Exploring the accuracy and predictability of the self-efficacy beliefs of seventh-grade mathematics students

Abstract

This research studied the self-efficacy beliefs of 107 seventh-grade mathematics students, particularly focusing on the accuracy and predictability of their beliefs. Path analysis showed that calibration accuracy had both direct and indirect effects on math performance, with indirect effects mediated through self-efficacy beliefs. Self-efficacy played a direct role in predicting students' math performance, postperformance self-evaluation, and postperformance judgments of effort. The effects of prior math achievement on math performance were mediated largely through the students' self-efficacy beliefs. The findings also did not reveal any gender differences in self-efficacy or calibration. Although the findings supported self-efficacy predictions, they also suggested important issues for future research, including accuracy of self-efficacy training in math problem solving and assessment of effort judgments prior and post performance.

Introduction

Self-efficacy beliefs refer to the perceived capability to learn or perform at a certain designated level. They are distinct from other self-beliefs in their specificity and close correspondence to measures of overt performance. Mathematical self-efficacy beliefs are typically assessed using self-ratings of skill regarding specific math problems (Schunk, 1981). Evidence shows that predictability of self-efficacy measures depends on their specificity and correspondence to actual math performance tasks (Zimmerman, 1995). Most research on self-efficacy has involved measures of self-efficacy that vary primarily in strength (from low to high). In her study of the generality dimension of self-efficacy, Bong (1997b) found that, although subject-matter-specific measures of efficacy better predict students' performance in the targeted area, these self-efficacy beliefs generalize to different subject matter areas that involve related underlying skills, such as history and English, which involve verbal processes.

Another important dimension of self-efficacy measures is their accuracy or calibration. Recent studies indicate that many students overestimate and a few students underestimate their self-efficacy Campillo et al., 1999, Pajares & Miller, 1994, Schunk, 1995. Optimistic judgments of capability may have motivational benefits, such as motivating students to continue learning even when their performance is deficient. However, few studies discuss the causes and effects of variations in self-efficacy calibration. The present research attempted to redress this issue. Among the potential causes of inaccuracy in students' efficacy self-calibration are variations in task difficulty. The role of task difficulty in self-efficacy judgments is a level dimension of this construct (Zimmerman, 1995). The effect of variations in task difficulty on students' calibration of self-efficacy is a relatively unexamined topic. However, task difficulty does affect the personal calibration on other self-appraisal tasks. For example, Schraw, Potenza, and Nebelsick-Gullet (1993) found that students were better calibrated and less overconfident in their postperformance self-evaluative judgments on an easy test than on a difficult test. If the students' inaccuracy in appraising their self-efficacy results from being unable to understand the task requirements or their performance capability, their accuracy should improve as they gain experience with the task.

Finally, research should explore variations in the method of assessing calibration. Ewers and Wood (1993) devised an early effort to assess the role of calibration in students' self-efficacy judgments. Using a 5-point scale, these researchers counted the number of overconfident self-appraisal predictions (rating 4 or 5 for corresponding problems solved incorrectly) and the number of underconfident self-efficacy predictions (rating 1 or 2 for corresponding problems passed). A limitation of this assessment approach is that it did not fully capture students' degree of overconfidence or underconfidence because higher and lower self-judgment scores on each scale were collapsed into inclusive categories. In more recent research, Schraw et al. (1993) and Yates (1990) developed an exact method for assessing calibration without grouping self-appraisal scores into an over- or underconfidence category; Pajares and colleagues later adapted this methodology to assess self-efficacy Pajares & Graham, 1999, Pajares & Miller, 1997. They labeled the two exact measures of self-efficacy calibration as bias and accuracy. Bias calibration measures direction of judgment errors and accuracy calibration measures the magnitude of the errors when performing a task. These researchers found that the correlation of both accuracy and bias calibration measures with math performance exceeded that of self-efficacy in magnitude; the present researcher later found that these differences in correlation were statistically significant (P<.01). Both calibration measures correlated significantly with self-efficacy. In these studies of self-efficacy, students generally reported overestimates of their math performances, but few students reported underestimates.

