An Optical Brain Imaging Study on the ... - ACM Digital Library

An Optical Brain Imaging Study on the Improvements in Mathematical Fluency from Game-based Learning Murat Perit Çakır METU Informatics Institute Ankara, Turkey [email protected]

Nur Akkuş Çakır Drexel University 3141 Chestnut Street Philadelphia, PA USA [email protected]

Hasan Ayaz Drexel University 3141 Chestnut Street Philadelphia, PA USA [email protected]

ABSTRACT

Frank J. Lee Drexel University 3141 Chestnut Street Philadelphia PA, USA [email protected]

activities ranging from worksheets, animations, and narrated examples are designed to help students develop such skills and conceptions, conventional methods often fail to motivate students to engage with the subject matter effectively and flexibly. The failure of conventional methods to engage students with math in meaningful and fun ways often leads to learning difficulties that fuel math anxiety among students.

In this study we examined the effectiveness of game-based learning in improving math fluency compared to a conventional drill and practice approach. An optical brain imaging method called functional near-infrared spectroscopy (fNIR) was utilized to assess changes in brain activation in prefrontal cortex related to cognitive load and working memory functions, so that the improvement gained by the increased attentional and cognitive training involved in a mobile game called MathDash could be examined in terms of how and why game-based learning can be effective. Overall, our experiment with college students indicated that Math Dash was equally effective in terms of improving computational fluency in comparison to the drill and practice approach.

The emergence of educational games allows for these issues to be addressed by the development of engaging and motivating games based on principles of computational fluency in order to improve learning outcomes. MathDash is a mobile game developed at Drexel University and designed to facilitate elementary math education by engaging students in the completion of multistep combination arithmetic problems. In 2012, MathDash came in first place at the Microsoft Imagine Cup in the mobile game design category, demonstrating its success at being both educational and engaging [3]. Users have a limited time to complete arithmetic problems within MathDash, and if they answer correctly, they are given more time to solve the next problem, as well as points. These points are extrinsic supplements to the intrinsic rewards of solving the math problem. This combination of extrinsic and intrinsic rewards is designed to maintain high levels of attention and engagement, facilitating the acquisition of basic arithmetic skills. This pattern of reward, both in the relief of a negative stressor (increased time limit) and positive feedback (point value) has been implicated in reinforcement learning [4]. The results of expert interviews and a focus group study conducted with middle school students suggests that MathDash succeeded at promoting computational fluency in students.

Author Keywords

Educational Games, Math Education, Functional Nearinfrared Spectroscopy, Computational Fluency, Working Memory ACM Classification Keywords

K.3.1. Computer Uses in Education. K.8. Personal Computing, Games INTRODUCTION

Developing computational fluency with numbers is a key objective in math education [1]. Computational fluency implies not only efficient and accurate execution of arithmetic operations, but also requires an understanding of the meaning of the operations and their interrelationships that facilitate their flexible use [2]. Abstract notions such as the equivalence of numerical expressions and algebraic principles like commutativity and associativity are grounded on such understandings. Although various

This study aims to evaluate the behavioral and neural effects of playing MathDash repeatedly on improving computational fluency through a controlled experiment. For that purpose a simplified experimental version of the original MathDash game was developed, which allows researchers to customize game-play parameters and to extract detailed log files for behavioral performance analysis. A controlled experiment was then conducted to contrast the performance and brain oxygenation measures of the MathDash group to that of a control group who were

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. CHI PLAY 2015, October 03 - 07, 2015, London, United Kingdom Copyright is held by the owner/author(s). Publication rights licensed to ACM. ACM 978-1-4503-3466-2/15/10…$15.00 DOI: http://dx.doi.org/10.1145/2793107.2793133

209

trained with non-gamified, computerized multiple-choice arithmetic questions. Although we included young adults rather than elementary school children as subjects, the study aimed to validate the use of the fNIR optical brain imaging technology for evaluating the game’s effectiveness in improving computational fluency in terms of changes in neural activation patterns.

outcomes with games, educational researchers should consider what theoretical lenses on learning they are using and what intervening variables those lenses predict as a whole [11]. Such an approach can inform and enhance possible studies, as it will provide a methodological framework in which researchers can design studies to investigate different factors affecting student motivation and achievement so that it would be possible to argue for new conceptual frameworks to guide future designs [10].

