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The Fermilab muon g-2 experiment aims to measure the anomalous magnetic dipole moment of the muon, aμ , to a precision of 140 ppb. The current value of aμ was measured at the Brookhaven g − 2 experiment, whose final result was published in 2006 with an uncertainty of 0.54 ppm [1]. The deviated from the Standard Model (SM) prediction by up to 3.6 σ, causing international intrigue that motivated the repetition of the experiment with increased statistics. The experiment's storage ring (SR) magnet was transported to Fermilab in 2013 to make use of its high-intensity muon beam. This will facilitate a 21-fold increase in statistics that will contribute most of the improved precision in the aμ measurement. In addition, improvements to the experimental hardware are intended to reduce the systematic uncertainty. A major improvement is a new straw tracking detector system, which will measure the beam profile continuously throughout the experiment, in order to mitigate sources of systematic error associated with the beam position and motion. The straw trackers will also be used to perform a muon electric dipole moment (EDM) search. The current world's best limit on the muon EDM was placed by the Brookhaven g − 2 experiment [2]. The signal for a muon EDM in the g − 2 experiment can be directly measured with the straw tracking detectors, so the upgraded tracking system is expected to enable a reduction in the current limit by a factor of 100. This thesis will describe the design and construction of the straw tracking detectors that took place at the University of Liverpool. The development and optimisation of a track extrapolation algorithm for propagating the track parameters of the decay positrons back to the muon decay position will be presented. The use of this algorithm in measuring the beam profile during the commissioning phase of the experiment will be discussed, and finally, the development of a muon EDM simulation and a preliminary sensitivity study using the track extrapolation algorithm will be presented. [1] Muon g − 2 Collaboration, G. W. Bennett et al., Final report of the E821 muon anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006) 072003. [2] Muon g-2 Collaboration, G. W. Bennett et al., Improved limit on the muon electric dipole moment, Phys. Rev. D 80 (2009) 052008.

For the more than 15 million children currently living in poverty in the United States, the risk for academic failure is high. With significantly greater likelihood of experiencing hunger, poor physical health, abuse and neglect, psychological disorders, developmental delays, and learning disabilities, it is not surprising that children living in poverty are five times more likely to drop out of school compared to children from higher socioeconomic backgrounds. However, despite these immense challenges, it must be noted that not all children experiencing economic hardship are failing in school. Parents, who are children's first teachers, play a critical role in helping their children to beat the odds and excel in school. Parents' promotion of children's academic resilience is especially crucial for Black children, who are three times more likely than White children to live in poverty. In order to develop interventions and strategies to support the academic success of low-income Black children, it is necessary to understand the specific attitudes, beliefs, and behaviors of low-income Black parents that are positively associated with children's academic achievement. Using a three-paper structure, this dissertation critically examined how socioeconomic status (SES) and race influence the attitudes, beliefs, and behaviors of low-income Black parents and, in turn, the academic achievement of low-income Black children. The first paper is a systematic review of literature that examined the mechanisms through which Black parents' racial socialization strategies promote academic achievement among low-income Black children in elementary school. Through an ecological systems lens, the systematic review identified child, parent, family, school, and community level factors that facilitate the effects of parental racial socialization practices on the academic achievement of low-income Black children. For the second paper, a confirmatory factor analysis--the first step of conducting general structural equation modeling (SEM)--was conducted in order to ensure that the Elementary School Success Profile (ESSP), an online multidimensional socio-environmental assessment tool used to identify risk and promotive factors for children's academic success, performed the same for low-income Black and White students when assessing the home educational environment and children's academic achievement. After Paper 2 findings indicated measurement invariance and demonstrated that the home educational environment and academic achievement of Black and White students would be measured the same way, multigroup general SEM was conducted in the third paper to test if the relationship between home educational environment and academic achievement was moderated by race. The final paper revealed that the relationship between home educational environment and children's academic achievement was moderated by race with low-income White students experiencing increases in academic achievement and low-income Black students experiencing declines in academic achievement despite both groups experiencing the same level of home educational support. Altogether, the three papers demonstrate the importance of disentangling the effects of SES from the effects of race in order to understand the unique needs and challenges faced by low-income Black families. Families who are low SES are not homogenous as they are affected and respond differently to socioeconomic risk factors based on race. By examining the protective effects of parental racial socialization strategies on the academic achievement of low-income Black children, the findings from this dissertation can be used to develop culturally relevant social interventions to support both Black parents and Black children. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Despite uncertainty related to student outcomes resulting from remediation (Bettinger & Long, 2009), eleven states mandate remedial education through common placement testing and standardized cutoff scores rather than permitting individual postsecondary institutions to establish remediation guidelines. Colorado, in particular, offers an exemplary look at how such policies have manifested on the state level. This policy analysis used a fixed effects model on panel data in order to determine the impact of statewide mandatory remediation policies on college graduation and persistence rates for states as a whole as well as at the two-year and four-year institutional levels. Examining the larger national context revealed statewide mandatory remediation policies offered no significant impact on state-level college degree completion or retention rates. A closer look at the state of Colorado showed similar null effects on community college graduation rates. However, institutional retention rates were significantly improved at all levels of higher education as a result of Colorado's statewide mandatory remediation policy. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

There is an enduring debate in the mathematics community concerning how to teach mathematics for understanding. Encouraging the development of mathematical reasoning among students is been a major goal of mathematics education. To encourage this development, students must practice mathematical reasoning in the classroom. The project reported here examines an episode of discourse taken as an example of effective teaching and learning. The unit of analysis was the discursive move, defined by its purpose in achieving a given learning goal. Elements of discourse considered include the type and description of the move in context, the classroom practices implied or observed, the perception of mathematics promoted, the diversity of perspectives presented, and the activity structure. These elements helped to identify features of the discourse that promote student reasoning.