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.

Ordering information so content flows logically

If you find yourself reading and rereading a paragraph of exposition with your eyes glazing over, it’s likely that the ideas are poorly connected. A good explanation of how to analyze and improve connectivity can be found in the article “The Science of Scientific Writing” by Gopen and Swan.

In short, each sentence should ideally begin with familiar information, which then introduces the important new information of the sentence. If each sentence starts with something recently mentioned, then there will be strong connectivity between sentences. Connectivity is important because, when there are gaps in connectivity, readers need to work to figure out how the sentences relate to each other.

Although the idea of beginning each sentence with familiar information is simple, identifying and fixing problems with connectivity can be challenging at first for both instructors and students, so connectivity is best taught when students are revising their writing rather than when they are writing their first drafts. During revision, students can first identify paragraphs that don’t seem to be “working” and can then analyze just these paragraphs to improve the information order and connectivity.

Connectivity is important during presentations, but using information order to create connectivity while speaking is perhaps more challenging than can be reasonably expected of students; instead, presenters can explicitly state how ideas are related to each other by using guiding text.

Although connectivity helps text to flow, sometimes flow is not desirable because we want readers to stop and think. Here is a description of what can happen when connectivity is taken too far.

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