Warrick's Secrets: Teaching Middle School Mathematics Through an Internet-based 3D Massively Multiplayer Role Playing Game
Purpose: The project leverages students' fascination with 3D digital entertainment and medieval fantasy stories to teach mathematics to middle school students by situating the mathematics in an appealing computer environment- an Internet-based massively multi-player role-playing game (MMPRPG) called Warrick's Secrets. The development team consists of individuals from the IT industry and researchers from three universities. Warrick's Secrets is the result of a Phase I SBIR completed for the US Department of Education in April 2001. Second stage development is on-going following the September 2001 awarding of a Phase II SBIR by the U.S. Department of Education. An MMPRPG is used to deliver National Council of Teachers of Mathematics (NCTM) Standards-based educational content. The system includes advanced 3D computer rendering capabilities and high quality 3D artwork since both have proven crucial to maintaining players' attention in the gaming community. Background & Theoretical Framework: What are Massively Multi-Player Role Playing Games? Warrick's Secrets is modeled on currently popular MMPRPG's such as, Ultima Online (UO), Everquest, and Microsoft's Asheron's Call (AC). Currently, more than 150,000 customers play Ultima Online- including players from 114 countries. (Walton, 2000). Sony's EverQuest and Microsoft's Asheron's Call both have a larger customer base than UO. A MMPRPG is a game with thousands of players gaming concurrently in real time. Role-playing indicates that a human player controls an in-game character's speech and actions. The virtual world is like the historical middle ages, including some degree of fantastic creatures (e.g., dragons) and magic. Related Research: Areas of mathematics education research for this project are situated perspectives on learning and constructivist views of representation. Mathematics viewed as socially constructed knowledge has strongly influenced other learning theories. Many researchers (Kieren, 2000; Steffe & Thompson, 2000; Sfard, 1998; and Cobb & Yackel, 1996) describe the theoretical underpinnings of their work in terms of "social constructivism." The learning theory that grounds many of these researchers, including those in the present project, may be traced to vonGlasersfeld's (1991) radical constructivism, and Piaget's (1970) genetic epistemology. Lave and Wenger (1991) describe situated learning as developing as a function of the activity, context, and culture in which it occurs. These ideas are important here because we consider how such theories apply to the development of educational interactive multimedia. An example of such multimedia research is the work of Herrington and Oliver (1997). Mathematical representation is considered from a constructivist perspective. Representation describes the form in which a problem is encountered- such as graphical, numerical, verbal, or symbolic representations. It also describes the learner's mental construct of the problem. One of the major advantages of the virtual environment for problem solving is that students have many opportunities to attempt solutions of mathematical tasks. This may increase the number and quality of the mental representations that the students apply to the problems. The project relied on the research of Cifarelli (1988) and Goodson-Espy (1994, 1998) to use the notion of reflective abstraction to explain how, as students work through multiple attempts to solve a problem, they may develop progressively more abstract mathematical conceptions. It has been observed that if students cope with recurrent mathematical themes, they are more likely to develop higher levels of reflective abstraction, and thus attain more powerful mathematical concepts. Methods: Subjects: The subjects included seven students from a middle school in the southern US. The subjects included two sixth graders, two seventh graders, two eighth graders, and one ninth grader. The subjects included one African-American, six Caucasians, four males, and three females. Data Sources and Analysis Method: The prototype testing took place at school on April 6, 2001. The individual sessions each lasted between 45-60 minutes. Students attempted all the problem scenarios and completed a questionnaire and participated in a concluding interview. Students were given a pen, paper, and a calculator. The problem set included two problem paths- an initial problem path dealing with percent and a second developing a series of questions about mixture problems. The data sources for the pilot study include: (1) videotapes and transcripts of the prototype testing sessions, (2) student written artifacts, (3) completed questionnaires, (4) observational field notes, and (5) researcher notes from the post-game interviews. Analysis of these data resulted in seven case studies. Results: The results of the game prototype testing include three parts: (1) a summary of student reactions, (2) the questionnaire results, and (3) seven case studies. Only brief excerpts of the results will be discussed below. Summary of Results: · All subjects expressed increased interest in working on mathematics problems that were situated in a computer gaming environment. · All subjects reported some level of self-confidence in solving mathematics problems but expressed less self-confidence in terms of solving word problems in a classic classroom or textbook setting. · One of the students specifically stated that he liked the graphics quality of that characters and that the quality was much higher than those of characters in computer game he had at home. · Several of the students indicated that they enjoyed being an active character in the game and that this improved their ability to interact with the mathematics. Students wanted to control the character's gender, skin color, clothing, ethnicity, character name, and skills. · All students indicated that they clearly understood what the problems were asking them to do. Students indicated that it was easier to solve the problems because the in-game flasks were displayed with measurement calibrations visible. Another student made a similar comment about the