Excellent Quote

I just came across this excellent quote:

“Human speech is like a cracked tin kettle, on which we hammer out tunes to make bears dance when we long to move the stars” (Gustave Flaubert, Madame Bovary).

While the most eloquent speaker can draw up emotion from deep with in us, make our bodies shiver, and our blood boil, there are so many more dimensions to experience about the world that our language leaves flat and lifeless.

Displacement

I'm sitting at Chuys and waiting. It is a festive atmosphere with lots of people enjoying each others company. Some are families some are co-workers. There are lots of kids running around. Occasionally, I'll see some one looking at me and it's been fun to watch their expressions change. At first they would give a quick glance and carry on with their conversation. Then their gaze began to linger a bit longer and an inquisitive look would flash across their faces. Now, as I catch their glance, I see pity.

The feelings that I'm feeling are strangely reminiscent of how I felt in Berlin. I had been there long enough to feel comfortable with the city, and, at the same time, I didn't have any one to call, or anything to do but wait. Wait until it was night, wait until it was day, wait until a party started. I was surrounded by people some of whom I had begun to recognized and some with whom I had become quite familiar. None of them seem to acknowledge me. There was a lot of activity, but I wasn't involved. I was invisible and just observing.

This I Believe

This has nothing with my ride or my training. I just found it encouraging to remember the hope that lives in innocence.

Tarak McLain, a six year old who is living in Austin, Texas was given an assignment to bring in 100 things to his class. He chose to bring in his beliefs...Here are the first 30. There is a link on the site to actually hear him reciting his beliefs as well.

Check out his "essay" from the collection This I Believe.

Last night I woke in the middle of the night dreaming that I had a classroom full of unruly students. It's been a while since I've had one of those dreams. I use to have them all the time. Part of it is probably because of feelings of inadequacy at work combined with running into one of my former students.

When I woke up I was thinking about how to teach Algebra. I wanted to relate the algebraic thinking to the world of a student. I know that none of them need "algebra" as math at that age, so I asked myself what algebraic thinking is outside of math. We say that it relates to everything and yet there are thousands of people who say that they don't know "algebra" and can't do "algebra". How are these people getting by without it if it is so important?

Simply put, they aren't. Sure, they don't have to manipulate equations with x's and y's. Instead they have to make substitutions where they set up scenarios in such a way that anyone could fill the role. e.g. Who could play a certain positon if so and so were injured? What would a dream team look like. What would it be like if so and so was on the date with so and so instead of so and so? They make mappings in their head of relations. e.g. Bret -> Quarter Back, Joe -> Fullback, etc. Susan -> Jack, April -> Manuel, Eric -> Jason...

One way to introduce the concept of "relations" (mappings) is to have the students find things that are related and display those things in some sort of form. You are almost guarenteed to get tables and maps. Then you can introduce a grid and represent the relation as a point in the grid. (can you say cartisian coordinates?) Finally, start mapping things in large numbers. You can use a computer and excel. You can relate every student in the school to a "zipcode" or a phone number, or the number of phone numbers in the phone, or any other collection of information about them. Then expand that to the city.

Once you start dealing with things that are too big to fit into a graph or a table or even a database, you would introduce sets of ordered pairs (domain and range) that have an infinite domain or an infinite range and show that only a piece of it is representable on a graph or a table or a map at a time. Then introduce the concept of a symbolic formula that represents the entire relation. Number of molecules in a volume is a constant times the volume.

Stick with writing out the descriptions for a while, then introduce the concept of using letters to stand for the quantites. Eventually, you will have to manipulate some of the formule and you will be able to introduce the letter x and y to stand for any quantities (abstract) and talk about generic manipulation of symbolic equations.

That...is how algebraic thinking leads to the need to learn "algebra".

Today I found Richard Galiano on You-Tube; here's the link:

http://www.youtube.com/watch?v=hLjqpIbwo54