2026 Theses Doctoral

Exploring the Factors Influencing Teachers’ Use of Proof and Justification in the Classroom

Barr, Davidson

Teachers must make decisions about the frequency and type of proof and justification included in their teaching. Researchers have identified that a teacher’s beliefs, knowledge, and context can influence their behavior, but less so in the subdomain of proof and justification. In addition, though a common term in the literature, how teachers conceptualize the “conceptual reach” of their students is not well understood.

This study explores the factors that affect a secondary school teachers’ use of proof. Seven participants from two independent schools in New Jersey were observed teaching one geometry and one non-geometry class, and follow-up interviews were conducted with each participant. Using an analytical framework, instances of proof and justification were counted and categorized. Interviews were coded to identify specific beliefs, knowledge, and contexts that influence a teacher’s use of proof and justification and find links to behaviors stemming from those factors.

Next, grounded theory was conducted on the interview transcripts to determine how teachers conceptualize the “conceptual reach” of their students. Additionally, evidence was collected to determine if conceptual reach is primarily a product of teacher beliefs, or primarily a characteristic of the students. The results of this study identified several beliefs, contexts and pieces of knowledge that influence teacher behavior when using proof and justification in the classroom. Findings also indicate that teacher behavior is primarily driven by the teachers’ perceptions and beliefs about the conceptual reach of their students rather than by the students’ conceptual reach directly.