collection bins used to represent the percentage problems. The students liked the visual representations of the problems. All of the students attempted all of the problem scenarios. Two of the subjects were able to solve all of the problems on the first try. Three of the subjects were able to solve all but one of the problems on the first atempt. · All of the subjects were able to attain the levels of reflective abstraction: Recognition and Representation in their problem-solving activities. Three of the subjects were able to attain the level of Structural Abstraction. Three of the students were able to complete the second problem pathway by building on their solution strategies for the previous problems. The relationships between reflective abstraction and problem-solving will be expressed in the full paper. Conclusions and Future Directions: Student Enthusiasm for this Genre: The favorite adjective used by the students to describe the game was, "Cool!" The students explained that the game made learning math easier for them because it placed the mathematics into a meaningful context for them. The students indicated that they were motivated to solve problems because they wanted to find out what would happen next in the game or because they wanted to gain access to the next magical tool that was described in the story. Character Creation and Communication: The students made numerous positive comments about the faces, clothes, and details such as being able to see the characters breathe. The students were intrigued by the ability to assume the role of a character in the game. They were greatly attracted by maneuvering their character arbitrarily in the virtual world. Students wanted to be able to choose gender, race, clothing, facial appearance, and other attributes of their character, including the character's name. This is a standard option in most MMPRPG's. Interactivity In The Game: The students were universally interested in gaining character mobility in the virtual world. They were fascinated by character head motion, lateral motion, climbing stairs, walking underwater, etc. Most of the students wanted to wander about in the game world before beginning the problem sequence. This activity allowed us to gain valuable data about the ease of character controls. Interactivity with objects in the game environment is a crucial factor in gaining and maintaining student interest. Problem Pathways: The students indicated that they found the collection bin representation for the initial percent problems to be very helpful in solving these problems. The students were very emphatic that the visual representations were extremely useful to them. The students' interactions with the flasks in the laboratory appear to have influenced their problem-solving success with the mixture-related problems. Based on the researchers' experiences in teaching very similar problems to college-aged students in traditional college algebra classes, the success rates of the middle school students on these problems were much higher. In the videotapes and post-session interviews, the students indicated that the visual nature of the representations were also useful in reducing their anxieties about this type of question. The students positively evaluated the hints that were provided for each task. Because of the visual representations of the problems and the scaffolded hints that could be accessed, students were more willing to attempt what they considered to be difficult problems. The students problem solving activities and successes indicate that carefully crafted problem pathways can be a successful teaching tool to assist students in making necessary conceptual connections via reflective abstraction. References Brown, Collins & Duguid (1989). Situated cognition and the culture of learning. Educational Researcher, 18 (1), 32-42. Cifarelli, V. V. (1988). The role of abstraction as a learning process in mathematical problem solving. Doctoral dissertation, Purdue University, Indiana. Cobb, P. & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31, 175-190. Goodson-Espy, T. (1994). A constructivist model of the transition from arithmetic to algebra: Problem solving in the context of linear inequality. Doctoral dissertation, George Peabody College of Vanderbilt University. Dissertation Abstracts International, 55, 34439. Goodson-Espy, T. (1998). The roles of reification and reflective abstraction in the development of abstract thought: Transitions from arithmetic to algebra. Educational Studies in Mathematics, 36, 219-245. Herrington, J. & Oliver, R. (1997). Multimedia, magic, and the way students respond to a situated learning environment. Australian Journal of Educational Technology, 13 (2), 127-143. Hershkowitz, R., Schwarz, B., & Dreyfus, T. (2001). Abstraction in Context: Epistemic Actions. Journal for Research in Mathematics Education, 32 (2), 195-222. Kieren, T. (2000). Dichotomies or binoculars: Reflections on the papers by Steffe and Thompson and by Lerman. Journal for Research in Mathematics Education, 31 (2), 228-233. Lave, J. (1988). Cognition in Practice: Mind, mathematics, and culture in everyday life. Cambridge, UK: Cambridge University Press. Lave, J. & Wenger, E. (1991). Situated Learning: Legitimate Peripheral Participation. Cambridge, UK: Cambridge University Press. National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics 2000. Reston, VA. Piaget, J. (1970). Genetic epistemology. (E. Duckworth, Trans.) New York: Columbia University Press. Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27 (2), 4-13. Sfard, A. (1994). The gains and pitfalls of reification- The case of algebra. Educational Studies in Mathematics, 26, 191-228. Steffe, L.P. & Thompson, P. (2000). Interaction or intersubjectivity? A reply to Lerman. Journal for Research in Mathematics Education, 31 (2), 191-209. von Glasersfeld, E. (1991). Abstraction, re-presentation, and reflection. In L. Steffe (Ed.), Epistemological Foundations of Mathematical Experience (pp.45-69). New York: Springer Verlag. Vygotsky, L. (1986). Thought and language. (E. Hanfmann & G. Vakar, Eds. and Trans.) Cambridge, MA: MIT Press (Original work published 1934). Walton, J. (2000). Physitron, Inc. Internal Market Data Report.