Multiple-Representation Online Learning System that ...

Session F2G

Multiple-Representation Online Learning System that Incorporates the Game of Monopoly 1

Yuan-Chen Liu1, Kuo-Tai Tang2, Tzu-Hua Huang3, Yi-Chun Chien4, Sue-Chun Chen5

Department of Computer Science, National Taipei University of Education, Taipei, Taiwan 106 [email protected] 2 Department of Management Information System, National Chengchi University, Taipei, Taiwan 116 [email protected] 3 Graduate School of Curriculum and Instruction, National Taipei University of Education, Taipei, Taiwan 106 [email protected] 4 Graduate School of Mathematics Education, National Taipei University of Education, Taipei, Taiwan 106 [email protected] 5 Graduate School of Educational Communications and Technology, National Taipei University of Education, Taipei, Taiwan 106 [email protected]

Abstract - Representation refers to “the process in which an external substance is represented by a more abstract or symbolized approach.” Representation conversion ability is one of the important factors that affect mathematic learning and problem-solving performance. Intensification or rectification of these abilities helps students acquire basic mathematic concepts. In other word, when a student is able to express the same mathematic concept through various representation forms or to freely convert the same representation into different forms, it means the student has thoroughly understood the mathematic concept. Therefore, the main purpose of this study is to develop a gaming learning system and explore students’ learning interest and condition after they use the system. The game is played after the manner of Monopoly. The target place is determined randomly by the point of the dice. When the student gets to the target place, the system will guide the student into different test screens. The feature of this gaming learning system is that it integrates multiple representations and cooperative learning. The system selects equivalent fractions as test units. The test screen divides the window of the same test group into 2 sub-screens and presents the same fraction question through different iconic representations. During the test, students are allowed to discuss with one another and observe team members’ answers. After an answer is given, the system will immediately give feedbacks via symbols or word representations. Research outcomes indicate over 80% of the students give positive evaluation of the system’s operational method and screen presentation. They also believe the system can significantly enhance students’ learning interest. Most students are willing to continue to play this kind of game after school. In other word, they are not against practicing through this gaming learning system during after-school hours. INTRODUCTION Mathematic understanding is about acquisition of a powerful representation system that has the flexibility to utilize multiple representations in order to engage in effective mathematic thinking and communicate with others [1]. Outcomes of numerous studies indicate representation has

diverse forms. Representation conversion ability is one of the important factors that affect mathematic learning and problem-solving performance. Intensification or rectification of these abilities helps students acquire basic mathematic concepts [2]-[3]. When a student is able to express the same mathematic concept through various representation forms or to freely convert the same representation into different forms, it means the student has thoroughly understood the mathematic concept. Representation conversion, therefore, is very significant in mathematic thinking. Shui [4] in his study indicates many have mistakenly believe that as long as the teacher divides his students into a few groups, let them discuss together and have them share their findings on the platform, it would be considered cooperative learning. As a matter of fact, this kind of grouping approach can be easily reduced to mere formality in which more capable students are often given heavier workload and less capable students often become wallpapers. Due to the fact students of the same team receive the same grade for the same question, poor planning may easily turn cooperation into copying. In response to the concern, this study incorporates the diversity of representations to expose students to different representation patterns. In other word, students are given the same question that their team members receive, but the question is presented through different image representation types in terms of symbols or words. According to Lin Yen-Hong [5], at a time of rapid development of multimedia technology, representation or conversion of these concepts can be done through many tools (various soft-/hardware packages). The study of Lesh [3] reveals that representations rendered by the computer can be observed and constructed by students and vested with representative meaning in order to demonstrate a more intense power of representation. Through the vb.net program this study designs a gaming learning system to display multiple representations of fraction. Thereby students receive assistance for development of accurate fraction concepts. Multiple representations ensure real responsibility sharing and real cooperation of group learning in order to attain the goal of learning. This is the primary direction of this study. In order to diversify cooperation approach, this study develops single-unit version and network cooperation version. The objectives of this study are as follows:

1-4244-1084-3/07/$25.00 ©2007 IEEE October 10 – 13, 2007, Milwaukee, WI 37th ASEE/IEEE Frontiers in Education Conference F2G-5

