PhET Interactive Simulations: Transformative Tools for TeachingChemistryEmily B. Moore,*,†,‡ Julia M. Chamberlain,‡ Robert Parson,§ and Katherine K. Perkins‡

†School of Education, University of Colorado Boulder, Boulder, Colorado 80309, United States‡Department of Physics, University of Colorado Boulder, Boulder, Colorado 80309, United States§Department of Chemistry and Biochemistry and JILA, University of Colorado Boulder, Boulder, Colorado 80309, United States

*S Supporting Information

ABSTRACT: Developing fluency across symbolic-, macroscopic-, and particulate-levelrepresentations is central to learning chemistry. Within the chemistry educationcommunity, animations and simulations that support multi-representational fluency areconsidered critical. With advances in the accessibility and sophistication of technology,interactive computer simulations are emerging as uniquely powerful tools to supportchemistry learning. In this article, we present examples and resources to support successfulimplementation of PhET interactive simulations. The PhET Interactive Simulationsproject at the University of Colorado Boulder has developed over 30 interactivesimulations for teaching and learning chemistry. PhET simulations provide dynamic accessto multiple representations, make the invisible visible, scaffold inquiry, and allow for safeand quick access to multiple trials, while being engaging and fun for students and teachers.The simulations are readily accessible online, and are designed to be flexible tools tosupport a wide-range of implementation styles and teaching environments. Here, weintroduce the PhET project, including the project’s goals and design principles. We thenhighlight two simulations for chemistry, Molecule Polarity and Beer’s Law Lab. Finally, we share examples (with resources) of thevariety of ways PhET simulations can be used to teach chemistryin lecture, laboratory, and homework.

KEYWORDS: First-Year Undergraduate/General, High School/Introductory Chemistry, Elementary/Middle School Science,Second-Year Undergraduate, Computer-Based Learning, Inquiry-Based/Discovery Learning, Internet/Web-Based Learning

Animations and simulations have long been recognized asimportant in the teaching and learning of chemistry.1−4

With increased access to technology in the classroom,interactive visualization tools have emerged as uniquelypowerful for transforming chemistry education. Interactivesimulations provide dynamic access to multiple representations,make the invisible visible, scaffold the inquiry process, andallow for multiple trials and rapid feedback cycles, while beingengaging and fun for students and teachers. Interactivesimulations are readily accessible online, which allows forflexible use.In this article, we introduce the PhET Interactive Simulations

project5 at University of Colorado Boulder. The educationaleffectiveness of interactive simulations depends on the qualityof the simulation design as well as its implementation withstudents.6,7 Here we highlight two chemistry simulations,Molecule Polarity and Beer’s Law Lab, and describe a range ofstrategies and resources for effective implementation of PhETsimulations in the classroomfrom use as in-class demos towriting simulation-based guided-inquiry activities. We includeSupporting Information and Web links to support both newand experienced PhET users.

■ PHET PROJECT GOALS AND DESIGN

Since 2002, the PhET project has developed 127 interactivesimulations (sims) for science and mathematics education, withover 30 sims for teaching chemistry and all available for freeonline.5 The project has broad pedagogical and accessibilitygoals that drive design and dissemination choices, shown inFigure 1. Notably, PhET sims aim to simultaneously supportcontent, process, and affective goals. Sims are widely usedacross K−12 and college levels (over 40 million uses worldwidein 2012), and are highly regarded for their quality and impact,as recognized by the NSF/Science Magazine VisualizationChallenge award and the 2011 Tech Award for TechnologyBenefitting Humanity.PhET sims are created by a team of content, education, and

interface design experts, along with experienced teachers andprofessional software developers. Each sim is also informed bystudent interviews. With the use of principles that leveragedesign to support students in achieving the diverse goals of thesims, PhET sims have a distinct look and feel.8 These designprinciplesinformed by the research and design experiencefrom the PhET project, and research from the scienceeducation and educational design communities3,9,10include

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• Interactivity: Sims allow students to interact with keyparameters for conceptual understanding (e.g., adding orremoving solute in solution).

• Dynamic Feedback: Each interaction results in immediatevisual feedback (e.g., solution color changes). Dynamicfeedback supports students to ask and answer their ownquestions as they explore a feature or phenomenon.

