Simple arithmetic lessons through an adaptive snake game

Simple arithmetic lessons through an adaptive snake game Maria Virvou, Spyros Papadimitriou Department of Informatics University of Piraeus Piraeus 18534, Greece [email protected]; [email protected] Abstract— Commercial games and educational games are different due to the fact that, the purpose of the first is fun while the second are primarily educative. Educational games may use motivational features of classic video games in order to help the students improve their learning skills in specific educational subjects. In this paper, we present a browser-based snake game, which is associated with the arithmetic operations context. Furthermore, the game contains adaptive attributes and provides students useful guides to overcome possible weaknesses. Keywords—educational games; arithmetic games; adaptivity; student modeling; error diagnosis I. INTRODUCTION Computer games play a significant part, not only in children's life but in adolescents' culture as well [1]. Researchers indicate that the average time a person spends playing digital games during a regular school day is two hours and a half [2]. However, it is widely agreed that computer games incorporate motivational and immersive features that may be used in learning process as well [3]. Educational games are different from commercial video games due to the fact that, their main objective is to assist students in learning a skill, while commercial games aim to entertainment [4]. The usage of fun and entertainment factors, that video games encompass, makes the educational process more enjoyable. Educational games are designed to help students improve their thinking and creativity and increase the feeling of fun while learning. Experimental findings have stated that educational games are great tools that promote learning skills [5]. Furthermore, studies have indicated that teachers need to recognize and accept the positive influence of educational games on students developing positive attitudes towards learning [5]. Adaptive educational games are one type of educational games. Researchers have proposed the integration of adaptive techniques and technologies into the video games [6]. User modeling may contribute to better recognize the knowledge level of a student in a specific domain. Afterwards, an adaptive educational game can take advantage of the student model information and make the necessary adjustments in order to provide student the correct guides while being in learning process. Several studies have shown that the usage of educational games lead to the improvement of education in elementary school [7]. In this paper we present an educational snake game, which contains various elements of adaptivity. It is associated with the educational subject of arithmetic in primary school and it is designed to test students’ understanding of the two major arithmetic operations (i.e. addition and subtraction). The adaptive attributes may help students recognize their possible weaknesses and recommend them respective ways to overcome their difficulties. II. THE SNAKE GAME 'Snake and Ladders' is one of the most classic and popular board games till today. It is a traditional game from ancient India that was brought to the UK in 1892 and first commercially published in the US as 'Chutes and Ladders'. The game consists of a game-board separated in numbered squares, a spinner or die and four pawns. Players start their game from the bottom left square of the game board, trying to reach the top right square, which is their main goal. Every move is defined by the value of the spinner or the die. In some cases, a pawn's move may end on a square, which contains the bottom edge of a ladder. Player can use the ladder to bypass several squares and move closer to the final target. However, there are cases where a player may end on a square where a snake exists. Therefore, it is considered that the snake attacks the player not only preventing him/her of approaching the final destination but constraining him/her to move backwards. First of all, Snake is a browser-based game meaning that it is not necessary for a user to buy a game board, pawns and a die. Browser-based educational games are simpler and shorter in length making them more accessible and affordable for the students [4]. A computer having internet access is enough for a student to start playing the game. Furthermore, it is an educational game concerning the domain of arithmetic in first classes of elementary school. Hence, the game incorporates two basic arithmetic operations, addition and subtraction. In view of this, we had to find a way to integrate the desired pedagogic features into the game. In order for the integration to take place, we took advantage of the fact that the player rolls the die and has to move depending on the arithmetic value of the die. The smallest integer value of the die is number one and the greatest number is six. These values correspond to a student with a basic level of knowledge in basic arithmetic operations. If the result of the die is number one, two or three, the student's goal is to solve the subtraction of the die’s value from the number of the square s/he is on. This means that s/he has to move backwards as many times as the die indicates. On the other hand, if the die’s result is number four, five or six, the player must move forward according to the die’s value. This selection of the arithmetic operation depending on the value of the die was made to facilitate the student to finish the game and don't get disappointed by moving often large steps backwards. Furthermore, subtraction is considered more difficult operation than addition, at least for the first classes of primary school. In addition, the color of the die changes respectively to its value in order to help the student know which type of arithmetic operations has to solve and move accordingly on the game board. In particular, if a subtraction takes place, the color of the die becomes blue. Red color of the die means that student has to solve an addition and move closer to the final destination. additionally submit his/her level at multiplication and division. Possible development of new games may make use of this feature as well. The initialization of the student model may be used to define the difficulty level even if the player plays for the first time. The student model divides the knowledge level for each operation in three categories as illustrated in Table I: beginner, intermediate and advanced. The knowledge level value helps the game to adapt to the needs of the student. For the beginner level, the die value ranges from one to six simulating the classic six-sided die. However, in the case of intermediate and advanced levels, the possible maximum die value may rise to thirty making the arithmetic operation more difficult to be solved. In these cases, the integrated feature of adaptivity increases the total number of squares needed to be crossed by the student's virtual pawn. The advanced game mode is illustrated in Figure 2. TABLE I. STUDENT KNOWLEDGE LEVEL Operation Type Fig. 1. Subtraction example. Player moves from square 5 to square 2. III. ADAPTIVITY IN SNAKE GAME It is widely acknowledged that there are many educational or adaptive games but it is hard to find a game that combines education and adaptivity. The Snake game incorporates a student modeling in order to add the feature of adaptivity in the game. Its' main role is to recognize students' possible