OT: Do 12 yrs old kids need graphing calcs?



#12

Interesting and funny article.

Funny article about TI graphing calcs


#13

The article was amusing, but the comments were the most significant highlight (lowlight?).

In the early '80s (the day of the TI-58/59 and HP-41), while a student in a large university's engineering program, I listened to a professor suggest that it was a shame that the school did not require the purchase of programmable calculators by its students. "10 years ago, students wouldn't have thought of completing an engineering degree without the help of a well-made $100 slide rule. It is not too big of a burden to expect them to spend $100 today on a programmable calculator."

I certainly did not need such a tool my freshman year (My TI-30 worked just fine), but I attempted to complete my sophomore year without one, with poor results. I had a tough time justifying $80 for my TI-58C in the fall of 1982, but when my parents (a CPA father and a math major mother) found out I was planning on getting through my junior year engineering classes with a "$10 calculator", they encouraged me to spend my money on something better.

It made a big difference in my academic performance, and I enjoyed my engineering classes all the more. Is this article a corollary? Maybe not. But the tongue-in-cheek arguments sound familiar.

Dan


#14

I bought my first Texas Instruments SR-50A at age 15 and the TI-58 at age 17 (couldn't afford the TI-59) and used them heavy.

We are now a family of six (49, 49, 20, 18, 15 and 14) and use SIX Texas Instruments TI-84 Plus S.E.!

Guess what, the two youngest know more about the Graphing calculators than we parents and/or even the two elder brothers.

Our daughter started age 12 to use her TI-84 and she knows every hidden functions in the dozens of menus.

Regards,
Joerg


#15

Sounds like an educated family, Joerg.

There seems to be a bias on this forum against kids using calculators in school, particularly graphing calculators. My experience as a math teacher is that the kids who lack what we would call the basic arithmetic and math skills are NOT the ones using the graphing (or other) calculators. No, the graphing calcualtors are, by and large, used by the kids with excellent math and arithmetic skills who want to explore more sophisticated math concepts, and the TI-84+SE is an excellent tool to do just that.

Here in the US, most kids in the middle grades (kids aged 11 to 14) do not use graphing calculators very much, it's the older kids (16-17) who benefit most from them, I'd say.

I've always known that some kids do use calculators as a crutch for not knowing the basics, but those kids are in the minority. By the way, I rarely take my TI-Nspire CAS to school, I find my trusty TI-83+ a tool that just works well.


#16

Hi Don,

It's good to hear from you that kids that use graphing calcs are generally good at arithmatic and maths skills. I know that technology is very much part of our world these days so I let my 8yr old check her maths on a 20S (don't worry, I'll make sure she can use "real" HPs too - she can do basic 4-banger RPN on the 35s). But I try to make sure she understands what she is calculating.

But when they start using calculators in class at primary school level I do worry that there's the potential for them to become button pushers without undertanding the underlying maths.


#17

Quote:
But when they start using calculators in class at primary school level I do worry that there's the potential for them to become button pushers without undertanding the underlying maths.

Agreed, Bart. I haven't spent any time in the primary school (grades 1-5 locally) classroom, but I suspect calculators are rarely, if ever, seen there. The early grades are where the kids are supposed to learn the basics. By middle school, most kids know how to do the basic operations with pencil and paper, and these kids can sometimes benefit by using calculators to explore more advanced concepts.

I think it is the responsibility and duty of the teacher to know when and how to use calculators, or any tool for that matter, in the classroom. Many older teachers don't want anything to do with electronic calculators or computers; they don't understand them and will not use them. And they really do a disservice to the kids who might, like Seth, get really motivated by them and want to explore advanced concepts.

#18

My son's 7th grade GT math class requires a TI-84+ SE. If you don't have one, they are provided, but only for classroom use. I was surprised to see how comfortable he was with the calculator while we were waiting for him to take the SAT. (They allow these things now on the SAT!)

For him, the calculator is a tool for a specific use--he doesn't give it anywhere the thought (or respect) that I gave my HP-41CV back in high school. Adding to what Don mentioned, these kids are using the calculators, much like computer software like Excel, as just another tool to turn to when solving a problem. Knowing when and how to apply the tool is the skill being acquired.

#19

Quote:
10 years ago, students wouldn't have thought of completing an engineering degree without the help of a well-made $100 slide rule.

Was there really ever a time when a top of the line slde rule cost $100.00?

Palmer


#20

There must have been a time they were expensive. My dad never let me touch his slide rule, but I could play with the first Sharp LED scientific he owned - even though they were pricey at the time too.

Anyone on the forum able to recall what actual prices of good slide rules were?


