Tuesday, August 28, 2012

The Numbers of Our Lives

A new semester, new classes and another new beginning. I'm always so nervous for the first half of the first class but I usually settle down once the students have laughed or smiled a few times. It's been the same since I taught my first fourth grade class in August 1972 and I wouldn't have it any other way.

There are a couple of things I really want to focus on in my undergraduate Teaching Elementary School Math and Science course this semester. I want my students to be able to see the relevance of school mathematics. I want them to see that it isn't just a means of balancing your check book or working out how to solve mathematical problems. I want them to go beyond the "do the math" syndrome that our culture seems to have fallen into when it comes to any form of quantitative experience. I want them to see the poetry and creative writing equivalents in mathemtics.

I want my students to appreciate the aesthetics of math in the same way that Vi Hart does. I want them to see how wonderful it is when you add two successive traingular numbers such as 3 and 6 and get a square number. Imagine three small wooden blocks next to each other so that a stack of 2 is next to 1; like a step. Now add a third stack of 3 to make another step and a total of 6. If you take another 3-step and invert it, it fits with the 6-step to make 9; two successive triangular numbers make a square number. You can make triangular numbers just by adding an additional step. 6 plus a stack of 4 is 10. Just like this: invert the 15 and it will fit with the 21 to make 36, a square number.

Isn't that just way cool? 

Sunday, August 12, 2012

Fourth Place in the Olympics

Go forth and multiply, come fourth and get nothing.

I would imagine it must be quite devastating to come fourth in an Olympic event especially if it is by the merest of a hundredth of a second or fraction of a centimeter. No medal, no standing on the podium, no name in the record books, nothing to take home and share with friends and coaches, and nothing to bite on.

On the other hand coming fourth means that you are the fourth best in the world at something. Of all the people on the earth only three can do that particular thing better than you can. This is the problem with ordinal numbers, they say so much and so little all at the same time. They also often tend to turn into nominal, or naming numbers, once they have been identified, such as in dates. Although July 4th is the fourth day in July it is more widely used to identify or name a particular day.

Of all the different uses of number, the ordinal use is the one we use when we want to compare things numerically. They are the type of number that seem to carry the greatest social meaning. When we are in elementary school it is way cooler to be a fourth grader than a first grader and it's probably better to live on fifth avenue or ninth street in New York rather than 12th Avenue or 42nd street.

Floors of buildings are identified first as ordinals but this can get really confusing. In most western cultures there is no 13th floor while in the east there is no 4th floor; each number being consider unlucky in their respective cultures. Then there is the confusion created in Britain where the first floor is above the ground floor making every high-rise building in the UK actually one floor higher than anywhere else in the world.

The Olympics really have been incredible to watch and a credit to London, my home town. I certainly wouldn't  mind coming fourth in any Olympic event.