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To construct single-unit cooperation and network cooperation online game-aided learning system in which multiple representations are employed in the game of cooperative learning. To explore system interface satisfaction, learning interest and cooperation of the fourth graders who have experience with the network cooperation online game-aided learning system. LITERATURE REVIEW

I. Multiple Representations of Decimals In mathematic education, representation is a fairly important concept. From different perspectives, scholars define “representation” differently. In general psychology, representation refers to “the process in which an external substance is represented by a more abstract or symbolized approach.” In information processing of cognitive psychology, it refers to “the course of information processing through which the information is coded and translated into another format for storage and presentation” [6]. Lesh et al. interpret the meaning of representation as “(observable) external realization of internal conceptualization.” So the meaning of “representation” is: A matter that exists in the heart in different forms such as figure, table, symbol, mental image, icon and example. Jiang [8] believes representation involves re-presentation of a matter or thought via certain form (physical or psychological) in order to attain the goal of communication. Representation is a cognitive structure constructed by the problem solver according to his interpretation of the question based on question-related knowledge. Therefore, the existence of a question can be represented in different forms via many meaningful methods [9], [10]. A translation approach formed according to personal understanding of fraction concept, fraction representation is used to help with thinking, communication and problem solving. Fraction representation, therefore, can be deemed expression of the thinking process of fraction representation and presentation of the outcome. It is a way to communicate with others. In elementary fraction curriculum, there are 3 frequently used representation models [11]: Area model, such as round fraction board, origami, geometry board; Linear model, such as fraction stripe, Cuisenaire, number line; Discrete model, such as plastic petal, apple, candy. In order to approximate elementary fraction courses, the questions of this system are presented through 3 image representation models – area, linear and discrete – in turn. Two students are assigned to a group, and the window is divided into the upper and lower portions – for each to receive the same question after different image representation models. Representation is a form of re-presentation of a matter or thought for the purpose of communication. When the meaning it represents is understood correctly, it can become an application and thinking material. Stephen & Mourat [12] believes representation permits individual pursuit of the outcome instantly because external representation can realize the significant relations expressed through the world of data or word in order to alleviate individual cognitive burden and give individuals more materials to work on a question. In the

face of problems, the use of representation gives students another alternative to consider the problems. Through various representations, this study helps students understand the abstract concept of “fraction.” The questions are presented through symbolic or word representations along with different image representations in order to help students make up for the representative ability they lack via another representation approach. II. Cooperative Learning Cooperative learning refers to forming a group with 2 or more people for participation in an activity in which group members must attain their common goal through coordination or communication [14]. Cooperative learning is learning method in which participating students assist on another. The teacher returns the learning responsibility to the students to give them more opportunities of class participation and intensify their learning interesting transforming them form passive knowledge recipients to active knowledge seekers. For teachers, the arrangement relieves them from the monotony of one-way lecturing and affords them the joy of interactive education [13]. According to the theoretic basis, social background, group structure, cooperative style and academic discipline, cooperative learning may involve different methods. In their study Huang Jheng-Jie and Lin Pei Shuen [15] identify more frequently employed cooperative learning models including Learning Together, Student Teams-Achievement Divisions, Teams-Games-Tournaments and Group Investigation. Development of information and network technology makes it possible for cooperative learning to accomplish the mission through computer network. This approach is normally termed computer supported cooperative learning (CSCL). Chong [16] defines “computerized cooperative learning” as a group of students discuss the learning material together and communicate with one another under the guidance of the computer and engage in learning activities in the atmosphere of mutual assistance and collaboration. Khan [17] defines network education as that which involves design of the teaching content via hypermedia and establishment of a very meaningful teaching environment through the attributes and resources of the Internet. The purpose is to help students develop the ability to engage in independent, self-motivated and continuous learning activities. Khan [17] identifies the major features of WBI including: interactive, multimedia, open system, online search, globalization for easy storage, globally applied standard, provision of Internet resources, diverse expert knowledge, electronic publication, control of learners. Secondary characteristics include: convenience, easy to use, online function support, substantiality, curricular safety, friendly environment, cost benefit, course content that can be easily developed, group learning, online evaluation, virtual culture. The primary characteristics have to be incorporated into the instruction design of WBI before the secondary can surface. The WBI environment must meet the following requirements [18]: y y

