Education

Brain Points: A Growth Mindset Incentive Structure Boosts Persistence in an Educational Game

Eleanor O’Rourke1, Kyla Haimovitz2, Christy Ballwebber1, Carol S. Dweck2, and Zoran Popović1 1Center for Game Science, Department of Computer Science & Engineering, University of Washington

2Department of Psychology, Stanford University {eorourke, christy, zoran}@cs.washington.edu, {kylah, dweck}@stanford.edu

ABSTRACT There is great interest in leveraging video games to improve student engagement and motivation. However, educational games are not uniformly effective, and little is known about how in-game rewards affect children’s learning-related be- havior. In this work, we argue that educational games can be improved by fundamentally changing their incentive struc- tures to promote the growth mindset, or the belief that in- telligence is malleable. We present “brain points,” a system that encourages the development of growth mindset behav- iors by directly incentivizing effort, use of strategy, and in- cremental progress. Through a study of 15,000 children, we show that the “brain points” system encourages more low- performing students to persist in the educational game Re- fraction when compared to a control, and increases overall time played, strategy use, and perseverance after challenge. We believe that this growth mindset incentive structure has great potential in many educational environments.

Author Keywords Educational games; growth mindset; incentive structures.

ACM Classification Keywords H.5.0 Information Interfaces and Presentation: General

INTRODUCTION Video games are famous for their ability to engage play- ers and motivate them to perform complex, time-consuming tasks. Most children today are exposed to games on a daily basis; 92% of children ages 2 to 17 play video games, for an average of 20 to 33 minutes per day [16]. As a result, there is a growing interest in leveraging games to address the prob- lem of student motivation in educational environments [11, 25, 23]. Game incentive structures, or the systems of rewards that are given to successful players, have elicited particular attention for their potential to motivate students [18]. How- ever, games have produced mixed learning outcomes in the classroom [14, 21, 23], and the effects of in-game praise and rewards on motivation and learning are not well understood.

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A growing body of research in psychology suggests that feed- back such as praise can have varying, and sometimes nega- tive, effects [24, 13]. Praising a student’s inherent ability has been shown to promote the fixed mindset, or the belief that in- telligence is unchangeable, while praising a student’s strate- gies or effort promotes the growth mindset, or the belief that intelligence is malleable [24, 13]. Studies have shown that children with a fixed mindset view mistakes, challenge, and effort as negative indicators of their intelligence, while chil- dren with growth mindset view effort as positive and chal- lenges as opportunities to learn [9, 15]. More importantly, holding a fixed mindset predicts static or decreasing academic performance over time, while holding a growth mindset pre- dicts academic improvement [3, 12].

Many laboratory and classroom studies have shown that chil- dren’s mindsets can be changed through careful intervention [3, 24, 17]. Directly teaching students that intelligence is malleable was shown to improve classroom motivation and grades compared to a control group [3]. Even minimal inter- ventions, such as praising children for their strategy or effort (e.g., “you must have worked really hard!”) instead of their ability (e.g., “you must be smart at this!”) as they solve prob- lems produces a growth mindset, as well as higher motiva- tion and task persistence [24, 17]. This research suggests that the praise and rewards given to students in educational games could impact their behavior, and even have negative conse- quences if rewards inadvertently support the fixed mindset.

In this work, we show that making a fundamental change to a game’s incentive structure can positively impact chil- dren’s behavior. We present “brain points,” a system that rewards students for their effort, use of strategy, and incre- mental progress. Unlike previous mindset interventions, this incentive structure provides children with real-time feedback as they work to develop growth mindset behaviors. Through a study of 15,000 children, we show that persistence and use of strategy is encouraged in the educational game Refraction through the introduction of this unorthodox incentive struc- ture. We believe this method of promoting the growth mind- set has great potential in many educational environments.

