Unknown Quantity

Every year since I was little I would create a wishlist of things that I wanted for Christmas. I always included at least a couple of "big ticket" items on the list, such as "World Peace" or "One million dollars" or "Cubs winning the world series."

[Ignoring the pink elephant in the room: how long it has been since I posted. . . just going to glide right by that.]

So what has been on my academic mind recently has been how to get the students to do more math. I'm not talking about practice problems that come from the textbook or even from my mind. I'm not talking about problems that are similar to those on standardized tests or my own assessments.

What I am thinking of is something that is closer to what mathematicians actually do. I'm vague on the details right now because I'm not exactly sure about them, but here is roughly what I'm thinking. Mathematicians don't typically work practice problems over and over again, but are instead involved in one (or more) of the following activities:

• Exploring the properties of some numeric/algebraic/etc pattern.
• Making a generalization about a pattern they see.
• Proving a conjecture they have made.
• Modeling the world around them with equations and data sets in order to answer some sort of question about the world.
• Researching the methods/work of other mathematicians.
  

So, why aren't my students doing more of this? Granted, they almost certainly would be going over ground already covered by previous mathematicians, but there is certainly value in finding your own way through something sometimes.

Now I just have to find a way to implement this idea and I need a long list of actual activities that students can do. Any thoughts, oh wise internet world?

Dallas Willard on creating disciples: "We [should] intend to make disciples and let converts 'happen,' rather than intending to make converts and letting disciples 'happen.' " Taken from The Divine Conspiracy.

What do you think of that?

So for the last couple of days my brother has been visiting. It is always fun when he comes to Indiana. We stayed up late most nights (well, late for me, kind of average for him). We had a good time discussing all the usual topics: movies, music, life, politics, etc.

However, he introduced me to a new "game" that he plays with him self. It is basically a solitaire version of 6 degrees of separation using wikipedia. Here are the basic rules:

1. Pick a topic which you would like to read about on wikipedia.
2. Start at the wikipedia homepage.
3. Only use the links available to you (don't use the search feature) in order to get from the homepage to the article you are looking for while passing through as few intermediate articles as possible.

It is a natural outlet for curiosity since you can read some of the intermediate pages that you land on. It is also a fun way to see the way that everything is connected.

Hopefully it is clear that neither my brother nor I exclusively use this method of looking stuff up on wikipedia, but it is an educational way to pass a half hour.