Resisting the TI
At my first school a few years back, we received a buttload of TIs that most teachers were not using. The AP gave me one. I told her I didn’t want it. She insisted, said I could work with the kids (bright kids, math service aides) in the office using it. What should I show them?
I found two families of graphs that I taught the kids.
Plug cos(At) and sin(Bt) in for x and y in parametric mode. Let A and B be 3-digit, relatively prime or almost relatively prime numbers. Set the window from (-1,1) to (1,-1). And run t from 0 to maybe 20pi. (Lissajou figures)
Another is in polar mode, r = 1 + theta/10 + cos(5theta) Let theta run to 20pi, set the window to +/-6 in each direction. (a spiraling 5-petal flower. Looks like a “leaf.”
So the kids had fun, and got good, and the AP saw, and agreed to take the calculator away. Victory was sweet.
JD2718 
You mean, you showed them how to make a pot leaf? LOL
I do not believe in using the calculator before pre-calculus and even then, I would do both calculator and non calculator excercises and I would alternate calculator and non-calculator exams. The calculator adds a new dimension to learning math, it allows us to explore areas that we were never able to get to before. It allows us to go deeper into an understanding of mathematics because we do not have to concentrate on calculations.
All this said, I believe students should know all their basics first. It is a sin that kids can’t do anything without this devise. They don’t know the trig (ex sin 90) anymore. They can’t recognize a simple trig graph. They don’t know the tricks that make computations easier, the ones I grew up with.
Last year I taught a class of seniors how to pass the math A regents using the TI 83. These were all kids who never passed more than one math class. All passed except for one. Am I proud of this? Absolutely not. But, that was the job I was given and I did it to the best of my ability. Do these kids know any math? Absolutely not. But, they are out of high school. If they choose to go to college, they will have to learn from scratch.
I believe in using calculators for what they’re good at: Quickly showing you the graph of a weird function, multiplying big numbers, or doing trig (and inverse trig) on non-standard angles. You don’t hear anyone lamenting that kids don’t know how to use trig tables anymore. You don’t hear anyone wishing we still had to look up logarithm values in the back of the book.
When I took trig and calculus in high school, we used the TI-85 and I think it benefitted us. On the other hand, we also had to memorize the standard positions on the unit circle (angles in radians and degrees, trig function values) and found it faster to use those from memory than to punch them in. There’s a whole unit of trig identities you can do that way. We learned the cosine and sine add/subtract formulas and used them to derive the double or half angle formulas as necessary (instead of memorizing those directly).
We also had to be able to graph A sin (Bx + C) – D for all A, B, C, and D by hand, for all six trig functions. So I’m not suggesting to compromise on these sorts of requirements. You’re the teacher and you decide when calculators are appropriate and when they’re not. A calculator won’t reason for you and we should disabuse students of that idea, quickly. But the calculator is a useful tool to allow students to tackle more complicated and interesting problems that would be too computationally gnarly otherwise.
I’m more with Ben on this one. But the TI’s have gotten way out of control.
Nan, it was not my intent. But that’s what the kids saw. By scaling the spiral part, I can change the shape of the petals so that it is no longer suggestion of, well, yeah, that.
I didn’t mean for this post to be a calculator rant, but since we’re here…
I rarely use them in Algebra I. I find more use for them in Algebra II, and trig, but not as a substitute for graphing… just as a quick grapher after they’ve mastered the basics. And I offer a once a week hand-graphing elective for upperclassmen.
We are cheating kids when we only teach them to graph using the calculator. Understanding comes from doing.
In calculus, we graph by hand, from clues and then check to see how close we come on the calculator. Kids love to see how our graphs are exactly correct.
I don’t agree with not using calculators to graph things… I recently did some math problems where you have to find the area between a 4 leaf rose and a cardioid, and I do not want to spend the time to algebraically calculate the intersects on those curves and then probably miss some of the intersects anyways because they wouldn’t show up.
Besides which, pulling trig graphs and triangles out of memory is just a waste of time and you won’t discover anything new from drawing sine curves over and over again just because you have no better way of doing it.
I am not sure who you are disagreeing with here.
“We are cheating kids when we only teach them to graph using the calculator. ” I agree with you.