The Impact of Context on Children's Performance in Solving Everyday Mathematical Problems with Real-World Settings

Article excerpt

Abstract. This study aimed to investigate children's performance and perception of problem difficulty in solving everyday mathematical problems with familiar versus unfamiliar contexts. In addition, the ways that children identify the similarities in problem-solving approaches between problem settings and everyday shopping were also examined. Forty-eight 4th-grade children participated in this study. Both quantitative and qualitative analyses were used. The results demonstrated that the familiar contexts neither enhance children's problem-solving performance nor decrease problem difficulty. More than half of the children did not identify the similarity in problem-solving approaches between problem settings and real shopping. When making judgments, even good problem-solvers were found to be distracted by superficial features in outward appearance and global mapping in similarity. This research highlights that children in the process of solving problems tend to be distracted by non-mathematical features in the problem settings. Some implications for instruction are given.

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In recent years, there has been an increasing emphasis within the field of mathematics education on the application of mathematics, such as the solving of problems posed in realistic contexts (Beishuizen, Gravemeijer, & van Lieshout, 1997; Gravmeijer, 1994). Many believe that integrating children's everyday knowledge and school mathematics would enable them to develop their understanding of mathematics by applying it to textually represented realistic problems; others argue for the application of mathematics to real life. Because cognitive activity in everyday life is socially defined, interpreted, and supported (Rogoff & Lave, 1984), it is plausible to suggest that a stronger connection between school mathematics and everyday life will enhance school learning.

It is well-known that problem solvers have less difficulty with problems in which the context makes it possible to retrieve learned knowledge and apply similar problem-solving experiences to formulate solutions (Bernardo, 1994). The term "context" is used here to describe the non-mathematical meanings present in the problem statement. Kulm (1984) stated that context helps to give meaning to the mathematical content. The verbal context or setting of a problem often provides a connection between mathematical content and its application. The context categories may include those that make the setting of the problem more or less relevant to the problem solvers' experience and interests.

The familiar/unfamiliar dichotomy is dependent upon the problem solvers themselves--that is, their backgrounds and experiences (Caldwell, 1984). Previous studies found that the level of familiarity with the context of a problem will affect the problem-solving process (Rogoff & Lave, 1984). Although prior research has shown that children have difficulty in unfamiliar contexts, little is known about how the familiarity of contexts and various quantities involved in problems affects children's performance and perception of difficulty in solving problems within real-world settings. This study seeks to address these issues by using mathematical problems with isomorphic structures involving multiplication in familiar versus unfamiliar contexts.

The Impact of Familiarity of Problem Context on Children's Performance in Solving Mathematical Problems

Contextual similarity was found to facilitate recall in a variety of earlier problem-solving studies (Bassok & Holyoak, 1989; Gick & Holyoak, 1983). Furthermore, familiarity with question terms matters for the feelings of knowing and facilitates understanding (Reder & Ritter, 1992). The hypothesis is that a familiar context provides a less abstract and more directly experienced grounding for the new domain, thus enhancing the use of particular strategies or activating known structures that allow for more efficient processing. …