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Calculator restrictions in schools
Message #1 Posted by David H Thompson on 29 Nov 2001, 11:15 p.m.

Hello group,

I am posting from Scotland where the use of calculators in science and maths in school exams is heavliy restricted.

Young adults in their final year before University are not allowed to use graphical calculators in exams. I can see that this is fair when a student has to use calculus to characterise stationary points in functions, but perhaps this says more about the Scottish outlook in science and maths. It is fair that better off students are unable to secure and advantage over poorer students, but perhaps the playing field should be levelled in a better way.

The fact that these calulators are barred has not lead to more time being spent on analysis, so there seems to be a double blow to students.

I am not thinking about reducing the emphasis on arithmetic and analytical skills, indeed without them a powerful calculator is meaningless; however, it's frightening to realise that students in Scotland in 2001 are restricted to calculators with the same funcionality as I used 20 years ago.

I write as a parent, and would be grateful to hear what other members of the group think.

Thanks very much, David

      
Re: Calculator restrictions in schools
Message #2 Posted by Ernie Malaga on 30 Nov 2001, 2:30 a.m.,
in response to message #1 by David H Thompson

David:

Your message reminded me of my troubles in college, back in 1974 in Lima, Peru. Back then, all calculators were forbidden (no exceptions). You were expected to use a SLIDE RULE, if you can imagine such a thing. A couple of years later the restriction was lifted and calculators started appearing here and there, much to everyone's relief.

Graphical calculators, of course, are an entirely different thing. For example, if college students are being tested for their knowledge of function maxima, a student with a graphical calculator has a device that allows him to cheat -- as if he were looking up the answers on someone else's test.

Then again, one wonders what's the use of learning to calculate function maxima (just to give an example) when a dumb calculator can do it in a small fraction of the time, and with much greater precision and dependability. It would be like expecting students to calculate cube roots by hand.

Cheers. -Ernie

            
Re: Calculator restrictions in schools
Message #3 Posted by Luca de Alfaro on 30 Nov 2001, 4:45 a.m.,
in response to message #2 by Ernie Malaga

I actually have mixed feelings about the use of graphing calculators in schools. From what I see at the TI site, it seems much of calculus is reduced to learning recipes for having calculators do the job...

But there is also another reason why I am not sure I am in favor of graphing calculators in schools. Sure, if you give them a function, they draw it for you. By having to draw them myself, I quickly learned tricks to decompose functions, and especially, to analyze them mentally before drawing them. I can stare at one, and with a few calculations, graph it in my mind. This is not only fast, but is fundamental to the ability of _designing_ functions. Suppose you have to design a function that goes to zero here, has a "rounded" maximum there, and so forth. If you have always relied upon a calculator to draw functions for you, it's likely you don't know where to begin from - trial and error doesn't really work well. If you are used to decomposing and analyzing functions mentally, you can quickly assemble the proper ingredients. Moreover, how much does a small graph really tell you? It gives you the outline of the function, but can you see from the graph which one is flatter at 0, x^2 or |x^3|?

On a related note, I wonder why people like and use so much these CAS systems. I can understand that people working out the equations of astronomical bodies need them, but this clearly does not explain all the use. What, then? I work with math every day. Usually, the difficulties I encounter are never related to pushing symbols around (gathering, factoring, whatever). The difficulties have to do with understanding whether a transformation is legal (can you exchange that limit with the summation?), or with how to decompose an expression in a fashion that opens the way to new manipulation (write a probability as the sum of probabilities conditioned by certain events, so that something turns out to be independent, and...). In other words, the symbol-pushing is really not the difficulty at all: understanding what to do with the expressions, or how to transform them, is. And I can't imagine that entering expressions in the slug-slow HP48 to do CAS is going to be faster than me doing it by hand with pencil and paper. I also like to have a record of the symbol-pushing, so I like to use pencil and paper anyway. Granted, I don't often have to do complicated integrals, but even for those, is HP48 CAS justified?

