Math(s) class is a calculator tutorial



#18

Hello all,

I am going to bring up something which I hope will stir controversy and discussion regarding education, learning, and the "correct" HP-Compaq market positioning for the educational market.

Having graduated from HS in 85 and College in 91, I never experienced the use of a calculator in math(s) class. Sure, we were allowed to use them in physics class, but math was MATH!

Reading some posts here, I am amazed to learn that teachers "build lesson plans around the TI-xxx" and "HP does not provide support for the educational market" and "Daddy will buy the child the Ti, because that is what the teacher uses".

Am I alone in thinking that this is a horrendous travesty?! Shouldn't the valuable time spent in maths be spent learning math? Shouldn't the calculator be a tool that is chosen and learned outside of the curriculum? (like for instance typing!) As technology marches on, doesn't the student who learned on a particular machine become dependent on it? (Aren't we even "dependent" on RPN!)

On the other hand, what are the positives? Does the calculator somehow make it possible for the teacher to provide better quality in the same time frame? Or do the children understand the concepts sooner? (Somehow I totally doubt that the latter is true.)

I for one am skeptical. Sure, the children may be able to learn to be proficient at producing *answers* using the calculator, but are they *understanding* any faster-better-deeper?

Ideally, we should hear some anecdotes from the younger set here---those who have actually experienced classes that were taught with a calculator. Like, I can't even imagine how this would go. Is it like, "OK everybody, find the f-shift key. Got it? Ok, now, you are going to press 'f-shift', 'solve'. Your screen should show a curve. OK, now push 'roots'. See the highlights....."


Regards and looking forward to commentary.


Bill Platt


#19

Your right Bill, this is a horrendous tragedy! They are teaching these kids a process and not teaching them to think independently. The current teaching philosophy is geared at getting higer scores on federal test to obatain money. It will kill us in the long run. I agree that the calculator is mererly a tool and the better the tool the more efficient the user. I feel we need to get back to teaching fundamentals! I have had an hp since my high scool days I graduated HS in '79 and college in '86 and have alwas been a loyal hp fan. My $.02 worth.


#20

Maybe I'm just getting old (graduated from high school in 64) but when I heard that my grand-daughter had to get a calculator for her kindergarten class starting this year, I was highly concerned for the reasons mentioned earlier (i.e., learning process over substance). On the other hand, maybe the instructors (kindergarten through college) spend most of the time on the actaul subject and use the calculator to maximize that time.

Tom Scott
Lander, Wy


#21

My son is starting 1st grade this fall. Last year, he had a great time in kindergarten. The teacher did use 1 computer a little bit, but really she seemed to be in agreement that technology should not be stressed.


Now, when we go on road trips, I sometimes give my son a calculator to play with. I feel strange about this--like am I encouraging the very thing I don't want to! Yet it seems to be OK. I'll give him a 20s, and he'll type in numbers. Then, I'll give him a 48, and he'll put numbers in it. And then he'll ask me question, like "why is this one have more numbersOr, "they are shaped differently" or "they are smaller." Once, he mamaged to get an exponent into the system, and that was fun--he wanted to know what htat did, so I showed him a huge pile of numbers and said that the exponent merely counts how many numbers. Then I show him how to make letters, and letters on the 20s by turning it upside down etc. Note that all ofthe good stuff was easier and more direct to do on paper--like showing the exponent thing. So the calculator is a "failure" in many teaching respects.

The result of this play has confirmed in me that at kindergarten, the calculator is not a serious teaching tool, but a fun diversion once in a while. At least he isn't playing with a gameboy?:~/

Regards,

Bill


#22

Last year I gave a pair of HP38G and a pair of 48G machines to a friend and her daughter. Said daughter was 8 at the time.

Is this a travesty? Is it so horrible? Did I suddenly reduce her brain mass by 30% and her effective IQ by 60 points?

Yeah yeah- anyone who graduated after 1970 or is horribly uneducated and *every* student in the old days could solve a quadratic in his head while simultaneously reciting the cubes of the Fibonacci series. While walking uphill both ways to and from school in the rain during an ice storm in May. Or something. Fine.

