraits Demonstrating the Interplay of Secondary Mathematics Teachers’ TPACK on their Integration of the Mathematical Practices
Chapter 15
Ayhan Kursat Erbas, Sarah Ledford, Chandra Hawley Orrill, Drew Polly
As teachers prepare to teach the Common Core State Standards for Mathematics (CCSSM), students’ exploration of patterns and relationships between... Sample PDF
Supporting Pattern Exploration and Algebraic Reasoning through the Use of Spreadsheets
Chapter 16
Jayme Linton, David Stegall
This chapter seeks to answer the guiding question: How does the TPACK (Technological Pedagogical Content Knowledge) framework influence how... Sample PDF
Common Core Standards for Mathematical Practice and TPACK: An Integrated Approach to Instruction
Chapter 17
Christie Martin, Drew Polly
The Common Core State Standards in Mathematics and English/Language Arts necessitate that teachers provide opportunities for their students to write... Sample PDF
Supporting the Common Core State Standards in Mathematics through Mathematics Journals
Chapter 18
Linda Boland
This chapter relates the classroom experiences of 44 teachers across the United States, implementing Investigations in Number, Data, and Space, an... Sample PDF
The Impact of Investigations and the Interactive Whiteboard on Students’ Mathematical Practice in Investigations Classrooms
Chapter 19
Patricio Herbst, Wendy Aaron, Vu Minh Chieu
This chapter describes how the authors have utilized digital graphics and Web 2.0 technologies to design an information technology environment... Sample PDF
LessonSketch: An Environment for Teachers to Examine Mathematical Practice and Learn about its Standards
Chapter 20
Sandra Madden
This chapter addresses the need to prepare and support teachers of mathematics in order that they will be able to co-construct with their students... Sample PDF
Supporting Teachers’ Instrumental Genesis with Dynamic Mathematical Software
Chapter 21
Theodore Kopcha, Keri Duncan Valentine
The purpose of this chapter is to present a framework for developing online professional development materials to support teachers as they adopt the... Sample PDF
A Framework for Developing Robust Online Professional Development Materials to Support Teacher Practice under the Common Core
Chapter 22
Amy Jensen Lehew, Drew Polly
This chapter describes the process of developing Web-based resources to support elementary school teachers’ implementation of the Common Core State... Sample PDF
The Use of Digital Resources to Support Elementary School Teachers’ Implementation of the Common Core State Standards
Chapter 23
Christine Browning, Alden Edson, Diane Rogers
This chapter focuses on how assessment for learning can be used to promote the development of student understanding of mathematics and mathematical... Sample PDF
Digitizing Students’ Voices: Assessing Mathematical Justification
Chapter 24
Nathan Borchelt, Axelle Faughn, Kathy Jaqua, Kate Best
Implementation of the Common Core State Standards in Mathematics has provided teacher educators a great opportunity to reexamine whether teacher... Sample PDF
TPACK Pathways that Facilitate CCSS Implementation for Secondary Mathematics Teacher Candidates
Chapter 25
Mary Grassetti, Silvy Brookby
The Standards for Mathematical Practice as delineated in the Common Core State Standards for Mathematics describe the processes, proficiencies, and... Sample PDF
Using the iPad to Develop Preservice Teachers’ Understanding of the Common Core State Standards for Mathematical Practice
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