I do like graphing calculators, but I use the graphing part not to graph functions, but to plot data: statistical data, curve-fitting, experiment results, etc etc. To me, this is the real bonus of graphing calculators.

Luca

                  
Re: Calculator restrictions in schools
Message #4 Posted by Vieira, Luiz C. (Brazil) on 30 Nov 2001, 2:50 p.m.,
in response to message #3 by Luca de Alfaro

Hi;

I'm a teacher (Computer Science, Math, Electronics, Telecomm) and I take a few classes for teaching how to use calculators. It's a tool. I tell the students that knowing the 'business' will lead to a correct reason; calculating correctly, will lead to a correct result. If reasoning depends on their knowledge - and it's expected it is up-to-date -, using the calculator will allow them to get results with enhanced precision.

Graphing calcs, anyway, allow text also, and there resides the problem: cheating, as mentioned by Ernie (Ola!). Cheating with a calculator that allows strings to be stored in variables is easy. This way, I allow any calculator in some tests, and I do not allow any in others (where reasoning is the focus). If a graphing calc IS to be used, then I allow students to form groups, so if at least one in a group has a graphing calc, the group will get to the final work. And I expect they will learn with each other.

I think this is fair.

Cheers.

                        
Re: Calculator restrictions in schools
Message #5 Posted by David Smith on 30 Nov 2001, 4:43 p.m.,
in response to message #4 by Vieira, Luiz C. (Brazil)

When I was taking a college calculus course taht covered limits, maxima, minima, etc I asked the professor if we could use a calculator on the exams. He looked a little puzzled and said "yes, but you will just be wasting your time".

I found it (HP25) a great tool to verify limits of functions. I would work the problem out and check the answer with the HP by substituting appropriate values (like 1E-20 or 1e20) in equations for x->0 or x->infinity. If the calculator gave a answer that matched mine all was well. If not I went back to check which was correct (almost always the HP).

After ace-ing the exams I showed the professor my use of the calculator and he was astounded. He did not think that numerical calculations would be of any use in such problems. He was most impressed with the abaility of the HP to produce meaningful results of functions as they approached extreme values (BTW, he had written several standard college texts and Schaums outlines on calculus and differential equations). He still allowed people to use calculators afterwards.

                              
Re: Calculator restrictions in schools
Message #6 Posted by Michael Meyer, M.D. on 30 Nov 2001, 10:06 p.m.,
in response to message #5 by David Smith

I remember an embarrassing moment due to using my calculator in college (1980). Taking statistics, I showed the professor that I'd programmed each distribution and formula into my calc, stored on magnetic cards. He'd announced that calculators were allowed in exams. I could make quick work of any statistical data.

In handing out the final, the professor announced to the entire class, "I wrote this exam with Mr. Meyer in mind." There was not a single problem to work on the final. Not one. Calculators, which sat on every desk, were of no help. Every question was based on theory.

Fortunately, I found that writing my own programs for math and physics also taught me the the theories. I aced the exam. Since it was our last class, I never did find out how the other students fared. It was still VERY embarrassing. Someone from that class is probably still cursing me today...

I do believe that calculator use should be taught as part of math and physics courses. I remember the argument for not using them... "what if you don't have a calculator?" But the argument for using them is greater; it allows teaching of more advanced topics more quickly. (If people are allowed to use matches, they'll forget how to make fire....)

Michael

                                    
Re: Calculator restrictions in schools
Message #7 Posted by Luca de Alfaro on 1 Dec 2001, 3:50 a.m.,
in response to message #6 by Michael Meyer, M.D.

Perhaps I need to make more precise what I wrote. I was not questioning at all the use of calculators in general. I was simply wondering whether the graphing function was really desirable, or worth it. I also used calculators to check roots, limits, draw a quick graph by hand, or so. But just as it is useful to take a written exam in a foreign language without a dictionary, sometimes it may be useful to have to do calculus without graphing - having to imagine the functions. Sometimes mental gymnastics is useful. Some exams could allow graphing calculators, but just as it is still important that people know how to do division with pencil and paper, so it is important that they know how to see function graphs in their mind.