• Multiple Representations: Students can explore anddevelop connections across multiple representations(e.g., coordinating pictorial and symbolic representationsof dipoles).

• Pedagogically Useful Actions: Sims allow actions that aredifficult or impossible in the real world, which canprovide insight that is otherwise difficult to achieve (e.g.,allowing students to change the electronegativity ofgeneric atoms and see the effect on bond dipoles).

• An Intuitive Interface: The intuitive interface supportsstudent engagement and exploration by minimizingbarriers to use (e.g., simple starting screen with optionsto build complexity) and emphasizing learning throughinteraction (e.g., obvious initial interactions providerelevant feedback). The intuitive interface allows forinstruction to focus on conceptual understanding, ratherthan on how to use the sim.

• Real World Connections: Where possible, the sims aredesigned to connect science concepts to students’everyday life.

• Challenges and Games: Sims are designed to be engagingand fun, sparking curiosity and a sense of challenge tomotivate student interaction and exploration.

• Implicit Scaf folding: The sims provide students withimplicit, rather than explicit, guidance. This results instudents being guided−without feeling guided.8,11 Im-plicit scaffolding is accomplished through careful choiceof sim scope, color and location of available objects,interactivity, feedback, and sequencing of conceptsthrough tabs.

In combination, these principles have produced a suite oftools that are transforming the educational experience ofstudents, supporting their understanding of chemistry conceptsthrough exploration, experimentation, and discussion while

being intuitive, engaging and fun. For more details on PhET’sgoals, design principles, and development process, seeLancaster et al.12

■ PHET FOR CHEMISTRYPhET chemistry sims address topics ranging from subatomicparticles to chemical dynamics. Through interactive represen-tations, the sims allow students to explore complex chemicalphenomena (e.g., dissolving) and multiple representations,spanning particulate, symbolic, and macroscopic levels. Ratherthan requiring accurate interpretation of a static visual model,students can engage with and discuss dynamic systems thatprovide feedback specifically designed to support studentlearning. A list of available chemistry sims and their alignmentwith the typical sequence in introductory undergraduatechemistry is included in the Supporting Information.Here, we highlight two recently developed sims, illustrating

available features and how these features support studentlearning.Molecule Polarity Sim

The Molecule Polarity sim addresses bond dipole and moleculepolarity. The topics are sequenced through three tabs, shown inFigure 2. The “Two Atoms” tab targets the relationship amongelectronegativity, bond dipole and dipole representations; the“Three Atoms” tab targets the relationship between bonddipoles and molecule dipole, and the “Real Molecules” taballows students to explore trends across example real molecules.In the “Two Atoms” tab, students can interact with a generic

two-atom molecule by rotating the molecule and changing theelectronegativity of each generic atom. As students interact withthe molecule, they can view and draw connections to thecorresponding changes in the bond dipole arrow, partialcharges, and bond character (more ionic to more covalent).Students can observe the effect of changing the electro-negativity of the generic atoms on electrostatic potential andelectron density surfaces. The two-atom molecule is situatedbetween two plates; students can turn on an electric field andsee how the molecule will rotate to align with the field,demonstrating a physical effect of the molecule’s polarity.In the “Three Atoms” tab, students can change the

electronegativities in a generic three-atom molecule and candrag atoms to change the bond angle. This additional featuresupports students in making sense of molecular dipole as thesum of bond dipoles. Students can visualize and investigate howthese interactions affect the bond dipole, partial charges, andthe molecule dipole. In the “Real Molecule” tab, students canchoose from a list of 19 real molecules to view in an embeddedJmol window. By comparing bond dipoles, molecular dipoles,partial charges and atom electronegativity values, students candetermine trends in molecule polarity and geometry.Beer’s Law Lab Sim

The Beer’s Law Lab sim, shown in Figure 3, addresses solutionconcentration and Beer’s Law, which relates the absorbance oflight to the properties of the solution. The “Concentration” tabtargets the concept of concentration and molarity, and theeffects of dilution and evaporation. The “Beer’s Law” tab targetsthe relationships among solution concentration, path length,molar absorptivity, and wavelength of a solution’s lightabsorbance.In the “Concentration” tab, students can engage in real-world

actions that change the solution concentration. A menu of eightsolutions lets students select from seven colorful inorganic

Figure 1. Pedagogical and Accessibility Goals. Image by PhETInteractive Simulations and used with permission.

