Determining How Order of Quantification Impacts Mathematical Logic
This task was adapted from the following reference:
Vroom, K. (2020). Guided reinvention as a context for investigating students’ thinking about mathematical language and for supporting students in gaining fluency (Doctoral dissertation). Dissertations and theses.
We intentionally chose a geometric context as an introductory task on multiply quantified statements. We believe that such a task has at least two advantages:
- Geometric examples promote deep, initial engagement with the underlying logic of a multiply quantified statement. In contrast, mathematical statements involving algebraic equations of at least two variables may predispose students to rely on procedural computation, offloading attention to the logic itself.
- Students' construction of diagrams for visualizing each statement may support attention to how quantification order impacts logic. When drawing a picture for a given statement in this task, the order in which students add components to and label variables on their diagram corresponds naturally with how the order of quantification determines the mathematical logic.