Some Discretion About the Future of Discrete Mathematics

With the remaining instructional time in the course trickling away so rapidly, Dr. E of Discrete Mathematics II has introduced a new lesson structure to continue engaging students in the material. At the beginning of each class, he will spin a virtual wheel with many divisions, upon which the names of the remaining lessons from the textbook will be written.

Wherever the wheel lands on a given day dictates which lesson will be taught, and the one selected will be removed after its completion to avoid the possibility of repeatedly teaching the same material. It must be noted that all of the remaining End-of-Chapter sections and all three appendices are included in this rotation.

There are many careful methodology but the one that takes precedence over any other is Dr. E’s desire to embody the discreteness inherent to the course. By offering a random lesson every class, he can effectively minimize the possibility of teaching lessons in an order that implies continuous motion, the polar opposite of what “discrete” represents. The suddenness of the change itself further plays into this philosophy of non-continuous movement throughout the year.

A second major reason for this abrupt alteration to the course structure, albeit significantly less important than adhering to the dictionary definition of discrete, is to ensure that students consistently pay complete and indivisible attention to the material. If the material can originate from any section in the textbook that was not previously taught, then students will thoroughly and meticulously study. He notes that this will only occur if they wish to maintain stable performance in Discrete II. Dr. E believes the ideal length of nightly studying should be around 32 hours.

If Dr. E deems this new model to function well, he will implement changes at undisclosed intervals. Some potential modifications include reintegration of past content that was last taught one month or longer ago in the wheel to guarantee having roughly 800 pages of content available to teach on any given day. Dr. E’s reasoning for not publicly announcing when the inclusion of past content will occur is simple: to stay in line with the essence of “discreteness” and instill it into his pupils’ hearts.

An additional future pathway to keep students on their toes is the sporadic addition of individual questions to assignments before they are due. This will not have any exceptions and can affect anything from a standard homework assignment to the final exam. Dr. E believes that, given his students’ present enjoyment of the course, they would be pleasantly surprised and excitedly plunge into additional opportunities to learn and practice.