Unpacking the Ambiguous Case to Develop Conceptual Knowledge and Representational Competence

The ambiguous case is a trigonometry topic for which high school students are often told “stay away from angle-side-side.” In many cases, however, these students do not get the opportunity to explore the underlying mathematical context that serves as the basis of this warning. After a briefly presenting an overview of the ambiguous case, the author describes a mathematical activity using simple homemade manipulatives to support secondary and post-secondary students’ work to unpack and understand the ambiguous case. It then discusses how this activity can support teachers’ understanding of representational competence and recommends general practices supporting students' purposeful and effective use of mathematical representations.