Wednesday, September 27, 2006

Graphing Calculators--and Tanks!

I stayed after school today to talk to a couple students. I hadn't planned to, but we just started talking after 6th period, and before we even knew it a half an hour had passed.

They asked several questions about my time in the military--which, actually, ended very near the time they were born! Still, I answered the questions and told war stories. It was a good time.

One of the questions, and I don't remember exactly what it was, launched me into a story about my rotations to the National Training Center in Fort Irwin, California. For those of you who don't know what the NTC is: it's over 600,000 acres of beautiful desert maneuver area, complete with its own OPposing FORce (OPFOR). Back in my day, the OPFOR adopted Soviet tactics, and their vehicles were all visually modified to look like Soviet weaponry. A visiting Russian general once pronounced the NTC's OPFOR the world's best trained Motorized Rifle Regiment--how could they not be, when they fought American army brigades several months a year!

I was with the 4th Infantry Division from Fort Carson, Colorado. Our mission at the time was to be prepared to deploy to Northern Europe to fight Warsaw Pact forces invading West Germany. How quaint that all sounds now! Anyway, we weren't a rapid deployment force or anything like that; in fact, we were pretty far down the totem pole when it came to getting repair parts or even fielding new equipment. When I arrived in late 1987 we still had Jeeps and were in the process of trading them in for Humvees! We still used Vietnam-era M113 Armored Personnel Carriers and M60 tanks, while the "more important" divisions had the Bradley Fighting Vehicles and M1 tanks that we still see used in Iraq today.

One of the NTC evaluators once said to us that brigades from the 4th Division often performed better than brigades with M1's and Bradleys. The reason, he said, was because units so equipped expected their superior equipment to win the battles for them, whereas units from the 4th, because our equipment was not noticeably superior to the faux Soviet equipment (except in night operations), relied on our tactics and battle plans to win the day.

At that point in the war story I saw a teachable moment, and I said, "That's why I don't let you use graphing calculators in pre-calculus class." I don't want the students to rely on their equipment to get the answers, I want them to rely on their brains. It worked for us in the 4th Infantry Division, it will work for my students, too.

27 comments:

nebraska girl said...

That is a great comparison. And great reasoning for not allowing the calculators. Our math teacher always made sure we could do the work without a calculator, and I've found life to be much easier because of this.

Anonymous said...

Bravo!

A calculator is a tool, not a crutch.

Scott McCall said...

why do tell us we should get a graphing calculator to help us, when we're not alowed to use them?

Darren said...

I *never* told you to get one, Scott.

Calculus teachers do, because they say that AP tests require them, but I don't allow them in pre-calc at all.

MikeAT said...

A little off the mark, but in the neighborhood.

I was in a conversation with some of my buddy’s at the reserve unit today and we got on the subject of movies and how you can’t let kids watch them anymore. One of my sergeants (she’s 25 with two kids) mentioned how she has problems with today entertainment. I told her in Casablanca, Humphrey Bogart and Ingrid Bergman had a “wild scene” where they met in his room and then you immediately moved to another scene in his room. You knew what happened but you didn’t need to see both naked on top of a bed (and thank God they haven’t tried to remake that classic of American cinema)

This movie was made in one week and it was one of 50 movies Ingrid Bergman made in 1942. I mentioned this because many people in what was a great movie industry have come to rely on special effects, violence and sex to fill up the time on a movie screen, when they should be relying on good scripts and acting.

Similar situation. Use your brains and a good plane instead of relying on some computer to do your job.

Brook Stevens said...

I feel left out i couldnt hear these war stories even though im sure i got my share of salty sea stories over the summer and yea baker says we absolutely need a graphing calculator for calc this year

Anonymous said...

Here at USAFA we arn't allowed to use graphing calculators. We are issued "honorlators" which are your standard scientific calculators. I actually didn't even own a scientific calculator until Darren's class.

I have never/nor will I ever own a graphing calculator.


I wonder who the OPFOR pretend to be these days.......North Korea? China?

Anonymous said...

What if you made the calculator that would help you on the test?

chris said...

What if you made the calculator?

Darren said...

For those of you who don't know, USAFA is the US Air Force Academy. I have a sneaking suspicion I know who that anonymous poster was :-)

And Chris, I doubt most people have the silicon technologies needed to make their own calculators. If anyone *did* have the capability to make their own, they'd be at a higher math level than my pre-calculus courses anyway! So in that regard, I guess it would be ok.

Brook Stevens said...

that might as well not be anonymous . . . USAFA

Anonymous said...

There is a problem with not being taught to use graphing calculators. This information is from collegeboard.com, you know the folks who issue the SAT 11 subject tests.


Regarding Mathematics Level 2

Mathematics Level 2 is a broad survey test intended for students who have taken college-preparatory mathematics for more than three years, including two years of algebra, one year of geometry, and elementary functions (precalculus) and/or trigonometry.

(NOTE: these are students exiting Pre-calculus)

Anticipated Skills

You're not expected to have studied every topic on the test, but you should anticipate the following:

* Number and Operations
* Algebra and Functions
* Geometry and Measurement (coordinate, three dimensional, and trigonometry)
* Data Analysis, Statistics and Probability

Regarding Calculator Use

It's NOT necessary to use a calculator to solve every question on the Mathematics Level 2 Subject Test, so it's important to know when and how to use one. For about 35-40 percent of the questions, there's no advantage, perhaps even a disadvantage, to using a calculator. For about 55-65 percent of the questions, a calculator may be useful or necessary.

If you're comfortable with both a scientific and graphing calculator, you should bring a graphing calculator. A graphing calculator may provide an advantage over a scientific calculator on some questions. Read more about acceptable calculators.

