▼
Posts: 2,448
Threads: 90
Joined: Jul 2005
I am an "olde skool" (or however the pseudoneohiphop generation would say it) hp calculator user and while I own two 48GX complete with cards and metakernel and once had ALG48 installed, I just don't really know or understand the graphing calculator utilization in school.
Yet pretty soon I am going to have to deal with that detail within my own household, and so I found the following statement, on the HP "Mastering the HP39GS and HP49GS" document interesting:
"The hp 39gs was released mainly in the United States and other regions, such as Australia, which do not allow a Computer Algebra System, or CAS, in their educational systems. The hp 40gs, on the other hand, was released mainly in Europe where a CAS has long been an expected ability for calculators used by high school students."
This has me even more fascinated. So in Europe, students don't need to practice algebra? Or am I missing something? What is the point of a computer algebra system in a calculator? I can see the utility in PC based programs for advanced analysis (Wolfram etc) but in a calculator for school use? How is this CAS business implementedand how/why are American and European schools different in this respect? (And isn't for instance Spain in it's own category here anyway?)
I have been a skeptic about early use of calculators in school. So far all I see them doing is reducing proficiency in arithmetic and number familiarity (like being able to see the answer to 7 X 14 rather than having to type it in...). Yet in the next few years I am going to have to support two students who will be required to own graphing calculators...
I have a feeling that this topic is probably evolving as we speak...
▼
Posts: 887
Threads: 9
Joined: Jul 2007
When our son was "required" to have a particular graphing calculator for a highschool class, I heavily doubted that he really needed it, and we didn't get one. He did fine without it, and said the other kids mostly used theirs to play games, trying to look busy when they weren't doing what they were supposed to at all. TI created the illusion of a need, then addressed that "need", and took a lot of parents' money.
Posts: 272
Threads: 12
Joined: Jun 2007
Quote:
I am an "olde skool" (or however the pseudoneohiphop generation would say it) hp calculator user and while I own two 48GX complete with cards and metakernel and once had ALG48 installed, I just don't really know or understand the graphing calculator utilization in school.
Bill,
People "learn" in different ways, I'm refering to audio, visual, and kinetic; audio can learn by hearing, visual learn best by seeing/reading, and kinetic are "hands on" learners.
So having the calculator draw a representation of an equation will help some of the students understand it better.
My daughter is in a Montessori school, I was surprised to see,
feel, and assemble the "Binomial Cube" in their classroom,
and someday I hope to do the same with their "Trinomial Cube".
Had those been available to me during my primary education, I think I would have "grasped" (literally!) those concepts quicker.
An Air Traffic Control manager once told me, once of the first tests given to prospective controllers is the diagram of an "unfolded" box (with designs on each side), followed by several drawings of isometric cubes. Only one of the isometric cubes can
be constructed out of the unfolded box. If the candidate can't choose the right cube, they are eliminated from further consideration. The candidate has failed to "visualize" a 3D object (a plane in the sky) with a 2D representation (the radar screen).
Ren
dona nobis pacem
▼
Posts: 801
Threads: 36
Joined: Nov 2005
Ren, even the visual students can forego the graphing calculator (and I hope no one introduces them to PC software like Matlab or Maple, or even Origin, yet!!) because the best visual (and handson) method is still taking a piece of graph paper, and sketching the function out after calculating several points with the function.
But I sympathize:
Just last night, my son questioned one of his own answers, a result from simply entering data into some automated program on the TI8something the school lent to him (he has a HP39G, but since "everybody else" is using the TI, he is also). I told him repeatedly to get paper and pencil and sketch it. In the end, he tried to graph it on the calculator, but the image was miniscule, so he settled for simply manually calculating y for his chosen value of x. I, knowing him, did not just let it end there, and since I no longer have graph paper around, I just flipped over a piece of scrap paper and plotted his given data freehand; it took less than a few minutes. Lucky for him, my freehand estimate was close to his manually (pressed the keys himself instead of using some calculator bot found in the ROM) calculated value...
... otherwise, it's upside the head time for him.
▼
Posts: 1,392
Threads: 142
Joined: Jun 2007
Quote:
even the visual students can forego the graphing calculator ... because the best visual (and handson) method is still taking a piece of graph paper, and sketching the function out after calculating several points with the function.
