School choice is a tool used to fight inequality and is important to consider how students are assigned to schools. The essays in this dissertation study mechanisms designed to improve and understand students' attendance at schools. Chapter 1 examines the inequality caused by the COVID-19 pandemic with respect to schools switching to a hybrid option. During the pandemic, school districts adopt hybrid schedules to continue the education of the students while maintaining social distance. In a hybrid schedule, students in the same classroom are usually divided into two groups, and students only in the same group can physically attend class together two days a week. School districts do not take the preferences of the students/parents over the days they would like to come to school into account during this procedure. In this paper, we propose a solution that divides students into groups based on their preferences. Our solution respects the number of classrooms initially reserved for each grade and enables possible efficiency gains by swapping classrooms across grades. Moreover, when there are two alternative schedules provided for students, our solution is immune to preference manipulations. In Chapter 2 we analyze the application of a reserve system to the Boston Mechanism. School choice enables disadvantaged students to have access to better schools and is an important tool in the fight against inequality. A reserve system sets aside a predetermined number of seats for under-represented groups. In this paper, we analyze the application of a reserve system under the Boston Mechanism. The Boston Mechanism is widely used by school districts in the US because it maximizes the number of students who receive their reported first choice. We show how the current inclusion of reserve systems to the Boston Mechanism by school districts, such as Charlotte-Mecklenburg, can negatively impact students. We propose a modified mechanism that respects reservations while eliminating waste. Moreover, it Pareto improves upon the current applications of reserve systems under the Boston Mechanism and is not outperformed in terms of incentives. In chapter 3 we develop a new methodology to estimate a student's true preference order. The estimation of student preferences from revealed choices typically uses a student's reported rank-order list. However, a student who chooses to not report a rank-order list of schools has revealed information about her beliefs of acceptance over her preferences but is often not included in current estimation strategies. In this paper, we adopt the bounds approach, introduced by Lu (2022), to estimate student preferences and compare it to the commonly used exploded logit model. We present simulation evidence that suggests the bounds approach has a smaller bias in the estimators while increasing the number of students in the data. [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://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]