Beyond answers: exploring the dual roles of framing and responding in students’ mathematical thinking
摘要
This study examined how middle school mathematics teachers and pre-service mathematics teachers (PMTs) frame students’ mathematical thinking (SMT) and respond to their ideas in the context of problem posing. Additionally, it investigated how teachers’ and PMTs’ framing of SMT influences their instructional responses. The data included responses from 20 teachers and 20 PMTs regarding three different solution processes for two problems, which were solved through additive and multiplicative reasoning. The results revealed that the participants tended to assess students’ answers as indicators of learning, problems to be addressed, foundations to build on, messages to be deciphered, and resources to be collected, respectively. The participants’ responding approaches are mainly determined as responsive problem posing, followed by considering students’ existing strategies and anticipating existing and future strategies. Additionally, the results showed that teachers’ and PMTs’ response approaches varied based on how they framed SMT.