Virtual Chichen Itzá

Transcription

1 Virtual Chichen Itzá Francisco Madera Ramírez 1 and Rocío Uicab Ballote 1 and Luis Basto Díaz 1 Universidad Autónoma de Yucatán Facultad de Matemáticas, Periférico Norte Tablaje 13615, Apartado Postal 172, Cordemex, C.P , Mérida, Yucatán, México 1 mramirez@uady.mx, 2 uballote@uady.mx, 3 luis.basto@uady.mx Abstract. We describe the design and development of an educational videogame to assist in the learning of mathematics fractions. Using didactic activities designed to help the understanding concept of the fraction, a videogame was elaborated regarding the primary level, children of 9-10 years old. Didactical challenges were transformed into 3D graphics of non photorealistic rendering to effectively cause fun and learning. This paper highlights key aspects of the design that we believe contributed towards making the game fun as well as educational. Keywords: 3D Game, Edutainment, Educational Games, Graphics Games. 1 Introduction The development of a computer game is widely used as a way of conveying mathematic concepts. There are several reasons for this: it stimulates creativity, it provides an immediate sense of achievement, it typically covers all the aspects of a course, and it is easy to find ideas by looking around and finding stimulation from one's environment and from students. Fun is quite often the very evidence of learning. The game becomes a formal system of challenges to stretch the brain, coupled with rewards to encourage the player to seek out the next learning high. In this sense, all games are educational, but certainly a game must teach a player how to play the game. The study of the fractions starts in the primary level when children have learned natural numbers. In this new numerical system, fractions or rational numbers, children should face new kind of problems such as the numbers are not in sequence, multiplication is not always possible to express as a summation, and the product is not always greater than its factors. In this work, we explore how to transform the concept of a fraction in a virtual 3D representation that causes entertaining, engaging, and motivating to the students. This paper proposes a method for game design that can enhance the strengths and reduce the weaknesses of informant design through its focus on the development. The paper proceeds as follows: Section 2 describes the related work about the videogames in the mathematics learning process, Section 3 gives a general description of the videogame concept. The avatar's actions are implemented in Section 4. In Section 5, we describe the challenges in detail, pointing out about the animation issues

2 considered to adjust the didactics to the scene. Conclusions and further work are presented in Section 6. 2 Related Work A lot of work has been done in the field of the educational videogames development, taking in mind the benefits of the learning process while playing. In the field of mathematics there have been some efforts to assist the learning: Mathemagic [1], ratio and proportion [2], fractions [3]. These games are really interesting and simple, there were implemented in 2D and utilise the basic principles of the concept they want to teach to. In [4], a didactic analysis of a variety of software applications is made, which basically consists of identify the mathematical objects (fractions, percentages, decimals) that can be employed in games. The analysis and design of the mathematical learning process must be dedicated as an essential role to the conceptualization moment, that is, moments in which the use of terms to identify operational invariants and the rules interpretation are fixed. In [5], several topics related to the use of videogames in education are discussed. The first part analyses the importance of the computers in schools, in particular primary and secondary levels. The second part makes the difference between the focuses of the videogames: entertainment or teaching. There are some design factors to maintain the player's interest: engaging narrative, easy learning curve, interactions, intuitive interface, and a logical feedback loop. 3 Game Concept The topic of fraction was determined with the results obtained in [6] and the surveys applied to teachers and students of some primary schools in Mexico. Basically, we identify preferences about videogames and specific math's topics which are difficult to learn. The information obtained reports that the interests of the students in year four, five and six, lies in action games such as Guitar Hero and Mario Bross. On the other hand, the most difficult topics to learn are divisions, fractions and problem arrangement. The best way to create challenge is to provide clear goals whose attainment is uncertain [7]. If the goal is unclear, the player will become frustrated. If the goal is too easy to attain, the player will become bored. Furthermore, if the goal is long range, there should be feedback given to the player that communicates progress towards the goal. This project aims to a develop didactic videogame oriented to the knowledge of the mayan culture in the southeast part of México. We chose Chichen Itzá, located in the Yucatán Peninsula, where the mayan culture had a great development in the ancient times. The videogame, illustrated in Fig 1, was developed with XNA and the assets were made with Blender and Gimp.