BACKGROUND Psychologists have been studying motivation and academic achievement for decades, and many of their discoveries have important implications for the designers of educational tech- nologies. Messages and rewards that support the growth mindset could be used to significantly improve the impact

of such systems. In this section, we provide background on mindset research and discuss previous efforts to integrate growth mindset interventions into classrooms and educational tools. We also describe existing work on educational games, and suggest ways that the growth mindset could be used to improve their effectiveness.

Theories of Intelligence Psychologist have shown that beliefs about the malleability of human attributes such as intelligence can have strong effects on motivation, reaction to challenge or failure, and academic achievement [3, 12, 15]. Individuals who hold a fixed mindset believe that they have a certain amount of intelligence, and that this is an unchangeable attribute. Studies have shown that people with a fixed mindset view challenging situations as “tests” of how much intelligence they have, and view effort and mistakes as indications of low ability [3, 15, 24]. On the other hand, individuals who hold a growth mindset believe that intelligence is malleable, and that people can increase their intelligence through hard work. They have been shown to value learning over performance, and view effort as a nec- essary part of the learning process [3, 15, 24]. These beliefs affect not only behavior but also academic achievement. In a longitudinal study of 373 seventh graders, Blackwell et al. showed that holding a growth mindset predicted improving grades over the two years of middle school, while holding a fixed mindset predicted static or decreasing grades [3].

A growing body of research shows that students’ mindsets, and subsequently their behaviors and academic performance, can be changed through intervention [24, 3, 1, 12, 17]. One type of intervention involves changing the type of praise given to children when they are successful. In a now-famous 1998 study, Muller and Dweck showed that praise can have negative consequences when it supports the fixed mindset [24]. They gave fifth grade students a set of achievable prob- lems and praised them for either their ability (“you must be smart at these problems”) or their effort (“you must have worked hard at these problems”). Then they gave students very challenging problems on which they did poorly. Finally, they gave students another set of the original achievable prob- lems. Students who received praise for their ability attributed their failure to lack of ability, and performed worse on the subsequent problem set, but students who received praise for their effort viewed the difficulty as a cue to try harder, and performed better on the subsequent problem set [24]. More recently, Gunderson et al. have confirmed the role of praise in mindsets, showing that the type of praise parents give to their young children at home predicts the child’s mindset and desire for challenge five years later [13].

Another type of intervention involves teaching the growth mindset directly. Blackwell et al. taught a group of seventh grade students that intelligence is malleable during an eight- session workshop through readings and discussions about the neural connections that are formed in the brain when it works hard [3]. Before the intervention, students’ math grades had been steadily decreasing (and this decline persisted for chil- dren in the control group), but after the intervention students grades improved significantly [3]. Aronson et al. also report

the positive impact of a growth mindset intervention on the academic achievement of both African American and white college students [1]. The GPAs of both the African American and white students in the experimental condition were higher at the end of the academic quarter than those in the control condition [1].

The effects of these interventions on student motivation and academic achievement are impressive, and it would clearly be beneficial to integrate similar programs into educational tech- nologies. Recently, efforts have been made to develop online materials that teach the growth mindset. Brainology, a for- purchase online program based on the Blackwell interven- tion, teaches students the scientific basis of the growth mind- set through readings and interactive exercises [4]. In ongoing work, Paunesku and colleagues are studying the impact of integrating a praise-based intervention into the online educa- tional website Khan Academy [19] with initial success [29]. However, we are not aware of any work that integrates the growth mindset into the incentive structures of educational games.

Games as an Educational Platform Video games are increasingly recognized as a compelling platform for instruction that could significantly improve stu- dent motivation in the classroom [11, 25, 23]. While em- pirical evidence supporting learning outcomes of educational games is mixed [14, 21, 23], there have been clear suc- cesses that highlight the potential of games as instructional tools. In a comparative review of STEM game studies, Mayo found that some games produce a 7 to 40% positive increase in learning outcomes [23]. Games have been shown to in- crease time-on-task, an important indicator for academic suc- cess [21, 20], and also increase student motivation [27]. Re- searchers have noted that successful educational games are those designed around effective pedagogical practices, per- haps explaining some of the mixed learning outcomes [23, 25]. These results indicate the importance of grounding edu- cational games in valid pedagogical theory.