The following section provides an overview of game-based learning in math education, introduces key skills and conceptions related to arithmetic such as computational fluency and number sense, and motivates the design decisions underlying MathDash by situating them within current curricular concerns in math education. This is followed by a description of the experimental design and the instruments used during the study. Next, the main findings of the study are reported. The paper concludes with a discussion of their findings and implications for future work.

Math Education & Games

A considerable number of students are not motivated to learn mathematics and do not really enjoy studying it; however, with game-based learning environments it is possible to change their attitudes towards learning mathematics [12]. Developing technology based individualized practice opportunities are considered to be an effective alternative to worksheets or whole-class practice, which dominate standard teaching practice in mathematics [13]. Some empirical studies revealed that digital math games can improve learners' achievement [14,15,16,12]. Kraus [17] examined the effect of a computer game on proficiency in basic addition facts in second grade and the results showed that subjects in the experimental group responded correctly, on the average, to twice as many items on the addition basic facts speed test as did the subjects in the control group.

RELATED WORK Educational Games & Pedagogy

The way students learn has dramatically changed due to the fact that they have grown up as “digital natives.” Unfortunately most educators today are digital immigrants and this causes a gap between the way they teach and the way students learn [5]. Digital natives spend a significant amount of their time consuming digital media, especially playing video games. Thus, educators are becoming more concerned with the importance of games in students’ lives and show more willingness to make use of the game experience to support learning in the classroom.

MathDash & Curricular Goals in Math Education

Mathematics education is a key aspect of the elementary and secondary level curriculum due to its implications for cognitive development and life-long success of students [18, 19]. In the US, the NCTM Standards [1] include statements about specific math competencies that students should develop from pre-kindergarten through grade 12, which have been incorporated into the math section of the recently established Common Core State Standards initiative adopted by several US states. For this study two domain experts evaluated MathDash in terms of its conformance with the Common Core State Standards for Mathematics from first through eighth grade, and commented that the game succeeds in targeting skill development especially for single-digit operations under the domain ‘operations and algebraic thinking’. These skills form the prerequisite for more advanced math concepts covered in higher grade levels such as the subheadings ‘fluently add and subtract multi-digit whole numbers using the standard algorithm’ in fourth grade and ‘apply and extend previous understanding of numbers to the system of rational numbers’ in sixth grade. Overall, all middle school students will potentially benefit from playing a game that requires them to practice single-digit integer arithmetic.

Children naturally learn through gameplay [6]. The connection between motivation, learning, and technology can be best seen through the video game phenomenon [7]. Modern children spend a significant amount of their time playing video games. Not only is the quantity of time significant, the quality of playtime reveal that children show a high level of engagement when they are playing video games [8]. By blending video games and curricula, it is possible to harnesses an inherent learning behavior in games towards educational goals. As students develop intrinsic motivation, a sense of “fun,” while learning they are more likely to be willing to learn the subject matter, thus more likely to spend their time and make an effort to succeed. Moreover, they are more likely to feel good about their learning and transfer the knowledge in different situations in the future [9]. However, not all video games have educational value and not all educational video games are fun. Kebritchi and Hirumi [10] mention that pedagogical foundations of educational games are of great importance for the educational study of game-based learning. Educational game designers should report on how those pedagogical foundations are reflected in the game experience. Moreover, while designing empirical studies on the learning

The educational goals set for elementary mathematics curriculum require students to demonstrate computational fluency and develop in-depth mastery about numbers and operations [2]. Their mathematical reasoning and

210

computational proficiency skills are essential for more effective mathematics instruction [20]. The exercises in MathDash are basic algebra exercises that require students to use strategic thinking to come up with a solution, as they often need to create the necessary numbers by combining the given numbers in different ways. MathDash does not present students with a singular correct answer; instead it aims to encourage flexibility in arithmetic thinking.