3 3.1 Learning Objectives We have adjusted the didactic activities in a virtual representation with animation in order to have each student engaged by several features of the same activity. We expect players to: a) Understand how to represent parts of an object by using fractions. b) Learn the different operations between fractions. c) Learn the equivalence between fractions. d) Understand how to manipulate proportions to calculate the result of a problem. Fig. 1. The mayan city of Chichen Itzá. 3.2 Modules The design of the game considers different levels to measure progress and involves 7 main modules depicted in Fig 2. Fig. 2. The modules of the videogame. The avatar module includes the functions to animate and visualize the avatar, the main actor of the game who can be manipulated by the user. The second module, collisions, contains the routines to detect collisions among the avatar and the other objects (temples, cenote, ball, deer, recipient, etc.). The sound module involves the sound effects routines which occurs when the avatar gets an object or achieves a challenge. The messages module interpretates the user progress to display or remove the correct message in the left corner of the screen. The map is a 2D image with a global view of the scene, and shows the avatar's motion by using a yellow point. The logic of the game is a sequential evolution of the challenges, starting with the most basic task, and increasing the cognitive level to help the user/student in the learning of fractions. Regarding the videogame as a didactic resource that provides

4 motivation and encourage to achieve the challenges, our didactic structure takes into account the topic of the fractions in several cognitive levels. The last module, didactic module, specifies the cognitive level to learn fractions, and determines how the task designed is adjusted to the scene. Several expressions are defined as tasks or operations which serve for the game definition. Such expressions are grouped in four areas: discrete approach, continuous approach, product, and proportions. 4 The Avatar s Actions Nine challenges ordered according to the level of difficulty and following the expressions defined. We believe this will provide easy learn and show the student's progress explicitly. In this sense, teachers will be able to test the students progress and apply feedback when required. These nine challenges were the base to game's design. At the start, the avatar plays the ball game and push the ball into the rings the number of times asked. In the second challenge the avatar goes to the 1,000-columns temple to build a column with the size required. Then he will go to the cenote to collect different kinds of flowers asked by the challenge. After that, the avatar should fill a recipient with water with the specified quantity. This recipient will help to the deer who is really thirsty, so that while he drinks water, the user computes the deer's age. In the sixth challenge, the avatar will go to the mango's trees to collect some of them, he has a maya tool called tira hule to get the mangos. Suddenly, the collar appears in front of him. This collar is formed by gems and it is incompleted, for this reason the avatar must determine de number of gems to be collected. Passsing this challenge, the avatar should build a 3x3 magic cube, carrying on some numbers to obtain a sum of such a cube, that is, the sum will be the same for the columns, raws, and diagonal. To meet the princess, the avatar should go to the main castle and catch equivalent blocks to fill the gaps of the stairs. This way he will be able to walk up to the top of the castle. The route of the challenges is illustrated in Fig. 3. The seventh challenge is not connected to the route since gems to be collected are randomly placed in the whole scene. Fig. 3. A top view of the route of the nine challenges.

5 5 The Challeges 5.1 The Ball Game Sum of fractions, result=1: 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1 The scene is a ball rink, where the avatar hits the ball to have it closer to one of the two rings. The aim of this level is to show the user that common actions are represented by fractions. Fig. 4. The first challenge: The Ball Game. 5.2 Building Columns Sum of decimal numbers to form an integer number: = 2. There are five columns labeled with a value, v(), that can be 0.25, 0.50, 0.75, 1.0, 1.25, 1.50 and The goal is to build a 2-size column, taking the first column as a pivot. This means that the sum of the used columns must be v(1). The number of columns to utilise depends on their sizes, that is, the goal could be achieved by using 1, 2, 3, or 4 columns. Fig. 5. The second challenge: Building a Big Column. 5.3 Collecting Flowers Sum of fractions, result<1: 1/6 + 1/6 + 1/6 = 3/6 There are 4 groups of flowers buoying in the natural sink hole. These flowers are coloured as yellow, orange, red and purple. A fraction for each color is required.

