Teaching Statement

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No one really needs a statistics teacher. The information is available from a variety of sources, whether through textbooks, study guides, papers, or more likely, online. This is especially true for introductory courses, which generally overlap in most of their topics between institutions and instructors. Lectures are even available for free through online courses. Anyone who wants to learn statistics is free to find these materials and learn all the topics that would be covered in an undergraduate or graduate course.

What students do need is a communicator. I’ve come to this conclusion after working as a teaching assistant for a variety of courses, from first-year college courses to upper-level graduate courses, and helping students as a private tutor with high school, undergraduate, and graduate level classes. The students I’ve worked with have included struggling high school students, non-statistics majors and college athletes just trying to fill a requirement, as well as math and statistics majors or graduate students. While there are obvious advantages to teaching a variety of courses at different levels, the greatest advantage comes from seeing the commonalities that run through all of them. In my time teaching (and taking) mathematics and statistics classes, I have often seen students focused on memorizing formulas rather than understanding concepts. My contention is that this is not the fault of the student, but of instructors that lead with equations in order to teach concepts, rather than putting the concepts first. When a concept is poorly understood, I’ve seen many students attempt to fall back on a formula, but it eventually becomes impossible to apply a formula to a problem you don’t understand.

Take, for a simple example, a high school student I was helping with angles of elevation and depression. This student had learned the textbook formula for each, but had difficulty putting them into practice - he understood the problems, just had difficulty putting the correct variable into the correct hole. I had him draw the picture and essentially retaught how sines and cosines work. Once he saw the picture and understood the relationships, he could solve the problem without using a formula, and follow it up by deriving the formulas on his own. He didn’t seem to understand at first that it was possible to solve problems without directly using the formula from the textbook.

This idea lends itself nicely to the topic of introductory statistics classes. Often, the material falls along the lines of “Here’s a formula for this; here’s a formula for that,” rather than getting at the general purpose of statistical methods, which is to gain knowledge from data. Understanding the how and why is crucial to applying some equation from an instructor’s lecture. Most importantly, learning concepts prepares students to deal with messy situations or modern data that don’t fit nicely into standard introductory setups. I feel that what students need is an instructor that is able to speak clearly about these topics, with a thorough enough understanding that he or she is able to speak colloquially as much as possible instead of overly-relying on quoting definitions verbatim. And while putting concepts first is nice for introductory courses, it’s absolutely essential for upper level undergraduate and graduate courses, where students are thinking outside the constraints of neatly formulated introductory ideas.

I had the opportunity to implement some of these ideas in an introductory course at Duke. I worked with a statistics professor to develop my own lab for his course that would cover linear regression with time series, applying ideas from his lectures to models and a type of data that most students had not seen before. Rather than have the students simply copy and paste code from notes, the lab I wrote guided students through the deriving the properties of the model and data. As this was an introductory course, much of the code was provided, and the lab focused largely on interpretation of the results in light of the properties they had derived. In addition to promoting better retention of material, this type of active learning better involves the students and allows them to make connections between the concepts learned in class and the data they work with in the lab.

Instructors will often assign reading before a class, so that the lecture is not the first time that students see the material. Some of the more ambitious students will do the reading, the vast majority realistically will not, but most would agree that there is some value to seeing topics before a long lecture. Active learning assignments, which can introduce the material in whole or in part, would allow for a structured version of this. My intention as an instructor would be to have short readings or videos and quick homeworks due before most classes, the idea being that the most useful homework assignments are those that include learning topics rather than just working problems. Short but relevant assignments allow individual students to learn at their own pace, rather than my lecture pace, and it ensures that every student has seen and thought some about the material before the lecture.

I will use my experience as a teaching assistant and especially as an individual tutor to focus on teaching from the students’ perspectives, focusing on their understanding rather than reading them a textbook. My experience has been that instructors focus too much on their concrete actions, i.e. making slides, writing down equations, etc. rather than focusing on the students’ learning. The role of the instructor is not to provide materials that are readily available online or in a textbook, but to communicate these ideas in a way that students will understand and be able to apply.