Maybe best for you, but not necessarily everyone. All kids learn differently. What works for one is often ineffective for others. We are all different, and the best teachers realize that and present ideas and concepts in as many ways as possible, hoping that at least one method will click for each student.
For example, consider finding the roots of the quadratic equation x^2 + 3x  28 = 0. I can think of at least nine ways of presenting this to students so that they can find the roots:
 As you said, plot several points on paper and sketch the graph (although it may not be accurate enough to pinpoint the roots of 4 and 7).
 Factoring into (x4) (x+7) = 0
 Completing the square.
 Quadratic formula (these first 4 use paper and pencil).
 Graphing on a calculator and observing the xintercepts.
 Graphing on a calculator and looking at the table where y1=0 and seeing the corresponding x values.
 Using the calc zeroes function.
 Using the application polysmlt to find the roots.
 Writing a BASIC program to implement the quadratic formula.
Now, no high school math teacher is likely to present all nine of these methods to his/her students, but the point is that some of these methods will click with some of the students, and the more students who end up understanding the conceptsthrough whatever method works best for themthe better.
▼
Posts: 2,448
Threads: 90
Joined: Jul 2005
...and ultimately, her education is complete when she understands all of the approaches (well, all but the machineoriented ones anyway...)
Thanks very much for all of your posts everyone. This has been very illuminating and Don, I see what you mean about tools and ways of learning. The point is find the way "in" and then the student has a chance to understand the other concepts that aren't so obvious to her...I just tried this idea tonight with mineand it was very useful. (The question was, why is the area of a triangle always b X h divided by 2. Why? And how you answer that can be obtuse or acute, pun intended:)
▼
Posts: 1,392
Threads: 142
Joined: Jun 2007
Quote:
The question was, why is the area of a triangle always b X h divided by 2. Why?
That's a great question from a student, and it got me thinking. Refer to this. If we draw two boxes around the triangle, Box 1 and Box 2, and we observe that exactly half of each box lies within the triangle ABC, and H is the height of both boxes, then it makes perfect sense that the area of triangle ABC is half of base times height.
What a great question!
▼
Posts: 2,448
Threads: 90
Joined: Jul 2005
Hey Don, yes, that's exactly what I did as an adhoc "proof"and I've asked the student to use the same idea to prove the general case of parallelograms, too. No answer just yet.
▼
Posts: 1,392
Threads: 142
Joined: Jun 2007
I know that we are all HP geeks, but I have found the TI34 MultiView calculator very well suited for students, especially in the middle grades (ages 1114). It has a unique feature, the OP1 and OP2 keys, which let you record a series of operations and variables and play them back. Not exactly "keystroke" programming, but very effective in some circumstances.
For example, the aforementioned quadratic equation. AFTER I teach my students how to solve the quadratic equation on paper, and they have demonstrated that knowledge, then we use the TI34 to set OP1 = (B+sqrt(B^{2}4AC))/(2A) and set OP2 = (Bsqrt(B^{2}4AC))/2A. Then they just store the appropriate coefficients into A, B, and C and press OP1 and OP2 for the two solutions. Pretty cool for a $15 calculator.
▼
Posts: 272
Threads: 12
Joined: Jun 2007
Don,
"Speaking" of TI calculators...
Yesterday I was in the local Staples (an office supply chain) and started pushing buttons on the TI Inspire.
It soon became obvious that the particular calculator I was using
had its "language" set for something other than English.
Without a manual, I was unable to find out to change it to English.
Even though the labels on the keys and keypad were English, I still
couldn't find the proper menu item to change it!
B^)
(yeah, yeah, I'm a "Monolingual 'Merican" )
Knowledge of Spanish, Arabic, and Mandarin didn't help me decipher the menus either!
Ren
dona nobis pacem
▼
Posts: 1,392
Threads: 142
Joined: Jun 2007
Yeah, Ren, I've never changed the language before so I had to look. From the first screen (press the home icon, upper right), with all the icons on it, select 8, system info. Then 2, system settings. Then the first dropdown box is the language selection.
