To examine this prediction, Schunk and Hanson (1985) asked elementary school children who were having difficulty in arithmetic to judge their capacity to solve 25 different pairs of subtraction problems. Each pair of problems was presented for 2 seconds, enough time for students to assess problem difficulty but not enough time to actually solve the problems. Students rated their capacity to solve each pair of problems on a 100-point scale ranging from "not sure" (10) to "maybe" (40) to "pretty sure" (70) to "really sure" (100). The average rating for the 25 problems constitutes a measure of Self-efficacy. Then students received instruction in how to solve subtraction problems. The number of problems that were correctly commpleted during instruction provides a measure of ease of learning. Finally, students took a 25-item subtraction test. The number of correct answers on the test constitutes a measure of achievement.

Is self-efficacy related to achievement in subtraction? The answer from Schunk and Hanson's (1985) study is clearly yes. The correlation between self-efficacy and achievement was high (r = .66). Furthermore, Schunk (1989) reported that similarly high rates were obtained across a series of studies in many domains (r = .46 to r = .90). Is self-efficacy related to ease of learning? Again, Schunk and Hanson's (1985) study produced a strong correlation between self-efficacy and ease of learning (r = .38), and Schunk (1989) reported that similarly high correlations were obtained in other studies (r = .33 to r = .42). In conclusion, performance during and after learning appears to be related to students' judgments of their capabilities for learning.

Another test of the achievement hypothesis concerns how changes in self-efficacy are related to changes in achievement. According to the theory, when a student's self-efficacy is raised, the student's academic performance also increases. For example, in Schunk and Hanson's (1985) study previously described, students rated their self-efficacy for subtraction. took a subtraction pretest, received instruction, and then again rated their self-efficacy for subtraction and took a subtraction posttest. Some students received instruction aimed at improving self-efficacy (student-model group). Students in the student-model group viewed two 45-minute videotapes presented on 2 consecutive days. The tapes portrayed a teacher writing subtraction problems on the board and a student successfully solving them. The student model verbalized aloud the steps in solving the problem and occasionally made positive statements such as "I can do that one" or "I like doing these." The student models in the videotape were selected to be similar to students in the study. When a student model finished a problem, the teacher stated that the solution was correct and then wrote another problem on the board, and so on throughout the videotape. After viewing the videotapes, the students received 40 minutes of workbook-based instruction on each of 5 consecutive school days. At the beginning of each session, each student was given a workbook containing a sheet explaining how to carry out the needed operations, two worked-out examples, and a series of pages with similar problems to solve. Students were free to consult with a proctor if they needed help. Other students received the same 5 days of workbook-based instruction but viewed videotapes showing a teacher solving the problems (teacher-model group) or saw no videotapes at all (no-model group).

The student-model group showed a large change in self-efficacy and in achievement, whereas the changes for the no-model and teacher-model groups were more modest. These results support the idea that modeling "can raise self-efficacy because it implicitly conveys to observers that they are capable of performing the modeled operation" (Schunk &: Hanson, 1985, p. 319). Thus, self-efficacy is not based solely on one's prior performance but is also influenced by observing peers. Importantly, the increase in self-efficacy is related to a concurrent increase in academic performance. Schunk and Hanson suggested that "teachers who systematically incorporate peer models into their instruction, at least with children who have skill deficiencies, may help promote children's skills and self-efficacy for acquiring them" (p. 321)

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