weaknesses in the domain of arithmetic and suggest specific game lessons which can help students overcome their difficulties. There are two types of student models: the short one and the long one. The short one keeps information about student's answers only for the current game s/he participates. On the other hand, the long-term model takes advantage of a database to create a history record for every student. In this case, the game provides the possibility of creating an account with a unique username and password. During the registration process, the game asks the student to fill the level of his/her knowledge for each arithmetic operation. Despite the fact that the game is related to addition and subtraction, the user can Knowledge Level Addition Beginner Intermediate Advanced Subtraction Beginner Intermediate Advanced As mentioned earlier, the ultimate goal of a player is to cross the tiles of the game board and reach the top right one which is the final destination. In order to accomplish this task, s/he has to solve arithmetic operations and obtain a sum of points, which is higher than a predefined threshold. If the last square is reached but the score points are less that the minimum limit, the game informs the player that the objective was not achieved. The score points are defined by the percentage of correct answers in the current game. If the percentage is less than 80, game communicates a relative message to student informing him/her that the goal is not achieved. Moreover, the number of total answers should be equal or greater than 20. In this way, the student-modeling component retrieves more information about student’s submissions and can produce more realistic results regarding the knowledge context. Every time the student rolls the die, s/he has to select the correct target by clicking on the numbered tiled s/he believes contains the right answer. The student-modeling component examines the correctness of the answer and updates the corresponding information of the student model. The game provides student with immediate feedback on an answer submitted (i.e. correct or incorrect). Furthermore, a sound is played depending on the correctness of the answer as an additional reporting feature. If the user is registered, these results are added to the student model in the database. The game also provides feedback on student's overall performance by reporting the total number of questions answered and the number answered correctly and incorrectly. At the end of the game, student-modeling component calculates the percentage of the correct answers for each arithmetic operation using the information retrieved from database. The calculation affects the student's knowledge level on each operation by comparing to specific integer values. For example, if the percentage of correct answers related to addition is less than 50, student's level in addition is adjusted to beginner. Similarly, if the percentage is equal or greater than 50 and less than 85, the level corresponds to intermediate user. Finally, a percentage of equal or greater than 85 promotes user to advanced level. Another significant attribute contained in the game is a timer running. Timer is an additional adaptive characteristic as the difficulty level of the game determines its speed. In the beginner mode, timer runs slowly and student has the opportunity to think more about the correct answer. Alternatively, s/he may count one by one the tiles that need to be crossed. This method of answering can help beginner students, especially youngest ones, to practice in counting numbers. If the difficulty level is above beginner’s, the timer runs faster, the die value may consist of two digits and the student's move should be quicker. Fig. 3. A list with student mistake types and corresponding suggestions. Fig. 2. Game running in advanced difficulty level containing more tiles. Fig. 4. A game lesson suitable for practicing. Finally, in order to offer additional feedback to students regarding their mistakes, the game performs error diagnosis. When a wrong answer is submitted, a process starts by receiving the numbers participating in the arithmetic operation and the respective result. The process continues attempting to detect possible frequent mistakes and connect them with the operation. The most common errors that may occur are operations including extras or the student executes incorrect operation such as addition instead of subtraction. At the end of interaction, the game informs students about the final result and presents a list with the types of errors the student made. For every error type, the game recommends the user to use specific game lessons that are provided for practice. In this way, there is a game lesson relating to addition with extras, a lesson without extras, subtraction of one digit numbers and many other educational game lessons. The main difference between the main game and the game lessons, is that student-modeling component is not used in the second case. IV. CONCLUSION In this paper, we have presented an educational snake game in which students have to reach to their final target by crossing several squares of a game board. A die’s value defines the arithmetic operation type that the student has to solve and declares the target square s/he has to move on. A studentmodeling component retrieves information about player's answers and recognizes his/her possible difficulties performing an error diagnosis. The difficulty level of the operations is adjusted depending on the knowledge level of the student. Moreover, the game provides students additional game lessons to help them outcome their weaknesses. Work in process currently occurs regarding new individual math games containing the operations of multiplication and subtraction as well. The multiple games will be connected to an already implemented and expandable educational game architecture, which can host several games of various domains and subjects. The main target is to take advantage of the adaptive characteristics of several math mini games, including snake, in order to help students practice in arithmetic operations in an enjoyable way. [3] [4] REFERENCES [1] [2] M. Virvou, C. Manos, G. Katsionis and K. Tourtoglou, “VR-ENGAGE: A Virtual Reality Educational Game that Incorporates Intelligence”. S. Mysirlaki, F. Paraskeva, "Digital games: Developing the issues of socio-cognitive learning theory in an attempt to shift an entertainment gadget to an educational tool", Digital Game and Intelligent Toy Enhanced Learning, 2007. DIGITEL '07. The First IEEE International Workshop on, 2007, pp. 147-151. [5] [6] [7] M. Demirbileka, S. L. Tamer, "Math teachers’ perspectives on using educational computer games in math education", Procedia Social and Behavioral Sciences 9 (2010) 709–716. S. Cotua, S. Aydınb, M. Filiza, "Students' conceptions about browsergame-based learning in mathematics education: TTNetvitamin case", World Conference on Educational Sciences 2009. S. Najdi, R.E. Sheikh, "Educational games: do they make a difference?", Procedia - Social and Behavioral Sciences 47 (2012) 48 – 51. N. Peirce, O. Conlan, V. Wade, "Adaptive Educational Games: Providing Non-invasive Personalised Learning Experiences", Digital Games and Intelligent Toys Based Education, 2008 Second IEEE International Conference. I. Polycarpou, J. Krause, C. Rader, C. Kembel, C. Poupore, E. Chiu, "Math-City: an educational game for K-12 mathematics", WCLTA 2010, Procedia Social and Behavioral Sciences 9 (2010) 845–850.