#21

I have a late '40s vintage K&E 4081-3 (10" log log duplex decitrig in their parlance). It's probably the most common general purpose "high end" model. The same slipstick in the 1962 catalog is (I think) the 68-1210, and the list price was $28.50.

According to an inflation calculator I found online, that works out to about $200.00 in today's dollars. ISTR Pickett's prices for an equivalent model in that late '60s was in the $15-20 range. Their metal rules aren't as luxurious as a bamboo Hemmi or a mahogany K&E, but they were cheaper to produce.

You can find a bunch of vintage K&E documents here.

FWIW, I bought a cute little NIB "As Used on the Apollo Missions!" Pickett N600ES 5" rule (new old stock) for about $50.00 a couple of years ago, along with several NOS (but not retail packaged) N500ES 10" rules for $15/each.

#22

Quote:
Anyone on the forum able to recall what actual prices of good slide rules were?

I purchased my K&E Log Log Dplex Decitrig <4081-3> in early 1947 for twenty dollars. I never found it necessary to get anything else.

I remember that sometime in the 1960's I saw my first Sterling all plastic log log slide rule but I can't remember the price. Peter Hopp's book describes the Sterling's as "... cheap plastic slide rules ..." I have several Sterling No. 594 Decimal Trig Log Log slide rules in my collection which carry a copyright 1965 nomenclature. The Pickett Microline 140 was another all plastic slide rule which must have carried a lower price. It seems to me that one nice thing about the all plastic slide rules was that the user wouldn't have to mess around with the adjusting screws.

Palmer

#23

Quote:
Anyone on the forum able to recall what actual prices of good slide rules were?
My grandfather gave me his K&E N4080-3 log log duplex trig slide rule with a leather case that is still in beautiful condition, and said it was a $50 slide rule. I think it's made of mahogany. I wonder how much of that number, if it was accurate, was for that outstanding leather case. You don't find many things made to that level of quality anymore. That was near the end of my years of using a slide rule, somewhere close to 1980.

Before that I used a less-prestigious metal Pickett N902-ES. I think I got it at a supermarket, but it did have a very smooth viscous sliding motion as long as I periodically put a tiny amount of Tri-Flow lubricant on it. I think I paid about $4.50 for it. The case was imitation leather and required care in handling to keep it from delaminating and shredding.

I also got a bamboo pocket slide rule, a Scientific Instruments Company (SIC) model 4500, whose less-expensive leather case had a clip and it fit in your shirt pocket, taking the space of maybe three pens. I think I paid closer to $10 for that one after it was somewhat yellowed on part of one side from having sat in the display case for many years with the sun shining on it in the afternoons.

Can anyone tell us if there was a push to get slide rules into schools after President Kennedy presented his vision to put a man on the moon by the end of the decade, and there was more push for engineering?

I was on the board of a private K-8 school for six years in the 1990's, one where my wife has taught for about 19 years. It was kind of funny to see the ideas about computers as they were becoming somewhat common. Schools wanted to look modern, so computers were perceived as a necessity even when they weren't very useful to students-- at least yet, and especially for lower grades.

< to be continued possibly in another more-relevant thread about misapplications of technology >


#24

Quote:
Schools wanted to look modern, so computers were perceived as a necessity even when they weren't very useful to students-- at least yet, and especially for lower grades.

And 30 years after the birth of the PC, they are still not very useful to students. We're still waiting for the "killer app" that will revolutionize education. We'll still be waiting in another 30 years.


#25

Quote:
And 30 years after the birth of the PC, they are still not very useful to students. We're still waiting for the "killer app" that will revolutionize education. We'll still be waiting in another 30 years.

I don't know that it is a "killer app" but the word processing capability has been widely used in classes in English composition and in writing term papers for many years. That certainly is a big improvement over the handwritten and typewitten (not even electric in most cases) methodology which was commonplace when I was in high school and college. But, I admit that one doesn't need a full up PC to do those tasks. Furthermore, I admit that too many word processor users don't seem to undersatand that a spell checker in not a context checker.

Palmer


#26

Hi Palmer,

"users don't seem to undersatand that a spell checker in not a context checker [sic].

You have me laughing at that gaffe!

#27

Quote:
Was there really ever a time when a top of the line slde rule cost $100.00?

Not in raw dollars uncorrected for inflation.

IMHO, the best (in quality and capability) and most expensive engineering slide rule ever made is the Dietzgen N1725. I bought one new in 1969 for $35. That equates to $206 in 2009. I still have it, but the last time I used it for actual professional work was 1974. That's when it was replaced by a TI SR-50 ($150 in 1974, or $658 in 2009!).

