The Role of Playing Games in Developing Algebraic Reasoning, Spatial Sense, and Problem-Solving
Lach, Tisa, Sakshaug, Lynae, Focus on Learning Problems in Mathematics
Introduction and Literature Review
Purpose and Relevance
Using games in the classroom to facilitate learning has been common practice among teachers for many years. Blum and Yocum (1996) supported instructional game-playing in the classroom because it provided an exciting and motivating strategy for students to practice skills already learned. They suggested that there are several benefits from using instructional games in the classroom. Games are naturally motivating and fun, games facilitate individualization of assessment and instruction, and games make the abstract concrete.
As a teaching tool games helped students become better problem solvers because playing games gave them a chance to work out problems and develop strategies for solving problems in a non-threatening environment. (Klein & Freitag, 1991; Olson & Platt, 1992 as cited in Blum & Yocum, 1996). Playing games provided opportunities for students to invent and test various strategies and procedures for solving problems. Kamii, Lewis and Livingston (1993) stated, "When children invent their own problem-solving strategies, they do not have to give up their own thinking, their understanding of [the concept] is strengthened and they develop better number sense" (p. 201). This also afforded students time to test their theories and strategies along with providing practice in multi-step problem-solving. "Playing games offers repeated use of ... strategies and invaluable practice of skills already learned. Practice becomes more effective because students become active participants in their own learning" (Ernest, 1986; Rakes & Kutzman, 1982; Wesson et al., 1988 as cited in Klein & Freitag, p. 303).
Playing games in the classroom provided a forum for students to have discourse with peers (Beigel, 1997; Wakefield, 1997). They discussed options, strategies and solutions and gained insight and understanding from each other as well. Wakefield further proposed that the social interaction during the playing of games not only helped student understanding, but played a large role in the game etiquette of following rules and fair play (1997).
Most studies in the field of using instructional games in the classroom focus on students with special needs as their subjects. Blum and Yocom mentioned three such studies that yielded positive results (1996). Beattie and Algozzine (1982) found that students with mild disabilities who practiced math facts and played instructional math games were on-task about 20% more than their peers and also received higher grades. Delquadri, Greenwood, Stretton and Hall (1983) found that by using an instructional spelling game, learning-disabled students were able to decrease their spelling errors equal to the level of their non-disabled peers. Mackay and Watson (1989) were able to show improvement of communication skills with severely learning-disabled students by using instructional games.
There were no studies found in which non-disabled students were used as subjects. This study looked at such groups.
The purpose of this study was to test the hypothesis that playing math-related games played a role in developing students' ability to solve problems involving algebraic reasoning and spatial sense.
Researchers chose the following from the NCTM Curriculum and Evaluation Standards for School Mathematics (1989), "spatial sense is an intuitive feel for one's surroundings and the objects in them" to define spatial sense (p. 49). Having spatial sense means understanding the relationships of objects, the sizes and shapes of figures and objects, and the direction, orientation and perspectives of objects (Liedtke, 1995). Based on these definitions, the following are examples of the use of spatial sense. Students with spatial sense are able to manipulate patterns and shapes or objects both physically and mentally in order to show an understanding of the properties of that pattern, shape, or object. …