Thesis (M.I.T.)--The Evergreen State College, 2010. / Title from title screen (viewed 7/7/2010). Includes bibliographical references (leaves 132-138).

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In this two-part dissertation, the sources of self-efficacy were investigated for elementary and middle school students in mathematics classrooms. In the first study, the Sources of Middle School Mathematics Scale (Usher & Pajares, 2009) was validated with a younger sample. Participants included 367 fourth- through sixth-grade students; these participants completed two surveys investigating their beliefs regarding their capabilities to perform successfully in mathematics. This study included an examination of the psychometric properties and a confirmatory factor analysis of the Sources of Middle School Mathematics Self-Efficacy Scale, and an investigation into the relative power of mastery experience, vicarious experience, social persuasions, and physiological state to predict self-efficacy. This scale demonstrates adequate reliability and validity to be used successfully with younger students. The goal of the second study was to examine social persuasions in greater detail by focusing on the feedback teachers provide to their students during mathematics instruction. The Teacher Feedback Scale (Burnett, 2002) and several self-efficacy measures were administered at two time points to a subset (N = 290) of the fourth- through sixth-grade students from Study 1. The reliability and validity of the Teacher Feedback Scale was explored, as well as the relative power of positive, negative, ability, and effort feedback to predict self-efficacy. Negative feedback was the strongest predictor of student mathematics self-efficacy; positive and ability feedback were also significant predictors. Effort feedback was not a significant predictor of self-efficacy. This dissertation makes a relevant contribution to the fields of educational and school psychology by providing additional evidence for the validity of these scales and by exploring teacher feedback through the lens of social cognitive theory. Results from this study can also be used to help mathematics teachers interact with their students in ways that will bolster self-efficacy.

The purpose of this study was to determine if there was a significant difference in total scores on the Mathematical Self-Efficacy Scale, the mathematics task self-efficacy portion of the scale, and the math-related school subjects self-efficacy portion of the scale for middle school students between students assigned to a homogeneously grouped accelerated math class and students assigned to a heterogeneously grouped math class. The instrument used to gather information for thus study on student self-efficacy was the Mathematics Self-Efficacy Scale (MSES). The MSES measures 2 domains of mathematics-related behaviors and capabilities. The Mathematics Task Self-Efficacy scale is designed to measure the level of confidence the student would have when successfully completing the given task. The Math-Related School Subjects Self-Efficacy scale is designed to measure the level of confidence the student would have when successfully completing a college level course with a final grade of an A or B. The 2 parts of the MSES may be individually scored or holistically scored to obtain a total score representing overall mathematical self-efficacy. Descriptive and inferential statistics were used to analyze the data for the 9 research questions. Participants in the study were randomly assigned to the heterogeneous or homogeneous groups by their schools and were not controlled by the researcher. Students within the groups were chosen as participants based on their math ability and scores on the seventh grade TCAP test. At the time of the survey these students attended either a K-8 elementary school or a middle school in Northeast Tennessee. The population consisted of 357 gifted or talented eighth grade math students in 6 school districts in Northeast Tennessee. The results of this study does not support or discourage the practice of acceleration by retaining 7 of the 9 null hypotheses that there are no significant difference in self-efficacy scores between homogeneous grouped eighth grade math students who were placed in accelerated coursework by taking Algebra I and those students who were heterogeneously grouped in a regular eighth grade math class.

The significance of this dissertation research is twofold with both methodological advancement and empirical update. In this dissertation research, quantile regression (QR) was introduced to social sciences researchers as a response to the weaknesses of the traditional mean-based regression often referred to as multiple regression. General advantages of QR includes being more flexible for modeling data with heterogeneous conditional distributions, more robust to outliers, and having richer characterization and description of the data. Results of QR allow researchers to not only describe a general trend of changes in the effects of the independent variables across a continuous distribution of the dependent variable but also provide information on characteristics of any shift in the distribution caused by the independent variables. These shifts pertain to location, scale, and shape shifts. This dissertation research reviewed graphical ways to examine location, scale, and shape shifts, and more importantly, developed statistical ways to quantify location, scale, and shape shifts (i.e., test for statistical significance of location, scale, and shape shifts). Overall, this dissertation demonstrated that the introduction of QR as an advanced statistical procedure will advance the quantitative landscape of social sciences research. The results of this dissertation showed that QR can detect the differential effects of independent variables on the dependent variables that mean-based regression cannot detect and therefore uncovers more detailed relationships. This quality of QR enables more in-depth research than mean-based regression in many fields. The results of this dissertation also showed that QR allows for the understanding of relationships between variables outside the mean of the data, making it useful in understanding outcomes that are non-normally distributed and that have non-linear relationships with the independent variables. Finally, this dissertation introduced ways to detect and describe distributional shifts caused by the independent variables. The median regression line describes the (central) location shift. In addition to the estimated location shifts, the other QR lines provide information about the scale and shape shifts. This dissertation developed the bootstrapping approach to test for statistical significance when comparing location, scale, and shape shifts between parameters within and between samples (i.e., studies). This dissertation research applied QR to the examination of individual differences in mathematics achievement and mathematics self-efficacy, using the 2003 and 2012 Programme for International Student Assessment (PISA) data. The QR results showed that the effects of many student characteristics were not constant across the mathematics outcomes distributions (i.e., mathematics achievement and mathematics self-efficacy). This suggested that individual differences were valued heterogeneously across the mathematics outcomes distributions. There was only one statistically significant location shift in terms of individual differences associated with family structure in both mathematics achievement and mathematics self-efficacy between 2003 and 2012. There was only one statistically significant scale shift in terms of individual differences associated with father SES in mathematics achievement for the middle 40 percent of the students between 2003 and 2012. There was only one statistically significant scale shift in terms of individual differences associated with gender in mathematics self-efficacy for the middle 40 percent of the students between 2003 and 2012. There was only one statistically significant shape shift in terms of individual differences associated with gender in mathematics self-efficacy between 2003 and 2012. Even though QR and LMR results can be similar in terms of statistical significance, they can differ dramatically in magnitude. Students’ age, gender, and socioeconomic status were typical examples in this study. The effect of student age generally became more positive as student mathematics achievement increased in 2003. This suggests that age had a stronger effect on better-performing students than lower-performing students in 2003. It also means that there are more age differences in the upper tail of student mathematics achievement distribution than in the lower tail.

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