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compounds, plus “drink mix”an everyday solution. Studentscan add solute either by shaking in solid crystalline particles orby dispensing a concentrated stock solution from a dropper.Students can explore the effects of adding solute and water tothe solution, removing solution through a drain, and removingwater by evaporation. Each action causes a correspondingchange in the solution’s color intensity, and a movable probeallows comparison to quantitative concentration values. Whensolute is added beyond the solubility limit for each compound,saturation occurs and a solid forms at the bottom of the beaker.In the “Beer’s Law” tab, students can dynamically control the

solution concentration and container width (path length) whileobserving the effects on a colored light beam as it passesthrough solution. This tab supports students’ coordination ofthe qualitative visual representation of colored light beamintensity and the corresponding quantitative values forabsorption and percent transmittance. A wavelength controlfor the visible spectrum allows students to investigate andcompare the absorbance of light across the visible spectrum fordifferent colored solutions.

■ STUDENT USE OF SIMS: A CLOSER LOOKObserving students using PhET sims provides valuable insightinto how sims work to implicitly scaffold productive studentinteractions and sense making, insight that can ground andinform the integration of sims into instruction. In the followingexample, two students (S1 and S2) in a class of 80 explored theMolecule Polarity sim prior to receiving a guided-inquiryactivity handout.13 At this point in class, they had been giveninstructions to “Just play with that sim for five or 10 min. Thinkabout how the molecule shape impacts the polarity. Try tounderstand what’s going on as you play.” Students had receivedno prior instruction on the topic of molecule polarity duringthis course. The following transcript describes what happenedover the first 1:19 (min:s) after the sim opened on S1’s laptop.

0:00 Molecule Polarity opens to the “Two Atoms” tab.0:02 S1: OK. So. OK. So let’s see here. [increases Atom B

electronegativity to maximum] I’m just messin’ around.0:21 S2: I think that’s what we’re supposed to do right now.

[increases to maximum then decreases to minimum Atom Aelectronegativity]

0:29 S1: OK. So if electron, er, if atom A is moreelectronegative [increases Atom A electronegativity]what does this mean?

0:38 S2: That’s the0:39 S1: That means it [the bond dipole arrow] gets smaller?

[moves Atom A electronegativity higher, then lower]0:40 S2: Yeah.0:45 S1: OK, and the same thing here. [moves Atom B

electronegativity slider higher, then lower] OK, so the lesselectronegative that is and the more that is, the fartherapart they’re gonna be. And if you bring ‘em [electro-negativity sliders for Atom A and Atom B] closertogether [moves Atom B electronegativity lower and Atom A

Figure 2. Molecule Polarity simulation tabs: “Two Atoms” (upper);“Three Atoms” (middle); “Real Molecules” (lower). Image by PhETInteractive Simulations and used with permission.

Figure 3. Beer’s Law Lab simulation tabs: “Concentration” (upper)and “Beer’s Law” (lower). Image by PhET Interactive Simulations andused with permission.

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electronegativity higher]OK. [moves Atom A electro-negativity slider higher and lower] Oh, it switches[direction of bond dipole arrow]. “Cause that’d bemore [Atom A’s electronegativity] and that’d be less[Atom B’s electronegativity]. [selects “Partial Charges”,then moves Atom A electronegativity to minimum and AtomB electronegativity to maximum]

1:18 S1: Makes sense, all right.1:19 S2: Yeah.

S1 quickly began interacting with the sim, exploring the atomelectronegativity feature and dipole representation. This patternof interaction is typical of students we have observed with simsin interviews and classrooms.12−16 The sims are designed sothat starting interactions are obvious and intuitive, and result inimmediate, productive feedback for sense making. The choiceof interactive features focuses attention on concepts, and theintuitive design ensures students quickly understand how tointeract with the sim. In this example, the generic two-atommolecule and the electronegativity sliders were inviting andintuitive, like colorful, real-world controls. The studentsimmediately began interacting with this sim feature and makingsense of the bond dipole representation.These students then discussed the relationships between the

electronegativity sliders and the periodic table, and explored thebond character feature. Next, they moved to the “Three Atoms”tab, where they grappled with the molecular dipole arrowrepresentation.

