When you drive an old car you get used to some rough sounds.
You also get very attuned to new, strange sounds. To the point where you almost don’t need an engine light to know when something’s not right.
So it is when you teach Algebra 1 frequent fliers, or in my current position, Track 3 Algebra II students with “Junioritis“. As my math coach in a previous district once told a room full of algebra teachers: “Your students have been going to school now for what, 11 or 12 years? Don’t fool yourself. They are not going to instantly start liking math all of a sudden just because you are their teacher this year.”
So we started a chapter on exponentials and logs last week. We kicked the whole thing off with a day of graphing exponential functions by making a table of values. How did it go, you ask?
“I didn’t get to the back page because the front page made me cry.”
How do we fix this? (Hint: The answer is not “Call the Car-X Man.”)
We go Back to Basics:
Opened up class with the odds of a perfect NCAA bracket, graphs included. Because, the first day of the tournament (mid-day games, yo) dominates my students’ attention like little else.
Then on to the bellringer – a Would You Rather on the evergreen task: would you rather have (insert giant sum of money) for a month’s work, or would you rather get one penny the first day, two pennies the second day, four cents on the third day, and so forth, with the daily pay rate doubling each day.
Several students lowered their shoulder and did the grunt work, either on calculator or on paper. And the answer became crystal clear. They actually “justified their answer with math”. Serious “light bulb” moments. (“Woah!……..”)
Then we walk through graphing an exponential with a fractional base, from the previous day’s assignment. Once I reminded (and showed) them that a negative exponent means write the reciprocal to the positive power, things fell into place. And hey, wait a minute. The shape of that graph looks very familiar. Like, we’ve seen it before. Maybe, today even…
They still freeze up any time they are asked to graph a function from an x-y table, but I think they left class that day having a little clearer view of the *concept* of an exponential function. For just one day, I’ll take it. Let’s just say I’m guardedly optimistic. We’ll do some review at the end of the week, and a partner quiz on the day before Spring Break.
Moral of the story: it’s my job to stay in tune with my students’ level of understanding, and back them up when it’s needed. Visuals, a chance to play with numbers, and a chance to manipulate graphs definitely helps.
Or I could sit in a corner and mutter H – E – Double – Hockey Sticks. Those are the options.