In this article, three instructional situations demonstrate the value of using an "unknown" student's work to allow the advancement of students' mathematical thinking as well as their engagement in the mathematical practice of critiquing the reasoning of others: (1) introducing alternative solution strategies; (2) critiquing inaccuracies…

That the quality of teachers' knowledge has direct impact on students' engagement and learning outcomes in mathematics is now well established. But questions about the nature of this knowledge and how to characterise that knowledge are important for mathematics educators. In the present study, we examine a strand of "Specialised Content…