Thanks Jeremy! While folks are likely using video resources in all kinds of ways (especially now), I think our videos focus on conceptual understanding in a way that a lot of other places (like YouTube and Khan Academy) don't. We focus a lot less on "how to solve this type of problem" and a lot more on "how to think about this concept." I think this means that they could be compatible in a classroom. Though I think there's a bit of a "but it's good for you" element too - students are likely going to go search out videos to help them solve a problem like the one on their homework more than a "here's how to think about this" video.

Matt

In addition to what Matt described, I think there are two important ways in which the Calcvids videos are different from most other videos.

First, our videos are mathematically correct. For example, Kahn Academy explains the concept of a derivative in terms of "the rate of change of a vertical variable over the rate of change of a horizontal variable"; these sorts of informal descriptions sound fine at first glance, but, when you think about what they're saying, they're simply incorrect. I think if you look at most of the Khan Academy videos—and many others—you'll find that they're rife with mathematical inaccuracies.

Second, our videos target particular ways of reasoning that the research literature has found to be productive for students to really understand the underlying concepts. So, for example, we ground all of the discussion of derivatives in terms of constant rates of change, and the ways "constant rate of change" is introduced, described, and depicted, are grounded in the idea of coordinating amounts of change between two varying quantities—a way of thinking that research has suggested as important for understanding calculus concepts.

Quantitative and covariational reasoning are the particular ways of thinking we designed our videos to support. If you're interested in reading about the theoretical design principles of our videos, feel free to check out the Resources page of our website (https://calcvids.org/instructorinfo/).

Thanks Monica! I hope they're helpful in folks with all the online instruction. And thanks for mentioning your project too - it looks very cool, and dissemination is definitely a tricky piece!

Matt

Thank you, Monica. If you or your colleagues have suggestions for how we might improve the videos, we would love your feedback. 

We'd love to scale up to other classes. Our funding ends this year, so we wouldn't be able to do it in the current project. But if there is enough interest in the community, we're hoping to apply for additional funding in the future.

That's a great question! In our videos, we generally tried to not tie them to any particular software, so that they could be used by instructors without requiring that their students have experience with particular technology. But we strongly encourage instructors to utilize mathematical software that will let their students do things like adjust graphing windows and make numerous approximations so that they can more easily explore the underlying mathematical concepts.

Thanks Paul! We've tried to walk that line of "intuitiveness" - which is pretty tricky sometimes. One setting that we wanted to really explore in the videos was the idea of constant rate of change and average rate of change. Students seem to often have an idea that these ideas are intuitive, until you start picking apart the ideas. Average rate of change is great for this - what is it an average of? Without just a computation, what does it mean to say you're traveling at an average rate of 45 mph? Building on intuition seems to be key here while also inspecting that intuition!

Thank you, Paul. If you do use the videos in your Calculus I Honors class, our project team would be interested to hear your suggestions about how we can improve the videos. 

Thanks Hong! We'd love to hear any feedback!

Our videos are designed to be used in many ways—we've had instructors use them as part of IBL classes, as part of flipped classes that incorporate group work, and as complements to more traditional lecture. The videos can definitely be used as the primary way to deliver material, and they should hit all of the topics that are addressed in a standard first-semester calculus class. On our website (calcvids.org) we also provide the Powerpoint files that were used to create the videos, so instructors can modify them and create their own versions of the videos, or use some of the resources in other ways in their classes.

Thanks Kathryn! To piggy-back off Aaron, I think the place that you might add to the videos (or add additional videos if you wanted) might be in the pure computation side. Because we focused a lot on the concepts, I've used more time in class when I've used the videos on working problems in groups. We certainly have examples in the more procedural sections (e.g. product rule, chain rule), and group work might be a good place to build on those to help the students use those ideas in practice.

Thank you! We created these videos with the curriculum of a standard first-semester calculus class in mind, so we haven't yet thought about whether and how they might be used in other contexts. But we'd love to hear about any ideas for other venues in which they might be useful, and to think about how the videos might be adapted for those settings.

Thank you!

The questions about the students' confusion are for our research - to help us understand how students watch and learn from the videos. Specifically, we've hypothesized that many students don't recognize moments when they don't understand something, and we're interested in learning more about the students and moments who do experience confusion; then we plan on looking at how these students interact with and learn from the videos.

We have made some significant changes to our videos over the past three years based on  feedback from students and instructors. And we'd love to get more ideas about how they could be improved!

Revising the UI and adding vocabulary is an interesting idea! We haven't yet thought about it, but we should definitely do some brainstorming. Most recently, we've been thinking about additional ways to make these materials available to instructors (e.g., ways to integrate the videos and assessments with a LMS), so we should think about UI/etc. as we do this!

Thank you!

We've been thinking a lot about the visualizations. We're hoping that they'll help make clear many of the things that textbooks and lecturers are trying to do when they describe dynamic imagery. When we dig through our data, we'll be looking to see whether students reference some of the animations in their descriptions.

However, I think that it would be even better to develop many of these visualizations as stand-alone GeoGebra applets, where students can experiment with manipulating values and controlling the animations themselves. I suspect that this interactivity (not quite embodiment, but closer to it?) would be more impactful than just watching the animations in the videos.