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Interactions around unexpected, incorrect, or dis-preferred responses can be powerful sites of learning for both teachers and students. The information that teachers uncover through probing student thinking can then guide their pedagogical response. We report on a study of prospective teachers' skills and capabilities around a particular problem of practice: eliciting student thinking when a student has an incorrect answer. In this case, if the student's thinking is sufficiently probed, the student is able to recognize the mistake and revise their work. Focusing on prospective teachers at the beginning of a teacher preparation program, we illustrate how knowledge of this kind of eliciting skill can be gathered through the use of a live teaching simulation. Our findings reveal that these prospective teachers were more fluent with eliciting the student's process than the student's conceptual understanding. Further, they focused more on eliciting the revised method and/or solution than asking about why the mistake was made. We consider the findings in terms of the skills brought by prospective teachers that could be built upon in teacher education, skills that need to be learned, and skills that need to be unlearned. [ABSTRACT FROM AUTHOR]

This article discusses the relationship of measure scores to classroom teaching and student learning. It discusses the formulated assumption as well as several observable inferences about the relationship of the measures of teachers' mathematical knowledge for teaching to their actual classroom mathematical work.