#28

I had a TI-86 that I used junior and senior year of high school. I also used it a bit in my freshman year of college, but for the rest of college (and graduate school), my poison of choice was MATLAB. My TI graphing calc has been used for basic arithmetic only and has now been supplanted by the HP-35 I picked up a few weeks ago. :)

-Tim

#29

This is just another reason my wife (a pubic school teacher) and I plan to educate our children ourselves.

My kids won't get anywhere near a calculator while they're learning math, though I do have a couple of "new old stock" Pickett slide rules stashed away for when the time is right. :-)

But I wear a wind-up mechanical watch, listen to vinyl records, and still work out problems with pencil and paper. If anyone finds out, I'll be kicked out of GenX for sure...


#30

I don't know your definition of GenX (1970 and later?) but for me, from the Generation that Has No Name (between Boom and X) I hear you. There seem to be many who bought into the tech world hook line sinker. Then there is me, with no cable, no cell, no laptop (yet) yes, record-player, yes tape recorder, yes HP-15c. No Graphing calculators for the kids just yet.

Maybe we won't get kicked out after all. At least there are two of us.


#31

Well, I predate the first Moon landing by a couple of years, but my parents were definitely Boomers ('45 and '48) so I must be GenX. 1970 places you right at the beginning, by the common definition.

But we are old GenX. The world of our youth was more like our parents' than that of those just a few years younger. When I was a kid, we rode in the backs of pickup trucks without anyone getting arrested, had three TV networks, played records, dialed phones, watched Cronkite, were annoyed by Guy Lombardo on New Year's Eve, laughed at little Japanese cars, and read about (but were never allowed to approach) computers that filled rooms.

Just a few years later, everything was different.

And so our approach to technology is different. In my case, I wind my watch every morning (and get a time hack from my NTP-synced computer about once a week), look stuff up in a paper dictionary (but have several hundred ebooks sourced from the Gutenberg Project and compiled/formatted with my own custom software), play vinyl records from my large collection (but was a very early employee of an Internet-connected, MP3-playing jukebox company), and tend to work out problems on paper (but I own a HP-12C, 33S, and 35S--and program all of them ... or write a program on my Linux-running, wireless-having, always-on submini Netbook).

Having learned things the hard way through necessity (like when I used to do speaker enclosure designs with a sheet of log/log paper, a pencil, and a simple scientific calculator), I find I have a much better grasp of what's going on under the hood than a lot of the younger people I've worked with. It has been a big advantage for me, and I'd like to pass it on to my kids.

But I do wonder if this isn't wrong-headed since technology is rapidly getting so complex that it takes lots of automation, not to mention blind faith, to do anything with all these neat toys. Maybe I shouldn't worry about it. After all, if we figured it out so will our kids.


#32

Hi John,

My experience is a lot like yours. I feel last the Last Victorian sometimes. (I remember the children I baby-sat making the "wrong noises" when playing cowboys and indians--they used the "eeeoow" sound from Star Wars with a six-shooter toy! We of course new what a six sounded like:0).

To the younger generation's credit, the young 20s who have come out of good colleges, (and that doesn't mean only Harvard -- can mean all sorts of "third tier" schools) whom I have worked with, are just as sharp as a tack can ever be. They carry TI-84s but rarely use them. They write databases instead. And they conceptualize very well, just with different tools.

#33

Quote:
When I was a kid, we ... ... read about (but were never allowed to approach) computers that filled rooms.

That's the way it was when I wrote my first digital program for a RemRand 1103 at the University of Minnesota in 1960. The 1103 didn't just fill a room, it filled a building. Users punched their programs onto paper tape using a Flexowriter. They submitted their paper tapes (very respectfully, I might add) to a computer operator. When the program was completed the output was another paper tape which the users printed out with the Flexowriter.

We were required to estimate the run time of our programs. If the run time exceeded our estimate by very much the operator aborted our program.

I carry no fondness for thos so-called "good old days".

Palmer


#34

Palmer, I suppose the ENIAC programmers would tell you that you had it easy. They had to enter their programs as ones and zeroes!

#35

I agree! Waiting a whole day for a 3 second job that was canceled just before it could print its results wasn't fun. I'm talking about the late seventies.

#36

Quote:
We were required to estimate the run time of our programs. If the run time exceeded our estimate by very much the operator aborted our program.

I carry no fondness for thos so-called "good old days".

Palmer


You may not miss those days just like I don't miss dealing with cassette tape "mass" storage for the TRS-80 Model 1 circa 1978, but I'll bet your experiences had a profound effect on your approach to technology just as mine did for me.

