19 April 2009

e to the i 2 pi

This xkcd reminds me of an old story. Kyle and I were at Sequoia Natl park, hiking through the trees and discussing science, math, and other sundries. At some point I said something which ended with the justification, "because e to the i 2 pi is one," and he almost laughed at me. Come on!

But when you use euler's formula, well, it's right there. So easy.

I love that.

So I justified it to Kyle on a little scrap of paper in my pocket... and for the rest of the afternoon we would shout it every once in awhile to the skies-- e to the i 2 pi is ONE!!!


09 April 2009

Project 2061

Today while my simulations were running, I skimmed through a book called "Science for All Americans." I have had it checked out for a few months, but finally I wasn't allowed to renew it anymore :) So this book is a report from a government group called Project 2061, tasked to improve the science, math, and technology curriculum.

I think the report made some very good points that (1) (quoting the text) "The present science textbooks and methods of instruction, far from helping, often actually impede progress toward scientific literacy. They emphasize the learning of answers more than the exploration of questions, memory at the expense of critical thought, bits and pieces of information instead of understandings in context, recitation over argument, reading in lieu of doing. They fail to encourage students to work together, to share ideas and information freely with each other, or to use modern instruments to extend their intellectual capacities."; (2) We try to cram too many things in our K-12 science and math curriculum, instead of teaching the very important things thoroughly; and so (3) We should really refocus from tabula rasa and try to design a math and science curriculum that emphasizes the very most important concepts while instilling skills and attitudes of scientists into the students.

Some of the concepts they said should be emphasized in "The Nature of Science" were good:

The world is understandable.
Scientific knowledge is durable.
Science demands evidence.
Science explains and predicts.
Scientists try to identify and avoid bias.
Science is not authoritarian.

Interestingly, in the chapter on mathematical skills which should be emphasized, four out of seven were concepts I use every day:

- Uncertainty
- Summarizing data
- Sampling
- Reasoning