Graphing Calculators

They are not just for graphing. I had to use one for a statistics course. It had the Z-test and T-test built in and greatly simplified the calculations. Graphing calculators add the benefit of displaying text and storing variables for a vast collection of stored equations.

The graph just gives the visual representation, which is helpful in understanding the concepts. The real data is derived from the tables associated with the data.

I've had four kids go through high school math now, and it seems to me that TI's calculator salesmen have done an amazing snowjob on the educational system. Kids are literally now taught what buttons to press, instead of what they're doing and why. I seriously doubt they're learning math any better than when I went through high school in the early '70's, just more expensively.

As for the graphing part, they get homework assignments to graph a function on the calculator, but they don't learn to draw graphs, and they have nothing to hand in so they don't know whether they did it right or not.

I agree with the snow job that is being done on us and the students. The lack of understanding of basic principals in mathematics and science scares the willies out of me. Its not the fault of the students they just aren't being taught what goes on. A niece of mine who had toped her year in high school had trouble when she went to university to study science because calculus had been deleted from the curriculum. How the hell can you study science or engineering if you don't even know what calculus is. It's like trying to study Shakespeare without being able to read or write.

I'd say that this may be true in some schools/areas, but not ALL. I went through public schools right up until 2 years ago when I enrolled at a private engineering school. I believe that I have a very good understanding of math, physics, and engineering principles given my age and had no trouble at all adapting to the more demanding educational requirements directly out of public schools. I was taught first how to do everything by hand, and then to use the calculator as a tool to speed up some time consuming calculations. I was however always in advanced math/science courses, so this may not be the norm around the nation?

As far as calculators themselves...I do agree that the graphing function is somewhat pointless. However, when it comes to entereing data to try to get a trend line, doing statistics, probablility, some calculus, conversions to/from obscure units, storing multiple variables, or executing programs you design, I find my graphing calculator to be an excellent investment and time saving tool. For example, why calculate all of your statistics (standard deviation, mean, variance, range, etc.) by hand when you can simply enter the data into a calculator table and push one button to display them all? Sure you can do this with a desktop computer, but you surely can't carry it around in your pocket.

Sorry I forgot to mention that I was speaking of Adelaide SA in Australia and apparently they are not teaching calculus in high school any more. As far a the graphing calculator goes I use a notebook computer and it goes everywhere with me. I use it for at least 12 hours a day and excel makes a graphing calculator look like an abacus. I only wish that I had it back in my university days instead of my HP-15, the one without the C. It is so unbelievably, mind bogglingly, incredibly and totally astronomically useful that I don't leave home without it and its no more difficult to carry around than the brief case that most people use to carry their fancy graphing calculator in.

I thought the calculator was perfected with the HP 15C. But then again, why does my cell phone need wallpaper and screen savers? Because someone thought it was cool. At least it employed some engineers and helps keep the price of indium up. Vermin-

Because if you get the TI-85, you get a huge conversion table. If you have any quantity in the MKS system, be it length, weight, pressure, energy, what-ever, you can convert to an American understandable value. Never have used the graphing function.

Definitely graphing is one of the least useful functions of these calculators. I feel like they arent necessary for high school level courses and probably impede the learning process more than anything, but in my EE courses in college it was invaluable. Application specific programs can even be downloaded from the web.

AP exams that require a calculator (Physics/Calc) allow you to use any non-QWERTY calculator (at least they did when I was in HS a few years ago...). With the ability to do plots, you could get it to find intercepts for you on the plot (useful for projectile motion problems...). Also, in college, profs would allow us use of calculators but not computers (that would have Maple or Mathematica installed). Because the computational abilities of the graphing calcualtors are fairly close to those of Maple in many respects (especially in more basic calculus and computation), they become a very attractive option to put as much firepower at you fingertips as possible. Who wants to spend half an hour solving a system of equations by hand when they can plug it into the calc/comp in 5 and have an answer within a minute? Besides, with tests having a limited time period, efficiency is the name of the game, and the newest graphing calc and it's rather powerful processor is what will get you there the fastest. That's the attraction, and why they're so popular. Straight from the mouth of a college student.

My high school calculus teacher would get around the calculator's abilities by telling us to solve an equation in terms of "X." At the time most people had a TI-82 or TI-85 so symbolic math had to be done by hand. The TI-92 could solve equations symbolically but no one had one do to their expense. Shortly after I graduated highschool, the TI-89 was released which puts the power of the TI-92 into the footprint of a normal graphing calculator. I'm not sure how teachers handle students that use this one. The other thing my calculus teacher allowed was any application we could program could be used on tests so long as it wasn't a database of notes (she checked). I thought this was a great idea because to write a program to perform some higher level math function requires knowledge and understanding of the underlying concepts. To this day I can still write TI BASIC programs like it is nobody's business!