6 Fig. 6. The third challenge: Collecting flowers. 5.4 Filling a Recipient Sum of decimal numbers: 3x100 ml + 6x5 ml + 3 x 1 ml = 333 ml A recipient should be filled with the required quantity in milliliters, named m. There are other three recipients of differents sizes which can be utilised to fill with water and therefore to put into the first recipient. Fig. 7. The fourth challenge: Filling a Recipient. 5.5 Computing the deer s age Apply proportions: 15/x = 10/8 The avatar needs to know the deers' age by considering his horn. The deer's horn indicates the age of a deer. A deer of 15 years old has 10 peaks, that means a deer with p peaks is px15/10 years old. Fig. 8. The fifth challenge: Computing the deer's age using the peaks of his horn

7 5.6 Throwing Mangos Product: 20 x ¼ = 5 There are 4 mango trees which the avatar can throw by using a maya tool called resortera. The assignment consists of using the tool to obtain a fraction of the n mangos: m/n. Fig. 9. The sixth challenge: Collecting mangos using a maya tool 5.7 The Gems of the Collar Sum of fractions, substraction: 1- ¾ = ¼ The avatar should find the gems of the collar. The collar is formed by n gems, but actually, there are only p of them. However, the challenge only inform about the fraction of the collar in such a way that the avatar have to determine the number of gems to be found. Fig. 10. The seventh challenge: The gems of the collar 5.8 The Magic cube Sum of fractions, result>1: 3/7 + X + 1/7 = 8/7 X=4/7 There is a set of fractions located in 3 rows and 3 columns, making a square of 3x3. A The sum of the elements of raw i should be E, and the sum of the elements of column j should be E as well. Fig. 11. The eightth challenge: constructing a magic cube, the sum of each raw and the sum of each column are equal.

8 5.9 Walking up to the Castle Equivalence of fractions: ½ = 3/6, ¾=9/12 The avatar walks up to the top of the castle where the princess is waiting for him. The task is not easy since there are some incompleted parts of the stairs which should be filled. An incompleted stair contains an empty room which indicates a fraction to be found with the blocks which are coming down from the top of the casttle. The avatar must catch the right block and put in the empty room. Then, the avatar can walk up again. Fig. 12. The ninth challenge: Finding the equivalent fractions to fill the gaps. 6 Conclusions We have presented MATYA3D, a didactic game-based 3D simulation about the history of the Mayan Culture Ages, that is utilised to learn fractions. We are allowing developers and educators to present material, regardless of domain, and establish methods to measure the efficacy of these new games and tools. Our proposed study on extended gameplay periods can help developers to create a smoother, more even learning curve. It would be possible to design controllable features that relate to the physics of the game (such as gravity and inertia), we plan to apply the videogame in primary schools and make the adjustments required, and finally our framework can be tailored for use as other math educational tool in other topics. References [1] MatheMagic, Playing with Numbers, [2] Ratio and Proportion, [3] Fractions, [4] Examples of business simulations and games developed, facultyresearch/business.htm. [5] British Educational Communications and Technology: Emerging Technologies for Learning. London, UK (2004). [6] A. Del Castillo and M. Villalba and J. Vargas and M. Castro and E. Galindo and M. Urrea, La Enseñanza de las Matemáticas en la Escuela Primaria. Material del diplomado impartido por la Sociedad Matemática Mexicana y la SEP, [7] T. Malone, What makes computers games fun? Byte, vol. 6 pp , 1981.