Juxtaposing cases of delegating versus withholding authority of mathematical ideation in early algebra classrooms

We will illustrate two cases of teachers implementing the same early algebra lesson exhibiting diametric forms of a teacher practice previously identified in the research literature as a means toward achieving equity—the delegation of mathematical authority. The teacher with greater student achievement gains on an early algebra assessment had greater occurrences of teacher moves that positioned students as having the power to rely on an intellectual authority situated internally or within the community of peers’ “taken-as-shared” knowledge. On the contrary, the teacher with lower gains exhibited greater occurrences of teacher moves that, in effect, resulted in withholding authority from students to form mathematical justifications. Illustrative excerpts of both cases are shared.