I run into this when working with younger programmers. They seem to be happy to grab whatever libraries they can find on the 'net, abstract them to death under umpteen layers of OOP, and assume the whole thing will run fine since they can just throw more hardware at it if necessary.

Having been scarred by my suffering with machines with 4k of RAM and 500kHz processors (and more recently, microcontrollers with 1k or less), I run screaming from this approach even though it works acceptably as often as not. In some ways this mirrors the mindset of Depression era survivors who hoard even in times of plenty.

But my project success rate is a lot better than the industry standard 50% so I think I'll keep petrifying my opinions until I reach curmudgeon Nirvana.

And I still don't think graphing calculators (or computers, mostly) have a place in primary or early secondary education. Now get off my lawn!

:-)

#37

Quote:

That's the way it was when I wrote my first digital program for a RemRand 1103 at the University of Minnesota in 1960. The 1103 didn't just fill a room, it filled a building. Users punched their programs onto paper tape using a Flexowriter. They submitted their paper tapes (very respectfully, I might add) to a computer operator. When the program was completed the output was another paper tape which the users printed out with the Flexowriter.

We were required to estimate the run time of our programs. If the run time exceeded our estimate by very much the operator aborted our program.

I carry no fondness for thos so-called "good old days".

Palmer



Yipes. I feel like a newborn! My first programming experience was a high school assignment to program either (I forget, I'm either really or not really a newborn) an income tax or a 3D tic tac toe game using punch cards on an IBM 1130. Needless to say, I found the DEC 20, PDP 11, and various VAXs a couple of years later in college to be almost infinitely more easy to program... even if my programs actually stunk. (I sure got used to debugging, even if I STILL hate it!)

Shortly after that, or during that time, I discovered my beloved HP-34C and that as a real JOY to program, and in addition, easier than any computer. It might have helped my health, as it enabled me to get some sleep on nights I had calculation-intensive assignments. (Unfortunately, I don't remember it being allowed for exams... )

#38

Please don't go overboard! Moderation in all things...

I speak from a great deal of personal experience. In grade school, I detested mathematics. I hated it because it was inflicted upon me, and I never developed a knack for mental arithmetic, no matter what tricks I tried. The fact was, I was quite slow with numbers. In fifth grade, speed of mental calculation was valued over everything else, and I simply crossed my arms and said "No, I refuse. If this is what math is, I want no part of it." So, while I excelled at every other topic, I declared that math was dead to me.

It wasn't until a year later in remedial math that I discovered that a calculator could relieve me of the burden of simple arithmetic, and I saw how wrong I was about math. It wasn't mathematics I hated: it was rote memorization and drills and mindless nonsense. The calculator literally opened up the world of math to me, and I found that I took to geometry, algebra, trigonometry, and calculus like a fish takes to water. It was night and day!

To this very day I hate arithmetic. It is mindless, and I still use a pocket calculator for everything but the most basic addition. It wasn't until I really got to use a calculating tool that I had the freedom that I needed to see that math could really be enjoyable.


#39

Great point of view, Seth (I think I met you at HCC 2007).

As a math teacher, I frequently look out at my students and the look on their faces is something like "what in the world are you talking about....this is all nonsense that we won't possibly use in real life." And I try to be honest with them and tell them they are right about that much of the time (especially box and whiskers plots and stem and leaf graphs, which I despise). But I do know, from experience in the real world, that there are math principles that you will need to know about, and so I stress those.

Capturing the attention of today's electronic generation is always a challenge. The Pythagorean theorem is just much less interesting than the latest Nintendo DS game. The trick is to find ways to make it interesting to the kids. For most public school teachers, with 150 kids per day, it is almost impossible to do that. For me, with 13 students per day, spread across three classes, it is much easier. I love my job. The only catch is, it is a volunteer position!

Don

#40

Seth, your experience is something we should all pay attention to. Indeed, why slash about with a buggy when when you can ride a bicycle or fly a plane instead.

At some point, maybe in freshmen college, one of us (was it me? was it Brian? Judy? Craig? can't remember) made the quip, "biology is actually chemistry, chemistry is actually physics, physics is definitely maths, and maths, well, that's philosophy for sure."

To your point, arithmetic, while it contains all the fundamental building blocks of Algebra and ultimately all of mathematics, yet is not, in its rote form, anything like the beauty, the utter beauty, of higher maths.

(Ironically, I think that while the "new maths" approach to arithmetic may be inefficient, there is something to be said for the obverse which sadly, is not used much even now: that is exactly what I said above; namely, that Algebra (distributive, associative, commutative etc) are already learned in 3rd grade, but without fancy names. I often wonder if there would be many more successful Algebraists (and fewer MacIntosh worshippers ;0) if only this disconnect were dealt with more effectively.

