Teaching Math Online
I have been teaching Calculus III (multivariable calculus) online since Spring 2013, one to three times a year. I began teaching Differential Equations online in Fall 2015, and have taught it two to three times a year since.
Before I started teaching online, I had not thought I could be satisfied with the quality of instruction in this format. But when I was asked by the chair of my department to develop an online course for Calculus III, I began to work on creating an online course that I could feel good about. I wanted to be sure that I could expect the students in my online classes to show work as clearly and use notation as carefully as my face-to-face students. Below I describe the major course components I designed to make this happen.
Here are links to two videos where I describe my approach, one was an interview recorded in March 2015 and the other is an AMS webinar on teaching math online I presented in July 2020. I also include a link to the slides for the AMS Webinar.
Online Course Components:
- Lecture Videos: The most important course component to achieve this goal was to record all my face-to-face lectures in a regular course. I used a wireless mic and a SmartBoard along with the SmartRecorder software to record my face-to-face lectures. [I have actually continued to record videos of all my face-to-face classes ever since, so that I can make the video recordings of the lectures available to students who missed class or wish to review.] To prepare these videos for inclusion in my online course, I used Camtasia to edit them, removing unneeded delays and content specific to running the face-to-face class. I also added a table of contents to these videos. This TOC allows students to easily keep track of which parts of the lecture they have watched to come back to it later, as needed, and allows them to quickly review particular examples as they do the homework.
- Graded Written Homework: I was concerned that this would be too difficult to assign, but it is not. My online students complete the same written homework and quizzes that I give in my face-to-face classes. The only difference is that I am not able to proctor the quizzes. For each assignment, students are required to complete these assignments by hand and submit a single PDF in my LMS (Blackboard) that includes all pages. I download all student PDF submissions into a single folder and then bulk print them into OneNote where I have set the default print option to print to multiple “pages” within an assignment Section of a course notebook. This means all pages of a single PDF are on a tab for each student. And all students are represented by a single tab on the assignment Section. I type the student name at the top of each page so that I know whose paper is whose and to act as the file name to use when saving these graded PDFs for return to the students in my LMS.
- Online Homework: I created a series of problem sets in WeBWorK, an OER (free) online homework system for each online course. These sets help keep students accountable for their learning of the content and also help me see their progress through the course. These problems are selected and designed to complement the graded written homework, requiring intermediate steps whenever possible and focusing on concept questions. Intermediate steps help train students to show the steps I would require if the problem were submitted as written work. They also greatly reduce student frustration and stress, helping them know where they are having trouble in longer problems.
- OER Textbooks: Although this component was added later to my Calculus III course (Fall 2018), I decided to make my change to OER in Differential Equations at the start as I created this online course. Using OER textbooks allows me to add links to the readings and textbook practice problems below each lecture video in my online course. It also allows me to save students money and ensure that they have access to the books from the start of the course and into the future.
As an example, here is a link to my OER Calculus III text on the LibreTexts platform:
It is a custom version of the OpenStax Calculus III book. So far I’ve added my own section (13.7 on Taylor Polynomials of a Function of Two Variables) and some subsections (see Section 12.1) and many dynamic rotatable figures and exercises. As a curator of the math content of LibreTexts, I would be glad to help other professors get started using and even customizing OER textbooks of your own on this platform.
- Online Course Discussions: Students are required to participate in regular class discussions on the LMS. These discussions help connect the students to each other, help me to get to know the students, and give them an opportunity to improve their understanding of the mathematical content by writing about it clearly. Discussions have been shown to increase student performance and retention in online courses since they provide an opportunity for students to feel connected to each other and to the professor. Discussion prompts I use include: Ask and answer each others questions about the content, Find and describe a new application of a course concept (e.g., cross products, dot products, first-order differential equations), Explain a concept learned in the previous week, Describe favorite concept from current unit, etc.
- Student Video Presentations: Students are required to create two to three 3-5 minute videos of themselves presenting a homework problem to their classmates. They are encouraged to write the problems out as they go, and to try to include visual verification of their answers, where possible. Students have surprised me by saying this was one of their favorite parts of the course. In addition to posting a link to their video and describing the content in a discussion post, students are required to view and comment on at least three of their classmates’ videos. Not only does this assignment help students master the content in the video problem they present, it also helps students to get to know each other and helps me, as the professor, get to know my students better.