How do preservice mathematics teachers analyze and respond to student errors in solving probability problems using tree diagrams?

Abstract

This case study examined the knowledge of preservice mathematics teachers (PMTs) in analyzing and responding to student errors. Participants were 41 master's level PMTs who had completed foundational mathematics education courses. They evaluated hypothetical student work solving a compound probability problem using a tree diagram. Through fine-grained qualitative analysis of written responses, researchers found PMTs proficiently identified and interpreted errors, employing both “show-tell” and “give-ask” response strategies. Key weaknesses included over-emphasis on procedures, low active utilization of errors, and communication barriers. The study highlights implications for enhancing PMTs' error-handling skills in teacher education and improving probability teaching.