And on another note, I am wondering what people use those CAS systems on the HP48 for. Nobody around me is doing it... and given that the HP48 is so slow, do they really gain anything?

Luca

                                          
One interesting note, Luca.
Message #8 Posted by Vieira, Luiz C. (Brazil) on 1 Dec 2001, 8:15 a.m.,
in response to message #7 by Luca de Alfaro

Hi;

I have been thinking the same about CAS (you mentioned 48 meaning 49, right?). I read the User`s Guide and felt amazed with the new features. What in fact called my attention was: when using all of this? I think of CAS as the CISC version (Complex Inserted Set of Curiosities), whereas Equation Lib is RISC (Reasonable Information Selected for Computation}: focussed in the needs. As tht 49`s O.S. is reloadable, I used to believe future options would be available. That was before ACO got closed...

I beleive you expressed your thoughts precisely. As I have made, I believe others also expressed their own thoughts. Your words, for me, mean your thoughts are closed to mine: the calculator with all features is a tool. Using or not is up to the user.

                                                
Re: One interesting note, Luca.
Message #9 Posted by Albert Graef on 1 Dec 2001, 10:31 p.m.,
in response to message #8 by Vieira, Luiz C. (Brazil)

I have been thinking the same about CAS (you mentioned 48 meaning 49, right?).

First, an earlier version of the 49G CAS is available for the 48G (search for "erable"). Second, the slowness of some functions of the 48G is an issue of the built-in firmware; you can get user-written software which effectively turns your 48G into something very close to the 49G. Not quite the same performance level as the 49G, because the 49G has an improved memory management system as well. But it's usable, and the 48G, as has been pointed out elsewhere, has a much nicer keyboard, just as nice as the older keystroke programmables. ;-)

Third, and most importantly, I wouldn't classify the CAS as a mere "set of curiosities". It's there to help you carry out boring routine calculations more quickly and reliably, just like the numeric features. Note that the HP CAS does not relieve you from the burden of planning your derivations, you still have to know what you are doing. (Even more so, because you have to be very precise when communicating with your calc.) The CAS certainly needs some time to learn before you can use it effectively, but it pays off, and IMHO it makes the calc even more fun to use.

Many students have noted that math classes involving the use of the full set of features of these sophisticated calculators are often more profound and difficult. That's because you concentrate on working with mathematical concepts in a creative and experimental manner, and on understanding the underlying mathematical theories. You have to work out how it's to be done, and the calc then does the tedious calculations for you, be they numeric or symbolic. I just wish I had something like the 48/49G when I was in school. :)

I agree that the 49G manual does not describe the CAS very well. To really explore all the possibilities of the 49G, it would have taken a 1000+ pages manual, and I think that HP thought that would be intimidating for new users. ;-) If you're really interested in some concrete examples on how to use the advanced functionality of the 49G, I suggest taking a look at Urroz' books "Science and Engineering Mathematics with the HP 49G", available from http://www.greatunpublished.com/. It's a good read.

I used to believe future options would be available. That was before ACO got closed...

The 49G CAS is already very capable. And Bernard Parisse, the author of erable and the 49G CAS, has announced on c.s.hp48 that he will continue to work on it, despite ACO's demise.

Albert

                                                      
Reasoning with Albert`s alert...
Message #10 Posted by Vieira, Luiz C. (Brazil) on 2 Dec 2001, 12:36 a.m.,
in response to message #9 by Albert Graef

Hi, Albert;

first of all, thanks! Good explanations and necessary calls are always welcome ;-)

You`re right in one major point: 49`s owner manual. Even the downloadable complements fail to show how to use the new features. Previous owner manuals (I can check for the HP25 Owner`s Manual and HP67/97) explore cases, not examples. New manuals, after 48 series, use only examples, and knowing that (e.g. CAS Commands) we can apply FCOEF to a vector like [1,2,3,-1] and get a rational polynomial '((x-1)^2)/(x-3)' easies a lot, but having this info in a context would help us plan next step with more confidence. Right?