Many researchers have explored how to most effectively in- tegrate learning theories into games, and leverage game fea- tures to maximize student motivation, persistence, and learn- ing [21, 7]. For example, Chase studied how the framing of tasks in a genetics game affects student persistence and learn- ing. She found that students who are told their performance is dependent on both chance and skill persist more after fail- ure than those who are told their performance is dependent on skill alone [7]. However, the effects of game features on student motivation are still not well understood.

To our knowledge, no existing research has explored how to improve in-game motivation and persistence through growth mindset incentives and feedback. We believe that educational games provide a set of properties that make them particularly conducive to introducing and incentivizing growth mindset concepts. Game narratives provide a forum for directly teach- ing about brain growth, weaving messages that support the growth mindset throughout the game world. Constant inter- active feedback provides a medium for showing students that

their effort translates into progress [10, 23]. But most impor- tantly, game incentive structures provide a way to support and reward behaviors consistent with the growth mindset, such as persistence and use of strategy.

Experimental Hypotheses The goal of this research was to study the impact of incen- tivizing productive effort and teaching the growth mindset in an educational game. To explore this question, we developed two versions of Refraction, a game designed to teach frac- tion concepts to elementary school students. The experimen- tal version teaches and rewards growth mindset behavior by leveraging the game’s narrative and incentive structure, while the control version provides a neutral view of intelligence. We expected children who played the experimental version to exhibit behaviors consistent with the growth mindset.

Hypothesis 1: Players in the experimental condition will be more persistent and more strategic than players in the control.

While we expected all players to be affected by the growth mindset intervention, we thought that players who struggle with Refraction would be most strongly influenced by our in- centive structure that rewards effort. We expected them to be more strongly motivated to persist in the game.

Hypothesis 2: Struggling players will be most strongly moti- vated by the experimental intervention.

In addition to observing general behavior, we wanted to ex- plicitly study how children in the two conditions reacted to challenge and failure. Following a similar model to that used in the 1998 Muller and Dweck study of the effects of praise on children [24], we designed an unusually challenging level to test children’s persistence and performance. We expected children who played the experimental version of Refraction to react well to challenge, struggle, and failure.

Hypothesis 3: Players in the experimental condition will re- act better to challenge than players in the control.

To evaluate these hypotheses, we released both versions of Refraction to BrainPOP, a popular educational website for el- ementary school students that provides a game portal [5]. We analyzed data from over 15,000 players to determine the ef- fects of incentivizing effort and teaching the growth mindset.

EXPERIMENT DESIGN To explore the effects of teaching and supporting the growth mindset in educational games, we created two versions of Re- fraction, a game designed by our research group. One version teaches the growth mindset directly through the game’s narra- tive, feedback, and incentive structures, while the other pro- vides a neutral mindset and the incentive structure commonly found in educational games. In this section, we describe the two versions of Refraction in detail and discuss the rationale behind our designs.

Refraction This educational puzzle game was designed by game re- searchers and learning science experts at the Center for Game

Figure 1. A level of Refraction. The pieces on the right are used to split lasers into fractional amounts and redirect them to satisfy the target spaceships. All ships must be satisfied at the same time to win.

Science to teach fraction concepts to elementary school stu- dents. The game was designed to support a conceptual under- standing of fractions rooted in the concept of splitting [22]. To play, a child must interact with a grid that contains laser sources, target spaceships, and asteroids, as shown in Fig- ure 1. The goal of the game is to satisfy target spaceships by splitting the laser into the correct fractional amounts and avoiding asteroids. The player uses pieces that either change the laser direction or split the laser into two or three equal parts to achieve this goal. To win, the player must correctly satisfy all the target spaceships at the same time. Refraction has been successful at attracting elementary school students, and has been played over 250,000 times on the educational website BrainPOP since its release in April 2012.

