Abstract
Justification has received an increased emphasis in more recent years and is considered an essential component of mathematical reasoning and sense making. Despite its importance to school mathematics, the practice of engaging students in constructing justifications remains a hurdle for teachers. This mixed methods research study explores the influences on levels of student-voiced mathematical justifications in 4th-12th grade classrooms. Interview data, teacher assessment data, and classroom observation data were analyzed to gain a deeper insight into the classroom practices of teachers who had received extensive professional development on mathematical justifications. Results from the quantitative study indicated that mathematical knowledge for teaching and teacher demonstration of constructing their own mathematical justifications did not have a strong relationship with the level of student-voiced justifications produced in their classrooms. Findings from the qualitative study included multiple themes identified across eight teachers’ data describing influences on the level of mathematical justifications produced in their classroom. Themes associated with high level student-voiced justifications include: press for reasoning, students are engaged in thinking mathematically, and build perseverance. Themes associated with low level student-voiced justifications include: emphasis placed on procedural understanding, teacher holds majority of mathematics authority, and students work in isolation. Overall findings from this dissertation study provide descriptive influences on levels of student-voiced mathematical justifications in the classroom. Findings can provide classroom teachers with implementation ideas to foster a classroom environment rich with high levels of student-voiced mathematical justifications. Further research could focus on developing a greater understanding of what influences levels of student-voiced justifications in broader and more diverse classroom settings. A possible influence on the level of student-voiced justification produced in the classroom that was apparent in the teacher interviews (but not researched extensively in this dissertation study) is teacher beliefs regarding effective teaching and learning.