Anyway, we all should find our own reasons to go deeper, as the tool is available and we have no limits using it; this is of no excuse, I admit I`m guilty not doing this <:-(

I would like only having the chance to load my 49 with Equation Lib instead of CAS when I needed, and load back CAS when I need it back. One of our regular contributors have posted here a link to an Eq. Lib for the HP49 at HPCALC.ORG, and that would be a good solution. (I don`t remember who post it; forgive-me you, who gave the info)

I used the poor expressions just for finding a (sad pun intended) comparison with CAS and CISC, as CAS has a lot of functionality not used so often, and Eq. Lib being general RISC, as it has sets of equations grouped in less entries, more often used.

Thanks again :-)

Cheers.

                                                            
Re: Reasoning with Albert`s alert...
Message #11 Posted by Albert Graef on 2 Dec 2001, 2:21 a.m.,
in response to message #10 by Vieira, Luiz C. (Brazil)

You`re right in one major point: 49`s owner manual.

Yes, this tiny brochure distributed with the calc barely scratches the surface, and HP's advanced user guide available for download is mostly a command listing with short descriptions. Needless to say that any new user will be pretty much lost with this. (Me too. But fortunately there's hpcalc.org.)

We're all victims of the tradeoff between what these electronic gadgets cost and what they do, which directly translates into the effort involved in producing appropriate documentation. Just take a look at the sad excuses of manuals which nowadays accompany most bits of PC hard- and software. Obviously, it would be nice to have something like the 48 AUR, and an additional CAS tutorial. Even that wouldn't be exhaustive, but I don't think that this is practical any more -- just imagine a calc with docs of the size of the full UNIX manual. ;-)

Anyway, Urroz' books are a good start for the mathematical features of the calc. For other things (programming) you'll mostly have to rely on documentation for the HP 48, which fortunately is pretty good.

I would like only having the chance to load my 49 with Equation Lib instead of CAS when I needed ...

You can have both. :) Eql49 is right here: http://www.hpcalc.org/hp49/math/misc/eql49r27.zip

I haven't explored it in any depth yet, but it appears that it has most of the stuff in the 48 equation library, and it's user-customizable too.

Albert

                                                                  
Thanks; I had lost this link...
Message #12 Posted by Vieira, Luiz C. (Brazil) on 2 Dec 2001, 11:24 a.m.,
in response to message #11 by Albert Graef

... and would you, please, post the references for Urroz`s books? Titles, editor(s), etc. I'll try finding them, mostly cause they have been mentioned in this forum a couple of times.

Good writings, Albert. Many thanks. That`s the kind of sharing I most apreciate here. And, God bless, people practice it a lot at this forum.

Cheers.

                                                                        
Re: Thanks; I had lost this link...
Message #13 Posted by Albert Graef on 2 Dec 2001, 2:01 p.m.,
in response to message #12 by Vieira, Luiz C. (Brazil)

Here's the reference you asked for: Gilberto Urroz: Science and Engineering Mathematics with the HP 49 G, GreatUNpublished, 2000. (2 volumes.) More info (including table of contents and samples) can be found on the author's website, see http://www.engineering.usu.edu/cee/faculty/gurro/HP49Vol1BookInfo.htm. If you're interested in user feedback, try a Google groups search: http://groups.google.com/groups?q=Urroz+49G&hl=en

The books are $25 each (for the hardcopy version). You can order the books online (either as hardcopy or as a downloadable pdf file) from www.greatunpublished.com. See: http://www.greatunpublished.com/bookstore/author.php3?accountID=GRTU00214. (If that link does not work for you, just go to the main page http://www.greatunpublished.com and do a "Search bookstore" for Urroz.)

And yes, most ppl from the HP calc community I've had contact with are very knowledgeable, friendly and helpful. It's a great community, and I'm sure it will survive HP going astray, at least until our HP calcs all fall apart. ;-)

Cheers, Albert


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