Game Narrative Both the experimental and control versions of Refraction are based on a central narrative. At the beginning of the game, players watch a 25 second introductory animation featuring Zuzu and Copper, characters who describe the game and its incentive structures. In the experimental version, we lever- age this animation to teach players about the growth mindset directly, using language based on that used in the Brainology curriculum [4] and the Blackwell intervention [3]. In the con- trol version, we present a neutral message about the impor- tance of fractions. The text and art used in the animations are nearly identical, differing only in the messages they present to players. Screenshots are shown in Figure 2 and the full an- imation scripts are included in Table 1. We do not use audio in the animations because we cannot guarantee that players will have access to speakers or headphones. To accommodate different reading speeds, we added “Next” buttons that allow players to manually advance to the next part of the animation when they have finished reading.

Incentive Structures Both versions of Refraction have point-based incentive struc- tures designed to reward different types of behavior. For the experimental version, we designed a system of “brain points”

(a) (b) (c)

Figure 2. Figure (a) shows a screenshot of the introductory animation that teaches the growth mindset in the experimental version of Refraction. Figure (b) shows a corresponding screenshot in the control, which presents a neutral mindset about the importance of fractions. The animations use identical art and text wherever possible. Figure (c) shows the brain points interface in the experimental version. In this version players earn points for effort, use of strategy, and incremental progress as they work to solve levels, while in the control version players earn points each time they complete a level.

Experimental Z: Hey Copper, guess what! Z: Did you know that when you work hard and struggle, your brain gets stronger and SMARTER? C: Whoa cool! Z: In this game, when you work out your brain and try new ideas, you’ll get BRAIN POINTS! C: I want to get lots of brain points! Let’s play, Zuzu! Control Z: Hey Copper, guess what! Z: Did you know that you use fractions in all kinds of MATH? C: Whoa cool! Z: In this game, when you make the fractions on the spaceships you’ll get FRACTION POINTS! C: I want to get lots of fraction points! Let’s play, Zuzu!

Table 1. The scripts for the introductory animations. The experimen- tal animation teaches the growth mindset, while the control animation presents a neutral message about the importance of fractions. Z indi- cates Zuzu’s line, and C indicates Copper’s line.

that rewards children for their effort, use of strategy, and in- cremental progress. These types of behaviors support “learn- ing” goals rather than “performance” goals, and rewarding similar behaviors with praise has been shown to promote the growth mindset [24, 13]. However, no existing growth mind- set interventions have used point-based reward systems, so this is an entirely new method of teaching the growth mindset that is particularly well suited to the game context.

Children earn brain points while they are working to solve levels. We use a combination of four metrics that capture de- sirable strategic behaviors to determine when players should receive points. The new hypothesis metric captures each new idea the child tries. It triggers when the child makes two suc- cessive new moves with distinct pieces. The board cleared metric emphasizes stepping back to consider the puzzle from a fresh perspective. It triggers when there are at least two pieces on the laser, and the child returns all the pieces to the starting bin. The math metric captures incremental mathe- matical progress. It triggers when the child makes a target fraction for the first time. Finally, the moves metric captures effort. It triggers when the child makes ten distinct moves.

To earn brain points, the child must trigger two of these met- rics. For example, a child might try a new hypothesis and then

clear the board, earning five points. We require two metrics to be triggered because this makes the system more difficult to game, since the child cannot repeat his last sequence of moves to earn another point. Gaming the system is a problem in many educational domains [2], so we wanted to ensure that our point system rewarded desirable behaviors without being overly transparent. All metric data, such as the number of moves made so far, are cleared when the child earns a point so that subsequent points are earned from scratch.

Brain points are given to players in increments of five to make them more exciting. Each time the child triggers two metrics, she earns five points. When this happens, a small animated brain icon with a short message appears, as shown in Fig- ure 2(c). The icon moves to the upper righthand corner of the screen, adding five to the total number of points shown in the brain points bar. The short message reflects the last metric the child triggered. The messages associated with the four metrics are “New Idea” for the new hypothesis metric, “Fresh Start” for the board cleared metric, “Math Effort” for the math metric, and “Working Hard” for the moves metric.

