By Susan Ruff
Johann’s presentation on partitions was carefully crafted. The math was completely correct, the board work was neat and legible, the delivery was professional, and the timing was perfect. But the talk was so dry and formal that the other students quickly reverted to the blank look that suggests they have more interesting things to think about.
In contrast, Karen’s presentation on generating functions gained and held the attention of many of the students. She successfully conveyed the beauty and power of generating functions . . . to the front half of the class. The rest couldn’t hear her, and they couldn’t tell from the board what she was saying because the board remained blank except for some scrawled examples of functions.
How in the world can I grade such diverse presentations? Each presentation succeeds in its own way, and each has weaknesses. Trying to compare them is like comparing apples and orangutans. Although these vignettes are fictional, they accurately represent the challenge of grading communication: Student presentations and papers are as varied as are the students themselves.
Ideally I’d like grades to support my verbal feedback by communicating both where students can improve and what they already do well. For example, Johann’s carefully crafted but rather dry presentation might receive an A for math, board work, and delivery, but a lower grade for audience engagement. In contrast, Karen’s presentation might receive an A for math and audience engagement, but lower grades for delivery and board work.
One challenge of using such a grading strategy is to create a categorization that successfully captures all of the aspects of what we consider to be an excellent presentation. To this end, one of the MAA minicourses of the 2013 Joint Mathematics Meetings asked participants to create categorized lists of characteristics of effective communication in various contexts. The results are here.
I’ve combined these lists with others created in the MIT Department of Mathematics to generate one general list of characteristics of effective mathematics papers and talks. The resulting list contains about 50 characteristics and reflects the communication priorities of more than 30 mathematicians at a variety of institutions. Here’s a summary:
Characteristics of Effective Student Mathematics Talks and Papers
- The math is correct.
- The constraints of the genre and/or assignment are satisfied.
- The audience can perceive the content (e.g., the content is legible, audible, and uses familiar or defined notation and terminology).
- The paper or talk is crafted to be understood by a member of the target audience who pays attention (e.g., the level of difficulty is appropriate; examples, figures, and explanations aid understanding; the paper/talk is carefully structured; sufficient detail is provided; the relevance of details is clear; wording is precise).
- Paying attention is easy because the content is presented in an interesting and engaging way (e.g., the talk/paper is tightly focused around an interesting topic, the introduction is compelling, important points are emphasized while tedious details are de-emphasized, style and tone are engaging, connections are made across disciplines, the audience is guided to discovery; the work is insightful, unique, or elegant).
I chose to use categories that are functional (e.g., helping the target audience to understand the content) instead of descriptive (e.g., quality of board work) because I believe that if students focus on the goal of communicating successfully, they’re likely to naturally see the importance of board work for achieving that goal. The breadth of each category is clarified by the full list of characteristics of effective student talks and papers.
Of course, this list is valuable not only for crafting effective grading rubrics, but also for guiding teaching. For example, it suggests questions I can use to guide a class discussion on giving an effective presentation. And when I become overly focused on students’ areas for improvement, a look at the list can remind me of all that they are already doing well. In the end, I want Karen to know that she has interesting things to say and she says them well, so she should say them loudly and visibly enough for all to benefit.
Many thanks to the participants in JMM 2013 Minicourse 7: Teaching and Assessing Mathematical Communication: Collaborative Development of Pedagogy, to the workshop co-leaders Mia Minnes and Joel Lewis, to the MAA and the NSF who supported the JMM workshop, and to the many mathematicians in the MIT Department of Mathematics who contributed helpful discussion and rubrics.