This study’s purpose was to explore science engagement and in/equity through science educators’ narratives of servant leadership at both the K-12 and higher education levels in the United States. The research question was: How have participants become and led others to become engaged in science? I took an arts-based approach using drawings and autobiographical data to initiate and create metissages focused on becoming engaged in science education. The findings were that: (1) Participants helped marginalized students understand the culture of science through pedagogical strategies that connected self and science; (2) Participants recognized and countered systemic forms of oppression for students who are marginalized in science education through outreach in STEM; and (3) Participants offset disengagement in science among underserved groups through meaningful relationships and presented non-dominant examples of scientific inquiry. I discuss their implications for professional development and provide recommendations for future research concerning leadership/followership aimed at promoting science equity.

The emphasis of undergraduate mathematics content is centered around abstract reasoning and proof, whereas students' pre-college mathematical experiences typically give them limited exposure to these concepts. Not surprisingly, many students struggle to make the transition to undergraduate mathematics in their first course on mathematical proof, known as a bridge course. In the process of this study, eight students of varied backgrounds were interviewed before during and after their bridge course at BYU. By combining the proof scheme frameworks of Harel and Sowder (1998) and Ko and Knuth (2009), I analyzed and categorized students’ initial proof schemes, observed their development throughout the semester, and their proof schemes upon completing the bridge course. It was found that the proof schemes used by the students improved only in avoiding empirical proofs after the initial interviews. Several instances of ritual proof schemes used to generate adequate proofs were found, calling into question the goals of the bridge course. Additionally, it was found that students’ proof understanding, production, and appreciation may not necessarily coincide with one another, calling into question this hypothesis from Harel and Sowder (1998).

This study is attempting to test the effectiveness of dynamic computer models such as GeoGebra and Desmos on high school students’ ability to understand key concepts with regards to the introduction of unit circle and the graphing of the sine and cosine functions. Algebra two high school students of varying ages were chosen and randomly placed into two groups. Both groups were given the same pre-assessment and an identical lesson. The two groups’ only difference occurred with the individual student practice portion of the lesson where one group did ‘traditional’ paper and pencil practice for graphing and solving while the other group used only computer models as their individual practice. Both groups were then reassessed by giving the same assessment again. Their levels of improvement were compared using standard statistical analysis and a mean comparison test. The results showed a statistically significant improvement in the student group that used the dynamic models versus the group that did not use the computer. The sample size was large enough to generate a confidence value of over 99% (99.3%) so we were able to reject the null hypothesis that there was no difference between the group results and accept the hypothesis that the student group that used the computer models improved by a statistically significant amount. The non computer group improved by 7.7 percent while the computer aided group improved by over 49 percent. This represented an 88 percent increase in the scores of the computer group when compared with the control group. I was able to definitively conclude that the dynamic software did have a significant and positive effect on the students' learning of the unit circle. It is hoped that this information will be used to help inform more effective instruction for high school and college students as they learn this topic. It also provides a strong argument for an increased emphasis on educating teachers to become more fluent in the use of dynamic models and software as both a demonstration tool and as an interactive tool for their students in a variety of math levels. These results may also have wider applications to many other math topics and math instruction in general.

No description available.

No description available.

No description available.

No description available.

The adoption of the Common Core State Standards has necessitated a change in the instructional practices used by many mathematics teachers. The new standards encourage problem solving and the development of conceptual understanding rather than rote memorization of formulas and rules. Researchers have demonstrated that formative assessment is a powerful instructional tool that, when implemented properly, can increase student achievement. The purpose of this quantitative study was to determine how mathematics teachers in Pennsylvania perceive the new standards; how they value and use formative assessment practices including involving students in their work, modeling quality work, providing feedback, and providing opportunities for peer and self-assessment; and how these variables are related to each other. The answers to these research questions could potentially guide future professional development for teachers. This study was guided by the theoretical framework of Bloom, Dewey, and Piaget who each stated that a constructivist approach to learning is necessary for student growth. Likert scale surveys were used and Pearson correlational studies were conducted to analyze the data from the 174 respondents. Results revealed that participants were generally not in favor of the Common Core State Standards, and there were few statistically significant relationships between teachers' value and use of the 4 formative assessment practices and their value of the standards. Participants appeared to have some misconceptions about the standards and the instructional practices that support implementation, suggesting a continued need for professional development. Attention to this professional learning could help to promote student achievement.

The number of high school graduates entering college needing to take developmental math courses is increasing. Gilmer State College (a pseudonym) introduced customized scheduling in which students identified as at risk after scoring low on the math entrance exam are placed in the developmental math course and additional courses that traditionally have a pass rate of 75% or better. The purpose of this study was to examine the difference in passing and retention rates between 1st-time college freshmen who attended Gilmer State College before the customized scheduling and after the customized scheduling was implemented. This study was based on Adelman's theoretical framework of academic momentum because students tend to continue their studies when experiencing initial success. In this causal-comparative study, archival passing and retention rates for students identified as at risk from the previous 5 years were compared to 137 students who took the developmental math as a part of the aforementioned customized schedule in the fall semester of 2017. The chi-square test indicated that there was not enough evidence to support an increase in student passing rates in developmental math courses when taken as part of a customized course schedule (p = 0.054) but did show a statistically significant difference in retention rates (p < 0.001). The results of this study might generate positive social change by providing a framework in which collegiate institutions can help to discover alternative methods of helping at risk students succeed academically.

Geometry has the distinction of being one of the oldest subjects given in the high-school. Its subject-matter was formulated and organized by the Greeks into a fine system of thought before the time of Christ. Since leaving the hands of the Greeks, geometry has received only a few minor changes, and these largely in recent years. Heretofore, the study of geometry has been made almost entirely dependent upon memory and reasoning. Geometricians have been slow in adopting the laboratory and observational methods. This thesis has been written to encourage the student in his work of observing geometrical forms, and in the construction of good designs and geometrical figures, and to obtain a better practical understanding of the figures and principles of geometry through the laboratory and observational work.