For the control version of Refraction, we designed a system of “fraction points” that reward children for completing levels. We chose to incentivize advancement through the level pro- gression because this is a commonly used metric of success in video games, as Schell notes in his popular game design book [28]. Players earn five fraction points every time they win a level, displayed on the summary screen described in the next section. The total number of fraction points earned so far are shown in the upper righthand corner of the screen.

Summary Screens Each time a child completes a level of Refraction, a summary screen is displayed. This screen is designed to reinforce the game narrative and provide an opportunity for children to re- flect on their success or progress. Identical art is used in the experimental and control versions, but different messages are given to support either the growth mindset or a neutral mind- set. The summary screen has three components: a progress indicator, a points message, and a praise message. Screen- shots of summary screens are shown in Figure 3.

(a) (b) (c)

Figure 3. Screenshots of the summary screens. Figure (a) shows the summary screen that is displayed when the child earns brain points in the experimental condition, and Figure (b) shows the screen that is displayed when the player does not earn brain points. Figure (c) shows the control condition summary screen that is displayed every time the player wins a level. In all cases, the mountain represents progress through the current Refraction planet. Copper physically climbs the mountain in the experimental summary screens to symbolize the player’s effort. In the control summary screen, Copper waits in his spaceship at the top of the mountain. The player advances to a new planet each time she earns 50 points.

Metric Growth Mindset Praise Messages New Hypothesis You worked hard and tried new ideas! Board Cleared You worked hard and got a fresh start!

Math You worked hard and used your math brain! Moves You worked out your brain and kept trying!

Table 2. The four growth mindset praise messages displayed at the bot- tom of the summary screen in the experimental version of Refraction. The praise message shown on a given screen is selected based on the brain points message the child saw most frequently during the level.

The Refraction world has seven different planets, each with unique level art. In both conditions, children advance to a new planet each time they collect 50 points, an exciting reward that highlights their progress through the game. Since this advancement is based on points, children in the experimental condition move forward based on their effort and strategy use, while children in the control condition move forward based on their performance. Each summary screen shows a moun- tain with ten dots that indicate the player’s progress through the planet. The player moves up one dot for every five points earned, and completed dots are shown in yellow. When the player reaches the top of the mountain, a reward animation shows the orange character Copper flying to the next planet.

In the experimental version, an animation shows Copper climbing the mountain every time the child earns brain points, as in Figure 3(a). This physical climbing metaphor was de- signed to symbolize the hard work required to earn brain points and support the growth mindset. In the control ver- sion, Copper waits at the top of the mountain in his spaceship while newly acquired dots are highlighted in yellow, as in Figure 3(c). This presents a more neutral message, showing progress without symbolizing effort.

At the top of the summary screen, a message tells the player how many points were earned. Since players in the exper- imental condition earn points based on their behavior, this number changes dynamically. If a player does not earn any brain points on a given level, a message apologizing for not giving the player an opportunity to struggle is displayed, as shown in Figure 3(b). This message is based on Dweck’s sug-

gested growth mindset response to situations that do not chal- lenge children or provide them with an opportunity to learn [9]. Players in the control condition always earn exactly five fraction points for each level completed.

At the bottom of the summary screen, a message praising the child’s work in this level is shown. In the experimental condi- tion, one of four messages is chosen, depending on which of the four brain point messages the player saw most frequently during the level. The possible messages, which are based on messages used in Muller and Dweck’s praise-based interven- tion [24], are shown in Table 2. In the control condition, a message summarizing the fractions the child made in this level is shown. If the child won a level with spaceships that required 1/6 and 1/9 laser power respectively, the message would read “You made 1/6 and 1/9 on that level!”

