We're keeping up with our experiment in a new rhythm: a video every two weeks!

Now available: the second half of Challenge 08, which continues the paper ripping-theme, and provides teachers and students with yet another pedagogically sound reason to make a mess.

Challenge 08, Part 1 explored a simple procedure for ripping up a piece of paper. Challenge 08, Part 2 presents a new procedure, with a small twist that leads to a whole bunch of new problems to investigate!

Enjoy!

Math can be messy sometimes. Grab some scratch paper and get a rippin' with Challenge 08: The Confetti Problem (Part 1).

Also, I'm going to try out a slight adjustment to the usual format. I've typically published one video per month, and that video has contained both a main challenge and some extension or elaboration.

This spring I'm going to try separating those two aspects. There will be two videos per month, connected to the same theme. The first video will contain the main challenge, and the second will have questions that extend or augment the ideas from the first.

I'll be interested to hear your thoughts on the new pacing! Plus, I look forward to seeing some response videos about Part 1. Stay tuned for Part 2 in about two weeks!

We've been inspired by the internationalization (or is it internationalisation?) efforts of other video producers, like Minute Physics and Numberphile to launch the Collaborative Mathematics Translation Project.

In an effort to make our videos available to as many people as possible, we'd like to recruit help creating subtitles in languages other than English. Here's how you can help out:

1. Choose your favo(u)rite challenge video from the translation project page, and download the English subtitles (a file called "challengeXX_en.srt").
2. Open up the subtitle file in a text editor and translate the text into your language of choice. (Please avoid changing the numbering and time information, as these are needed to synchronize the text with the video.)
3. Use our contact page to let us know when you've completed a translation. We'll get the updated subtitle file from you, enable it as an option on the video, and post the file on the project page. We'd also like to add your name to our credits!

Mange takk på forhånd for deres hjelp! ;)

Challenge 07 from Collaborative Mathematics is here! Watch the video, try out the probability experiment, and send in your data. Or, tackle it theoretically!

Plus: we've received a great response to Challenge 06 from Dani, and a fantastic new approach to Challenge 03 from Paul.

There are several very cool blogs out there -- among them Math Mistakes and Bridging the Gap -- that highlight the value of thinking deeply about student responses, the mistakes they make, and the explanations they give for doing things the way they do.

One of the ideas behind Collaborative Mathematics has always been that participants could learn something from exploring other people's solutions, in addition to exploring the challenges. Some of the response videos in the archive contain mistakes, and I think that's fantastic. Rather than being an answer key of tidy solutions, they represent a library of arguments and ideas that require additional critical thinking.

One aspect of this is that I avoid posting my own answers to the challenges. I don't want my way of solving a problem to be interpreted as "the right way" just because I'm the one who posed the challenge in the first place. Over the next few posts, though, I would like to share my thoughts on a particular solution as a way to talk about my own mathematical curiosity, and what I've learned from a really creative approach to one of the video challenges.

But before I start going on and on about what I think, I want to give you a chance to explore for yourselves. Here's what I suggest:

• Take a few minutes to visit the archive page for Challenge 03: Finger Counting.
• Solve the challenge on your own, if you haven't already.
• Watch a few of the response videos.
  
• In particular, watch Maile's solution and see what makes you curious.

Next time I'll share how I've come to think about the mathematics of Maile's approach.

I recently received response videos to a number of earlier challenges, so I'll summarize the updates here. Click the links below to visit the archive page for each challenge, where the new videos are highlighted. Plus, you can watch the original challenge video and the other responses, and take on the follow-up challenges.

• A new solution to Challenge 01, in which our problem solvers go back to the beginning and hope to count the even "Ermer Numbers".
  
• A new solution to Challenge 03, in which our problem solvers take on the most popular challenge from the spring, "Finger Counting".
  
• A new solution to Challenge 04, in which our problem solver sets about to explain how we know we have found the minimum number of button presses on the less-than-useful "Two-key Calculator".
  
• A new solution to Challenge 05, in which our problem solvers bust out the rulers for a practical approach to "International Paper".
  

This month's challenge is brought to you in part by my good friend Scott, who originally shared the problem with me. Jump over to the front page to check it out!

The first response videos have arrived! Check them out, and explore some follow-up challenges, by visiting the Challenge 05 page in the archive!

None of the videos (so far) have taken up the challenge of describing a new piece of paper for us to explore, so I'd like to encourage you to put on your problem-posing shoes!

• What if the paper had been a square? A golden rectangle?
• Describe a piece of paper such that exactly one-third of the paper is inside the largest circle that can be drawn. Can you find a real piece of paper that fits your description?
  
• What other questions could we pose?