I’ve been thinking about what I think a truly great mathematics education website would look like. Dan and David have produced some awesome mock-ups of the future of mathematics textbooks, and I love their work, but I can think of more features I would add.

  1. There should be space available for students to ask and answer questions, just like MathOverflow. It would probably need to be moderated, and perhaps seeded with people with some knowledge of mathematics willing to attempt to anwer questions, but I suspect many of the interactions would be peer to peer. The level of mathematics discussed on MathOverflow and the sometimes snarky responses to people who ask lower-level questions lead me to believe that this type of discussion space should be have a different community standard – one that expects children to be participating in it.
  2. There should be a mixture of styles of problems from the directed-style problems with embedded, mediated peer to peer interactions that Dan and David are dreaming up  to open-ended problems and/or puzzles wherein students choose what tools they want to use to try and solve the problems.
  3. There should be a library of exploration spaces available for students. I’m thinking Logo, origami, and other types of similar resources would be available here, along with discussion space to share any discoveries and/or projects students develop.
  4. At least part of the site should be dedicated to sharing some of the wonder of mathematics. Perhaps this looks like a blog where some of the most fascinating and elegant mathematical ideas through-out history could be shared. The primary purpose of this section of the site would be to inspire, not to teach.
  5. The site could include a toolkit of different mathematical techniques students could use to solve mathematics problems. Alternatively, solving specific problems on the site opens up new tools in the toolkit. Students could also have a toolkit of skills they have developed themselves, and bookmarked to remember for later, much like programmers do as they build their own code libraries.

I can imagine that trying to introduce this all at once might be overwhelming or too challenging, so these features would have to be introduced over-time, but the ability for students to connect with each other to have discussions about mathematics would have to be front and centre from the very beginning.

What other features would you include?