To summarize, the three participants used their SMK to participate in discussions
related to subject matter by raising questions, investigating solutions, and connecting with
PCK. Fatima took the opportunity to pose questions that resulted in the exploration of the
multiplicative relationships afforded by the tasks and initiated a whole-group discussion
about SMK. Faith’s participation in the tasks centered on the representations used by the
assessment items to engage students in the mathematics. Kathy’s input involved investigating
a solution to a problem. While Fatima’s and Faith’s use of their SMK influenced
their learning and the learning of the group, Kathy’s contribution did not advance the PCK
or SMK goals of the task sequence for the group but rather allowed her to make sense of
her group member’s strategy and clarify the mathematical issue for herself.