3:14 [Selects “Three Atoms” tab.]3:16 S1: [rotates molecule] Oh, wow. [moves Atom C

electronegativity f rom ‘less’ to middle, pauses, then movesto ‘more’]

3:21 S1: OK.3:29 S1: So what is this [molecular dipole arrow] pointing to?

I’m trying to think how this works here. [moves Atom Celectronegativity f rom ‘more’ to ‘less’] More, less[movesAtom B electronegativity f rom the middle to ‘less’ then to‘more’, then back to the middle, moves Atom C electro-negativity f rom ‘more’ to the middle, pauses, then to ‘less’,selects “Partial Charges”, then “Bond Dipole”]

4:05 S1: OK. So those are just like when we were lookin’ atthe two [Two Atoms tab].

4:14 S2: Yeah.4:16 S1: So it’s [bond dipole] always gonna be pointing

toward the negative. And then what does this [moleculardipole] signify?

4:25 S2: The dipole. I guess that’sI don’t know.4:30 S1: I don’t know how to explain that.4:32 S2: Maybe the sum of the two bond dipoles.4:34 S1: Uh huh.

The sequencing of the tabs provided scaffolding to supportthese students’ efforts to make sense of the challenging conceptof molecule polarity; their experience with bond polarity in the“Two Atoms” tab allowed them to progress toward under-standing the molecular dipole.The sim provided a range of opportunities for conceptually

rich, student-centered activities and discussions. Within thisclassroom, the teacher leveraged the implicit scaffolding withinthe sim to allow students to discover and make sense of keyrelationships and representations. After 10 min of open play,the students were primed to engage in and contribute todiscussions around these topicsfacilitated by the teacher anda guided-inquiry activity (see In-Class Student Use section, and

Supporting Information for Molecule Polarity guided-inquiryactivity). The tool has transformed the way studentsapproached this subject, encouraging sense making and conceptinvention instead of relying solely on rote memorization andpattern recognition.

■ TEACHING WITH PHET SIMS

PhET sims are designed to support a wide range of teachingneeds. They can help address a range of learning goalscontent, process, and affective goalsand can be incorporatedinto teacher demos, interactive discussions, in-class activities,laboratories and homework. The design features that supportexploration and engagement by students also serve to supportthe dynamic role of the teacher, providing the uniqueopportunity to explore and illustrate concepts in response tostudent questions in real time. In this section, we describeseveral ways of using the two sims highlighted above based onobservations and faculty accounts of sim use, and includeexample classroom-tested supporting materials in the Support-ing Information. In the following descriptions, we focus on theteacher facilitation aspects of sim use; studies have shownimproved student learning and engagement when using sims inthese types of contexts.15,16

Teacher-Led Sim Use

Sims can be used in a variety of ways in the classroom todiscover, demonstrate, communicate, apply, or test an idea.PhET sims provide unique opportunities for teachers to engagestudents in actively processing and applying the ideas in thesims.In a traditional “Lecture Demo” approach,14,15 the teacher

uses a sim that is projected onto a screen. For example, theMolecule Polarity sim’s “Three Atoms” tab can be used todemonstrate that the molecular dipole is the sum of the bonddipoles. The teacher opens the sim with the “Bond Dipole”arrow representation showing. When the molecular dipole isintroduced, the teacher adds the “Molecular Dipole” arrow. Theteacher can then illustrate various ways to change the bonddipoles, allowing students to visualize the relationship betweenbond and molecular dipoles.To increase active participation and processing by students,

the teacher can use a sim to support an interactive discussion.In a recent classroom use of the Molecule Polarity sim, theteacher asked students “When will a triatomic molecule bepolar?” A student responded, “When all the electronegativityvalues are the same, the atom is non-polar.” To guide thediscussion toward investigating bond dipoles, the teacher asked,“What happens when electronegativity values are different?”After students discussed this scenario with their peers, theteacher was able to easily “do the experiment”, leveraging thefeatures of the sim to create the case of differing electro-negativity values. This approach could further increase studentengagement by asking students to explore the sim on theirpersonal computers, using a guiding question followed by aninteractive class discussion.Sims also couple naturally with concept tests administered

with personal response systems (“clicker questions”).17 Forexample, in a recent lecture the Beer’s Law Lab sim“Concentration” tab was used. The teacher asked students“What will happen to the concentration when water is added todouble the solution volume−will it increase, decrease, or staythe same?” (Figure 4). After providing time for discussion andrecording responses, the teacher increased the solution volume