Incorporation of various audio-visual media, which is capable of generating deep impressions to help with memory and understanding. Web-based learning provides a non-coercive, more

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flexible learning environment that allows synchronous and asynchronous interactive education and mutual cooperation or group discussion. Internet search engines can be utilized to look for and download data for enhancing the learning content. Utilization of computer tools facilitates data collection, organization, modification and analysis.

III. Gaming Computer Assisted Learning Wu [19] defines computer games as “game software that can be played on the computer for recreational and educational purposes.” The so-called gaming CAI and educational game are in essence a type of CAI discs. They were originally educational-function-oriented materials, but are designed as recreational and educational software for the purpose of integrating entertainment in education [20]. Many educationists study all kinds of learning theories only to realize in the end that no matter how good they are teaching materials or teaching methods alone cannot allow children to learn happily in games. Gaming CAI is a product that incorporates the gaming theory and CAI technology. In-depth analysis of computer games reveals that its most fascinating characteristics are as follows: It has a goal; the score is recorded; it comes with sound effect; random production. Jhuang [21] in his study discovers: Among the systems that incorporate learning and compute games (1) most have stopped at the CBI (Computer-Based Instruction) stage; only a small portion is structured on the basis of WBI (Web-Based Instruction); (2) the interaction of most systems is between the learner and the computer with information feedback from the virtual learning companion (or teacher); it is in essence an individual learning approach that lacks real interaction between the learners; (3) the interactive modes provided by a few systems are competitive social interactions that lack benevolent cooperative social interactions. Therefore, this study adopts the WBI cooperative approach. Through the network students can communicate with one another and are no longer limited to interaction with the computer. Cooperative social interactions become a reality via questions of different representations. SYSTEM ANALYSIS I. System Framework The master-servant framework normally divides the application program and operational system into several components: client end, server end and databank. The only thing stored in the user’s computer is the client end program. Most of the remaining programs are stored in the network server and databank. The client end, server and databank may be kept in different networks. For example, the client end may be located in the company’s LAN; the server and databank may be situated in the Internet or in another company’s LAN. These separated networks are linked by the WAN. In a least sophisticated situation, the client end, server and databank may be all situated in the same LAN. The master-servant framework offers more flexibility and better system responsibility sharing. The structure of the

master-servant framework is shown in Figure 1: II. System Screen The gaming part consists of 2 main components: the map menu and the test menu. The map menu is the primary menu in the game process while the test menu is closed immediately after each test is completed and reopened prior to the next test. So the test questions introduced each time are all different. The gaming processes of the single-unit version and network cooperation version are largely the same. The single-unit version assigns 2 persons to a computer; the network cooperation version assigns 1 person to each computer. Therefore, the map menu of the network cooperation version includes something that the map menu of the single-unit version does not have: dice rolling and packet transmission of the walk. The game screens are shown in Figure 2, Figure 3 and Figure 4. The network cooperation version is the expansion of the single-unit version. The network cooperation version requires 1 computer for each student. So logon time of team members will not be the same, and a waiting mechanism is needed. In other word, the greatest discrepancy between the two lies in the fact that logon to the network cooperation version entails transmission of the packet to the server for the server to notify the team members. RESEARCH OUTCOMES Filling out of the learning survey form involves 3 categories: system interface, learning interest and cooperation. The calculation is based on “very agreeable” (5 points), “agreeable” (4 points), “no comment (3 points), “disagreeable” (2 points) and “very disagreeable” (1 point). Each category includes 5 questions. From the table of System Interface Use Survey Statistics below we learn that over 80% of the students respond positively to the operational method and screen display of the system. Especially noteworthy is that over 90% of the students are either very agreeable or agreeable with the game screen. Over 81.2% of the students feel that the game operation is simple and that the game rule is easy to understand (Table 1). From the table of Cooperation Survey Statistics below we learn that over 59% of the students care about the score of the team. Over 84% of the students indicate they care about how their team members answer the questions. Therefore, the impact of this game seems to be more significant on interaction between students than on the score. The outcome is shown in Table 3. Statistical analysis of various dimensions of the learning survey form shows students respond highly positively to the gaming learning in terms of system interface, learning interest and cooperation. In other word, students do not reject the idea of utilizing gaming learning during after-school hours. We are convinced that a perfected, more lively gaming learning system can be very attractive to students. In the future we perhaps can make students more willing to practice repeatedly through gaming approaches.

