Beyond the Given: Stretching Mathematical Thinking Through Journaling. Issue 10 (26th November 2017) - Hamdan, May
Abstract: This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one that they themselves can justify. This experiment was conducted in the Discrete Mathematical Structures course; as it contains several subtopics, each of which uses a discrete set of elements with specific conditions. The textbook does not mention how those conditions are effectively put to use, and often uses the natural numbers as the default domain. Students are required to identify in their journals the exact properties that the elements need to have, justify how they are being put to use, and in ambitious cases attempt to sharpen them if possible. This activity can be adapted to different contexts and is not specific to the topic of Discrete Mathematical Structures.