May this Luddite growl about graphing calculator use on the AP Calc exam?

[Jane in NC]

Granted, I studied a lot of math in the pre-calculator dependency era. But even today, after a certain point in mathematics study, a calculator is never used since the device does not help you prove your way out of a paper bag.

 

That said, I have tried to adapt to teaching Calculus in this era during which the calculator is not only an accepted instrument but a required one on the AP exam. There are times when the calculator is optional, times when the calculator is not permitted and times when it is mandatory for full credit. There are integrals and equations that a student is expected to use a calculator to solve--although the student needs to know when the calculator is the mandatory tool.

 

I'm going to be honest: this came as a surprise to me. Some of the prep books that I have seen only emphasize Calculus (imagine that!) But has the College Board made it absolutely clear that the graphing calculator must be used for certain problems? They do state that a course goal is to "use technology to help solve problems, experiment, interpret results, and verify conclusions". I think what is frustrating me is the knowledge that many fine colleges in this country do not permit calculator usage throughout the Calculus sequence.

 

Parents of those students who have been there and done that: Since the College Board publishes the free response questions, I can see examples of how they expect students to use a calculator on these kinds of questions. But what about the multiple choice? Are these all doable with a brain? Or do they include problems that require approximate solutions determined via technology? Anyone know?

 

Thanks,

Jane

 

P.S. According to this PDF, students should know not only how to use the graphing function, but how to evaluate derivatives and integrals on calculator and solve equations.

 

P.P.S. The PDF in the postscript is chapter one of a book on preparing for the AP Calc exam by Skylight Publishing. I just realized the company also makes available the last chapter of the book which supplies annotated solutions to the AP Free Response questions. While the College Board does provide a rubric, this page will lead you to more detailed answers with good notes on presentation, some common errors, etc. This looks very helpful!

Edited February 19, 2010 by jane.kulesza
Bonus chapter!

[Ruth in Canada]

and so far they have all said that calculators are not allowed on calculus exams at university.

[Caroline]

Yes, there are a couple of multiple choice questions that require calculator use. However, even in the calculator section, most questions do not require a calculator.

 

If you google PDF AP Calculus multiple choice released, you can find some copies on-line, even though they are not supposed to be there.

 

I am a non-calculator calculus girl. However, I do teach my students the calculator. On the exam, it is not only required for some questions, but also for speed.

[Kathy in Richmond]

Hi Jane,

 

I have a 2003 released exam for AP Calc BC, so I can help you with your question about the multiple choice part of the test. Part B of Section I (the multiple choice part of the exam) states that "a graphing calculator is required for some of the questions on this part". That's a true statement in our experience. Some require a calculator to make any progress, some require one just to evaluate the final answer, and some others don't require a calculator at all in this section. The student really has to know when to use the calculator and how to use it efficiently.

 

Some examples I found:

 

(1) A particle moves on the x-axis with velocity v(t) = cos (2 - t^2). At t=0, the position of the particle is 3. What is the position of the particle when its velocity is first equal to zero? (followed by 5 choices of numerical answers given to three decimal places).

 

(2) A particle moves in the xy-plane so that its position at any time t is given by x(t) = t^2 and y(t) = sin(4t). What is the speed of the particle when t=3? (followed by 5 choices of numbers to three decimal places)

 

The pdf linked in your post lists the four calculator techniques that are required on the AP exam. My look at the released exam and my two kids' experience would say that they're accurate. All four techniques are usually tested somewhere in the multiple choice or FRQs.

 

I'm with you, though, Jane. My kids and I think the non-calculator questions are a lot more interesting and fun and actually test a higher level of thinking!

 

~Kathy

[Jane in NC]

So it looks like, in addition to prepping for the Calculus part of the exam, I also need to work on how best to use the calculator on that part of the test which permits its usage. (This has never been a part of any Calculus course that I have taught. :rant:)

 

My son had never used the solver feature on his calculator until this week. I have not wanted him to get into the habit of depending on technology to solve equations but it was clear when he was working on some Free Response Questions that he had to solve an equation numerically. I truly am taken aback.

 

My word, those calculus courses without calculators must come as a complete shock to some students when they reach college!

 

Thanks for your responses and sympathy. I think I'll now have a quiet moment with my slide rule. ;)

 

Jane

[kiana]

My word, those calculus courses without calculators must come as a complete shock to some students when they reach college!

 

I'm not so sure it's "when they reach college" as "when they reach the AP exam". Many universities still do not allow or limit graphing calculator usage.

[asta]

On the exam, it is not only required for some questions, but also for speed.

 

I was going to point this out: the exam is timed as if the student is doing those problems with a graphing calculator, NOT by hand. If your student is writing them out, they are putting themselves at a disadvantage relative to the other students.

 

I feel that it is just one more example of "how well you have learned how to take a test" vs "how well you know a subject", but what do I know. If the world goes to sh!t, homeschoolers will be in charge, because they will be the only ones who know how to do math and engineering w/o a calculator.

 

 

a

[vonfirmath]

Thanks for your responses and sympathy. I think I'll now have a quiet moment with my slide rule. ;)

 

Jane

 

*laugh* My physics teacher my senior year of HS insisted we use slide rules, and ONLY slide rules for the first semester (before Christmas). She wanted to make REALLY sure we knew what magnitude of answer we were expecting before we did the problem. We also did lots and lots of conversions. (she provided the slide rules. Even in 1990, going out and buying a slide rules was really not an option)

 

We were allowed to use a regular calculator the second semester, once she KNEW we had down what size of answer we were expecting without the calculator telling us that answer. To this day, I do conversions the way she taught it, though, writing everything out thoroughly and making sure that I can cancel out all the units of measure except the ones I am expecting at the end.

[distancia]

What I would like to know is: who is the "they" that keeps insisting our children (students) need to use calculators--especially the advanced graphing calculators--at such an early age?

 

When my D was in public school she took Algebra 1 in 8th grade (skipping pre-Algebra) and we had to buy a TI-84 for her classroom use. The girl hadn't even mastered fractions, decimals, and percents, so she never learned how to "think" the problem through, nor the accuracy of her answer.

 

Shaking my head...:confused: