The relation between mathematical achievement in early childhood and future academic success is well established. However, the effect of instruction on mathematical performance is less well-documented and often reliant upon self-report instruction measures and standardized achievement measures. Therefore, this study seeks to use observational data to examine the role of classroom mathematics instruction in the growth of adaptive early mathematical skills across the kindergarten school year. The first research aim identified the relation between children's math skills at school entry and the rate at which their math skills grew during kindergarten. The second research aim determined whether student characteristics, such as age or sex of the child, predicted different mathematical skills. The third research aim examined the effect of observed classroom mathematics instruction on the growth of children's early mathematical skills. Four schools, fourteen classrooms, and 98 children were recruited to investigate these research aims. Children completed counting and addition measures three times during the school year from an individualized assessment novel to the United States, called Math Garden. Teachers recorded an entire school day using an audio recorder in the middle of the school year. First, longitudinal multilevel models were used to identify the relation between school-entry skills and the rate of growth on counting and addition capabilities. Second, multilevel models determined whether student characteristics predicted counting or addition abilities at the beginning of the school year, or growth across the kindergarten year. Last, multilevel models assessed whether content, quantity, and quality of kindergarten classroom mathematics instruction predicted the growth of children's counting and addition skills. In this sample, children grew significantly in both counting and addition skills across the kindergarten year. However, the rate of growth for addition capabilities was four times that of counting skills. Children with low entry skills showed a larger rate of growth in both skills across the school year. Children's age in the beginning of school and sex of the child did not predict entry or growth in counting abilities, however, boys performed better than girls on addition in the beginning of the school year. The quantity, quality, and content of classroom mathematics instruction did not predict growth in counting or addition abilities across the kindergarten year. This study was one of the first to use audio recordings to investigate kindergarten classroom mathematics instruction and its contribution to early mathematical growth. Children with the lowest levels of math skills grew the most across the kindergarten year, suggesting a focus on basic skills continues to consume early grades. Inconsistencies in sex differences on early mathematical tasks highlight the need for future work to address skill proficiency as an essential context. The results suggesting classroom mathematics instruction did not contribute to children's growth in early mathematical skills highlighted important methodological differences between previous research, as well as a need for more robust measurement in assessing classroom mathematics instruction for future work. [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.]