The problem isn't the *calculators*. My friend's daughter is doing quite well with her calculators - outside of school. She's figured out how to structure most of the measurements involved in making a grape arbor, she knows what fourier series means, she's fine. the calculator is not sucking her brains out through her nose. Oh- maybe it makes things a bit more fun since the machine will do the boring bits of adding and subtracting. Granted- she's a special case, but her in school math bores her to tears. The only thing keeping her interested at this point seems to be her favorite calculator (alas, it's the 38G, not the 48G)

And I've yet to see a teacher allow a calculator for anything that hadn't already been taught (the way the high schools in one part of CA I'm familiar with do it- first, you learn trig. THEN, you learn trig on a TI).

Learning is a lifelong process. If using a calculator rots your brain in school, it rots your brain now. Fess up- how many of you are going to sell me all your HPs cheap because of this?

Another issue- and a fairly important one- is the need for students to adapt to technology early. Oh- it may not matter if we get bombed back to the stone age, but given the structure of our society right now, technophilia is a trait that is likely to improve your prosperity.

I find the influences that try to prevent children from gaining skills in the use of computers harmful. (And when you get past 4 * 7, a calculator is a computer and can teach you a lot about how to think about them.)


If you believe that having a calculator automatically means a child will never learn to add, that's your prerogative, of course. As for me- I'm hoping the son will go for the 32Sii instead of the 20s, but who knows :)


Christof
(accept that there is humor in this, along with the grit)


#23

Bravo! I was going to post something like this, but you beat me to it -- and did it better than I could have. I only wish to add a bit more:

What matters (or what _should_ matter) in education is building the ability to analyze a problem: take it apart, see its components, and then come up with a solution. If you don't have that ability, the spiffiest calculator in the world won't make up for the lack. If you already have it, it makes no difference whether you employ paper and pencil, a slide rule, or a graphing calculator to get the answer.

One way or the other, then, calculators should NOT be banned. Banning them is equivalent to forcing students to walk in a thunderstorm when they could be riding their cars.

Another 2¢.

-Ernie

#24

hrm, I seem to have written fourier in one spot when I should have written Fibonacci again.

ah well.

and the current approach to introducing, selling, and manufacturing calculators- and computers- really does suck. I'm in full agreement. But I think they *do* need to be there, and early.

-C

#25

Quote:
If you believe that having a calculator automatically means a child will never learn to add, that's your prerogative, of course.

Well, I don't think it's automatic; I can add, and I had a load of calculators at school, but only in later years (15+), so my experience isn't directly germane. (Plus, in Scotland in the 1970s, arithmetic was a separately-taught subject from mathematics, and attempted to provide a reasonable education in day-to-day number work for those who weren't studying maths proper.)

However, here is a story from the other day which might be a small data point that tells us something about something.

I was buying a calculator on eBay (no surprise there), and had to get a money order to pay for it. I went to the closest Western Union agent to my home, which happened to be a bureau-de-change in a travel agent. The total cost of the money order was £27.49 plus a £12.00 fee.

The manager had to get a calculator to add these two numbers together.

Once he'd figured out that I owed him £39.49, I gave him £40 in cash. He then asked me if I had a penny, to make the change he had to give me easier.

A puzzled look must have come over my face, because he clarified that he didn't have any pennies. So I thought: "ah, he's going to give me fifty-*two* pence, so he wants a penny back."

So I gave him a penny. He then gave me a fifty pence piece in return, and indicated he was done.

I pointed out that he had owed me 51 pence in change.

After a few moments looking at me, he then looked at the penny in his hand, and the fifty pence piece in mine, smiled the smile of a problem well solved, and handed the penny back to me.

At this point, I thought I was in one of those splitting-the-bill puzzles where a dollar "goes missing" between the waiter and the diners, and really didn't fancy having to draw diagrams to explain what was going on.

So I repeated that I'd been owed 51 pence, and that so far, I'd only been given 50. After an even longer period of looking at me funny, the guy said it had been a long day, took a penny from his cash drawer (which previously he'd claimed he didn't have), and handed it to me.

Now, I would just like to point out, for those who didn't spot it the first time, that this guy RUNS A BUREAU-DE-CHANGE! Yet, apparently he can't add small currency values, nor correctly reckon change, in his head.

Thank goodness that he can work a calculator, eh?

