Mathematical Communication is a developing collection of resources for engaging students in writing and speaking about mathematics, whether for the purpose of learning mathematics or of learning to communicate as mathematicians.

Professional Communication

Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis. This week students learn about uniform convergence (Rudin pp. 150-154).

Authors: This recitation was developed by Susan Ruff. The software engineering research is joint with Michael Carter, the case study is by Les Perelman, and the Active Listening story is by Fisher, Kopelman, and Schneider.

Communication objectives: Communicate professionally

Recitation: This recitation has three parts,

  • a summary of research into the professional communication skills needed by software engineers,
  • an explanation of one of those skills (active listening),
  • and a case study from industry of (un)professional communication (an e-mail “flame war”) followed by the active-listening exercise of identifying why each player acted as they did as well as a discussion of when and how the flame war could have been diffused.

Research on software engineering communication

Individual: Review summary of research into the communication skills needed by software engineers (applicable to all professionals)

Mini-lecture & class discussion:
Briefly summarize research. Tell students that each skill has associated details or story from interviews of software engineers, so invite them to ask for more details. Give a few more minutes to look at the handout (the table from the paper linked above), and address questions as they arise, until conversation slows.

Active listening

Note that active listening is considered one of the most important skills by software engineers, is expected of recent graduates by hiring managers, and is seen as lacking in recent graduates. Summarize meaning, purpose, (& difficulty) of active listening.

To illustrate difficulty of active listening, give example from literature. There’s an ambiguous illustration that can be seen either as an old woman or as a young woman. Researchers modified the illustration so it was clearly an old woman and preconditioned one group by showing them that illustration. To another group they showed a version of the illustration that had been modified to be clearly the young woman. When they showed the ambiguous image to each group, each person saw the image they’d been preconditioned to see. When members from one group tried to convince members from the other, they could not do so. Seeing from another person’s point of view when you have your own preconceptions can be *very* difficult. So active & effective listening takes effort.

Case study from industry

Break students into 2-4 groups of 2-3 students each. Give each group a letter A or B.
Have students read Les Perelman’s e-mail flame war case study and answer the associated discussion questions as a group. The final question has two versions, one for group A and one for group B. Tell students to practice the active listening strategy of trying to put yourself in the other person’s shoes to understand what they’re saying and why.

Class discussion: What are the purposes of each communication (stated or unstated, professional or unprofessional)? How could each person have achieved their professionally acceptable purpose(s) professionally?

Points to address:
Remain professional.
Don’t send e-mail when you’re angry. Go for a walk, sleep on it, do whatever’s necessary to avoid sending e-mail when angry, even in urgent situations.
When possible for “sensitive” situations, talk in person or on the phone instead of by e-mail. (It’s hard to convey tone accurately by e-mail, and it’s easier to adjust to reactions of the audience in person or on the phone. People are more likely to be polite/respectful in person and on the phone.)

Instructor observations

Timing note: The e-mail flame wars part of the class requires at least a half hour. A half hour does not permit time to discuss everyone’s answers, but does give enough time to discuss the most important points about how to communicate professionally in a stressful situation.

This recitation has been offered twice. The first time it was offered, the research results were interesting to students because they were new results. The second term the recitation was given students responded that the points addressed by the recitation (particularly the discussion of the case study) were obvious.

This professional communication recitation is no longer offered along with Real Analysis, both because it is seen as unimportant to students who have not yet spent time in industry and because it is specific to engineering rather than to mathematics.

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