Adaptive Level Progression In order to effectively incentivize effort in the experimental version of Refraction, it was important to design a level pro- gression that would provide every player with an opportunity to struggle, irrespective of their incoming skill level. To ad- dress this requirement, we created an adaptive level progres- sion that was used in both versions of the game. Our design is based on the mastery learning model used in many knowl- edge tracing systems, in which students must display mas- tery of a concept before advancing to the subsequent concept [8]. The adaptive progression covers eleven mathematical concepts typically included in Refraction, which are listed in Table 3. We designed ten levels for each concept: one tutorial level that introduces the concept without providing additional pieces, and nine puzzles in which the player must correctly choose between splitter pieces to create the correctly valued fractions.

All children play the eleven concepts in the order listed in Ta- ble 3, but they move through the concepts at different speeds depending on their skill level. Every child plays the tutorial level for a given concept, and is then given levels from that concept until she either wins two levels under a performance threshold, or completes all nine levels for the concept. To

win a level below the performance threshold, the player must complete the level in less than 1.5 times the minimum num- ber of moves required to beat the level without making any mathematical mistakes. Mistakes are defined as moves that split the laser to make fractional values that are not needed to solve the level. For example, if a child is working on a level with a 1/9 target spaceship, she should never split the laser to make 1/2 or 1/4.

Every child will play between three and ten levels for each concept. The levels are given to all players in the same order, so every child plays the same first three levels for a concept, and some will continue on to play more levels. This means that many more children play the first three levels than play the ninth and tenth level.

Skipping Levels For the growth mindset version of Refraction, we wanted players to think about their progress in terms of effort and strategy, symbolized by brain points, rather than in terms of the number of levels they have completed. As a result, we de- signed the summary screens and adaptive level progression in a way that minimizes the visibility of speed by making it dif- ficult for children to compare the number of levels they have completed. One downside of this design is that it provides no way for players to back out of levels when they get stuck.

To address this issue and deter frustrated players from quit- ting the game, we added a “New Level” button that appears in each level after three minutes of play. Children are required to work on each level for at least three minutes, but then they are given an opportunity to move forward when they are stuck. To ensure that children notice the button, a tutorial message is displayed the first time it appears.

When a child clicks the “New Level” button, a summary screen is displayed. In the experimental version, if the child earns brain points before clicking the button, the standard summary screen shown in Figure 3(a) is displayed. If the child does not earn any brain points, the message “Work harder and use your brain on the next level to earn points!” is displayed in a screen similar to Figure 3(b). In the control version, children only earn points when they win levels, so the same summary screen with the message “Try again on a new level! To move up the mountain, save the spaceships!” is always shown. In all cases, the summary screen has a “Back” button that returns to the level and a “Next” button that ad- vances to the next level in the current concept.

Challenge Levels In addition to observing children’s behavior as they interact with the standard game levels, we wanted to measure how they react to a particularly challenging level. In their 1998 study of praise, Muller and Dweck saw that failing to solve a very difficult problem affected children differently based on whether they received fixed or growth mindset praise [24]. We designed a similar test for Refraction players by giving them a “challenge level” 30 minutes after they started the game. This level had two 1/2 spaceships, and presented a

Order Concept Order Concept 1 Halves 6 Halves and Fourths 2 Thirds 7 Thirds and Ninths 3 Fourths 8 Halves and Sixths 4 Ninths 9 Thirds and Sixths 5 Sixths 10 Fourths and Sixths

11 Sixths and Ninths

Table 3. The fraction concepts covered in Refracion’s adaptive level pro- gression. All children play the concepts in this order, but they advance through concepts at different speeds based on their performance.

Experimental Timing Message Tutorial You won’t earn points on this level, but it will let you challenge your

brain and make it grow stronger! Skip You didn’t master that challenge yet, but you can keep growing your

brain by earning points on the next level! Win You beat the challenge! You really worked out your brain on that level.

Control Timing Message Tutorial You won’t earn points on this level, but it will let you show off your

fraction skills! Skip You didn’t beat that challenge, but you can use your fraction skills to

earn points on the next level instead! Win You beat the challenge! You really used your fraction skills on that

level.

Table 4. The three challenge level messages for each condition. The first message is shown during the challenge level tutorial, the second is shown when the level is skipped, and the third is shown when the level is won.

tricky and unintuitive spatial problem. We used simple frac- tions because we could not guarantee that all players would have reached more complex concepts.

