<p> <b>Purpose:</b> The purpose of this phenomenological qualitative study was to describe how expert teachers at the high school level perceive the impact of rigor, relevance, and personalized learning on the learning experience and achievement of gifted and talented (GATE) students. </p><p> <b>Methodology:</b> Data collected for this study included classroom observations, interviews, and documents. The target population consisted of public high school teachers of gifted learners in grades 9&ndash;12. Moreover, teacher participants were chosen using both purposeful and emergent sampling procedures. </p><p> <b>Findings:</b> For this phenomenological study, there were 15 teacher participants from both Los Angeles and Orange County. The study utilized mixed methods to develop a valid understanding of natural occurrences related to the research questions. Additionally, the researcher employed the used of thick descriptions as another method of advancing external validity. </p><p> <b>Conclusions:</b> Experts in education indicated personalized learning and the rigor and relevance framework were effective methods for learners and specifically gifted learners. </p><p> <b>Recommendations:</b> The research did not produce a unified methodology incorporating differentiation, personalized learning, rigor, and relevance in a single framework. Implications suggested a need to develop a concise framework incorporating these theories to implement student-centered curricula, effective in-class strategies, and a defined approach for students becoming active participants in their own learning.</p><p>

<p> The purpose of this study was to determine if there was a significant difference in total scores on the <i>Mathematical Self-Efficacy Scale, </i> 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. </p><p> The instrument used to gather information for thus study on student self-efficacy was the <i>Mathematics Self-Efficacy Scale</i> (MSES). The MSES measures 2 domains of mathematics-related behaviors and capabilities. The <i> Mathematics Task Self-Efficacy</i> scale is designed to measure the level of confidence the student would have when successfully completing the given task. The <i>Math-Related School Subjects Self-Efficacy</i> 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.</p><p> 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.</p><p> 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.</p>