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Although students’ invented strategies typically prove to be meaningful and effective in improving the student’s mathematical understanding, very little is known about how teachers interpret and respond to student-invented strategies. As part of a larger effort to characterize mathematics knowledge for teaching, this study examined, through a teaching-scenario task, the nature of one hundred ten elementary preservice teachers’ reasoning and responses to a student’s invented strategy for whole number subtraction. This study also examined challenges reported by preservice teachers attempting to connect the student’s informal strategy to the traditional method. Implications for teacher educators and future researchers are discussed in accordance with the findings of the study.