Path analysis was used to test the predictive and mediational role of self-efficacy beliefs in mathematical problem solving. Results revealed that math self-efficacy was more predictive of problem solving than was math self-concept, perceived usefulness of mathematics, prior experience with mathematics, or gender (N = 350). Self-efficacy also mediated the effect of gender and prior experience on self-concept, perceived usefulness, and problem solving. Gender and prior experience influenced self-concept, perceived usefulness, and problem solving largely through the mediational role of self-efficacy. Men had higher performance, self-efficacy, and self-concept and lower anxiety, but these differences were due largely to the influence of self-efficacy, for gender had a direct effect only on self-efficacy and a prior experience variable. Results support the hypothesized role of self-efficacy in A. Bandura's (1986) social cognitive theory.Social cognitive theory suggests that self-efficacy, "people's judgments of their capabilities to organize and execute courses of action required to attain designated types of performances" (Bandura, 1986, p. 391), strongly influences the choices people make, the effort they expend, and how long they persevere in the face of challenge. According to Bandura (1986), how people behave can often be better predicted by their beliefs about their capabilities than by what they are actually capable of accomplishing, for these beliefs help determine what individuals do with the knowledge and skills they have.Although researchers have established that self-efficacy is a strong predictor of behavior (Maddux, Norton, & Stoltenberg, 1986), research on the relationship between self-efficacy and academic performance in areas such as mathematics is still limited (Bouffard-Bouchard, 1989). Studies of math self-efficacy have been largely correlational, and researchers have emphasized the need to construct causal models with which to conceptualize and test hypothesized relationships (Hackett & Betz, 1989;Meece, Wigfield, & Eccles, 1990). When causal modeling has been used, most models have excluded key variables identified as influencing math performance (most notably, self-concept), or the theoretical framework used to hypothesize relationships was not based on social cognitive theory. Thus, results have added little to a better understanding of self-efficacy's influence. Bandura (1986) mance; that is, when these determinants are controlled, self-efficacy judgments are better predictors of performance. Bandura also argued that constructs such as selfconcept, perceived usefulness, and anxiety are "common mechanisms" of personal agency in the sense that they, like self-efficacy beliefs, also influence an outcome. However, these mechanisms are, to a great extent, the result of selfefficacy judgments-their influence is largely due to the confidence with which individuals approach a task. Consequently, although strong correlational relationships are observed between these mechanisms and related outcomes, ...

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In this study, 391 students were asked to provide 3 types of mathematics self-efficacy judgments: confidence to solve mathematics problems, confidence to succeed in math-related courses, and confidence to perform math-related tasks. Criterial tasks were solution of math problems and choice of math-related majors. As hypothesized, students' reported confidence to solve the problems they were later asked to solve was a more powerful predictor of that performance than was either their confidence to perform math-related tasks or to succeed in math-related courses. Similarly, confidence to succeed in math-related courses was a stronger predictor of choice of math-related majors than was either confidence to solve problems or to perform math-related tasks. Results support A. Bandura's (1986) contention that, because judgments of self-efficacy are task specific, measures of self-efficacy should be tailored to the criterial task being assessed and the domain of functioning being analyzed to increase prediction.

We randomly surveyed 1,576 Florida special education teachers to examine factors that contribute to their propensity to leave or stay in the special education classroom or transfer to a new school. The variables identified, based on extensive review of the literature, included background, classroom, school district, and personal factors. We tracked our respondents for 2 years using a multinomial logit model to identify significant predictors of leaving, staying, or transferring. Results indicate that teachers left special education teaching primarily due to insufficient certification, perceptions of high stress, and perceptions of poor school climate. Special educators who transferred to a different school or district had perceptions of high stress and perceptions of poor school climate and were significantly younger than stayers.

Thirty-four matched pairs of sixth-and seventh-grade students were selected from 358 participants in a comparison of an explicit concreteto-representational-to-abstract (CRA) sequence of instruction with traditional instruction for teaching algebraic transformation equations. Each pair of students had been previously labeled with a specific learning disability or as at risk for difficulties in algebra. Students were matched according to achievement score, age, pretest score, and class performance. The same math teacher taught both members of each matched pair, but in different classes. All students were taught in inclusive settings under the instruction of a middle school mathematics teacher. Results indicated that students who learned how to solve algebra transformation equations through CRA outperformed peers receiving traditional instruction on both postinstruction and follow-up tests. Additionally, error pattern analysis indicated that students who used the CRA sequence of instruction performed fewer procedural errors when solving for variables.Abstract thinking requires a person to work with information that is not readily represented at the concrete or pictorial level (Hawker & Cowley, 1997). To work with abstract information is to understand theoretical properties and think beyond what a person can touch or see. On a practical level, an ability to work with abstract concepts allows one to work with predictions of what may happen and expectations about what is happening elsewhere. Abstract knowledge may also be considered a conscious awareness that a symbol stands for some Requests for reprints should be sent to Bradley S. Witzel, Ph.D., Winthrop University, Richard Riley College of Education, Department of Curriculum and Instruction, Rock Hill, SC 29733. Electronic inquiries may be sent to witzelb@winthrop.edu.

The authors investigated the nature of gender differences in the writing self-beliefs of elementary school students in Grades 3, 4, and 5 (N = 363). Girls were judged superior writers, but there were no gender differences in writing self-efficacy after controlling for writing aptitude. However, girls expressed that they were better writers than were other boys or girls in their class or in their school to a greater degree than did boys. Only writing self-efficacy beliefs and aptitude predicted writing performance in a path model that included writing apprehension, self-efficacy for self-regulation, and perceived usefulness of writing. Self-efficacy mediated the effects of aptitude and self-efficacy for self-regulation on performance. Writing self-concept was higher and apprehension lower for students in Grade 3 than in Grade 5. Data were consistent with A. Bandura's (1986) social cognitive theory and suggest that boys and girls may use a different metric when responding to traditional self-efficacy scales.

We review the effects of contingency schedules that require a particular amount of one response for the chance to perform another response during experimental sessions having some fixed duration. Increasing the size of the response requirement often produces an increase in the total amount of that response but a de-

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