I agree with the efficiency comments. While in college taking a controls course, factoring and solving complex equations was common place. Each problem required several 2-3 pages of scrap paper and a lot of time. My professor was more concerned about the derivation of the transfer functions instead of the tedious (but not too difficult) process of manipulating and solving them. He encouraged us to use any tools available to help speed up the process. The TI-89 has functions for both complex factoring and complex solving. Spend 2 minutes entering the equations and poof, you've got useful data!

In Michigan, Graphic Calculators are intended to impress the parents. Too often the parent is forced to spend hours each night working with the son or daughter that years ago would be truly educated during school hours. Perhaps teachers, like youngsters today, have too short attention spans to use paper. The small screens do not help understanding but they do look "cool" to the unknowing parent. I recommend, just for the fun of it, asking the instructor to demonstrate the work on paper- it can be telling.

It seems that a few have mentioned there favorite calculators, mostly TI's. I had to use a TI in a stat class, and had to re-learn how to use it. The calculator I used through college was the HP-48gx, with its RPN it took some getting used to, but I love it, and all other calculators are now backwards. During college I collected a few programs for it, and once when changing batteries, I lost all of my data. Does anyone have the Ye Olde Notepad for the HP-48 series? I also had a program, I think it had the letters USA in it, that was an animation of a woman in a bikini, does anyone have that? The main reason I want the animation is to show up the guys with the TI's, I have yet to see an animation on the TI.

When I was in highschool, the TI-83 was the graphing calculator of choice. For some reason (cost / availability) I had purchased a Casio Model. As stated above, a good portion of math class was dedicated to learning the TI-83-specific button sequences. Those of us with different models were forced to teach ourselves.

We used the graphing functions for a few different things: finding solutions to equations, looking at the shape of different equations and finding intersections between two equations. In province-wide standard tests, we were required to sketch what we saw on the screen, as well as indicate what range and domain we were looking at. This reduced the amount of manual calculations and allowed more complicated problems to be solved.

In University, the Engineering Faculty layed out very specific guidelines on what type (and in many cases, which model) of calculator were allowed to be used in each class. Calculators had to have a colored sticker, identifying them as programmable or non-programmable, and approved for use by the faculty. (Calculators could be bought with stickers attached already from the bookstore, or taken to the faculty for inspection.)

While I agree that this increases the level of fairness, the part that bothers me the most is after trading in my Casio for an approved TI model, I didn't have a single course that programmable (graphing) calculators were allowed.

REAL old curmudgeon here..... When I was in school, the argument was over whether
we ought to be allowed the use of slide rules.
I can remember that graphing was particularly enlightening to me because
it gave me an understanding of how the functions actually behaved.
Having it instantly available might have speeded that process but what I see around me now
is people who can't even do arithmetic without a 'box`.
I wonder whether allowing the use of these tools without competence in their
underlying principles is a good thing.
From what I see around me it is not being managed well at all.

SLIDE RULES RULE!!! Calculators are for accountants not engineers!

I suppose a graphing calculator would allow students to not understand the relationship between position, velocity and acceleration, for example, but it might enable them to show someone else which buttons to push to get the graph to show up.

I don't think the US will ever get back to the moon, or Mars, or anywhere else, before another country does. The plans for the Saturn IV rocket are lost or destroyed. Don't know that it would do any good if they still existed. Reminds me of the old movie, "Time Machine," where Rod Whatshisname goes so far into the future that people were completely ignorant and Warlocks ruled the world.

I'm worried about our children and our educational system.

You'll probably be pleased to hear then that my calculus lecturer (at an Australian university) has a simple rule about which brand / model / type of calculator can be used in exams... no calculators allowed! All graph drawing of complex functions etc has to be done from scratch. I don't think it's going to get Australia to the moon, but it's a good motivator to have all your maths chops and common trig ratios firmly in your head...

The essence of your questions boils down to another question: Who is using the calculator? The fact that students might use graphics calculators has more to do with the fact that graphing capability is incorporated into most "scientific" (formerly, slide rule) calculators. Why? Mostly because having the graphic has lot's of shelf appeal at the store. If the who who is using the calculator is a student at high school or at high-scool equivalent college, chances are good that that student might get little or no use out of the graphic display, or even the calculator itself once the Grade has been bestowed. For others, or more serious types, the graphing feature comes in very handy for quickly envisioning many functions, on the fly so to speak. So, it would not make a lot of sense to disparage TI for importing such devices simply because some will not get much use out of them, or appreciate their features fully. Some might even remember the college days of yore when the greatest use gotten from SLR calculators was having something to carry around in its holster on one's belt.