Designing a computer tutorial to correct a common student misconception in mathematics
Edith Aurora Graf, Earl B. Hunt · 2000
The goal of the research described in these three experiments was to inform the design of a computer tutorial for helping students correctly represent algebraic equations. Specifically, tutorials were designed to help students construct equations for statements of the “Students and Professors” type (Clement, Lochhead et al., 1979; Clement and et al., 1981). The first two studies contrasted the effectiveness of the classic “DIAGNOSER” format (Hunt and Minstrell, 1994) with a format that required participants to enter written self-explanations of their responses. Students who make thoughtful verbal self-explanations learn better, and eliciting verbal self-explanations from students helps them to learn (Chi, Bassok et al., 1989; Chi and Bassok, 1989; Chi, de Leeuw et al., 1994; Pirolli and Recker, 1994; Berardi Coletta, Buyer et al., 1995; Bielaczyc, Pirolli et al., 1995; Neuman and Schwarz, 1998; Renkl, Stark et al., 1998). In the first experiment, students learned to set up the equations correctly, but may have relied on a clever but nonmathematical heuristic to do this. This is consistent with case studies done by Rosnick and Clement (1980) which showed that while students learn to set up equations correctly, it is often without a complete understanding of their meaning. In the first two experiments, there was no apparent benefit of asking students to justify their equations (either through a multiple-choice reason or a written self-explanation). There are many qualifications on this finding, however. Results involving the effects of word problem context (Bernardo and Okagaki, 1994) and word problems (Wollman, 1983; Mark, Koedinger et al., 1998; Borchert, 2000) informed the design for the computer tutorial tested in the third experiment. During the tutorial, students in the experimental groups either (A) solved a concrete word problem prior to constructing each equation, or (B) received a general solution method after constructing each equation. Although performance in the word problem groups was very high relative to other groups during training (replicating Bernardo & Okakgaki, 1994 and Borchert, 2000), students did not transfer this skill to a paper and pencil test, where the solution group showed the highest performance. Possible reasons for this result are addressed. Finally, applications of these findings to new web-based computer tutorials being developed are discussed.