Bits and Pieces (Mostly Links)

When I'm going through my google reader and find stuff I like, I often leave tabs open for days, waiting for me to find the time to think about a post more. Then I clean up all the tabs, and wish I could post about everything I'm reading. Here's a collection of things I've noticed in the past month or so...

• Jason says this proof, that only perfect squares have rational square roots, is insanely simple, but it's not simple enough for me to figure out with this cold I have. 
• "The answer is π²/6: What’s the question?" (at Republic of Math) ends with this cool idea:
  

  Here’s a simple yet revealing question to ask people at all levels of mathematical attainment: “The answer is 10. What is the question?”

  Try it on a few people, preferably in groups: the answers may amaze you.

  I can guarantee people will try, and you and they will be amused by the different answers given.

• Mathematician as Explorer. I saved it 2 or 3 weeks ago, and just now read it. I like stories about how interconnected mathematical topics are.
• Measuring the Measuring Device
• Seems like I'm always marking articles in Plus Magazine to save. This one on bones has more science than math, so here's an older one I liked, about ants finding their way home.
•  Here's another critique of Khan, perhaps the most useful I've seen so far. I think Salman Khan explained things well enough to help his cousin, and then went wild putting content online. That content has been very helpful to students wanting explanations right when they're ready for it. But that doesn't mean Khan is an especially good teacher. Alexandre Borovik thinks carefully about how to move a student forward, wherever they are at the moment. His alternate hints are so much better than Khan's.
• Too bad PiFactory doesn't seem to be posting these days. He has some good stuff on his site. How to Think Like a Mathematician describes some good classroom interaction, and I liked this game described in Wizard Math:
  

  There are 35 players standing in a circle. As the games wizard walks round the circle she kills every second player until only player survives. The players are numbered one through 35. Which player lives?

•  Some thoughts about the different kinds of memory, at Republic of Math.
• A new blog that I'll be following, by Rebecca Hanson, has this:
  

  I want my students to learn to fight for what they instinctively feel is correct.  I want them to experience how arbitrary mathematical vocabulary is.  Once we decide that answer that fight is curtailed so we never do.  I'm making a point.  "Who cares what anyone else says? - If it's not true to you don't accept it."

This list by Seth Godin reminds me of another list I once saw, that included things like cook a meal, keep a checking account balanced, and fix a toilet that's running:

What's high school for?

Perhaps we could endeavor to teach our future [students] the following:

• How to focus intently on a problem until it's solved.
• The benefit of postponing short-term satisfaction in exchange for long-term success.
• How to read critically.
• The power of being able to lead groups of peers without receiving clear delegated authority.
• An understanding of the extraordinary power of the scientific method, in just about any situation or endeavor.
• How to persuasively present ideas in multiple forms, especially in writing and before a group.
• Project management. Self-management and the management of ideas, projects and people.
• Personal finance. Understanding the truth about money and debt and leverage.
• An insatiable desire (and the ability) to learn more. Forever.
• Most of all, the self-reliance that comes from understanding that relentless hard work can be applied to solve problems worth solving.