xvi, 115 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / There is convincing evidence that many students struggle to learn mathematics proficiently. One plausible contributor to the low math achievement is the quantity and quality of learning opportunities provided in classrooms. These opportunities may fall short of addressing the learning needs of students, especially those at risk for failure in mathematics. Against this backdrop, the purpose of the dissertation was to validate a direct observation instrument. The Coding of Academic Teacher-Student interactions (CATS) observation instrument systematically measures the instructional interactions that occur between teachers and students during kindergarten mathematics instruction. The dissertation harvested data from the Early Learning in Mathematics: Efficacy Trials in Kindergarten Classrooms (ELM-ETKC) project, a randomized control efficacy trial. ELM-ETKC is investigating the efficacy of the Early Learning in Mathematics curriculum within 65 kindergarten classrooms across three school districts in the state of Oregon. The dissertation utilized student and classroom-level information collected in 65 ELM-ETKC kindergarten classrooms across the 2008-2009 school year. At the student level, data included scores from 929 kindergarten students on the Test of Early Mathematics Ability-Third Edition (TEMA) and two curriculum-based measures: Oral Counting and Number Identification. Information at the classroom level included observational data from 191 classroom observations. Utilizing the extant data, the dissertation addressed research questions related to content validity, discriminant validity, and criterion-predictive validity. Additionally, the study examined if observers could reliably use the CATS instrument in classrooms. To address two of the research questions, the dissertation employed a hierarchical design and fit multilevel models that nested (a) observations within classrooms and (b) student posttest TEMA scores within classrooms. Predictors of the models included student risk status and rates of observed instructional behaviors. The study found promising evidence for using the CATS instrument to collect information about the quantity and quality of kindergarten mathematics instruction. Independent observers reached acceptable interobserver agreement across the observations. The CATS instrument demonstrated high levels of content validity, as well as sensitivity to treatment conditions. Results also found statistically significant relationships between the mean rate of instructional behaviors and student posttest TEMA scores. Implications for future research and practice are provided. / Committee in charge: Robert Homer, Chairperson, Special Education and Clinical Sciences; Christopher Murray, Member, Special Education and Clinical Sciences; Scott Baker, Member, Special Education and Clinical Sciences; Joe Stevens, Member, Educational Methodology, Policy, and Leadership; Thomas Dishion, Outside Member, Psychology