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Session F2G CONCLUSIONS AND RECOMMENDATIONS The primary purpose of this study is to construct a single-unit and CSCL online game-aided learning system that is fascinating to students. Multiple representations are employed for the cooperative learning of this game while system achievement is not the concern of this study. Following the experiment, students fill out the learning survey form in order for the researcher to understand their need and degree of satisfaction, which will serve as the basis for designing similar game systems in the future. Research outcomes show that most students love the game screen of this gaming system and are willing to utilize this system after school, and that there is no significant discrepancy between the high-achieving group and the low-achieving group in terms of the degree of fondness. The gaming system, therefore, is supposed to have positive impact on most students’ learning interest. Yet, instructions are required to help students understand how the game is played. It is worth mention that most students desire to know where the mistake is when they give a wrong answer. Real-time feedback therefore is very important and indispensable. If it can be done in an interactive way, or students can receive individualized assistance via the feedback, it will help students more with their meta cognition. So system design cannot do away with the real-time feedback mechanism, which instead should be intensified or equipped with more details. REFERENCES [1]

[2]

[3]

[4]

[5]

Yu Tze-Da (1995), Connotation of Mathematic Learning and Comprehension – Analysis from the Perspective of Psychology, National Taichung University Graduate School of Elementary Education Symposium of Elementary Education Studies, 3, 31-45. Lesh, R. (1979). Mathematical Learning Disabilities: Considerations for Identification, Diagnosis, Remediation. In Lesh, R., Mierkiewicz, D., & Kantowski, M. (Eds.), Applied Mathematical Problem Solving (pp.111-180). Columbu: ERIC/SMEAC. Lesh, R., Post, T. & Behr, M. (1987). Representations and translations among representation in mathematics learning and problem solving. In C. Janvier (Ed.).Problems of representation in the teaching and learning of mathematics (pp.33-40). NJ: Lawrence Erlbaum. Shui Wei-Jheng (2002), Design and Development of Collaborative Joint Note-Tanking Learning System, National Taipei University of Education Graduate School of Educational Communications and Technology master’s thesis. Lin Yen-Hong (2002), Diagnosis of Fifth Graders’ Fraction

Fig.1 Master-Servant Framework

[6] [7]

[8]

[9]

[10]

[11] [12]

[13]

[14]

[15] [16]

[17] [18] [19] [20]

[21]

