online teaching

Teaching Mathematics Online

**Join the conversation on this subject at the On Teaching and Learning Mathematics blog**

In the current public health crisis, we are all working quickly to move our classes out of the classroom. Fortunately, even if online teaching and learning are new to you, there is a lot of experience to draw on. On this page we have compiled the best resources we can find for practical strategies that will help you plan and run your course, including web-based resources for a deeper dive into assessment, learning activities, and other aspects of online instruction. Check back often as we update this page with additional information.

laptop with post it notesSet realistic expectations for yourself and your students

  • In the current situation you don’t need to become an expert in online course delivery. Your course won’t be perfect, and it won’t be the same as it was in the classroom, and that is ok. Give yourself permission to just do the best you can do. Many of your students don’t have much experience learning online, and they are adjusting too. Set realistic expectations for yourself, your course, and your students.
  • Keep flexibility and empathy in the forefront. Some students may not have ideal learning or internet environments — they have family responsibilities, lack privacy or quiet space, have unreliable internet access, be in other time zones, be online at a library or other public space, or have any number of distractions or obstacles.
  • To the extent that your institution allows it, be particularly flexible with deadlines, independent study, and extended incompletes. Focus on what your students need in order to learn, rather than on structure or deadlines. We are in an unusual situation and this flexibility will make it easier on all of you.
  • There are many tools available: Zoom, Skype, Dropbox, Blackboard, Canvas, Slack, VoiceThread, email, online chats, video chats, MS teams, Google docs, and many others. Investigate if there are particular platforms or tools that your institution already uses. Even if you are not familiar with them, your students might be and your institution is more likely to offer support for those platforms. Coordinating with your colleagues to use similar tools will allow you to support one another.
  • Let your students know that many internet providers are offering free internet service for a fixed period. That does not mean it will be easy for everyone, but it should help many students. Some students will still need to be online in a library or other public space.
  • Unless your institution requires something different, it is ok to build the course week by week and adjust as you go. You don’t need to have it all figured out in advance.
  • Some publishers and other organizations are providing access to resources during this current crisis. Even if these are not your ideal choice for assessment, you may be able to make them work for you in order to complete this semester.
  • While we all strive to offer the best learning experiences we can, in the current quick transition, consider the mantra, " 'Better' is the enemy of 'good enough'."

Preparing to teach online

For comprehensive training on teaching online, enroll in the free, self-paced course Interested in Teaching Online from the State University of New York. 

Design your course group chat on laptop

  • Most institutions have an office that supports online learning. Check their website to see what training, technology, consulting, or other services they have to offer.
  • Does your institution use a Learning Management System (LMS)? These are structured learning environments, like Blackboard, Moodle, or Canvas, and are specifically designed for online learning. Your students are likely to be familiar with the LMS from other courses, and you might have access to campus resources for support.
  • You may be required to use the LMS to ensure FERPA and accessibility requirements are met. Your campus may have resources to guide you with this. If needed, there are services online that will caption or transcribe videos. YouTube and Zoom have automatic, if imperfect, captioning services.
  • Prioritize the learning goals for your course. What are the most important things for your students to come away with? As with any teaching, focus on what you want students to learn rather than what you need to teach.
  • Are other faculty teaching sections of the same course? It might help to work together.

Set ground rules

  • Be transparent. Communicate very clearly with students about expectations, and about why you are making decisions and setting priorities. You can also be open about how you’re all in this together. This will reduce anxiety for everyone.
  • Every week, provide a list of deliverables: read this, start this, submit that. What should they be working on, where, and with whom? Where and how should their work be submitted?
  • I always remind students at the start of an online course that even if they are in the course platform frequently, if they don’t speak up and participate, no one knows they’re there. The same applies to instructors — communicate often.
  • Establish netiquette rules up front. Be clear about expectations for respectful and professional communication. “Tone” can easily be misunderstood online.
  • Encourage your students to compose their work before posting it online, using Word, LaTeX, by hand, or whatever works in your context. Composing responses directly in a chat box leads to less effective communication.
  • Students can solve problems on paper, scan or take a picture of the solution, and upload it somewhere. Let them know that you can’t grade it if the image is unclear. Avoid using email for submitting assignments. It gets messy quickly. But provide a clear alternative.
  • Consider a combination of synchronous (everyone there at the same time) and asynchronous instruction. Synchronous instruction allows for more direct interaction, but it can be challenging for everyone to make timing work in the new normal. There are many ways to engage students asynchronously instead. If you decide to ask everyone to be there at the same time, use the same time slot that your class was originally scheduled for.
    • Synchronous teaching builds on the classroom norms established in face-to-face instruction in the first part of the semester, and offers more immediate personal engagement. It may reduce miscommunication and isolation.
    • Asynchronous teaching allows more flexibility with scheduling, which may be important for students and faculty with family, work, or other obligations, or with challenges accessing needed technology. It can increase cognitive engagement as students explore the course material at their own pace.
  • If you use video, use small chunks, no more than about 5 minutes at a time. This allows students to stay focused. Also think about the easy parts of production quality — adjust the lighting to be clear, don’t move around too much, and avoid other distractions that are within your control (until your cat runs across your keyboard or your toddler comes into the room). It might help to use the microphone on your earbuds rather than your computer.
  • Test all technology. Do microphones, electronic whiteboards, video cameras work? Can the online platform handle the number of students who will login? But also remember that technical snafus happen. Communicate with your students with humor and you can all figure it out as you go along.

