geometry that has game-like properties, that is, elements of games that ..... Gee, J. P., What Video Games Have to Teach Us About Learning and Literacy.
Mily’s World: A Coordinate Geometry Learning Environment with Game-like Properties Dovan Rai, Joseph E. Beck, Neil T. Heffernan Computer Science, Worcester Polytechnic Institute {dovan, josephbeck, nth}@wpi.edu
Abstract. Mily’s World is a learning environment for coordinate geometry that has game-like properties, that is, elements of games that are engaging such as cover story, graphical representation, and animated feedback. This paper proposes that adding game-like properties to a computer tutor results in more student engagement and interest in the material. However, in addition to taking instructional time away, adding such properties imposes new limitations and difficulties in constructing content. Therefore, we have taken a measured and minimalist approach to making the original environment more game-like by weighing each additional component in terms of retaining all the learning features of a tutor and minimizing the new limitations, while exploiting the benefits of games. Sixty six students used the system who had also used Assistment, a web based tutor. Although the students were not totally enthusiastic about Mily, they still preferred it over Assistment. We also analyzed how different student subpopulations receive the new intervention, and that found that the students who find real-world examples and pictures helpful for solving math reported liking Mily more. Keywords: educational game, motivation, authentic educational datamining, visualization, endogenous fantasy
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activities,
Introduction
Although games are engaging to motivate students, they tend to take up time that could have been used for instruction and have been empirically shown to be less effective than intelligent tutors when it comes to learning gains [1]. Hence, instead of completely integrating educational content into a game framework, we instead choose to incorporate into the tutor those features of games that are motivational but do not overly detract from learning. Based on this choice, we created Mily’s World, a learning environment for coordinate geometry with game-like properties. We define game-like properties as elements of games that are responsible for their engaging nature such as points and rewards, graphics, fantasy, interactive feedback, speeded
trials, leveling up, etc. Our reason for taking this viewpoint is that we wish to make computer tutors more engaging and game-like, but do not want to start by trying to design an educational game. Instead, we are taking a measured and minimalist approach by incrementally making a complete tutor more game-like by weighing each additional component in terms of retaining all the learning features of a tutor and minimizing the limitations, while exploiting the benefits of games. Our hypothesis is that the sweet spot of educational efficacy and engagement is closer to computer tutors than it is to educational games. Therefore, we feel that a strategy of gradually and incrementally adding game-like properties to a tutor is productive. The ASSISTment system is a web-based tutoring program for 4th to 10th grade mathematics. It tutors students on items they get wrong, thus providing integrated assisting of students while they are being assessed. To make ASSISTments more game-like, we created Mily’s World. This environment has a series of 8th grade (approximately 13-year olds) coordinate geometry problems wrapped in a visual cover story. Students help characters in the cover story solve coordinate geometry problems to move the story forward. The complexity of problems and the richness of story grow as the students proceed. Similar to a classic ITS, students will receive tutorial help as they stumble on problems and misconceptions. We now provide a brief overview of the world and the types of activities students perform. In the following section, we define game-like properties and link our design to those. Mily, a 9-year old girl, is the protagonist who has a puppy and some friends with whom she plays soccer. Students are engaged in many different math-related tasks. For example, they calculate Mily‘s height and the distance between her and her puppy based on the coordinates of their heads. This is a very simple warm-up to make students familiar with the environment. As they proceed, students help Mily decide the name of the puppy and then help create a doghouse (see Fig 2). When students give the correct answer for slopes, the doghouse wall and roofs are built gradually and then a new doghouse pops up. The puppy develops a bad habit of chewing socks; so Mily ties him to a post. Students have to help her find the coordinates of a position to place the socks where the puppy cannot reach them. Afterwards, Mily goes out with her friends to play soccer wearing the socks that the students have kept the puppy from chewing. Here, students have to calculate slopes and equations of the path of the ball as Mily and her friends play (see Fig 3).
