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How to teach children RPN



#12

It has come to the time when my sister must learn to use a calculator (she is starting to use one in class in 6th grade). Next year she will probably be taking Algebra, or at least Pre-Algebra. The question is, how do I teach her RPN.

I realize that many will object at using a calculator at all in 6th/7th grade, but her teacher wants her to use a calculator, and the preaching about buying a TI-83+ is already beginning. So, I have a few months to get her addicted to RPN.

She doesn't mind learning RPN because then she gets to use the "pretty silver calculator" (hey, the new design attracts some people at least... new RPN users). I plan on giving her the 33s (at least for the next year while I still have my school's 32sii), so it is simply a matter of teaching her to use the calculator.

I have a few questions/thoughts. Should I teacher her only the 4 functions (and few other functions) so that she learns the math, or teach her the quick way now (ie: equation solver, base conversions, etc)?

Also, what is the best way of teaching RPN? In the past, to my peers, I explain the stack system and do a few sample problems. After that, I generally just give them some problems to try. Is repetition enough? (I learned by using the 32sii all the time in my math class, even though at first I was slower with it and would make errors)

Finally, once I get this "project" going, I plan on writing a "How to teach kids RPN" paper. I would like any suggestions that you all can give.

-Ben Salinas


#13

Ben, by coincidence, I am in the process of teaching my daughter (14, in the 8th grade) and my son (11, in the 5th grade) about RPN and HP calculators. I have been pondering the same questions that you raise.

Thus far, my approach is slightly different because the two children are different. For my son, I am focusing only on the 4 basic functions. He is of course aware that the calculator does much more, but except for occasional demos, I am steering him away for them, for now. The most important thing, for both children, is that I am using a 48 so that they can see the stack in operation. I had originally intended to use one of the many RPN aplets available on the Internet, but it turned out that the 48 was simply easier. Every few days, I work with him a bit, doing elementary operations, and I make sure to leave the 48 out and readily available to him so he can "play" with it any time he wants.

For my daughter, who is literally light years more mature, I am slowly going over most of the numerical functions, including (eventually) solve and probably plot. Again, it is the same routine, but over a greater span of functionalities. My daughter has already been exposed to TI's and AOS, so for her it's also a question of "unlearning" some things. She's no RPN fan, yet, but I think it's starting to dawn on her. I overheard her tell her brother that she's probably going to have to make use of the calculator next year, when she starts high school. She knows the 48 is capable of doing symbolic math, but hasn't gotten into it enough to really see the advantages.

So, my bottom line is 1) use spaced, rather than massed, learning and 2) be sure they have free access (including possible breakage!) Make it a long term project and go slowly...

#14

Hello, Ben;

I guess the best way of teaching a kid how to use RPN is showing that calculators using RPN (or "the [ENTER] key") allow them to perform simple operations like they do with pencil and paper. And this is the main "explanation" HP used to write in the calculator's manuals.

Think of the way kids learn how to add two numbers. They are not introduced to algebraic notation in the very beginning, instead the teacher "stacks" the two numbers to be added FIRST (and when the first number is finished you tell the calculator so with the [ENTER] key...) and then he writes a + (plus) sign in order to indicate what to do with them. There is no [=] sign used when we actually "perform" a math operation. I always use the [=] sign to refer to the algebraic NOTATION, that is a way to represent a math OPERATION.

RPN is a notation as well, but it is closer to the operation performed by kids when learning math. And I guess addition is the very first of them, right?

I guess Steve has a point when using the HP48 and showing the stack contents. That's very important. Anyway, after having the RPN "mechanics" understood, going further is easy. I guess that the "power tools" you mentioned must be mastered after having a better understood of them without the calculator. I'm not against using the calculator to "understand" the process of finding a root; in fact I think it may even make it easier to understand, but I would try having her effectively using the calculator after knowing what is a "numeric root finder" about. I don't know the HP38G, but I guess it would be the best tool for this particular job.

Back to RPN: try this:

2 (finished? tell the calculator so with [ENTER])
3 (finished? Now tell the calculator what you want it to do)
_____+

5 (see? That's what happens with paper and pencil...)

I would let her try for a while. If she does not get acquainted with the [ENTER] key after a while, at least the "pretty silver calculator" can also be used as an algebraic, right? As a teacher (although I'm in Brazil and you're in USA), I'd never let a student without a second option. Algebraic notation is also a powerful tool, and using it depends on knowledge. As RPN also does.

My 2ยข.

Cheers.

Luiz (Brazil)


Edited: 6 May 2004, 12:23 a.m.

