Month: February 2008

The Origin of Life on Earth and Logarithms

Today in Algebra II I went off the beaten track. I wanted to make logarithms useful to them. Yeah, I could talk about the Richter Scale, or pH scale, or decibels, but when it comes down to it, logarithms really only become intuitive, natural, and beautiful once you reach calculus. Plus, these examples seem like such cop outs. If the are only good for weird measuring systems, then they aren’t really worth teaching in math class (not that I would be opposed in, say, a chemistry or physics class).

When I was in North Carolina for a math teacher conference, I went to a talk on logarithms, and the speaker reminded me that one great use of logarithms is for displaying data (either on a log scale, or a semi-log plot).

So today, I talked about my students being science journalists and representing data (confession: I cribbed this idea from the NC conference too): namely, I wanted them to create a timeline of major events in the evolution of life, from the existence of prokaryotes (3,000,000,000 years ago) to the emergence of homo sapiens, to the advent of writing (6,000 years ago).

Plotting all the relevant moments on a standard timeline yields a major problem: the events that happened closer to now (e.g. emergence of homo sapiens, taming of fire, writing) all overlap on the timeline — because the scale (of now to 3,000,000,000) is so large. The difference between something happening 6,000 years ago and 15,000 years ago on a scale this large is negligible.

So I taught them how to plot on a logarithmic scale: the events all become spread out, but you lose the ease of pulling off the data immediately from the graph. It’s harder to interpret the data, but it all becomes visible.

I think they learned something from this activity. If I had planned it better, I would have asked them to each find their own set of data to plot on a log scale.

Teaching Portfolio

My math department is losing it’s department head, and two long-term members to retirement. And since the hiring season has now gotten underway, I’ve been looking at the resumes and personal statements of potential candidates. One of them had an online portfolio, with student quotations, sample tests and quizzes, videos of him teaching, and lots of other useful pieces of flotsam and jetsam.

Of course, my critical eye went first to the terrible website design.

But the idea, and the content, were good. And so, in the spirit of picking projects to focus my mind on so I don’t get depressed, I have decided to make my own portfolio.

http://www.virb.com/samjshah

It’s only in the beginning stages, but the idea behind it is go beyond creating something that will be useful when job hunting; it is going to be the place where I document my success, and show off who I am as a person and as a teacher (the two are inseparable). It’s going to archive the little things that just don’t fit or belong on a resume. (Small two day conferences I attended, quotations from students, good smartboards I’ve created, writings from grad school, etc.)

Which means that lots of flotsam and jetsam are going to be carefully placed in there. I want to put on this page all the things I would want to see/read if I were looking into hiring someone.

Logarithms

Logarithms. Confusing, unintuitive, blasted made-up things! I am teaching my Algebra II classes logs for the first time today, and since I didn’t have much time to do my planning last night (I went to the school dance concert, and by the time I got home, I was too tired to function), I made only a mediocre lesson plan.

I think if I had given myself more time to plan things out, I could have made an interesting lesson — one that made logs seem less like things that pop out of nowhere, and more like these concrete natural things that simply had to exist because them not existing would be even more horrifying.

Sort of like I tried to do when I introduced imaginary numbers.

I didn’t do a terrible job, but I know how confusing logs can be, so I wanted to do a bang up job. Instead I simply took the book’s presentation wholesale and translated that to Smartboard. Next year I’ll try to look what other teachers do.