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Article Excerpt
Many students enter mathematics courses with a poor attitude toward mathematics (Gal & Ginsburg, 1994), making attitude as important a consideration as achievement in mathematics (Cognition and Technology Group at Vanderbilt (CTGV), 1992; Marsh, Cairns, Relich, Barnes, & Debus, 1984; Sedighian & Sedighian, 1996). Pedagogical agents are often touted for their ability to address affective variables in learning (Moreno, Mayer, Spires, & Lester, 2001; Baylor, 2000), as are games for both attitude and achievement (Baltra, 1990; Fery & Ponserre, 2001; Kent, 1999). However, few studies have examined the effect of combining agents and games, and none has examined their effect on attitude toward mathematics. This study was designed to determine the effect of contextual pedagogical advisement (CPA) and competition on attitude toward mathematics in a computer-based simulation game. A total of 123 seventh- and eighth-grade students were randomly assigned to one of five conditions formed by crossing the two independent variables and adding a control group. Results indicate that contextual pedagogical advisement can result in lower anxiety toward mathematics scores, especially under competitive conditions.
LITERATURE REVIEW
Attitude Toward Mathematics
Many researchers posit that learners' attitudes and beliefs toward subject matter, especially mathematics, are as important as achievement (Cognition and Technology Group at Vanderbilt (CTGV), 1992; Lent, Brown, & Larkin, 1984; Marsh, Cairns, Relich, Barnes, & Debus, 1984; Sedighian & Sedighian, 1996). With mathematics in particular, this linking of attitudes, motivation, and beliefs to achievement can be of particular importance because many researchers report students have a poor attitude toward mathematics when they enter mathematics-related courses (Gal & Ginsburg, 1994).
Performance in mathematical problem solving is also related to beliefs about mathematics (Schoenfeld, 1983, 1985), and attitude toward mathematics can determine the likelihood of continued study and perseverance (Lehman, 1987). Conversely, poor attitude toward content can result in poor learning and performance in mathematics areas (Barling & Beattie, 1983; Gal & Ginsburg, 1994; Kraiger, Ford, & Salas 1993; Stumpf, Brief, & Hart-man, 1987). Attitudes, therefore, perhaps especially in mathematics, are important considerations in learning.
GAMING AND ATTITUDE TOWARD MATHEMATICS
A review of the literature lends support to their claim that games are good for improving or ameliorating the negative effects of attitude and motivation (Druckman, 1995). A review by VanSickle (1986) looked at 42 studies of simulation games and found an effect size of .16 for attitude toward subject matter in favor of gaming versus other forms in half of the studies. A meta-analysis of 21 simulation games showed a significant increase in attitude toward subject matter and toward instruction at the p = .01 level when compared to control groups, (Remmer & Jernstedt, 1982). Other research has also shown that attitude toward content can be influenced by using games (Barak, Engle, Katzir, and Fisher, 1987; Malouf, 1988; Pascale, 1974). This positive effect of games on attitude has been shown for mathematics in particular (Sedighian & Sedighian, 1996; Pascale, 1974), leading researchers to argue for their use in this area. According to the National Council of Teachers of Mathematics, (as cited in Bright, Harvey, & Wheeler, 1985), mathematics games may be the best way to ensure that students get the basic mathematics skills they need to be successful in life, while at the same time promoting an enjoyment of mathematics and motivation to learn mathematics. Heyman (1982) agrees: "Simulation games contribute to young people's learning in the affective domain" (p. 4), and the incorporation of game-like features and simulation elements can promote motivation to learn (Brophy, 1987).
Seginer (1980) further argues that gaming may not be as affected by the learner's sense of confidence and control as traditional instruction is. This implies that learners with poor self-efficacy or attitudes toward the content (as is often the case with mathematics) may do better under game-based instruction than under traditional instruction.
However, the literature is unclear on just what conditions or aspects of games are key to promoting positive attitudes toward the content or for ameliorating the effects of negative attitudes toward the content. The key may lie in Malone and Lepper's (1987) theory of intrinsic motivation in games. Intrinsic motivation (motivation that stems from internal events such as goals or affective responses rather than from external events such as rewards) is promoted by four factors: creating a sense of challenge and accomplishment, promoting curiosity, encouraging a sense of personal control, and making use of endogenous fantasy elements.
