Logs and Exponents
My precalculus class got a real lecture today, because apparently they were never exposed to logs in their Algebra 2 class. I’m not sure that I completely believe them on that, but it’s been clear that they do need some help understanding negative and fractional exponents. It was an old-school lecture with notes, and my only concession to “student-centered learning” was that I made them do the examples on their own, pausing mid-stream to go around and look at their papers. They took beautiful notes. I wish every day was like this one. When I finally got around to saying my bit about how exponents and logs are really just different ways of describing the same relationship, I got my reward of the day from one of the laziest (and smartest) students:
How come every other math teacher we’ve had made this seem so hard?
I told him they just have to make it fill up a whole unit of the class, and not to tell anyone else how easy this stuff really is. The only aspect of exponent and logarithm laws that we didn’t get to was changing bases on logs. I figure we can hit that on Monday. The Laws of Logarithms page at Oak Road was really helpful in reminding me how to derive the “rules” for multiplying, dividing, etc.
Hi
have been browsing for easy ways to learn log and exponent algebra.
I struggled with advanced logs and derivative manipulation at school, and am now 48 years old, and thought I should revisit the field and see if my wiser but older brain can pick it up. So often, the penny drops when you have somethign explained in a different way.
I am further motivated because I have been studying up on probability and stats to help me make better investment decisions, and mess a little with trading shares. Position sizing of each trade depends very much on probability, and that is getting me back into frequency distributions which rely on logs….
Anyway, you sound like a passionate teacher, and I would encourage you to never undervalue what you do.
One of the most certain ways for any commercial endeavour to streamline processes and produce goods and services more efficiently, is via the application of maths.
And every generation is a tabula rasa (blank slate) that needs to learn this stuff. If one generation misses it, then that can seriously impact a country’s GDP for 20-30 years.
ANyway, I’d encourage you to keep exploring different paradigms for presenting logs and calculus to students. I am confident there is a method of getting the penny to drop for 80% of students aged 15-17 to be comfortable with these fields. It just requires the appropriate use of visual/spatial/logical mix for each individual.
All the best with your teaching career, and never be disappointed if you feel you need more of a challenge or a break from the same old thing. You can always go back fresher after a break. Our forefathers never did the same thing day in day out all their lives….much more variety….the human spirit needs it.
Cheers
Bruce, Brisbane, Australia
Comment by Bruce — April 24, 2008 @ 7:23 pm