The challenge was framed as a special level separate from the standard game. We used an exciting animation to intro- duce the level, and designed a new background to accompany it. We wanted to measure whether any effects caused by the growth mindset intervention would transfer to levels where effort is not explicitly rewarded, so we did not give children points during the challenge level. We added a bright orange “New Level” button to the sidebar so that players could skip at any point. We also added a tutorial message highlighting the presence of the “New Level” button to make sure players knew it was available. The challenge level was identical in the two conditions except for the text displayed to children. There are three challenge-related messages: one shown at the beginning of the level, one shown when the child wins the level, and one shown when the child skips the level. These messages can be seen in Table 4.

METHOD To gain an understanding of the effects of incentivizing pro- ductive effort and teaching the growth mindset in educational games, we studied how children play the experimental and control versions of Refraction on the popular educational website BrainPOP [5]. BrainPOP is best known for its cur- riculum resources, but it also provides an educational game portal designed for use in the classroom. The BrainPOP Ed- ucators community has over 210,000 members [6], and the website is used as a resource in around 20% of elementary schools in the United States (Traci Kampel, personal com- munication).

One benefit of using the BrainPOP game portal to study the impact of our growth mindset intervention is that it provides us with access to a large, diverse population of students, and allows us to quickly learn whether our intervention has promise in the classroom. However, one downside of this resource is that we know very little about the children who visit BrainPOP or the contexts in which they play. We can- not collect any demographic information, and while we know that the website is primarily used in schools, we cannot tell whether children are playing in the classroom, in a computer lab, or at an after-school program. We mitigate the effects of these uncontrolled variables by evenly distributing them be- tween conditions through the use of randomization and large sample sizes. We are also unable to directly measuring learn- ing through formal pre and post tests in this environment. In- stead, we analyze how our intervention impacts observable in-game behaviors such as persistence, use of strategy, and reaction to challenge. These are key components of learning that capture how students react to our growth mindset system.

Our study has a single between-subjects factor intervention with two levels: experiment or control. To collect our data, we set up Refraction to randomly assign new players to ei- ther the experimental or control version of the game, and logged all interactions players made with the game or its in- terface. We only included new players who were not famil- iar with Refraction in our analysis, and only used data from a player’s first session to control for issues with shared comput- ers in schools. To track players, we stored their progress in the Flash cache, which allowed us to selectively include new players and exclude return sessions. One drawback of this method is that a player who clears the cache or changes com- puters will be treated as a new player by our system. While we cannot assess the seriousness of this risk, its effects will be evenly distributed across conditions. Furthermore, it is un- likely that children will clear the cache because this option is inconvenient to access and it deletes all saved game progress.

Another challenge of studying student behavior online is that average play times are typically small. Previous research con- ducted on BrainPOP shows that children play Refraction for about three minutes on average [26]. We expected our brain points system to influence student behavior even during this short period of play because previous studies have shown that very minimal interventions, such as praising children for their effort or strategies, can improve motivation and persistence [24, 17]. However, we filtered our data to ensure that all stu- dents included in our analysis had an opportunity to be influ- enced by our growth mindset intervention. The first growth mindset message presented to students is the introductory an- imation, so for both conditions we only included those who watched the entire introductory animation and made at least one move in the game. We also conducted our analysis with a stricter filtering criterion that only included students who completed the first four levels of the game. After four levels, 99% of players in the experimental condition have received brain points and seen the summary screen. Both analyses showed the same patterns of significance and led to the same conclusions, so we chose to present results for the looser fil- tering method that included more students in the analysis.

After filtering, our data set contained 15,491 players, with 7,807 players in the experimental condition and 7,684 in the control condition. These data were collected between September 3 and September 13, 2013. Refraction was fea- tured on the front page of BrainPOP’s game portal between September 3 and September 5, allowing us to attract large numbers of students. Since the data sets for the two condi- tions had different numbers of players, we randomly selected 7,500 players from each condition to include in our analysis.

