This dissertation is devoted to a history of the New York State elementary school teacher certification requirements, specifically in mathematics, during the nineteenth century. In the last half of nineteenth century, teacher education and uniform certification procedures were beginning to become the norm in the educational systems throughout the United States. The purpose of this study was to determine the ways an individual could obtain a elementary school teachers' certificate in New York State at the genesis of teacher certification examinations and to establish an understanding of what mathematical knowledge was required for elementary school teachers in order to obtain a State Certificate. This study analyzes multiple primary sources, including annual reports from New York State and New York City, along with the State Certificate examinations. The examinations in arithmetic, algebra and geometry are analyzed for the mathematics topic of the questions, the number of steps needed to complete the question and the categorizing of the questions according to Bloom's taxonomy (CBT). Five examinations of each subject, arithmetic, algebra and geometry, are analyzed, from the years 1875 to 1898. The topics addressed on the examinations, the number of steps to complete the questions and the CBT of each question are determined and used to establish the required mathematical knowledge of the elementary school teacher. The analysis of the mathematics examinations for State Certificates showed that the content required for elementary school teachers were comparative to the high school mathematics curriculum at the time. The content on the examinations for mathematics was more than the course of study they were going to be teaching in the elementary schools. They were required to have a broad and sophisticated mathematical education, however, less sophisticated than offered in the University. Also on the mathematics examinations, teachers were not assessed in what is now called pedagogical content knowledge. [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.]