Edited: 8 Dec 2009, 10:35 p.m.

#41

Quote:
It wasn't until a year later in remedial math that I discovered that a calculator could relieve me of the burden of simple arithmetic, and I saw how wrong I was about math. It wasn't mathematics I hated: it was rote memorization and drills and mindless nonsense. The calculator literally opened up the world of math to me
That sounds dangerous. If you can't get a reasonably close estimate in your head, you won't know when the answers the calculator gives you are garbage resulting from human error.

When our boys were in high school and a graphing calculator was supposedly required, they said the only real graphics that went on in class were games played in such a way so as to make the student appear to be hard at work. I'd say if the kid needs help to visualize the function graphed, then he probably doesn't understand what the graph is telling him anyway, so no learning has taken place.

#42

As someone who was equipped with various scientific and graphing calculators throughout school, I can see both sides of this one. On the one hand, if the teacher is doing no more than making them crunch numbers like automatons, then there's no real value.

Now, instruct a student how to REALLY use a calculator, and they'll gain an advantage. I was the type that had no trouble writing programs in class to simplify my work. If the students in class can make inferences and use the machine in novel ways without constant handholding, all the better. But if your lectures sound like, "Now, press Y=, enter this equation, press Window, enter this range, and press Graph," then you're doing it wrong.

I say, tell them to buy whatever calculator they like, and they can read the manual for themselves if they want to learn how to apply the tool.

...And then use a 48GX for all your classroom demos, of course. ;)

#43

I think the answer to the question that is the title of this thread is NO. I base that on my ancient experience. When I entered Georgia Tech as a freshman in electrical engineering, the only required "calculator/computer" was a decent slide rule. The year was 1970.

I bought my first scientific calculator (a TI SR-50) six months after graduation in 1974. Many, many of my professional peers in the engineering world did not have their own electronic calculator then, or for several years afterwards.

Yet, somehow we survived in our profession, and managed to produce some useful output. That leads me to have little doubt that advanced calculators are not *needed* by 12 year olds.

A completely different question is "Are graphing calculators useful in the mathematical education of a 12 year old?" I suspect that the answer is YES...such calculators certainly can be an educational asset. Every generation uses tools that were not available to earlier generations.

#44

The real tragedy is that these kids who are buying Ti84's will just eventually have to buy a TI89 later. They might as well just buy those first instead.


#45

Do you drive a horse and buggy? Don't feel that what was good enough for you is fine for your kids. You are forming their matrix of beliefs, let them form their own. One writer above in this thread showed the younger the kid the faster he was at using the new gadgets. TI has an integrated teaching system that is easier for teachers so they will use it. It is so sad that HP lost all advantage at a critical period, forever lost. Now they are doomed to algebraic. Sam


#46

Quote:
TI has an integrated teaching system that is easier for teachers so they will use it.

Bingo.

The "easier" part, that is.

Do keep in mind that teachers don't determine curriculum in any meaningful way. TI sells their system to the powers that be as a pre-packaged course that even mediocre teachers can walk the kids through.

#47

Sort of a coming out: Without my Casio fx-81p, I probably never had developed any interest in math due to a dyscalculia. A calculator helps you to experiment with numbers, which is essential for people like me to understand them.

What I really don't understand is the goal of this textbook style entry method. Intermediate results are hidden when entering long expressions, and thus your insights are reduced to the final result.

I'm quite sure I'd have gained a lot more of improvement with a PRN calculator.


#48

Tom, exactly my experience with RPN. You are able to pause in mid problem and change units or correct yourself, not easy at all in algebraic. I learned relations I would not have known with algebraic.
Algebraic hides the nuts and bolts to pursue one number. A friend said his calculations seldom result in one number. I know how to do repeated calculations using the repeating register, I edon't know how in algebraic, it may ne possible. I find RPN faster and more versatile. I rewrote all the teextbook formulas for easier use in the calculator. Sam


#49

Quote:
Algebraic hides the nuts and bolts to pursue one number.

The idea that "Algebraic hides the nuts and bolts ..." is really not true for the so-called A.O.S. machines but is a persistent myth in the RPN community.
Quote:
I know how to do repeated calculations using the repeating register, I don't know how in algebraic, it may be possible. I find RPN faster and more versatile. I rewrote all the teextbook formulas for easier use in the calculator. Sam

For real versatility in repeated calculations I find that it is difficult to do better than the playback modes in the graphing calculators where the user isn't limited to only repeating the value from the t register.

Palmer


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