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by adding water and related the change to the molarityrelationship. The teacher could have elicited student reasoningon why the observed behavior occurred, and then have askedhow the concentration of the solution changes if the amount ofsolute is doubled before saturation is reached, and again aftersaturation is reached. Such discussions help develop students’ability to solve problems by qualitative reasoning and sensemaking around chemical processes, instead of relying solely onmathematical formulas.For more tips on writing clicker questions with sims see

Supporting Information. For more information about usingsims in the classroom, see our video tutorials.18

Sim Use with Written Guided-Inquiry Activity

Sims are specifically designed to support inquiry-based learning,making them excellent for use with guided-inquiry activities inthe lecture class,13 laboratory, and recitations.12 From class-room observations across K−12 and undergraduate classrooms,the PhET group has developed tips for writing activities thatcomplement sims by supporting development of studentprocess skills, content understanding, and affective goals. Werecommend the following:

• Identifying two to three learning objectives, aligned withthe design of the sim, to be addressed by the activity.Activities that attempt to do too much can becomeoverly prescriptive, minimizing opportunities for student-driven inquiry.

• Taking advantage of sim-specific features by structuringquestions around interactive components of the sim andutilizing games or challenges designed into the sim.

• Keeping the activity worksheets relatively sparse toencourage students to focus on sense making with thesim rather than filling in answers.

• Scaffolding students’ understanding through the use ofConcept Tables (Figure 5)structured areas thateffectively cue students toward discovering and makingsense of particular sim features and scenarios.

• Avoiding the use of explicit sim use directions: “moveslider to the left”.

These activity tips aim to encourage the development ofactivities that guide productive exploration and sense makingwith the sim, and keep students actively thinking throughoutthe activity. For examples of guided-inquiry activities designedaround PhET sims, see Supporting Information.

In-Class Student Use

In this style of sim use, the teacher (or teaching assistant) asksstudents to bring their laptops to class (or recitation) to engagein an in-class activity with a sim.13 For tips on successful simuse with student laptops, see Supporting Information. For theexample activity described below (included in the SupportingInformation), students are in groups with shared computers,and use the Molecule Polarity sim while working through aguided-inquiry activity facilitated by the teacher. The activityhas a modular, four-part structure, allowing the flexibility tochoose a stopping point and ask students to finish outside ofclass.Part I of the activity includes a prompt for students to

explore the Molecule Polarity sim for 5 minutes. This openexploration time with the sim allows students to find all simfeatures and to begin asking and answering their ownconceptual questions−as in the student transcript exampleabove.Part II of the activity focuses attention on exploration of the

representations in the “Two Atoms” tab. Students are asked toexplain the ways to change the polarity of the generic two atommolecule, cueing students to find that dif ferences in atomelectronegativity affect bond polarity. Through the use of aConcept Table (shown in Figure 5, Concept Table 1), studentsare cued to connect the various representations in the sim (e.g.,bond dipole arrow and partial charge symbols) with theirunderstanding of molecule polarity. The teacher could facilitatea class discussion around group responses to the ConceptTable, and highlight or expand on student ideas.Part III of the activity focuses attention on exploring the

“Three Atoms” tab, with questions that guide students’ inquiryto include a second factor affecting polaritythe spatial

Figure 4. Example clicker question for use with Beer’s Law Labsimulation. Image by PhET Interactive Simulations and used withpermission.

Figure 5. Example of two Concept Tables from an activity utilizing theMolecule Polarity simulation. Image by PhET Interactive Simulationsand used with permission.

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arrangement of atoms. Students are prompted to find new waysto change the polarity of the generic three-atom molecule, andasked how changing the bond angle affects polarity, high-lighting the significance of the spatial arrangement of atoms inmolecular polarity. Students are then asked to determine therelationship between bond dipoles and molecular dipole. Afterstudents have worked on responses to this question, the teachercould facilitate a discussion around student responses, resultingin a group consensus. Next, students are asked a challengequestion “Can a non-polar molecule contain polar bonds?” andto use examples to illustrate their ideas.Part IV of the activity provides an opportunity for students to

explore molecular polarity in the context of real molecules.With the use of a Concept Table (Figure 5, Concept Table 2),students are cued to predict the bond and molecular polarity ofreal molecules, and then to check their prediction with the sim.

