|Whenever I'm discussing increasing and decreasing, local (relative)
extrema, polynomials, slopes of tangents lines or limits, I use Pierre the
Mountain Climbing Ant!
Here are some examples of how:
Increasing and Decreasing...
I just tell them that, for this, Pierre always crawls from
left to right - just like we read.
If Pierre is crawling uphill, the function is increasing. If Pierre
is crawling downhill, the function is decreasing. (Ok, this is isn't earth
shattering... they get better! This is just the student's first
introduction to Pierre.)
The fun part is to draw Pierre on the graph... The trick is to make
a really pathetic stick drawing ant:
I call these roller coaster graphs and draw Pierre and his friends
taking a ride:
I always draw all the bodies first, then put all
the arms in the air... Then I pause to admire my work and put the "Weeeee!"
on. Delivery is everything. ;-)
My students always remember what a polynomial is, since they can't
get this stupid picture out of their minds. I've seen their notes... They
all draw the ants... and the "Weeee!"
What will happen if Pierre and his friends try to ride a polynomial
That last drop is going to be a doozee!
This is where Pierre is most effective as a learning tool. By this
time, the students are quite fond of him.
Simply have Pierre (the Mountain Climbing Ant) crawl on the graph...
What is Pierre's altitude (as in mountain climbing - not the trig thing)
when he's crawling over to x=3?
Pierre looks more like
a sick cow on this one!
Since I've started to use Pierre and the altitude
thing, my students are doing MUCH better on this concept... and they're
to Karen's Tricks of the Trade