Unlike prior studies that investigated calibration as an academic outcome, the present study investigated calibration to predict self-efficacy strength and academic performance. This required a change in methodology to assess calibration with a separate but parallel task in order to avoid using the same data as both predictor and outcome. Historically, researchers have used earlier self-efficacy indexes to predict later self-efficacy and academic performance measures; for example, Schunk (1983) used self-efficacy with learning progress to predict posttest self-efficacy and academic performance measures. The issue of calibration in students' self-efficacy judgments is pedagogically important because poor calibration may undermine the predictive power of students' self-efficacy judgments. On the other hand, the inclusion of the calibration dimension along with the strength dimension of self-efficacy could increase the predictability of students' academic motivation and performance. Many at-risk students have reported unrealistically high self-efficacy and an unwillingness to change their study methods because of this overconfidence (Zimmerman, Bonner, & Kovach, 1996). If teachers use students' self-efficacy judgments to guide their instruction, they need to know how well-calibrated the students' judgments are and how they can use that information to forecast students' academic performance.

Studies present conflicting evidence on the role of gender in self-efficacy judgments as well as in calibration. Some research reports gender differences in calibration among fifth graders (Ewers & Wood, 1993), but not among middle school (Pajares & Graham, 1999) or high school students (Pajares & Kranzler, 1995). These findings of weak gender effects resemble those of students' mathematics achievement in general. Hyde, Fennema, Ryan, Frost, and Hopp (1990) conducted a meta-analysis to test gender differences in students' mathematics beliefs and achievement. The effect size of gender differences was small and generally nonsignificant, but there was a positive gender effect on math self-concept and confidence that favored males. In view of these mixed findings, the role of gender in students' calibration of math self-efficacy requires additional study, particularly in conjunction with variations in task difficulty.

The present research investigated the role of calibration in students' math self-efficacy judgments and potential causes of inaccurate self-efficacy beliefs, such as task difficulty and gender. Another possible source of inaccuracy in calibration is students' prior achievement in math. High achievers may be better at estimating their capability to solve a particular math problem than low achievers. Prior math achievement may explain why gifted students seem to be more accurate in estimating their self-efficacy (Pajares & Graham, 1999).

Another key question concerns how differences impact the accuracy of students' self-efficacy beliefs before they render postperformance judgments, such as self-evaluations and judgments of effort. Concerning effort, Pintrich et al., 1991, Pintrich et al., 1993 found a positive and significant correlation between course-referenced perceptions of efficacy among college students and effort regulation on the Motivated Strategies for Learning Questionnaire (MSLQ); Bong (1997a) replicated this finding. Pajares and Graham (1999) also found positive correlations between self-efficacy and effort (which they termed engagement). In these studies, greater self-belief in one's ability seemed to produce greater effort to succeed. As for self-evaluation, Schunk (1996) reported that increases in self-evaluative feedback led to enhanced learning on a math task. In addition, Zimmerman and Bandura (1994) found that self-efficacy in writing skill was linked causally to students' self-evaluative standards. However, recent research has not explored the influence of students' accuracy in self-efficacy calibration on their postperformance self-evaluative judgments.

The present study used path analysis procedures to assess the influence of prior achievement and gender on students' calibration accuracy. As discussed earlier, students' calibration judgments were expected to play a mediational role between the effects of prior achievement and gender, and students' mathematics self-efficacy beliefs and test performance. Along with self-efficacy judgments and math performance, calibration accuracy was expected to predict postperformance measures of effort attributions and self-evaluative judgments. In terms of task difficulty (e.g., easy, moderate, and difficult math problems), the researcher hypothesized that linear trends would occur between difficulty and self-efficacy and between difficulty and calibration. Finally, the researcher hypothesized that the indexes of calibration would increase the predictability of math performance when combined with self-efficacy measures.