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.

Excessive connectivity: too much of a good thing

Here’s a description of what can happen if connectivity is taken to an extreme. This is from a comment written to a student:

This paper exhibits excellent connectivity. I’m glad that you’ve gone through the exercise of figuring out how to create connectivity between every adjacent pair of sentences in the paper, because now you’ll clearly be able to use that tool whenever you need to.

Applying connectivity continuously, though, introduces problems. When there is strong connectivity between each pair of sentences in a paper, for the reader it’s like you’re on a train that won’t stop to let you off. Each sentence hands you off to the next which then pulls you along to the next, and you can only wonder where you’ll wind up. So although connectivity is a powerful tool for helping the reader along, it’s also important to have techniques for signaling to the reader that it’s time to stop and think. (Such techniques include displaying an equation, referring to a figure, starting a new paragraph, or carefully breaking connectivity.) It’s also important to stop now and then to supply some guiding text.

I suggest that you write your next paper without much thought to connectivity. As you revise, use your first intuitions for how best to improve the text. When you think the paper is in good shape, set it aside at least overnight. When you return to the paper, notice any paragraphs that are more difficult to read than others. Analyze only these paragraphs for connectivity, and use connectivity as *one* tool in your toolkit for making the paragraph work better. You will find that it is often a very helpful tool—but not always.

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