The Effect of External Representations on Compare Word Problems: Supporting Mental Model Construction

Abstract

This study explored the effectiveness of external representations presented together with compare word problems, and whether such effectiveness was moderated by working memory. Participants were 49 secondary school students. Each participant solved 48 problems presented in 4 presentation types that included 2 difficulty treatments (number of steps and language consistency). Data from errors and response times indicated that adding a graph to compare word problems helped accuracy (d =.60) and response time (d =.44). This effect was larger for difficult and cognitively demanding problems. Findings suggest that external representations might help problem-solvers build a mental model of the described problem situation. In addition, working memory was not found to moderate the effectiveness of external representations.

Keywords:

• compare word problems
• external representations
• word problem solving

Notes

Baddeley (2000) also suggested an additional component of the model, the episodic buffer, which integrates and temporarily stores information from the articulatory loop and the visuospatial sketchpad and enables the exchange of information between the central executive and long-term memory.

Compare word problems with compare set (CP3, CP4) or reference set (CP5, CP6) as unknown set and different directions of the relational statement (more than: CP3, CP5; and less than: CP4, CP6). Different studies have used similar word problems even with undergraduate students (e.g., Hegarty, Mayer, & Monk, 1995).

TABLE 1 Sample of Experimental Problems Used in the Study

The use of the verification task instead of the production task eliminates individual differences related to the execution of the necessary computations. The verification task has been supported in different studies related to chronometric research on mental arithmetic and word problem solving (see Ashcraft, Fierman, & Bartolotta, 1984; DeStefano & LeFevre, 2004; or Swanson, Cooney, & Brock, 1993, for a similar argument).