Reading Discrete Mathematics: A Semester-long Assignment in Communication

Steven M. Hetzler and Robert M. Tardiff

Salisbury University

The authors use a semester-long team assignment in a Discrete Mathematics course to improve students’ abilities to read and write mathematics. This talk will summarize the assignment and evaluation procedures, the reasons we think the assignment works, the course topics about which students read and write, and some features of previous versions of the assignment which have been revised. We will also present some samples of student work, to show what students capabilities are and to show the potential for student improvement.

The primary objective of the assignment is to improve student reading abilities and reading attitudes in mathematics. Many math instructors have lamented that students are weak math readers and do not recognize the importance of reading math in their textbooks. By providing feedback from the instructor as well as from a small group of peers, we use this assignment as formative evaluation of the students’ reading skills. We employ frequent encouragement and praise of quality work and correction of weaknesses spread across an entire semester to strive progressively toward improved reading. Also, we employ this assignment across an entire semester, not just one time, to stress how important it is to read math when trying to learn math.

Each team of approximately four students summarizes every section of the text that we cover in class. The task of writing the summary rotates through the group, but each team member is expected to respond to each rough-draft summary. This process of draft, response, and final version is intended to give weaker students a chance to read good summaries and to receive more feedback than the instructor alone can provide. When the final version of the summary is written, the instructor grades it on a four-point scale. Summaries will receive all four points if they contain all the significant ideas of a section, employ examples effectively to illustrate the key concepts, and clearly communicate with other students.

In this course, students have the opportunity to summarize a variety of mathematical topics. It is an introduction to discrete structures for mathematics, statistics, and computer science majors. It therefore includes numerous applications, such as Combinatorics, digraphs, and networks. The course is also an introduction to mathematical logic and proof, so students read about topics such as argument form, logical equivalence, direct and indirect proof, and the Principle of Mathematical Induction. Finally, we use this course to prepare students for advanced abstract math topics, such as number theory, equivalence relations, and group theory. Such a variety stretches a student’s reading abilities, probably outside of any special favorites she or he may have.

Since this is the third semester in which this assignment has been used, a number of modifications have been made. A sample summary of the first section of the text has been written to get the students started. The grading scheme has been changed; too many students didn’t take the assignment seriously, to the significant detriment of their teammates. We have also tried to balance the work required for this assignment with all the other responsibilities of the course. This balance applies not only to students, homework, and exam studying, but to instructors, grading, and class preparation!

We will present evidence that student reading and summary-writing abilities are improving in this course, through this assignment. We hope that others will find this assignment useful in addressing these significant learning objectives.