Prompt 4: Respond
This prompt really didn’t speak to me when I initially read the email from Sam and Julie. That was Wednesday, the first day kids reported to school for the year. All I could really do that day was introduce myself, hand out books, read through the agenda and syllabus, and maybe ask a few kids how their they spent their summers. The usual.
Today was different. Today I taught. And the picture of the graphing calculators rises to the top.
We have a seven period day at my high school; I get one planning period and six classes to teach (I’ll save this rant for another day, but I want to mention I have five preps this year. I only ever teach one class more than once.). Bookending my day are AP Calculus AB in the morning and AP Calculus BC in the afternoon. This year, to begin each of these classes, I’m going off-book for the Precalculus review. After teaching Calc for 2 years, I feel like I have a pretty good handle on what topics my students should know well before we hit Limits.
In my opinion (subject to change), the most important concept is recognizing functions in their algebraic form and visualizing the graph mentally. I’ve noticed that the students who work problems with the most speed and precision are the ones who best understand the analytic and graphical connection of a function.
So in Calc AB, I start talking about Parent Functions. y=x, y=x^2, yada, yada, yada. What does the graph of y=x look like class? Crickets. And I know I’ve got a wall to climb.
Similar story in Calc BC. I give a worksheet with the graph of a piecewise function, f. I ask them to graph y=|f(x)|, y=f(-x), y=(x-1), yada, yada, yada. Better results than AB, but nothing to write home about.
New goal: If I teach these kids anything this year, it better be for them to recognize 10 or 12 parent functions and their corresponding graphs. And they’re going to know how to translate them all over the place. And this stuff is going to be automatic. If they can do this, I hold, the Calculus will have more meaning, make more sense, be easier. And what high school student doesn’t want his homework to be easier?
On this Friday night, I’m concerned. Functions and graphs and translations are things they should know. Right? My Precalc review should last days, not weeks. *blurg*
So where does the graphing calculator come into play? THEY ALL HAVE THEM. Our math department hands out TI-8x’s like Fire Sauce packets in the drive-thru at Taco Bell to students who don’t have one of their own. Even more, these students have had them for 2-3 years.
How do I respond to the picture? I want to stand on my desk and loudly ask my Calculus students what they’ve been doing with those $120 paperweights they carry around. They do more than add and subtract and play Tetris, I want to sarcastically exclaim. But I don’t. And I won’t. I don’t know the circumstances of their knowledge gaps, so I won’t hold them guilty. What I will do is make sure I incorporate the “Y=” button on the graphing calculator into every Calculus lesson I teach until I can see some light at the end of the tunnel.
Hold me to that last promise there, blog readers. My students will benefit. And so will I.