The objectives for this study were to develop a checklist specifically focused on evaluating preservice elementary teachers' mathematics lesson plans through the lens of Universal Design for Learning (UDL) and to analyze some mathematics lesson plans using the UDL-oriented checklist. Information on the principles, guidelines, and checkpoints of UDL and existing checklists were used to structure the new checklist. Two rounds of expert review resulted in a list of 73 strategies considered essential for mathematics lesson planning; those were included in the Universal Design for Learning -- Mathematics Lesson Plan Checklist (UDL-MLP Checklist). The strategies, referred to as UDL criteria in the checklist, were divided into two lists: the priority criteria and the accommodation criteria. The priority criteria were considered important for mathematics lesson plans regardless of the mathematical topics and students' special needs. The accommodation criteria would provide support for teaching some mathematical topics and would need to be addressed in the lesson plan depending on the special needs of the students. The research question guiding this study was: Using the checklist developed for this study, what criteria of Universal Design for Learning are present in preservice elementary teachers' mathematics lesson plans, and in what ways do preservice elementary teachers provide evidence of those criteria? Eighteen preservice elementary teachers' mathematics lesson plans were collected and reviewed using the UDL-MLP Checklist. The descriptions of plans by preservice elementary teachers (e.g., activities they designed, instructional strategies they planned to use, or methods they used to evaluate students) were considered as evidence of UDL criteria. Evidence of 49 UDL criteria was presented in the 18 mathematics lesson plans. The frequency of evidence for UDL guidelines 7 and 8 (Providing Options for Recruiting Interest and Sustaining Effort & Persistence) and UDL guidelines 2 and 3 (Providing Options for Language Symbols and Comprehension) was notably higher than for other UDL guidelines. Additionally, this study identified the lesson plan sections where evidence for each UDL criterion was located and provided a representative example from one lesson plan illustrating how each UDL criterion was used in a specific mathematics context. [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.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]