researchers claim human mind has limits and “…if too much energy goes into figuring out what 9 plus 8 equals, little is left to understand the concepts underlying multidigit subtraction, long division, or complex multiplication” (p. 21). They indicate that students who do not have the skill to automatically see arithmetic facts and relationships such as “32 is 8 more than 24” or “16 is half of 32” may fall behind and fail to develop a sound understanding of the particular mathematical concepts discussed in the class. According to Geary [21], arithmetical development depends on students’ ability to develop procedures and memory representations to execute and retrieve automatically, and the ability to develop a conceptual understanding of these procedures. Having mental calculation shortcuts enables students develop both their number sense and mathematical fluency [13], which is one of the essential sub-skills for high level math [26]. Students who cannot retrieve basic combinations automatically have more difficulty in discussing mathematical concepts involved in algebraic equations. Gersten et al. [13] argues that students who cannot do fast retrieval of arithmetic combinations such as 6 + 4 = 10, will get lost when teachers assume they can effortlessly retrieve this information.

Students need to have well-developed strategies to be fluent and accurate with arithmetic combinations [21,13], but the standard in-class activities might not provide enough practice to construct such strategies. Jordan et. al [22] examined students’ mathematical competency development in a longitudinal study and found that children with mathematical difficulty have deficiencies in calculation fluency as a defining feature. MathDash provides a gaming experience in which students need to practice basic arithmetic combinations in a variety of ways. Furthermore, Math Dash provides opportunities for students to acquire a foundational understanding of mathematics by requiring them to connect operations and understand the relationships between them to solve a given equation, instead of making them perform these operations separately. Russell [2] emphasizes the importance of gaining an integrated understanding of procedures rather than learning them as compartmentalized pieces of knowledge. Students generally learn to compute basic operations without understanding, which is as important as fluency to solve complex problems [21]. Math Dash’s design equally pursues these two goals and aims to enhance students’ understanding of the foundations of operations and mathematical fluency.

Moreover, according to Gerstain et al. [13], an important indicator of numerical competence is concerned not only with the ease of retrieving the answer to basic expressions such as 4 + 4, but also the ability to recognize the relevance of such expressions for solving new problems. For instance, a new expression such as 4 + 5 can be decomposed as (4 + 4) + 1, which would allow the learner to make use of their prior knowledge of the expression 4 + 4. Storing and retrieving such information from memory with ease to facilitate the recognition of such relationships help students develop the necessary procedural and conceptual skills to grasp more abstract mathematical principles such as the commutativity and associativity laws of arithmetic.

Another important goal in math education is to help students develop “number sense.” Berch [25] reviewed various definitions of number sense in the math education literature and compiled a list of the components of this construct. According to Berch [25], number sense enables students to “…achieve everything from understanding the meaning of numbers to developing strategies for solving complex math problems; from making simple magnitude comparisons to inventing procedures for conducting numerical operations; and from recognizing gross numerical errors to using quantitative methods for communicating, processing, and interpreting information” (p. 334). Research suggests that number sense is generally developed with informal instruction before students start kindergarten [21,23,13]. However many researchers also agree that number sense development should still be reinforced in higher grade levels [24, 13], because such instructional support can help students deal with the difficulties of early mathematics classes [23].

Number combination skill is foundational to higher order performance and has a profound effect on mathematical proficiency, thus the deficiencies should be intervened as early as possible. The intention of any intervention should be to foster the development of number combination skills so that students will not be left behind in the following years. Computers with their rich multimedia design options can lead to major changes in this situation [27]. According to Griffin [24] the growth of higher-level math abilities depend on the growth of core skills such as associating quantities with numbers and thinking about numbers without needing the presence of physical objects, which generally take place at ages five or six. When students have deficiencies in the core structures, they will experience serious difficulty in catching up with their peers. In their longitudinal study about children’s early mathematical development Aubrey et al. [28] emphasized the importance of mathematical knowledge and its relation to later achievement. Students that have less understanding of math will probably remain low achievers.

Gersten & Chard [20] argue that number sense is binding for both automaticity in math and solving basic arithmetic computations. They emphasize that knowing 15 is much further away from 8 as compared to 11 requires an awareness of 8 + 7 and 8 + 3. They also point out that

211

MathDash as Instructional Design

good game should provide clear feedback with failure but should not cause them to feel discouraged [9]. In MathDash players receive immediate corrective feedback and positive reinforcements. When they figure out the correct equation they gain points and when they come up with a wrong equation they are provided with information about what is erroneous with their calculation and still have chance to rework the equation until it is correct. Furthermore, the game offers prompts until independent mastery has been achieved within the given time frame. If a player takes an extended amount of time on a single equation, a solution that is readily available in the current state flashes in the equation bar, indicating a possible solution to the player.