DATA ANALYSIS AND RESULTS We study the effects of our growth mindset intervention on children’s behavior by analyzing a number of outcome mea- sures, each of which is described in detail below. Before per- forming this analysis, we evaluated the Kolmogorov-Smirnov test to assess the normality of our data, and found that it was statistically significant for all of our outcome measures. We therefore use non-parametric statistical methods: a Wilcoxon rank sums test and an r measure of effect size for continu- ous variables, and a Chi-square statistic and a Cramer’s V measure of effect size for nominal variables. We report ef- fect sizes in addition to p-values to show the magnitude of the differences between our populations, since we are likely to find many significant differences due to our large sample sizes. For both tests, effect sizes with values less than 0.1 are considered very small, 0.1 are small, 0.3 are moderate, and 0.5 or greater are large.

The Growth Mindset Intervention Increases Persistence We expected children who played the experimental version of Refraction to be more persistent than those who played the control version. To evaluate this hypothesis, we analyzed two outcome measures: the amount of time children spent play- ing the game, and the number of unique levels they played. Since BrainPOP offers many other games that teach fraction concepts, we expected children to quit Refraction when they became bored or frustrated. As a result, these measures cap- ture how long children are willing to persist before choosing to leave the game.

We calculate active time by counting the number of seconds each child played Refraction, excluding menu navigation and idle periods with more than thirty seconds between actions. Our analysis showed that intervention has a significant effect on active time played, with children in the experimental con- dition playing a median of 118 seconds, compared to 89 for the control condition (Z=-8.61, p<0.0001, r=0.07). A graph of the active time for both conditions is shown in Figure 4.

We calculate the number of unique levels each child played by counting levels with at least one game action. Since Re- fraction has an adaptive level progression, each child plays a different set of levels based on their incoming skill. How- ever, since children are randomly assigned to either the ex- perimental or control condition, we expect skill to be evenly distributed across conditions. Our analysis showed that in- tervention has a significant effect on levels played (Z=-9.04, p<0.0001, r=0.07). Children in the experimental condition played more levels, a mean of 6.7 levels compared to 5.5 for those in the control. The median was 2 in both conditions.

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Figure 4. A graph showing the percentage of players in each condition who are still playing after a given number of active minutes. Children in the experimental brain points condition play significantly longer.

These results suggest that children who play the growth mind- set version of Refraction are more persistent than those who play the control version. They stay in the game significantly longer and play significantly more levels. However, both of these effects are very small. Given the BrainPOP environ- ment, where the majority of children play for less than three minutes, this is not surprising. Therefore, the fact that we ob- serve a 33% increase in median time played is encouraging, despite the small effect size.

The Intervention Promotes Growth Mindset Behavior We expected children who played the experimental version of Refraction to display behaviors consistent with the growth mindset more frequently than those who played the control version. To evaluate this hypothesis, we analyzed an outcome measure that combines the four metrics used to award brain points to children in the experimental version. Recall from the Experiment Design section that we used a new hypothesis metric, an empty board metric, a math metric, and a moves metric to decide when to give brain points. In both versions of Refraction, we log an event every time one of the four metrics is triggered. We combine these four metrics to measure how frequently children exhibit the behaviors incentivized by the brain points system.

To combine the metrics, we summed the number of times each metric was triggered during play. Since children in the experimental condition play for significantly longer, they have more opportunities to trigger these metrics. To control for the amount of time played, we divided our combined met- ric by the number of minutes of active time played. This pro- duced the average number of metric triggers per minute, our strategy outcome measure. Our analysis showed that inter- vention had a significant effect on this combined measure. Children in the experimental condition triggered an average of 2.49 metrics per minute, compared to 2.18 triggers per minute for the control (Z=-8.18, p<0.0001, r=0.07).

These results show that children who play the growth mindset version of Refraction learn to use the strategies incentivized by the brain points system. While the size of this effect is small, it is encouraging to see that such a short intervention

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