# Research

Middle school instructional practices often are not developmentally appropriate for young adolescents (Eccles, Wigfield, Midgley, Reuman, MacIver & Feldhaufer, 1993). Students at this age possess the ability to reason, evaluate, and become autonomous. However, many school environments consist primarily of rote learning and other low-level cognitive processes, as well as tightly controlled environments. At the same time, social relationships take on new importance for adolescents, yet many teachers enforce work in isolation (Eccles, et al., 1993). Students will never truly engage in learning if they are not allowed independence in the classroom (Deci, Vallerand, Pelletier, & Ryan, 1991). In response, Fantasy Sports and Mathematics addresses the social and cognitive needs of middle-school students in large part because it is based on a pedagogy that is student-centered. Students work collaboratively in groups to draft players, compute their weekly points, check their peers' answers, and create their graphs. Consequently, students become active learners. This socially interactive classroom approach provides for higher levels of thought processes (Barwell, Leung, Morgan, & Street, 2002). When students are allowed to work in small groups, student achievement increases (Burns, 1988).

Scaffolded instruction improves transfer of responsibility (Gallimore & Tharp, 1990). As students gradually learn, teachers withdraw so the transfer of responsibility for learning lies with students. This transfer holds students accountable for their learning and is characteristic of a mastery-goal structure which leads to lower incidences of avoidance strategies (Turner, Meyer, Anderman, Midgley, Green, & Kang, 2002). Fantasy Sports and Mathematics places the onus of responsibility for learning on students. The teachers' role is as a guide, and students rely on their peers for assistance. The teachers' role is less didactic so students can become active learners and negotiate their own mathematical meanings. Students in autonomous classroom environments enjoy mathematical tasks more than students who are in authoritative classroom formats (Deci, 1975; Deci & Ryan, 1987).

There is no set age at which algebra should be introduced to students (Mills, Ablard, & Gustin, 1994). In Piagetian terms, children reach different stages at different times. Some children can reason abstractly sooner than others and have developed the necessary cognitive skills for algebra in earlier grades than when algebra is typically introduced (Mills, et al., 1993). Fantasy Sports and Mathematics introduces algebraic concepts in the fifth grade. At the onset of the game, students compute their weekly points non-algebraically. After a few weeks, teachers have the option of introducing algebraic equations that contains several variables. Students comprehend the rationale behind the progression from a non-algebraic method to a algebraic method, and students understand that the variables represent concrete data from sports statistics. All too often, students who are introduced to algebra in middle school do not comprehend the meaning of variables in equations because they do not understand where the data originates from, nor do they understand the relevance of the equations in their everyday lives. Fantasy Sports and Mathematics addresses these issues by providing opportunities for students to understand how algebra can simplify mathematics by eliminating several steps in the computational process.

Completing algebra in middle school has become a priority for many students (as well as for parents) because students must be ready for geometry in the ninth grade if they are to take Advanced Placement calculus as seniors in high school. Only 36% of students who do not take Algebra I or geometry attend college, and fewer than half of low-income students take these courses (Kirkland, 2002). Students who are otherwise intimidated by the sudden onset of algebra perhaps would be more confident if they had exposure to algebra in earlier grades. It is plausible that the introduction of algebraic material in elementary school can increase student confidence when they approach more complex material in later years. Moreover, a by-product of introducing algebra in the early grades is the positive effect it may have on teachers' perceptions of the abilities of their students. Higher teacher perceptions of the ability of students are important because academic learning is increased when teachers have positive views about the abilities of their students (Bandura, 1992).

Traditional math pedagogy emphasizes procedural skills over conceptual skills. Current educational reform emphasizes conceptual skills (NCTM, 1989). Competing theories exist as to which skill develops first. Some educators believe that conceptual knowledge can improve procedural skills, and that this relationship is unidirectional (Putnam, Heaton, Prewat, & Remillard, 1992). However, one theory suggests that the link between procedural and conceptual skills is bi-directional. That is, skills are developed iteratively with an increase in one skill resulting in an increase in the other skill. Therefore, both skills must be taught for maximum learning to occur (Siegler & Abibali, 2001). Fantasy Sports and Mathematics addresses this issue by including both procedural and conceptual skills. Practice worksheets are balanced with graphing activities and higher-order thinking skills to allow conceptual and procedural skills to develop simultaneously.