Concept and Remedial Education, National University of Tainan master’s thesis. Chang Chun-Hsing (1998), Education Psychology, Taipei: Dong Hua. Lesh, R. (1987).The Evolution of Problem Representation in the Presence of Powerful Conceptual Amplifiers. Problems of Representation in the Teaching and Learning of Mathematics. NJ: Lawrence Erlbaum. Jiang Chi-Bang (1994), Exploration of the Design of Number and Calculation Activity of New Teaching Materials from the Perspective of Representation, compiled by Taiwan Province Elementary School Teacher’s Workshop Association: Introduction to New Elementary School Mathematic Curriculum (Junior Classes) (pp.60-76). Taipei: Taiwan Province Elementary School Teacher’s Workshop Association. Yang Rei-Jhi (1994), Mathematic Problem-Solving Thinking Process of Fifth and Sixth Graders of Different Abilities, National Taiwan Normal University Graduate School of Science Education doctorate dissertation. Yeh An-Chi (2000), Case Study Pertaining to Enhancement of Elementary Student’s Creative Problem Solving Ability – Development of Problem Representation, National Kaohsiung Normal University Graduate School of Science Education master’s thesis. Watanabe, T. (2002). Representations in Teaching and Learning Fractions. Teaching Children Mathematics, 8(8), 457-463. Stephen, J.＆ Mourat A.(2001).The role of representation(s) in developing mathematical understanding. Theory Into Practice, 40(2),118-125. Huang Chien-Yu (1999), Junior High Physics and Chemistry Teacher’s Tentative Implementation of Cooperative Learning, National Kaohsiung Normal University Graduate School of Science Education master’s thesis. Wang Dai-Yi (2002), Achievement of Animation-Webpage-Aided Geometry Learning – Case Study of Sixth Graders’ Prism and Pyramid Units, National Chiao Tung University Graduate Institute of Computer Science master’s thesis. Huang Jheng-Jie and Lin Pei Shuen (1995), Cooperative Learning, Taipei: Wu-Nan. Chong Shu-Chuan (1996), Effect of Mixed-Gender and Mixed-Ability Grouping on Achievement and Attitude of Computer-Aided Cooperative Learning, Journal of Elementary and Secondary Education, 2, 81-105. Khan, B.H.(1998).Web-based instruction: An introduction. Educational Media International, 35(2), 63-71. Wen Ming-Cheng (2000), Exploration of Cross-Century Network Education, Friends of Teachers, 396, 10-16. Wu Tie-Hsiung (1988), Impact of Computer Software Games, The Third Wave, 66, 64-71. Cheng Kai-Yu (2000), Impact of Computer Games on Fourth Grader’s Two-Dimensional Space Concept Development, Chinese Culture University Graduate Institute of Applied Science of Living master’s thesis. Jhuang Shi-Wei (2003), Design of Cooperative and Competitive Model of Online Mathematic Games, National Taipei University of Education Graduate School of Mathematic Educational master’s thesis.

Fig.2 Single-Unit Cooperation Version Test Menu Screen

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Session F2G

Fig.3 Network Cooperation Version Test Menu Screen

Fig.4 Single-Unit Cooperation Version & Network Cooperation Version Map Menu

Questions

Very Agreeable

Agreeable

No Comment

Disagreeab le

Very Disagreeab

Table 1 System Interface Use Survey Statistics No. of Students/Whole Class (%)

(1) Game operation is easy to learn (2) Game rule is easy to understand (3) Following the instruction of the computer, I often run into trouble (4) I am able to understand the meaning of all the questions displayed on the screen (5) I like the game screen very much

50 56.3 3.1

31.3 31.3 18.8

18.8 9.3 53.1

0 3.1 15.6

0 0 9.3

34.4

34.4

25.0

6.3

0

71.8

18.8

9.3

0

0

Questions

Very Agreeable

Agreeable

No Comment

Disagreeab le

Very Disagreeab

Table 2 Learning Interest Survey Statistics No. of Students/Whole Class (%)

(6) I feel time flies when utilizing this online game to study math (7) I feel very happy when utilizing this online game to study math (8) In the next class I am willing to use this game to do math (9) I am are willing to continue to play this kind of game after school if it is available (10) Experience with this online makes me enjoy studying math more

53.1

31.3

12.5

3.1

0

50.0

31.2

12.5

6.3

0

50.0 53.1

34.4 21.9

9.3 21.9

6.3 3.1

0 0

34.4

37.5

21.9

6.3

0

Questions

Very Agreeable

Agreeable

No Comment

Disagreeab le

Very Disagreeab

Table 3 Cooperation Survey Statistics No. of Students/Whole Class (%)

(11) I care about the score of the team (12) I care about whether my team members answer the question correctly (13) Questions of the team members inspire me to think (14) I engage in active discussion with my team members (15) If my answer is wrong, I would like to know where the mistake is

34.4 43.8

25.0 37.5

21.9 18.8

0 0

18.8 0

43.8 34.4 50.0

28.1 37.5 34.4

25.0 21.9 9.3

3.1 6.3 6.3

0 0 0

1-4244-1084-3/07/$25.00 ©2007 IEEE October 10 – 13, 2007, Milwaukee, WI 37th ASEE/IEEE Frontiers in Education Conference F2G-9