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Conceptual Framework
2.1 Why “tutor with game-like properties” rather than educational games Despite the intuitive appeal of educational games, there are limitations inherent in those games dealing with conventional curriculum. In addition to taking instructional time away, the cognitive overload can be a major limitation. We have taken a strategy to minimize extraneous details when it gets in the way of effective learning, making a balance between stimulation and overload. After all, educational games should not be competing against regular games but instead with other educational materials to get students‘ attention. We have used the following two strategies:
Simple game-like environment: Regular games can afford to have new and complex environments with complicated rules since students will spend hours learning the basics. But for educational games, the goal is for students to learn the content, and so students should not be overwhelmed by too many details. Even if the educational games are able to add emotional interest with seductive details, they cannot succeed if they cannot evoke cognitive interest in the content [21]. Specifically, the students who are already struggling to figure out problems can be confused and irritated by the complexity of the game environment. We want to have simple, familiar environments and tasks with details just enough to add context.
Fig 1: Screenshot: ASSISTment, slope problem
Minimalist visual presentation: The presentation should be simple and intuitive so that it helps to off-load details rather than overload working memory. In our context of coordinate geometry, while a concrete scenario is desirable, making too realistic a visual presentation can be counter-intuitive [5]. In Mily’s World, a concrete scenario is presented with real objects like a dog and a doghouse whereas graphics are minimalistic, stick-like figures and wireframe structures that are closer to symbolic representation. If the pictures are too realistic, e. g: if the house is shown in 3-D isomorphic form with patterned roofs, we assume that students will have difficulty to figure out slope. Similarly, a doghouse in wireframe structure is more intuitive as students can clearly see the connection between slope of the line and slope of the roof. 2.2 Game-like properties and emotional interest Games have a property that they are engaging to those who play them. More formally, games arouse sensory and emotional interest [6, 15]. Therefore, our goal is to include properties that will have similar effects. Based on our content, we have included some game-like properties. Though a lot of education materials have the properties listed below, we call them game-like properties based on their interactivity, fantasy and concreteness.
Authentic activities: Rather than working on isolated, de-contextualized, abstract problems, students want to work in an interesting context [6]. When there is realworld context, students find the problems meaningful. For example: Mily’s World has a sock problem where the students have to figure out the coordinates of a place to keep socks away from the puppy so that the puppy does not chew them. The students had a sense of delight and achievement after solving this problem. It would be hard to elicit similar interest in an equivalent abstract problem.
Fig 2: Screenshot: Mily’s World, doghouse problem
Visual representation: Adding pictures relevant to the problems and activities make them more tangible and interesting. Storyline: Integrating the problems in a coherent cover story can make the learning more holistic. Adding narrative has been found to increase motivation in ITS [23]. Animated immediate feedback: The animated feedback like walls drawn gradually, rendered doghouse emerging after wireframe solved, and puppy chewing socks add interactivity to the tutor. Badge collection: Students can collect badges after completing each problem set, which give them sense of achievement and progress. Each badge is for a problem set which is associated with a skill. For example students receive ‗puppy badge‘ after completing the warm up problems and a ‗doghouse badge‘ after solving the slope problems. Choosing game-like properties depends on the content and domain. Rich graphics can be a good option for history or biology but not for geometry (to avoid overloading the student’s visual processing abilities). We have not included speed, as our goal for this lesson, unlike activities designed to increase mathematical fluency, is for students to reflect upon the problems.
2.3 Game-like properties and cognitive interest Within a learning environment, the material can be viewed as occurring in layers. At the base level is an abstract problem description, above that is a word problem, above that is a continuing storyline, etc. Our hypothesis is that since Mily’s World is composed of more layers than a classic ITS, it will lead to students becoming more engaged in the activity, and increase their cognitive interest (desire to learn about the material). We propose that the carefully integrated game components can make math problems more meaningful and challenging and also aid in more easily understanding the content, and thus arousing cognitive interest. (Testing such a view was beyond the scope of this study, but we are planning such a study for March 2010) Our approach extends some of the existing research literature in this area, as follows: Authentic activities: Learning is more efficient and effective when it is embedded in realistic and relevant contexts [2]. In Mily’s World, students are engaged in everyday activities like building a doghouse, playing soccer and solving mathematical problems along the way. Visual representation: Successful problem-solvers build mental models from word problems [3]. Graphics not only add appeal but they can help develop mental models, thus reducing the burden on working memory and processing [4]. Interactive visual immediate feedback: With visual immediate feedback, students can tell what the error was and how it relates to the correct solution [7]. For instance, the puppy can chew socks if they are placed at wrong coordinates (e.g. ―I liked the dog. He was really cute. Also it helped to understand why I got the problem wrong.‖). Well-ordered problems: In good computer games, the problems players face are ordered such that the earlier problems are well built to lead players to form hypotheses that work well for later, harder problems. It matters how the problem space is organized—that‘s why games have levels [15]. In Mily’s World, different levels correspond to different problem sets, and the complexity of levels increases successively. Students first get warm up problems (manipulate one coordinate pair to calculate height, and then two pairs to calculate distance), then build a doghouse (intuition based simple problems with minimal computations), and then finally get the soccer problems (elaborate calculations). This property of sequencing educational content is used by instructional designers as well [10]. Integration of game and educational content: If math is used just as a means to perform other non- mathematical, supposedly fun stuff, students will get the sense that math is not fun. They can feel that they are being fooled into having fun doing what they would prefer not to do if it were only math without the fun context [9]. Therefore, Mily’s World has endogenous fantasy [16], that is, the students genuinely have to use their math skills to solve the story problems. Unlike exogenous fantasy where student solve arbitrary problems to get reward like a new doghouse, here the doghouse itself is made of slopes and has coordinates embedded on it.