#26

Sure it bothers me. It bothere me a lot. School (and university) classes should be about learning concepts, not how to use particular tools!.
When I was at school, we were allowed to use calculators, but we were never taught how to use them. We were expected to read the instruction book and figure it out.
In UK schools, it appears, 'computing' classes consist of learning how to use the current versions of Word and Excel. Ouch!. No matter what your views on Microsoft products (and mine are not repeatable in a public forum!), schools should not teach what keys to press. They should teach the _concepts_ behindword processing (how to correctly format various types of document, when to use particular types of font, etc) and spreatsheets. Learning what keys to press is something you find out for yourself in an afternoon with the program's documentation.
Incidentally, I once read something that I strongly agree with. It basically said that OK, calculators are here to stay, and therefore most students probably don't need to do endless long division examples any more. But if you are going to let
school students use calculators, then they have to learn how to use said calculators correctly. THey have to learn about truncation and rounding errors. They have to learn that because a statement is mathematically true it does not mean it's a useful method for calculation. They should learn about iterative processes, and so on.
In other words, let students use the 'new' tools, but make sure they understand the concepts relating to said tools.


#27

I agree with you. My nephew had to get a TI-83 for junior high this year. The manual was on a CD. No printed manual other than here is where the batteries go. I had to spend 2 days over a weekend printing out over 800 pages so he could start learning how to use it. So if a number of students don't have a way to print out the manual that is on the CD or if they buy their calculator in a pawn shop to save money, there is no manual for them. The teacher will have to spend most of the class time telling all of them press this key, them that key. The fundamentals need to come first then the calculators can be used as aids not crutches.

#28

At the grade/middle school level, calculator usage should be minimal. At the high school level, calculator and computer usage should be encouraged with the proper (hard to do) balance between old time skills and machine use.

A good example of what happens when the old fashioned diehard Luddite types take over is being argued several threads down, with the banning of calculators for national PE tests.

Trying to reason with the Luddites is like trying to talk with religious fundamentalists, it can't be done. In a nutshell: if you don't like calculators and computers, don't use them - but when you infringe on my wish to use them, @#$%!

J.C. Randerson


#29

Let's be sure to bring religion into the discussion. Anyone care to make a political issue out of it?

#30

My HS son just took a trig class at the community college, in which he was required to use a TI-83+. This fall, he is taking calc at the same college, and is required to use an 86. He was told that an 89 would do, but that the 86 was better suited to the course. I suppose that for his calc 2 course, he will need to buy an 89, and then a 92 (or whatever) as he continues on. I graduated HS in 82, and used a sharp 506H until my senior year in engineering school, which is when I received a 41CV as an anniversary gift from my sweet wife.

I don't have a problem with the use of calculators in class, once the concepts and processes involved have been learned. I do have a problem with the use of the calculator in performing the work, when the student has not learned to do the work w/o the calculator. I also don't appreciate fact that the classes are structured around specific calculators, as I can't afford to buy every TI calculator. More importantly, we should be able to do the work if the calculator we learned on dies, and we have to use a different model, or (no, don't even think it) a pencil.


#31

This is exactly the sort of baloney I was afraid of--just making mathematics class into a seminar for appliance operators. Ughhhhh. I think the teach needs a pep talk--actually, the faculty board or whathaveyou.


regards,


Bill

#32

That is odd, and disturbing.

I'm very much in favor of technology in the classroom, but requiring different machines for different math courses - especially at a community college- seems very bad.

I'd suggest having some discussion with the college, or local newspaper. I can accept suggesting one calculator, but not requiring multiples!

and there is still the statement "first you teach trig, then you teeach trig on a calc"

-C

#33

I just want to say that I think this thread has been really good--I certainly have learned some interesting and useful ideas! Thanks to all (past and future) for posting!


Regards,

Bill

#34

Personally, I do agree with the opinion of e.g. Tony (see his post above). But still, I'm thinking that calculators -- espec. graphing calculators -- can be reasonably and sensible used for supporting and complementing teaching (at least) undergraduate math classes. I sincerely believe that graphing calculators can enter math classrooms for the benefit of both, the learning folks to delight them for math in a "playing" manner and for the mathematics itself to make she -- right, I'm mathematician and I do love her :-) a lot -- more attractive in modern, technology driven world. By the way, I'm currently reading a textbook titled "HP48G/GX: Investigations in Mathematics" which IMHO clearly shows that and how calculators can be used to actually teach mathematics. The "instructors" at the college mentioned there use calculators for teaching math since the advent of the HP-28 and so do have a profound experience in that matter. If someone would be interested in the book, I can post information on the authors, the publisher and where one probably can get a copy.

Jürgen


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