#15

I have tried to pattern some of my own manual-writing after HP's manuals for the 41 and 71. When I got them, I just started at the beginning of the first manual, and just kept going. When I got to the end, I felt like I knew the material, even though I never got to "the hard part". Unfortunately good manual-writing is a rare art.

When I started in Forth (which is stack-oriented and RPN), I used Leo Brodie's book, "Starting Forth". Some time later after getting some experience in Forth, I read "Thinking Forth" (which is really more about programming philosophy). I mention these books because of the sense of humor and all the simple little cartoons with characters that keep coming up, illustrating various concepts. They're almost enough to make it worth reading the book even for someone not interested in Forth. These books have been out of print for many years, but do take a look at them if you ever find access to them.

Before your booklet is written however, I would just keep it simple. It sounds like your goal is to make them think in RPN, not necessarily understand everything the calculator can do. The basic four functions and a couple of extras like square root or log should do the job. I mention the extras as examples of functions that only operate on one stack item, not two.

I would call the "+" "add" (not "plus"), the "-" "subtract" (not "minus"), and so on, because you're telling the machine what you want to do. It should make it seem more natural instead of "backwards." That will help with the acceptance. In Forth the IF-THEN condition is RPN too, and beginners think it makes no sense until it is explained differently. Instead of IF <condition> THEN <actions>, it's <condition> IF <actions> THEN. You make the illustration: You're going to put your shoes on. First you ask the question, "Are you lacking socks?" IF so, put socks on, and THEN put the shoes on.


#16

This post is for everyone, not a direct answer to the previous post.



"Instead of IF <condition> THEN <actions>, it's <condition> IF <actions> THEN.
You make the illustration: You're going to put your shoes on.

First you ask the question, "Are you lacking socks?" IF so, put socks on, and THEN put the shoes on."



More Forth like sentence would be:

Are you lacking socks IF put socks on THEN



Sorry, but Reverse Polish Notation does not make much sense in English or any other (human) language.

That's just the way it is.



Actually you can put IF anywhere before the THEN in the same program block when using RPL in HP calcs.

<< -> n << n DUP IF THEN DUP SIN SWAP / END >> >>

<< -> n << n IF DUP THEN DUP SIN SWAP / END >> >>

<< -> n << IF n DUP THEN DUP SIN SWAP / END >> >>

BUT not before the "<<"

Yes, RPL is not pure Forth.

The earlier machines like the HP-41 series used RCL__ STO25 SF13 etc. non-RPN structure.

These are now more Forth like in the 48/49 series:

15. 'X' STO

-55 SF



I think I will take a look at my HP-71B Forth/Assembler ROM in my Summer vocation...

{VPN} AXL


#17

A little OT--

> I think I will take a look at my HP-71B Forth/Assembler ROM in my Summer vocation...

The 71 is where I got started in Forth. It was not the easiest, because in spite of what I just said in the last post about HP manuals, this particular one assumed you already knew Forth and only needed to know the particulars of Forth on the 71, while the book "Starting Forth" assumed you had something to practice on. So in a way, the two books were left pointing at each other. This might have some relevance to the original poster's desire to write a book to help kids learn RPN.

I have nothing but praise for the HP-71's BASIC implementation, especially when the many contributions from the user groups are added. After using it, I was _extremely_ disappointed with the Rocky Mountain BASIC HP used on the bigger computers. It was a step down. Unfortunately the 71's implementation of Forth was not nearly as good. After learning Forth though, I was able to drastically improve the performance of many built-in words-- up to 13x-- even without using assembly language!

#18

While everyone here thinks how GREAT RPN is, just remember, "If someone never has, they don't miss." I personally prefer RPN, but I don't mind using AOS all that much. I detest EOS, but guess what? That is exactly how math is Taught! It wastes keystrokes and is the slowest way to work problems, but with todays calculators, memory is so cheap and 90% of your students don't care and don't mind. This herd rules the market place. Hp could make a calculator that would sell to 5% of us (guarenteed and it would be a nice sized chunk of the overall pie), but marketing would flip, because they want a product that can concievably sell to 95% of the market (but with Hp's pricing policy, only us 5% who like quality over quantity, would even be interested).

Sadly, I believe Hp Marketing has only pulled their heads halfway out of that dark warm crevice.

I wish Hp would subscibe to the old philoshy of offering the best calculator available instead of looking at market niche.

I would suggest only 3 calculators, an entry level RPN based upon the Hp20s (RPN/algebraic selectable w/2-8+K RAM or just keep making the present Hp33s), an Hp43sx high end pocket calculator, and their present high end 49G+.

