In summary, we claim that Fatima made advancing contributions that focused on and
extended the subject matter goals embedded within the tasks. She used the opportunities
the task sequences provided to draw upon her MKT of equipartitioning and rational
number to extend her SMK, relating the learner’s logic presented by the professional
learning tasks with her mathematical perspective. Similarly, Faith’s strong equipartitioning
MKT allowed her to participate in SMK discussions. However, her rational number MKT
may have moderated this participation and resulted in connecting contributions that related
subject matter discussions to issues of teaching and learning rather than extending them. In
subject matter discussions, Kathy made clarifying contributions that supported her in
understanding the mathematical issues in subject matter discussions. However, her less
developed MKT of both equipartitioning and rational number may have limited her
influence over the group’s progress toward the embedded subject matter goals. Thus, these
teachers’ MKT mediated their participation in subject matter discussions that arose from
professional learning tasks purposefully designed to support their learning of the LT.