Preservice teachers’ response and feedback type to correct and incorrect student-invented strategies for subtracting whole numbers

• The role PSTs’ specialized content knowledge (SCK) plays in their ability to respond to student-invented strategies was investigated.
• SCK seemed to relate to PSTs’ tendency to create student-centered approaches.
• However, there was no such relationship between SCK and PSTs’ feedback type.
• Seven factors were identified as influencing PSTs in responding to student work.
• Six challenges were reported in connecting student strategies to a traditional method.

Despite the important role of teachers’ interpreting and responding to student ideas in teaching mathematics, there are many unanswered questions related to teacher learning and the role of errors in student-invented strategies. This study examined the reasoning and responses of 140 preservice teachers (PSTs) to students’ correct and incorrect strategies for whole number subtraction, as well as the PSTs’ perceived challenges in connecting student strategies to traditional methods. The study also investigated the role that PSTs’ specialized content knowledge plays in their ability to respond to correct and incorrect student-invented strategies, with respect to student-centeredness and feedback type. Results reveal that although some PSTs interpreted the validity and generalizability of the student methods incorrectly and justified them from the procedural aspect of each method, PSTs’ specialized content knowledge (e.g., the mathematical depth of the PSTs’ interpretation of student work) seemed to relate to their tendency to create student-centered approaches. However, specialized content knowledge did not seem to support PSTs’ feedback type in the domain of whole-number subtraction.