How do students prepare to meet the challenges of a test (where the college board says the calculator may provide them with an advantage and further states, "it's important to know when and how to use one.") without having ever been taught to do so?

Darren said...

I know this will raise a stink: I don't view it as my responsibility to teach students what they need for the SAT. I teach them the California Math Standards. If they're in pre-calc and think they'll need a graphing calculator on the SAT II, they can read the manual that comes with the calculator!

What you're also not considering is the practical limitations of teaching them to use these boxes. Since I legally can't require them to buy a calculator, which one shall I teach? The cheaper Casio, or one of the myriad TI calculators, each of which is different?

Sara said...

Ooh, I get to tell my favorite "math geek" story now! When I was a senior taking BC Calculus my teacher (formerly a teacher at USAFA - I think, although it might have been USNA) told us the first day of class that his goal was to prepare us so well for the AP exam that we would feel it was the easiest test we took all year. With that it mind, he proceeded to teach Calculus (including multivariate!) ENTIRELY WITHOUT THE USE OF A GRAPHING CALCULATOR! Or any calculator. We did everything by hand. Definite integrals, ugly fractions and decimals, trigonometric evaluations... everything. We learned about how and when to round our answers, about significant figures and danged if I'll ever forget ANYTHING on the unit circle. So I was using the "I've got an AP exam this afternoon" get out jail free card to study with some friends at Starbucks the morning before the exam, and asked a friend who had a different teacher what was the most important thing to know before the exam. I was thinking about the FTC, but he responded "Math 9" referring to a command on the TI-83, and I had never heard of it! I thought it was insane that the calculator could do definite integration, so I pretended like I still didn't know, took my calculator into the exam, didn't use it, did the free work portion of the exam in purple crayon and proved my teacher right by getting a 5 on the exam, earning 6 hours of college credit and being thouroughly bored in the remaining 2 hours of the Calc sequence and the Multivariate course. (I tell this story to the kids I teach now, but none of them believe me... they still think they need the box.)

Anonymous said...

A student reading a manual alone is hardly an adequate substitute for being taught how and when to use a calculator for questions on a mandatory test. (a very important test used to determine their future acceptance into college) State standards do nothing to help students get into college. Advanced math classes (such as pre-calculus) should be considered college prep and SAT prep should be part of the classroom learning. I agree with no calculator use for lower level math classes that are only required to graduate from high school. However, students enrolled in pre-calculus are college bound and should be receiving the necessary instruction to do well on the SAT11. The AB and BC teachers at Rio REQUIRE an advanced graphing calculator for thier classes.

Darren said...

Please read Sara's comment again.

Anonymous said...

Please read the information from collegeboard.com again.

Anonymous said...

Also the SAT11 is a timed test. There is not adequate time provided to do all the problems without a calculator.

Darren said...

The College Board doesn't dictate the standards of my course. The State of California does.

If a student can't learn how to use a graphing calculator from reading the manual, I wonder how well they'll do in college.

Sara said...

SAT II has little to do with college acceptance. They're subject area tests that most schools use only to grant students credit for introductory coursework in an area where they've already demonstrated competency. SAT I still doesn't require a calculator, although one is allowed.

http://collegeboard.com/student/testing/sat/testday/calc.html

Darren, you're doing right. If you're teaching kids to use their brains, they don't need the box. Thanks to your warm welcome, I'm eschewing total internet anonymity and using my blogger account here. This conversation is worth having.

Sara said...

Oh, and SAT II isn't required. If it were, what about all those poor souls who could barely pass Algebra 1? How would they get into a good college? (Don't even get me started on this one!)

Anonymous said...

Sara your confidence to post about a topic you obviously know little about is alarming. The SAT11 is REQUIRED by all UC's in California, and MOST of the more competetive private schools. The UC's are on a point system, and points are assigned for each of several areas, including two SAT11 tests. Other schools use the SAT11 to assist in their overall determination of a students profile. Some schools require as many as three SAT11 tests the UC system no longer accepts the SAT11 level 1 math test. Most privates prefer or require the level 2 as well. I find your attitude about blowing off important college tests foolish. Should we dumb down all our math courses to help out those poor souls who can't even pass Algebra 1? They don't belong in the UC system. Should public school no longer serve the students who want to go to a UC or quality private school?

Anonymous said...

I think you are confusing AP testing with the SAT11 Sara.

Darren said...

I find it telling that an institution as elite as the Air Force Academy does not use graphing calculators when teaching calculus.

MikeAT said...

"The College Board doesn't dictate the standards of my course. The State of California does.

If a student can't learn how to use a graphing calculator from reading the manual, I wonder how well they'll do in college."

Darren, these are CA public education graduates. You’re going off an on limb thinking they can read! :)

Barry Garelick said...

Students who depend on calculators have problems seeing that x + 60*17 = 60*14 can be solved without a calculator by using the distributive principle: x = 60*14 - 60*17 = 60(14 - 17) = 60*(-3)=-180. By being dependent on plugging in numbers to get an answer, students miss out on important features of math which play significant roles in advanced math classes, where fewer numbers are used and equations contain mostly letters.

Fritz J. said...

Calculators are marvelous little gizmos and I simply love them. I remember the first time I saw one back in the 70's and when the price finally dropped to where I could afford one, I have never been without since that time. I happen to prefer the ones that operate in RPN, but use the system you like best.

Having said that, I would agree that calculators are of limited use in the classroom. The object of any class is to teach the student how to solve certain problems and doing it the old fashioned way with pencil and paper will quickly show which of the students truly understands the process. Who knows, there may come a time when you will be forced to solve the problem without the aid of a calculator and if you have always depended on one, you may find yourself unable to do so.