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              <p>This paper uses analysis of shared video data to discuss teacher responses to public student apparent error. Drawing upon conceptions of student thinking and theories of agency, authority, and mathematical identities, we argue that certain ways of responding to public student apparent error have the potential to elevate student thinking and empower students with mathematical agency, authority, and standing. We also suggest that such teaching practices may be a high-leverage site to develop equitable mathematics teaching.</p>
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