    Design your course

  • Some universities offer online tutoring, writing, or other forms of support. Check what is available to your students. You can also refer students to websites like Virtual Nerd, Math is Fun, Khan Academy, or Math Forum. If you hold virtual office hours or offer extra help, try to work with several students at a time so they can support one another and you can use your time effectively.
  • There are applets available online for students to create and manipulate graphs. One of my favorites is Desmos, but there are many others.

These resources provide solid guidance to help you get started online:

Stanford University Teach Anywhere

The Chronicle of Higher Education: Move Online Now

Get Up and Running with Temporary Remote Teaching: A Plan for Instructors who Lecture

Get Up and Running with Temporary Remote Teaching: A Plan for Instructors who Use Interactions in Class

Planning to Teach Online: Four Essential teaching Functions

Seven Practices for the Online Classroom

A mathematician describing his online multivariable calculus course

Hybrid courses use a mix of online and face-to-face practices, as you can see in A Scalable Hybrid Introductory ODE Course

Define and communicate expectations for your students

elearning on laptopLearning activities

  • Your online course doesn't need to replicate everything in your face-to-face course. Instead of starting with your previous course design and trying to adapt it all to be online, start with your goals for the course and the tools you have available, and figure out what's feasible.
  • Some group and interactive activities can be adapted to an online setting. For group work, develop ways that all students are held accountable to their group. Assigning group grades is one option (this also reduces your grading load). Some instructors require students to make individual submissions of assignments, and then assign everyone in the group the lowest grade; this is great motivation for them to make sure their group-mates understand what they’re doing.
  • To keep students engaged, have frequent, small assignments with clearly-communicated due dates, and create learning activities that require students to interact at specified intervals. If you are requiring them to engage in collaboration or discussion, communicate clearly about how often you expect them to be online. I usually tell my students that they should be online 2-3 hours per week, on a minimum of 3 separate days.
  • Ask open-ended questions. Discussion happens when there is struggle or debate, which doesn’t happen easily with yes-no questions. Ask students to interact about how or why, not what or whether.
  • Here are a few activities that have worked well with my online students:
    • Write out or type the solution to a problem (or problems) using words and sentences and a minimum of mathematical notation. This is challenging! But it also requires a different level of understanding of the mathematics. Communicating about mathematics deepens understanding.
    • Students solve a problem and share it online with a partner, a group, or the rest of the class. They provide feedback on a specific number of others’ solutions (for example, if they are in a group of 6, I might require them to comment on 2 other solutions) within a few days. Then they submit a written solution to the problem, using someone else’s strategy. This requires them to communicate with their classmates enough to understand someone else’s reasoning.
    • Give them personalized problems to solve. For example, in one assignment about compound interest with regular savings contributions, each student submitted calculations for their personal retirement savings plan. They identified how many years they had until retirement, how much money they wanted to have access to each month, and then calculated their required monthly contributions. This way, everyone could help one another because they were working on the same task, but each had to do independent calculations.

Ideas for online learning activities:

Tips for students to participate in online group work and projects

YouTube playlist: Ideas for new online faculty


  • Some textbook publishers have online test banks. Google forms has a feature for creating tests and quizzes in an easy-to-use form, and for multiple-choice and fill-in responses, the quizzes can self-grade. In addition, some companies and organizations are providing access to resources during this current crisis. Even if these are not your ideal choice for assessment, you may be able to make them work for you in order to complete this semester. As my advisor would tell me when I was writing my dissertation, “ ‘Better’ is the enemy of ‘good enough’ .”
  • No matter what you do to defeat cheating, someone will find a way to work around it. One option is to require students to find a proctor of their own (often a librarian or local teacher) who will attest to their independent work, but this may be challenging for those who are self-isolating or maintaining the recommended social distancing. You could also assume that all work is open book and open notes and design assignments accordingly.
  • Talk openly with your students about what they need to know in order to be ready for next semester’s courses. If they don’t do the work honestly, they are really cheating themselves. One contributor to a discussion about online learning hosted by MAA’s Rachael Levy suggested, “I think it’s worth asking what kind of deception we’re trying to prevent. Do we want to keep our students from deceiving us on assessments, or themselves? Because I think the second one is the real danger, and might be better to address directly."
  • You can find tools for formative and summative assessment that expose both students' mathematical knowledge and their reasoning, helping teachers guide students toward improvement and monitoring their progress at the Mathematics Assessment Project.
  • Learn more about basic concepts in Assessing Teaching and Learning, and expand your planning and implementation of sound assessment practices. 

More about online assessment:

Assessing student learning

Authentic Assessments

Self-grading quizzes in Google Forms


This is by no means a comprehensive list of what to do or how to do it. There are as many ways to teach online as there are online instructors (maybe more). To share your ideas and questions, visit the Online Teaching and Learning blog . We can all help each other manage this transition and provide our students with quality learning opportunities.

Some of these ideas are drawn from resources developed by Open SUNY Center for Online Teaching Excellence of the State University of New York, and the Institute for Teaching, Learning, and Academic Leadership at the University at Albany.