Introducing Web Sketchpad at the 2021 NCTM Annual Meeting

NCTM’s Virtual 2021 Annual Meeting ran from April 21 through May 1, and in Session 299 Daniel Scher, Karen Hollebrands, and I presented an on-demand video workshop to introduce Web Sketchpad (WSP). Even if you weren’t able to attend the conference, you can still take advantage of this workshop, and we will be glad to provide whatever support you need; just let us know by posting your comments or questions on this blog post. The video itself appears at the end of this post.

The Presentation

Our workshop begins with two short segments (#1 and #2 on the presentation webpage) that focus on WSP’s simple, easily-used interface and on its approach to tools. We then take a deeper look at how tailoring tools to a task helps focus students’ attention on the mathematics rather than the superficial details of the task (#3).

In segment #4 we take a deep dive into the relationship between functions in geometry and functions in algebra, and we create and use Dynagraphs as a way to put variation and movement into students’ understanding of Cartesian graphs.

Segment #5 is a deep dive into congruence from a transformation point of view, at the end of which you’ll create a construction that leads to the proof of the SSS Theorem.

Segment #6 addresses how best to use WSP with students in both virtual and in-person classes, and segments #7 and #8 sum up the current status and expected future of Web Sketchpad.

A Virtual Workshop?

Given our deep commitment to doing mathematics as the best route to learning and understanding mathematics, we originally proposed a workshop rather than a presentation.

Why would we want to tell you stuff about math and show you pretty demos when you could much more profitably create your own mathematical objects, tinker with dynamic models, and use Web Sketchpad’s virtual math environment to connect concrete physical experiences to abstract mathematical understanding?

But instead, Session 299 was designated to be an on-demand video, not a workshop. On the positive side, conference attendees can watch the video at their convenience, possibly even in short bits and pieces spread out over several days. On the negative side is the difficulty of interacting with other workshop participants, asking questions, and getting appropriate feedback from the workshop leaders.

The only viable course, we decided, is to do our best to overcome the difficulties. to do our best to enable “viewers” of our video to become “participants” in a shared experience. We have created four elements in our effort to support this shared experience:

  1. The video for this workshop: https://www.youtube.com/watch?v=EZRNsSUoSuk&t=144s)
  2. The presentation webpage, with all the WSP websketches, hint videos, and supporting material.
  3. The discussion/Q&A site, which is right here on this blog page.
  4. The session handout, available here.

We envision two different ways to use these resources: group and individual.

Group Scenario

The group scenario is an effort to turn the disadvantages of a virtual workshop into advantages that you can share with other teachers. You and several teachers from your school or your larger community can meet to view the video, either in person or using Zoom. At specific times in the video, we will tell you to pause the video and use your own computer to try out the activity. You and your fellow teachers can each go to the presentation webpage and talk about the activity as you are engaging in it. (We hope you will also send us your thoughts and questions as comments on this blog page.) When you’re all ready, you can restart the video and see how well (or badly!) we’ve anticipated your comments/questions.

In this scenario, you and your colleagues have the freedom to work through the entire workshop in a single sitting, or to break it up into several pieces over two or three days.

Individual Scenario

In this scenario you’re on your own. First open all three resources (video, presentation webpage, and this blog) on your computer., and then follow the same process described above: start the video, pause when we ask you to do so, engage in the WSP activity on the presentation webpage, and submit your thoughts and questions as comments on this blog page. Then restart the video and repeat the process. As mentioned above, feel free to break the workshop into pieces that you engage with over several days.

Whichever scenario you choose, we’ll try our best to reply to blog posts quickly, and in the meantime you may notice helpful comments and questions from other participants, just as your own comments and questions may be of use to them. To provide helpful context, we suggest that you begin each comment/question you submit with the activity number from the presentation webpage (for instance, “#4b” for the “Construct a Dynagraph” activity). If your comment/question refers to the video presentation, please include the specific time within the video that prompted your comment/question

Questions and Comments

As you submit questions and comments below, remember to begin with the relevant activity number from the presentation webpage (such as “#4a”). Similarly, if you refer to the video, it will be helpful to give the time in the video to which you’re referring.

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