Laboratory Student Use

Sims can be coupled with laboratory activities to deepenconceptual understanding of experiments and to developrepresentational competence. Students can be assigned a pre-lab activity, where they explore a concept prior to conductingrelated physical experiments in a laboratory setting. Sims canalso be used during the laboratory, with physical experimenta-tion coupled with exploration of the sim. In this example, wecoupled the Sugar and Salt Solutions sim with a commonchemistry labmeasuring the conductivity of differentsolutions. The activity’s learning goals include the following:supporting students to differentiate between ionic and covalentcompounds based on composition and physical behavior, andto represent solutions using chemical formulas and particulatelevel drawings.The Sugar and Salt Solutions sim (see Supporting

Information for a full description) allows students to addionic and covalently bonded solutes to water, and to observehow each solute dissolves at the macroscopic and particulatelevels. In this lab activity, included in Supporting Information,students are first prompted to explore the “Macro” tab of thesim, which shows only what one could observe macroscopically.Students are then prompted (through the use of a ConceptTable) to explore whether sugar or salt solutions conductelectricity, to relate this to whether the solute contains ionic orcovalent bonds, and to determine how the conductivity changeswith solution concentration.Next, students are asked to explore the “Micro” tab of the

sim, which shows a particulate level view of the dissolvingprocess. Students are prompted to compare how sugar and saltdissolve in solution, and relate their observations to thepresence of ionic or covalent bonds. On the basis of theirobservations, students are then asked to explain theconductivity results found during exploration of the “Macro”tab.This sim work is then followed by a series of lab experiments,

where students test the conductivity of solutions (e.g., sucrose,sodium chloride, and ethanol). Once students complete the labexperiments, they are asked to explore the “Water” tab of thesim, which shows a two-dimensional view of water solvation ofsodium chloride and sucrose. On the basis of their experiencewith the “Water” tab, students are prompted to draw particulatelevel representations of solutions.

Homework

Homework assignments can have students investigate a simdiscovering trends, ideas, or questionsto prime students prior

to covering the topic in class. Or, sims can be used to deepen,reinforce, or extend conceptual understanding of the topic.Questions involving the use of sims can also be incorporatedinto Learning Management Systems, including multiple-choicequestions that allow for automated grading. An examplehomework assignment using the Beer’s Law Lab sim, includingquestions appropriate for a Learning Management System, isincluded in Supporting Information.

■ UPCOMING RESOURCESThe PhET Interactive Simulations project continues to developnew interactive sims for chemistry while shifting its simdevelopment to HTML5, a Web browser technology that iscompatible with tablets. We are also currently developing a“Teach with PhET” Web site, to accompany the existing PhETWeb site. This new Web site will contain detailed professionaldevelopment materials and resources for teaching with PhETsims, including video tutorials, guidelines and tips for sim useacross a range of implementation styles, examples of authenticclassroom use, and expanded sim specific teacher guides withvideo introductions to individual sims.

■ CONCLUSIONA principal goal of the PhET Interactive Simulations project isto transform the educational environments of both teachers andstudents. PhET sims are research-based tools for teachingchemistry that support the development of process skills,content learning, and affective goals, in a way that is free, easilyaccessible, and flexible. In this article, we introduced the PhETproject, highlighted two sims for chemistry, and described arange of approaches for integrating PhET sims into classroomsand courses. We hope the examples, guidance, and linksprovided here will encourage chemistry teachers new to sims toconsider ways of implementing PhET sims in their courses, andinspire experienced sim users to continue finding and sharingeffective and creative ways of using the sims. Additionalsupporting materials for sims, including activities submitted byusers, are available at our Web site.5

■ ASSOCIATED CONTENT*S Supporting Information

Table listing a typical undergraduate general chemistry coursesequence aligned with existing PhET sims; support fordeveloping clicker questions; tips for encouraging students tobring laptops to class; example activities (in-class, lab, recitationand homework); description of the Sugar and Salt Solutionssim. This material is available via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author

*E-mail: Emily.Moore@colorado.edu.

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank the PhET team for their contributions anddedication. We also thank participating teachers and studentsfor their contributions to these efforts. This work wassupported by the National Science Foundation (DUE-

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1226321). Supporting Information materials is by PhETInteraction Simulations and used with permission.

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