Instructional designers can use most of the characteristics of intrinsic motivation through game design, as games can be designed to give clear goals with uncertain outcomes, they can include different levels of difficulty and can provide performance feedback [29]. MathDash’s game design was based on the assumption that when students are provided with various ways of basic arithmetic and abstract thinking in a repetitive fashion, with learning support such as feedback, positive reinforcement and scaffolds; and with an intrinsically motivating instructional design, the exercise will be more fun than standard exercises such as worksheets. The goal is to focus attention on the flexibility of mathematical thinking and fluency, thus promoting fast arithmetic fact retrieval and eventually reduce math anxiety. Malone [9] suggests a framework for intrinsically motivating instructional design with three main characteristics; challenge, fantasy and curiosity.

Secondly, according to Malone [9] fantasies make learning more appealing. There are two kinds of fantasies, intrinsic and extrinsic fantasy. Intrinsic fantasies are when the necessary skill and the fantasy of the game depend on each other, whereas extrinsic ones are when the fantasy depends on the skill, but the skill does not. He also claims that intrinsic fantasies are more effective as they provide images that help to create emotionally and cognitively engaging learning environments. Many educational games employ extrinsic fantasies even though they are considered educational "sugar coating" [29]. MathDash provides intrinsic fantasies for mathematical learning content as the target skill is number combination and it is appealed by the fantasy context of the game as players practice the target skill by various atom combinations to solve an equation.

Challenge is attained through personally meaningful goals, which are designed at an appropriate level of difficulty, in a way to build self-esteem [9]. MathDash offers adjustable difficulty levels so that students can have a choice about the amount of challenge. Students can move forward as they demonstrate increased levels of number combination skills. In the game, players are presented with a set of atoms that contain numbers and an equation to be solved. If the player does not have the desired atoms on the screen, the player can choose to combine atoms. Combining atoms results in a new atom that has a value equal to the sum of the combined atoms. If the result is larger than nine, two new atoms are created, one for each digit of the result. The ability to combine atoms results in endless possibilities that keeps player thinking ahead. It's the act of playing with the numbers to come up with a solution that counts.

Thirdly, Malone [9] argues that curiosity can take two forms, sensory curiosity and cognitive curiosity. Audio and visual effects can stimulate sensory curiosity while cognitive curiosity is linked to construction of knowledge for a less ambiguous understanding and desire to learn more. MathDash appeals to sensory curiosity with its audio and visual presentation. The game has a visual appeal with its colorful design and original graphical representation. It also includes music and sound effects related to the game features.

To establish uncertainty variable difficulty levels, multiple level goals, hidden information, and randomness can be used [9]. In MathDash, as the equations are solved, the player is awarded points and the progress bar gradually increases with correct answers. If the progress bar becomes completely filled, the player proceeds to the next level. If the progress bar empties, the game ends and the player is taken back to the main menu. As time progresses the progress bar continually decreases. This effect becomes greater as the player progresses through levels. During the course of the game, there are a number of power-ups and hazards that will appear on the screen. Power-ups provide a benefit to the player to help get through the levels and to increase the player's score while going through the level. Hazards work against the player, preventing the player from being able to take full advantage of the available atoms. Taking advantage of power-ups and avoiding hazards are key to getting through later levels.

METHODS

27 right-hand dominant participants in the age range 18-36 (mean = 26.2, sd = 4.9) participated in this study. All subjects were undergraduate and graduate students at Drexel University and METU Informatics Institute. The majority of the students were studying towards degrees in cognitive science and computer science, whereas the remaining students had business and digital media/design backgrounds. 10 participants were randomly assigned to the control group, whereas 17 participants constituted the experiment group. The study was approved by the Institutional Review Board at Drexel University and the METU Human Subjects Ethics Committee. In the pre- and post-test, participants were asked to answer multiple-choice arithmetic questions implemented in Open Sesame [30]. Each session included 32 questions in random order (see Figure 1 below). Half of the questions included a