The extent to which a game attends to these four factors is, they argue, directly related to whether the game is intrinsically motivating. By extension, learning games that attend to these four factors will be more intrinsically motivating than those that do not. It is logical to conclude therefore, that if we want to use learning games to promote positive attitudes toward content such as mathematics, we should attend to these four elements.
One aspect in particular, the role of endogenous vs. exogenous fantasy, may hold particular relevance in this regard. When attempting to design instructional games, designers often struggle to integrate the content with the game because content in curriculum is often separate from authentic contexts. This can lead to edutainment titles that are examples of what Seymore Papert calls a Shavian Reversal, which is a genetics term referring to a situation where the offspring inherits the worst characteristics of both parents.
Specifically, games should strive to keep content and fantasy elements endogenous (contextually related) to the game. For instance, a game in which the instructional content does not make use of the endogenous fantasy elements of the game (e.g., an embedded tutorial that is minimally tied to the game world) is less likely to affect attitude toward the content. To that end, designers should find ways to integrate the content within the game world. By extension, then, it may also be the case that advisement should be endogenous to the game. Because pedagogical agents can take on roles that are endogenous to the game fantasy world, they may be an ideal way of integrating content and advisement.
One of the purposes of this study was to examine the role of a computer-based game on attitude toward the content (i.e., mathematics). Specifically, it was hypothesized that a game in which the content and the advisement were endogenous to the fantasy of the game would lead to improved attitude toward mathematics.
Competition
While many posit that games are motivational, the role of competition, often a part of games, is less clear. According to Klein, Freitag, and Wolf (1990), "[some] educators argue that instructional games are effective for providing motivating practice of newly acquired skills and information.... Other scholars argue that the competition element decreases student motivation" (p. 330). Competition does not function identically in all situations, however.
For instance, for competition to promote motivation, performance, and learning, students must perform at less than their maximum level of performance in noncompetitive conditions. While this may often be true, it also follows that if students are already at a maximum for other reasons (such as extrinsic or intrinsic motivation/reward/punishment), then competition is less likely to produce large improvement (Thompson, 1972). Competition alone cannot make learners function beyond their maximum ability unless they have help, such as a coach, mentor, or advisor.
This phenomenon, which is similar to Vygotsky's (1978) scaffolding approach to learning, would lead us to conclude that competition, or challenge, as Malone might call it, should be just advanced enough to create the sense of an "uncertain outcome" (Malone, 1981) but not so much that the learners begin to doubt they can accomplish the goal.
The connection between attitude and performance under competitive and noncompetitive conditions has been found in several studies. Atkinson and O'Connor (1963) found that homogenous ability classes showed improvement under competition (all students were of the same ability) but only among those highly motivated to succeed with low anxiety about failure. Success in team-based mathematics competitions is most likely to be attributed to the motivation or attitude of the student and sponsor (of the team) (Spalt, 1988).
Some of the research on attitude and competition has supported the notion that competition can lead to positive attitudes and affective responses. Competition in academic games can promote interest and learning (Jacobs & Dempsey, 1993; Dempsey, Lucassen, Gilley, & Rasmussen, 1993). Other research indicates that competition can lead to negative attitudes and affective responses. Those who are not good at content, or who cannot beat other players with faster reaction times may consistently "lose," leading to disaffection. Competition can also cause stress, which may interfere with learning (Lancaster, 1988), which can then result in confounding emotional responses (Brown, 1989) and reduce intrinsic motivation (when exogenous, like scores).
One theory, achievement goal theory, may also shed light on the role of competition. This social-cognitive theory of motivation (Ames, 1984; Dweck & Elliott, 1983; Maehr, 1984; Nicholls, 1984), contends that the type of goal adopted by learners during a learning task can influence performance and motivation. According to Urdan and Maehr (1995), there are three basic kinds of goals that can be adopted by learners. Performance goals are goals that focus on how the learner's performance compares to others. Mastery goals focus on mastering the content to be learned. Social goals often focus on extrinsic rewards such as social standing or approval.
The type of goal adopted by the learner has been shown to impact motivation and performance in mathematics. Wolters, Yu, and Pintrich (1996) conducted a study of these three different goals on motivation, self-regulation, and performance. Among their findings was that those who adopted performance goals had more positive outcomes on all three areas (motivation, cognition, and performance). When the competitive element in a game is between learners, a learner and perceived peers, or the learner and a social agent (a computer-generated character, for instance), then one might see that this finding could explain...
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