Online instructional videos in mathematics have been on the rise for quite some time, but now, due to worldwide events, more teachers than ever may be thrust into a situation where they have to teach mathematics remotely.

If you’re a mathematics teacher, how should you approach the idea of using videos to teach your students? We have been studying flipped instruction in middle school and high school mathematics classrooms for several years (with funding from the National Science Foundation) and we’ve analyzed hundreds of videos. Here are some of our suggestions.

**MAKING THE VIDEOS (OR NOT)**

**You don’t actually have to make your own video! **It takes quite a bit of time and effort, and there are already tens of thousands of videos online addressing topics in middle and high school mathematics. We advise finding some videos that will work reasonably well for your students (many are posted on YouTube or Vimeo) and then using your time to plan follow-up activities for students (more on that below) and providing individualized feedback on students’ work.

If you do seek out existing videos, there are a few things you should keep in mind.

- Look for videos that are
**not too long**—4 to 6 minutes is basically the sweet spot, and for a complex topic, it’s better to have multiple 5-minute videos than it is to have one 20-minute video. - Check the
**mathematical quality**of the video. You will want to confirm that there are no major errors, first of all, but also you are looking for videos that use appropriate mathematical language considering your group of students and it is best if the video provides some motivation for the topic being learned and some conceptual development of the ideas (connections to prior topics, integration of representations, explanations of why a procedure works). - Since worked examples are the main ingredient in mathematics videos, look for
**well-chosen worked examples**. There should be a range of worked examples, not just several that are very prototypical. The worked examples should also illuminate various aspects of the topic. So if we were looking for a video on factoring trinomials, we would prefer a video that includes examples with positive coefficients, negative coefficients, and one with a leading coefficient instead of just three fairly straightforward examples. Also, if you can find it, it’s great to have videos that explicitly highlight common mistakes instead of just showing the correct way to do things.

If you are having trouble finding those things in videos (“there’s a common mistake that I want to highlight, but no one else seems to be bringing it up!”), or if you strongly feel that you want to have your own voice and style in the videos for your students, then you may decide to go ahead and **make the effort to create new videos**. In that case…

- Make videos that are
**not too long**. The same guideline applies to you—4 to 6 minutes is recommended. The other guidelines above are also worth bearing in mind. - Although voiceover videos are the easiest to make, it has been found to be beneficial for students if they can
**see your face**. So you might consider video-recording yourself at a board or with a screen display behind you, or you could do picture-in-picture video. A simple way to do picture-in-picture is to have your webcam displayed in a small window on your screen and then have your presentation slides or digital workspace taking up the rest of the screen. Then you can use a screen capture app (several are listed here or you can get creative with Skype or Zoom recorded calls) to grab your entire screen, which includes your presentation and the small little image of your face. Examples of a full-on lecture video and a picture-in-picture video are shown below.

- Build your video around
**clear and relevant visual objects**that you can talk about. These might be equations, tables, graphs, or a diagram of how ideas are related. The main idea here is to show something that encapsulates the main idea you are teaching, and then talk about it and highlight various aspects as you are talking. Or to put it another way, don’t fill up the screen with lots of text and don’t read everything aloud in a stilted way. **Avoid distractions in your video**. Don’t spend time trying to find fancy emojis to “spruce up” your video and don’t try to incorporate fancy transition effects or whirly-gigs. The visual space is very important, so it should be clearly focused on the mathematical ideas and it should be well organized rather than crowded or distracting. You should also avoid audio distractions. Try to record somewhere that is relatively quiet, free from background noises. You should also pay attention to your audio recording quality. Being too far (have to strain to hear) or too close to your microphone (clipping and distortion) is also distracting and can reduce the learning potential of the video.

**ENGAGING STUDENTS AND CHECKING FOR UNDERSTANDING**

Even with a stellar video, if students don’t watch the video, they aren’t going to receive the content portion of your lesson. Therefore, you want to increase the odds that they will watch the video by adding in some accountability and also making it a bit more interactive. Here are some suggestions for how to do this.

- Consider how to include
**interactive activities**within or alongside your videos. You could use EdPuzzle to embed questions or Padlet to point students toward questions, encourage students to use the YouTube comment features, or have them complete and submit a follow-up activity. - These interactive features not only allow for some accountability, they also serve as a formative assessment to gauge students’ learning. After students watch the video, it is important to
**check for understanding**. These checks shouldn’t just be conducting a procedure shown in the video, they should also ask students to consider the big ideas. We encourage you to ask students to share their own understandings via a summary of big ideas, visual notes, a quick video discussion, etc. You should focus on what they should have learned generally, not specific instances of problems. You can also ask students to generate similar problems to those in the video or to consider different problems and note any questions they have. If students are struggling to understand, it means you need to consider other ways to support their learning.

**OTHER USES OF VIDEO**

Teacher-created instructional videos are not the only way to use videos remotely. Here are some other suggestions for using video.

- You could have your
**students make videos**(FlipGrid works well for this) and send them to you or to one another. These videos could be to summarize ideas you presented in a video, summarize their understanding of a topic, or to explain their thinking on a problem. For example, you could have them explore a Desmos activity and then create a screencast of what they noticed as they explored. Allowing students to make videos can keep it fresh and exciting for them. It can also form a record of what they’ve learned. - Your videos
**don’t have to be lecture-type videos**. You could also create videos that show a novel solution to a problem, provide a rationale or application for a topic, or set-up an interesting investigation the students will work on. Use this time to think of interesting ways to engage students in mathematical practices and applications.

*Some of these ideas will be presented in an article forthcoming in *Mathematics Teacher: Learning and Thinking, *published by the National Council of Teachers of Mathematics*. *The views expressed here are those of the authors, Zandra de Araujo and Samuel Otten, and do not necessarily reflect those of the National Science Foundation*.

This is awesome and greatly appreciated. Thank you.

With wishes for prosperity and success.

Marla A.

member NCTM

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Thanks for sharing. I also want to add the idea of using video to highlight math in the real-world. Videos can be used to spark interest in a subject or provide a relevant context for how the math is used in the real-world.

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Yes, for sure! Good point. If you have any you like to use feel free to share! 🙂

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