In an intrinsically motivating design, students should get some performance feedback to be motivated by the goal. A

212

single missing part (e.g. 1 + 1 = _ ), where the subject had to choose the correct answer (e.g. 2) among the given three options. In the remaining half, equations with two missing places were displayed (e.g. 4 - _ = _ ), and the subjects were required to select among the three pairs that would correctly complete the given equation (e.g. 2,2). In each trial, a fixation cross was displayed for 4 seconds before the equation was displayed. Participants were expected to respond within 10 seconds by clicking on one of the three options presented under the equation. When the user clicks on an option, a color-coded fixation screen is shown for 1 second, where a green fixation dot signifies a correct response, whereas a red fixation dot signifies an incorrect response. This is followed by the regular fixation screen with the white dot, separating each trial for five seconds. Each trial took a maximum of 15 seconds to complete. Participants completed 32 trials during pre- and post-tests, where 16 trials included equations with one unknown, and 16 trials included equations with two unknowns. Trials were presented in a pseudo-random order.

available among the numbers in the screen. In such cases subjects can drag a number onto another to initiate an addition move. For instance, if the user drags 1 over 8 in the situation depicted in Figure 2 below, a new green number, 9, will be produced, and numbers 1 and 8 will disappear. The user could then use this number with the already available number 6 to solve the equation in Figure 2. When the user combines two numbers whose sum is a two-digit number such as 14, then two single digit numbers 1 and 4 will appear on the screen. In other words, the green bubbles represent single digit numbers only.

In the control condition, subjects continue to answer multiple choice questions, where they went through 8 blocks each of which are separated by a rest period of 20 seconds. Within each block subjects were presented 10 equations sampled randomly from a repository of arithmetic questions, so each participant responded to a total number of 80 questions. Each trial has the same temporal structure as the pre- and post-test trials, which allowed a maximum duration of 15 seconds for each question. Thus, the control task would take at most 22 minutes. Behavioral logs indicated that on average the control group participants spent 11 minutes to complete the 80 questions during the experiment.

Figure 2. The screen shot of the experimental version of the Math Dash interface.

The blue bar at the top represents the remaining time in the current trial. The numbers in green move around randomly in the screen and after a certain duration they disappear and a new number spawns and replaces it. The number on the top right represents the current score. For each correct answer subjects were awarded 20 points. For each combination move they did they were awarded 10 more points (e.g. if the subject performs 2 combinations that lead to a correct solution, then he/she is awarded (2 x 10) + 20 = 40 points). The experimental version of Math Dash did not have the same graphical display and sound effects of the original game, but it had the same game play mechanism and it provided more advanced data logging capabilities and game customization support (e.g. various parameters such as the block lengths, the algorithm for choosing numbers in the bubbles, the duration of the visibility of the bubble can be provided to generate different game conditions).

Figure 1. The time-course of each trial used during pre- and post-tests as well as the control condition.

In the experiment condition, subjects played an experimental version of the MathDash game. The game was implemented in Unity and deployed in the Android platform. Subjects used the touchscreen of a 9-inch Samsung tablet to play the game. The game requires subjects to solve a given equation at the bottom of the screen by dragging appropriate numbers in green into the empty slots. The required numbers may not always be

Subjects in the game condition completed eight two-minute game blocks. Each block was randomly assigned a type, from one to four, based on two game play parameters that define task complexity. In a type 1 block, subjects were presented equations with one unknown and the required number to solve the equation was highly likely to be

213

spawned by the game engine (i.e. it will become available soon). In a type 2 block, subjects were presented equations with a single unknown, but the spawning algorithm randomly selects numbers, so the required number is not as likely to appear as it is in type 1. In this case, subjects are more likely required to usemore likely to use combinations to generate the number they need to solve the given equation. In a type 3 block, subjects were presented equations with two unknowns and the spawning algorithm gave more weight to the numbers that can be used to solve the equation at hand. Finally, in a type 4 block, subjects were presented equations with two unknowns, but the number spawning algorithm acted randomly without any bias towards potential solutions. The questions were sampled from the same pool of arithmetic questions used for the control group. The behavioral logs suggested that, on average, participants in the experiment group attempted 168 equations in 16 minutes.

