The purpose of this embedded sequential explanatory case study with a quantitative→qualitative two-strand design of inquiry was to explain how the quality of teacher-student relationships and the gap of cognitive styles between teachers and students impact student achievement. The population for the quantitative strand of research was comprised of 11 career and technical education (CTE) teachers and 210 CTE students, representing six disciplines within CTE. The study occurred in a suburban high school in western North Carolina. Leader-member Exchange (LMX) theory and Adaption-innovation theory guided the research.

In the quantitative strand, the Kirton Adaption-Innovation Inventory was used to measure the cognitive style of teachers and students, a researcher developed survey was used to measure dyadic intensity, the Leader-Member Excellence—Shared-Leadership Exchange instrument was used to measure the perceived quality of dyadic relationships between teachers and students, and the North Carolina CTE end of course tests were used to measure student achievement in CTE classes. Additionally, demographic information was collected from teacher and student participants. In the qualitative strand, four teachers and eight students were interviewed. The purpose of the qualitative strand was to investigate how teachers and students describe their dyadic relationships. Data from both the quantitative and qualitative strands were mixed to allow for a stronger interpretation and explanation of the quantitative and qualitative results.

Statistically significant relationships were identified among the various dimensions of teacher-student relationships. There was a weak, positive relationship between dyadic intensity and student GPA. A weak, positive relationship was found between dyadic intensity and teacher LMX. There was a weak, positive relationship between dyadic intensity and student LMX. There was a weak, positive relationship between student GPA and teacher LMX. A moderate, positive relationship was found between student GPA and student LMX. A moderate, positive relationship was found between student GPA and student achievement. Additionally, there was a moderate, positive relationship between teacher LMX and student LMX. A path analysis of quantitative data indicated that student GPA had a significant effect on teacher LMX. Teacher LMX and student GPA had a significant effect on student LMX. Lastly, student GPA had a significant effect on student achievement. Qualitative data validated the quantitative findings. Further, five themes surfaced from the qualitative data providing support for additional findings.

The researcher recommended future investigation of the impacts of leader-member exchange and cognitive style on student achievement using alternative indicators of student achievement, an exploration of how involvement in a career and technical student organization (CTSO) interacts with teacher-student relationships and student achievement through the lens of leader-member exchange, and an examination of the impacts of leader-member exchange and cognitive style on student achievement outside of the context of CTE. The quality of teacher-student relationships from both the teacher's perspective and the student's perspective are affected by a student's grade point average. Student grade point average has a significant effect on student achievement. Much remains unknown about the antecedents of teacher-student relationships and how the relationships between teachers and students may interact with student achievement.