Concreteness fading: As mentioned above, the problems get harder as the student progresses through the learning environment. As the problems get harder, they tend to be more abstract and it is harder and sometimes counterintuitive to have concrete representations. Therefore, we have used a strategy to make the representations more concrete at first and less so as we proceed. For example, Mily is shown in full figure in doghouse problem (fig 2). But in soccer problem (fig 3), once Mily and her friends are introduced in person, they are abstracted to mere dots. Research has demonstrated that initial concrete grounding facilitates interpretation in later problems [5].
Fig 3: Screenshot: Mily’s World, soccer problem
Integration of concepts: Typically mathematics concepts are presented as independent entities. In contrast, in Mily’s World, students have to answer various questions on coordinates and concepts of slope, such as in the activity to create a doghouse. By using multiple math skills in the context of one activity, we hope that students will have representation other than each skill as a separate entity. Storyline: Word problems are effective, but students have to first devote time and attention to understand the context and scenario for every word problem. If we use a coherent cover story, the initial story context can be reused for multiple problems, thus saving student effort. For example, once a student is introduced to Mily and her puppy, they can solve the successive problems based on the same scenario.
3 Participants “Mily’s World‖ was assigned as homework to 8th grade students (12-14 year olds) in a school in the suburb of a small city in the Northeastern USA. Sixty six students started the exercise and 58 students completed it. There were 16 math questions and
12 survey questions and one open ended feedback question. Before the students worked on the problems, we asked their attitudes and preferences with math (whether they like math, whether they find real-world examples helpful or confusing, etc.) and asked about their views on Mily’s World after they worked on the problems. Zooming in subpopulations of student Game playing is a very subjective experience affected by player‘s proficiency, preference, and expectations. The impact of game-like properties with different student subgroups can shed light on the nature of games, what they affect and what they offer. Knowledge level: There are competing hypotheses here for whom game-like properties will be beneficial. One possibility is that by adding game-like properties, weaker students will be more engaged with the material and will learn more. Alternately, perhaps the overhead imposed by the interface will hurt weaker student’s learning, while stronger students are the ones who benefit from the motivational increase. Math anxiety: Some students have math anxiety [20], that is, they are extremely nervous about their ability to perform math and personalize failure in solving math problems. Can these students perform better if math comes in a friendlier, tangible interface? Mily’s World has a non-threatening and non-competitive environment, where the player is in a position of power to help the younger characters. Gender: Gender is always an important issue when it comes to games. Studies have shown that boys and girls prefer different kinds of fantasy and features [16]. As we mentioned earlier, Mily’s World is also a cognitive intervention rather than mere addition of interesting elements. The abstract math problems are mapped into real world context and corresponding pictures are added. These new interventions can be supportive for some but can add confusion for other. Hence, we asked them additional two questions and divided them accordingly: Do you find real-world examples helpful for solving math problem? a) Yes, examples are helpful b) No, they make it more confusing Do pictures help you learn math? a) Yes, pictures help me b) I am not sure
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c) No, pictures don‘t help me
Results
We asked the students two questions on their preference of Mily’s World. On the question whether they like Mily’s World, 20% said they liked it, another 20% said they did not like it and 60% said they find it ok. We also asked them about their preference between Mily’s World and Assistment. 52% preferred Mily’s World, 13% preferred Assistment and 35% had no preference; this preference for Mily’s World is reliable at P