towards that location, which increases the concentration of Hb02 and washes away the HbR. As the neural population returns back to its baseline activity level, the concentrations of HbR and HbO also come back to their baseline levels.

fNIR Optical Brain Imaging

While the subjects solved arithmetic problems the neural activity in their prefrontal cortex was monitored by a functional near-infrared spectroscopy (fNIR) system developed at Drexel University (Philadelphia, PA), manufactured and supplied by fNIR Devices LLC (Potomac, MD; www.fnirdevices.com). The system is composed of three modules: a flexible headpiece (sensor pad), which holds 4 light sources and 10 detectors to obtain oxygenation measures at 16 optodes on the prefrontal cortex; a control box for hardware management; and a computer that runs the data COBI Studio software [31] for data acquisition (Figures 3 & 4). The sensor has a sourcedetector separation of 2.5cm, which allows for approximately 1.25cm penetration depth. This system can monitor changes in relative concentrations of oxy and deoxy-hemoglobin at a temporal resolution of 2Hz. The locations of 16 regions on the cortical surface monitored by fNIR are displayed in Figure 3, which correspond to Broadmann areas 9,10,44 and 45.

Figure 3. fNIR sensor (top, left), projection of measurement locations (optodes) on brain surface image (top, right), optodes identified on fNIR sensor (bottom) [45] .

fNIR is a neuroimaging modality that enables continuous, noninvasive, and portable monitoring of changes in blood oxygenation and blood volume related to human brain function [32]. Neuronal activity is determined with respect to the changes in oxygenation since variation in cerebral hemodynamics are related to functional brain activity through a mechanism which is known as neurovascular coupling [33]. Neurons require energy to get activated, which is supplied by the metabolization of glucose. The metabolization process requires oxygen, supplied by the hemoglobin molecules present in the capillaries. When a group of neurons fire, they initially consume the oxygen present in their vicinity, which will produce an initial increase in the concentration of deoxy-hemoglobin (HbR) and a dip in the concentration of oxy-hemoglobin (HbO). In the order of 4-6 seconds, the vascular system responds to this local energy need by supplying more oxygenated blood

Figure 4. A subject wearing the fNIR sensor while playing with Math Dash on a tablet computer. The brain signals are collected by the computer located behind the participant.

fNIR uses infrared light to monitor the changes in HbR and HbO molecules in an area of the brain under the forehead called the prefrontal cortex. fNIR can monitor activity in 16 different locations called optodes distributed on the prefrontal cortex. Existing neuro-imaging studies suggest that the prefrontal cortex has a special role in the processing of higher order cognitive functions such as working memory management, sequential processing of sensory and memory input, as well as response inhibition [46,47] and decision making [34]. fNIRS can monitor regions such as left/right dorsolateral prefrontal cortex (dlPFC), left/right dorsomedial prefrontal cortex (dmPFC) and frontopolar cortex which are known to be associated with the

214

aforementioned higher order cognitive processes. Since fNIR sensors are placed on the forehead, veins within the skin can potentially contribute to the fNIR signal. However, recent studies that combine multiple neuroimaging modalities found that the cerebral cortex is the primary contributor to the fNIR signal [39, 40, 41].

raw light intensity measures obtained by the fNIR sensor were first low-pass filtered with a finite impulse response, linear phase filter with order 20 and cut-off frequency of 0.1 Hz to attenuate the high frequency noise, respiration and cardiac cycle effects [32]. Next, motion artifacts due to excessive movement of the head were filtered by using the sliding windows motion artifact filter [42]. Saturated channels (if any), in which light intensity at the detector was higher than the analog-to-digital converter limit were excluded. Filtered raw measures were converted into oxyhemoglobin (HbO) and deoxy-hemoglobin (HbR) concentration changes by applying the Modified-Beer Lambert law.

RESULTS

At the behavioral level, control and game groups were compared in terms of their accuracy and average response times to the 32 multiple choice questions they were presented in the pre- and post-tests. The average accuracy values were above 95% for both pre- and post-test results of both groups. Hence, main comparisons between the control and game groups were done based on their average response times. A two-way mixed ANOVA where response time is taken as a within subjects variable found a significant main effect of test, F(1,24)=42.35, p