Concerns about low mathematics achievement have created a push to increase national mathematics proficiency levels through research and policy. Efforts have largely focused on early mathematics interventions for students with or at risk for mathematics learning difficulties implemented within multi-tiered response to intervention (RTI) frameworks. Within these models, important educational decisions are based upon instructional response, making meaningful categorization of student responsiveness to intervention paramount. Across research and practice, intervention outcomes are typically thought of as a binary, with students considered either responsive or non-responsive to intervention. However, defining and categorizing responsiveness in more complex ways may reveal important differences between subgroups of students who exhibit distinct patterns of responsiveness over time. The present study explored patterns of response to an early mathematics intervention using data from the ROOTS Efficacy Project. Participants included kindergarten students at risk for mathematics difficulties who were randomly assigned to the ROOTS intervention condition (n = 880). Results of a latent profile analysis indicated that variability in response to a generally effective intervention was best captured by a more complex categorization framework encompassing four distinct response profiles: a moderate-risk, mildly responsive group; a moderate-risk, delayed response group, a high-risk, strongly responsive group; and a lower-risk, non-responsive group. Membership in each response profile group was predicted by pre-intervention performance on measures of both early mathematics and cognitive skills (visual-spatial, fluid reasoning, and working memory). On average, students with lower initial math skill and cognitive performance demonstrated stronger intervention response. Implications for future research and practice are discussed. [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.]