Fantasy Sports and Mathematics assessment is closely aligned with curriculum. Practice worksheets and quizzes are mirror images of each other. Confidence plays a greater role in student learning and assessment if tests more closely match the instruction (Wiggins, 1989). Social-cognitive theorists believe that students' self-confidence as they read and solve problems plays a role in determining the amount of effort and time they put forth. Students who work longer are less anxious; thus, their probability of success is enhanced (Bandura, 1997; Schunk, 1991).

Students who exhibit poor attitudes toward mathematics tend to perform poorly on tests. Attitude can influence perseverance (Carrol, 1963). Attitude also affects energy input and engagement (Middleton & Toluk, 1999). Fantasy Sports and Mathematics is a game designed to engage students by tapping into their natural competitive urges. Interest may be heightened because students can observe their players on television, read about their players in newspapers, and use online resources to gather data. In addition, the very nature of the game is such that it may promote social interaction in the classroom, which provides for a higher quality of experience when compared to traditional classrooms. Quality of experience is related to interest in mathematics, and interest in mathematics is a significant predictor of experience in grades, class, and course level (Schiefele et al., 1995). Moreover, intrinsic motivation is steered toward activities that are inherently interesting, enjoyable, or challenging (Csikszentmihalyi & Nakamura, 1989; Deci & Ryan, 1985). Thus, it seems plausible that intrinsic motivation in mathematics can only be maintained by positive emotional experiences in the discipline.

Increasing students' interest in mathematics and becoming aware of the importance of mathematics in life are among the least emphasized goals of high school teachers (Weiss, 1990). Teachers' favorite instructional methods are lecture, discussion, and textbook work, while their least favorite pedagogical methods are use of hands-on materials, use of computers, and group work. Fantasy Sports and Mathematics attempts to bridge this dichotomy between teacher attitudes and characteristics of standards-based curricula by providing hands-on activities along with the inclusion of technology, both of which are student-centered activities that promote a higher level of student interest (Weiss, 1990). Indeed, interest and achievement influence each other (Schiefele et al., 1995).

Visual imagery is a major factor in information processing (Bishop, 1989). Meaning is constructed cognitively as verbal, visual, or a combination of both (Kosslyn, 1983). The ability of students to understand and solve problems may be influenced by the method in which the material is presented. Most individuals' schemas are more powerful for pictures than for words (Larkin et al., 1987). Student understanding may be facilitated if the schemas involved in the learning process are associated with pictures or diagrams because the cognitive load associated with visual aids does not entail as much working memory as does the cognitive load with words (Lowrie et al., 2001). A major difference between Fantasy Sports and Mathematics and traditional math units is that many practice worksheets are designed to use in conjunction with a graph, thereby addressing the visual learners. In addition, Fantasy Sports and Mathematics' hands-on features (graphing, the use of newspapers, and the use of technology) address all learning styles. The inclusion of all learning modalities helps to shift the environment from a transmission model to a knowledge construction model, a goal of NCTM (NCTM 1989, 1991).

Challenge gives students intrinsic rewards and leads to building higher knowledge (Meyer, Turner, & Spencer, 1997). For example, Fantasy Sports and Mathematics gives students opportunities to create bar and line graphs using fractional intervals along the vertical axis', which is unusual and initially difficult for many students in middle school. In traditional mathematics instruction, students interpret data by studying graphs in their textbooks. However, Fantasy Sports and Mathematics gives students opportunities to generate their own meanings because they create their own graphs.

Eighty percent of students in eighth grade have difficulty with problems that involve fractions, decimals, and percentages (Mullis, Dossey, Owen, & Phillips, 1993). Much of the content of Fantasy Sports and Mathematics involves one or more of the three concepts, and the game exposes students to these concepts for a period as long as several months (depending on the sport). Multiple exposures to mathematical content are essential for maximum learning and retention (NCTM, 1989). Moreover, the visual representation of fractions, decimals, and percentages on graphs helps students to understand relationships between proportional qualities and numeric representations.

Motivating students may depend on the connections made between subject matter and students' experiences outside the classroom (McNair, 2000). Such a relationship may be especially vital for students in urban environments because their life experience is often the farthest from traditional school curriculum experience (McNair, 2000). Students from less-affluent backgrounds may have difficulty engaging in class if the subject matter does not connect with their reality (Bruckerhoff, 1995). Given the nature of the subject matter, it is plausible that Fantasy Sports and Mathematics is closer to the reality of urban youth than traditional mathematics curriculum. Curricula that attempt to make connections with the experiences of urban youth outside of school have the possibility of increasing their interest, engagement, and achievement. The need to make stronger connections between mathematics and students' lives outside the classroom is a major recommendation by NCTM (NCTM, 1989, 1991).