A Strong Schema Can Interfere with Learning: The Case of Children’s Typical Addition Schema

A Strong Schema Can Interfere with Learning: The Case of Children's Typical Addition Schema Nicole M. McNeil (nmmcneil@students.wisc.edu) Department of Psychology, 1202 W. Johnson Street Madison, WI 53706 USA Martha W. Alibali (mwalibali@facstaff.wisc.edu) Department of Psychology, 1202 W. Johnson Street Madison, WI 53706 USA Abstract This study investigated whether children's schema for typical addition interferes with their ability to learn about mathematical equivalence. In a pretest, elementary school children (1) solved a set of math equivalence problems (e.g., 3 + 4 + 5 = 3 + __), (2) reconstructed equivalence problems after viewing them briefly, and (3) provided definitions of the equal sign. Children were categorized according to the number of measures (out of 3) on which they exhibited the typical addition schema. Children then received one of four interventions that presented new information about equivalence problems. Finally, children completed a posttest similar to the pretest. From pretest to posttest, children who exhibited the addition schema on all three measures were the least likely to change their strategy for solving the problems, followed by children who exhibited the schema on two or one of the measures. All of the children who did not exhibit the schema on any of the three measures changed. It is important to note that all children used incorrect strategies at pretest, so it was the addition schema in particular that was associated with change resistance. Thus, a strong schema can interfere with learning. Furthermore, children's addition schema may put them at risk for difficulties in learning higher-level mathematics. Some behaviors and ideas are particularly difficult for individuals to acquire, even after numerous attempts have been made by the individuals to learn them or by instructors to teach them. Consider, for example, a woman who has always counted on her fingers when solving addition problems. She does not wish to count on her fingers; in fact, she finds it to be an infuriating habit. However, no matter how hard she tries to memorize the addition facts, she always seems to resort to counting on her fingers. Consider also a father who is trying to learn a second language as an adult. The father is frustrated because his daughter, who is only five years old, is learning so much more quickly than he is. Why is it so difficult for the woman to memorize the addition facts and for the father to learn a second language? One reason may have to do with the organization and strength of the behaviors and ideas they already possess. The woman's knowledge about addition may be organized into a strong schema that interferes with her memorizing of the addition facts, and the father's knowledge about his first language may be organized into a strong schema that interferes with his learning of the second language. A schema can be defined as a higher-level assembly of knowledge that is unitized in that it supersedes its constituent parts and acts as a whole (cf. Smolensky, 1986; see also Hayes-Roth, 1977; Hebb, 1949). Once established, schemata can serve as selective mechanisms that determine how environmental stimuli are encoded, interpreted, and stored in memory. In general, schemata enable fast and efficient processing of environmental stimuli. However, this efficiency can come with a price, especially if a particular schema is inaccurate or lacking in some way. When a schema is strong, it resists change (e.g., Allport, 1954; Bartlett, 1932; Bruner, 1957; Schutzwohl, 1998). Individuals who have a strong schema have been shown to resist learning new information when it is more specific than (Adelson, 1984; Thorndyke & Hayes-Roth, 1979), not applicable to (Voss, Vesonder, & Spilich, 1980), or discrepant with (Marchant, Robinson, Anderson, & Schadewald, 1991; Markus, 1977) their current schema. Indeed, individuals who have a strong schema often actively resist change by modifying or distorting environmental input so that it corresponds to their schema (Bartlett, 1932; Bruner & Postman, 1949; Guion, Flege, Akahane-Yamada, & Pruitt, 2000; Hannigan & Reinitz, 2001). Importantly, the stronger a schema is, the more resistant it is to changing (see Luchins, 1932). Although the strength of a schema has clear behavioral consequences, it is not always obvious how to operationalize schema strength apriori. Some theories suggest that strength may be determined by how practiced particular action procedures are (Luchins, 1942), while others suggest that it may be derived from tightly organized perceptual (Flege, Bohn, & Jang, 1997; Intraub & Bodamer, 1993) or conceptual (Wellman & Gelman, 1992) information. These accounts need not oppose one another, though, because any given schema is likely constructed out of various related sub-schemata (Smolensky, 1986). We propose that schema strength depends on the relationship