I wouldn't bother to make anything else as the price difference between the present 48 and 49 doesn't warrent this ($35-???). Who buys a 48 unless they need a serial port (I like that feature though myself) and the calculator may be in harms way a lot. Regardless, $35 to step up to a much faster calculator, means the 48g is really just a white elephant.

But most professionals don't want a huge graphics calculator (heck, even in college, I liked my 42s better, I just missed units conversions in Physics and ME courses).

A graphics calculator is really nothing more than a sophisticated cheap math package in a portable case that can also serve as a calculator. But it doesn't travel well, its just that no one likes to toss out a well know tool, but I prefer the smaller package of a real calculator. But I don't want to sacrifice much more than graphing either.


#19

"I would suggest only 3 calculators, an entry level RPN based upon the Hp20s (RPN/algebraic selectable w/2-8+K RAM or just keep making the present Hp33s), an Hp43sx high end pocket calculator, and their present high end 49G+."



I disagree.

You need several models (all programmable):

0) A Basic *non*-programmable scientific - a crippled 33s

1A) An approved calc for test: the 33s (make it slightly narrower)

1B) A financial scientific combo model: 33B

2G) A Basic graphing with numeric solve/integrate only. (Flash ROM)- make it small and name it HP-37G

3GX) Advanced graphing with all the goodies (Flash ROM/RAM)- name it HP 50GX (good serial port)



That is the minimum list in my opinion

{VPN} AXL


#20

Hello Veli!

I have an overdue apology to make as I never actually expected to see the Hp 49G+ and accused you of taking some type of mental stimulants for thinking such.

That said, I feel that the Hp39/40G calculator is a wasted marketing adventure, since it doesn't offer RPN and is basically a Ti clone that will lose to Ti.

Therefore, I feel the basic graphics calculator market is lost to the Ti-83. Give it up and don't bother to pursue. Would you buy an Hp39G and not buy an Hp49G+. Sell only one high end Graphics and dump everything else.

As far as pocket calcs, I would have never bothered with the 33s, but made an Hp20s w/RPN and limited programability w/o alpha numerics. This should have allowed it on nearly every exam.

Since Hp now makes and distributes an Hp33s, continue to sell, but my main gripe against the 33s is PRICE and features. Truthfully that is what hurt the 32s also. These are $30-40 calculators selling for $50-60 and failing to sell.

An Hp43s on the other hand could justify an $80+ price (much like the Hp17Bi+ presently does). But an Hp43s released now would rob lots of sales from the Hp48GII (maybe all). Therefore, I still say an ideal product line doesn't bother to address product niche but offer the best at three levels.

The best at three levels is a low end pocket programmable that the 33s could fill, but would have to be priced at $30 to be that calculator.

The best possible pocket calc (fabled 43s) $60-90 price range.

The best possible graphics: an Hp49G+ or newer evolution.

Hp has the 33s on the market as the highest end pocket calculator available, and if there were never nothing better, I would embrace it. However, I just so happen to own an Hp42s and therefore have tasted better. There is no comparision for features and capabilities. People with a 32s who think its the best, just never had to bump into the upper limits of the 32s or need extensive use of matrix functions or use the superior soft menu system of the 42s.

The 33s is truthfully a low end pocket programmable which just happens to rule the roost because there are no challengers and the NCEES is effectively nailing an artificial ceiling on calculator development here in the USA.

I rant on too much.

Thanks for your input.

#21

I recommend reporting the teacher to the school board for severely hindering your daughter's ability to learn mathematics by-hand... Especially with a TI, yuck.

Many years ago, my dad gave me a TI-30 for Christmas with a book called "Calculator Math Made Easy" or something like that. The book had nifty illustrations and lots of examples (e.g., "plan your trip across the country... how many miles is it to X and Y, how long will that take if you're travelling an average of 60 mph..." etc.) Of course, solving these problems by the book included hand-holding the TI AOS way...

You know what? I could solve every problem in the book wth my TI-30! But when it came to trig in high school, I was, um, a bit lax... Because doing them by hand isn't the same as using an appliance.

Here's my suggestion: put together a comic book with basic sixth-grade (or higher?) problems all solved using RPN with an HP-whatever you have at-hand. That'll fix those TI-loving landlubbers!

#22

I have been using RPN for a few years now. Maybe this will help you out:

* I like the suggestion of using the HP48/49 series to let the student see how the stack works.

* Practice, practice, practice; the HP manuals are good with a few practice manuals.

* Start with arithmatic and roots. Then build from there. In her case, it might be a slower build than most of us (who know the trig/equation operations).

* Patience, patience, patience


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