So I’m trying to write my dissertation proposal, i.e., the first three chapters of my dissertation. Sometimes when I am doing this I get super frustrated because I know what I want to say, but I can’t think of the right words to say it in. When this happens, sometimes I will say to myself, “just write some words:” I give up on fancy words and focus on conveying the *substance* of what I want to say. Like, here’s the general idea, in language that would be in an informal email, because that’s pretty easy to write. Once these words are on the page, I can come back later, when my brain is producing nice fancy words again, and fix the style.

Here’s an example of a paragraph that resulted from this technique:

Calculus I is super important okay. Lots of people take it, whether as a foundation for a math major or as a service course that provides them with the mathematical tools necessary to succeed in another discipline. Since it’s so super important, we should be teaching it well, but unfortunately a lot of people, and a lot of students in particular, feel like we’re not. So, we need to figure out what works, and then do that all over the place. This way we can make sure everyone is getting what they need out of calculus. This chapter introduces my proposed study, which looks at four different ways of teaching calculus to see if any of them are better than any of the others. I’ll look at various reasons why calculus is so important, ranging from questions of national economic standing to individual student outcomes. I’ll explain the relationship of my study to an ongoing national MAA study. I’ll even say some words about why this topic resonates with me personally. Then, at the very end, I’ll tell you what my research questions are.

After refinement, this paragraph turned into two paragraphs that I’m pretty happy with:

Calculus I is a course of great importance in college education. It is a required course in the college careers of many students, whether as a foundation for a math major or as a service course providing them with the mathematical tools necessary to succeed in another discipline. Given its broad importance and utility, Calculus I should be taught well; unfortunately, many students experience their calculus classes as uninspiring, dull, or unproductive, and up to a quarter of the students in any given calculus class will not achieve a passing grade (Bressoud, 2011). Therefore, the mathematics education community is obligated to find and document productive approaches to calculus, then disseminate these approaches for use across the nation. Only in this way will all students obtain from their calculus classes the tools, skills, and attitudes they need to succeed in their education and careers.

This chapter introduces my proposed study, which examines four different pedagogical approaches to teaching calculus and compares their effects on student outcomes, including conceptual and procedural achievement, persistence in STEM major tracks, and attitudes and beliefs about mathematics. I will discuss several reasons why calculus education is so important, ranging from questions of national economic standing to individual student outcomes. I will explain the relationship of my study to an ongoing national MAA study of successful institutions. I will explain why studying the teaching of college calculus resonates personally with me. Finally, I will conclude by presenting the research questions that will drive this study.

I’m sure this technique is not novel, but it has been useful for me, and hopefully it will be useful for others!