Don
Posts: 335
Threads: 12
Joined: Dec 2007
Quote:
Arabic, and Mandarin
Is there anybody out there who has a calculator that speaks Arabic or Mandarin??? ;)
Quote:
dona nobis pacem
... or Latin
▼
Posts: 272
Threads: 12
Joined: Jun 2007
Quote:
... or Latin
Would it use Roman Numerals?
B^)
▼
Posts: 335
Threads: 12
Joined: Dec 2007
Quote:
Would it use Roman Numerals?
I doubt it. My calcs all use Arabic numerals and don't even think of speaking Arabic! ;)
Posts: 4,587
Threads: 105
Joined: Jul 2005
I had a similar approach in mind: You easily prove the area of a parallelogram is base times height, and then you divide it into 2 congruent triangles.
Posts: 1,392
Threads: 142
Joined: Jun 2007
Hi Bill. This subject has come up several times before on the forum. Lots of people have very strong ideas on this subject. Some of these people have actually been in classrooms in which calculators were used by students. As a middle school math teacher for the past 3 years (after leaving the software field after 28 years), here are some of my observations relative to this subject:
 I've never encountered a student who really cares that much about calculators; certainly not like members of this forum, for instance. Calculators cannot compete with ipods.
 Many teachers let students use their own calculators. No middle school math teacher I have encountered has required a specific calculator. I'm sure that's different in high school.
 For those classrooms equipped with schoolfurnished calculators, TI reigns supreme. I've never seen an HP calculator in a middle school classroom (except my own, of course!).
 Some kids know their math facts and operations and some don't. This has more to do with whether they were taught their facts adequately rather than calculator usage.
 In high school, if a math teacher requires or recommends a specific calculator brand and model, I'd go along with that. TI graphing calcs are actually pretty good.
 I would imagine most high school math teachers would not allow their students to use a CASequipped calculator, like the HP 50g or TI NSpire.
 My own opinion is that calculator use neither helps nor hinders kids' ability to learn and understand math. The quality of the teacher and parental involvement are much more important.
Posts: 167
Threads: 13
Joined: Sep 2008
I teach Physics to 1118 year olds in the U.K. In this school (and I believe in the U.K. generally) Casio calculators reign supreme, particularly the FX83 natural display calculator. This isn't a graphing calculator, still less a CAS machine, and it is all that the students are required to have at school, even if they choose to study mathematics to age 18. I'm not sure what the situation is in the rest of Europe, but CAS calculators aren't in use here. Graphing calculators seem to have faded away; they were more popular in this school some years ago. They are not required now.
At age 16 the compulsory maths exams for everyone include at least one noncalculator paper. This year the maths and Physics papers to be taken by those applying to study Physics at Oxford University were both noncalculator papers. Students still have to learn arithmetic and algebra!
As a Physics teacher, I like students to have calculators so that I can set real problems. I don't like it when someone insists that "20/(60x60)=20" because her calculator says so, and won't admit that she forgot the brackets (no RPN!). To be honest, with such people I doubt that calculators are the problem. On balance, I like calculators. I would hate to return to the 4figure log tables I used at school.
Going further, I'd even be happy with students having (for example) an HP50g: if a student was bright enough to figure out how to use one, the maths itself would pose no problem! The difficulty comes when a calculator gives answers without the need for thought. Maybe the problem lies with the type of question that is set: the sort of question that can be answered trivially with a calculator might not be a good test of mathematics (or physics) ability.
▼
Posts: 54
Threads: 2
Joined: Jul 2008
He, he, "20/(60x60)=20".
I also live in the UK. Last year I've witnessed an unbelievable "calculator" moment on TV. Can't recall exactly which channel, but it was a quiz show in which the producers lined up a number of primary school children against a grownup. Shame I didn't write down which exact channel and programme it was... I am pretty sure it wasn't BBC, but that's about it. I am really clueless about daytime telly.
Anyway, at one point, the grownup got a question, "what is 5 + 3 x 0 ?" and failed to produce any answer in 30 seconds or so. The competing child did produce an answer, "zero!"
To much of my horror, as one of my sons also managed to get it so horribly wrong, and say "zero" straight away, the presenter (the producers) accepted the answer as correct!!!
It took me an hour to explain to my son (who was then 11) what went wrong, but even though he remembered what the teacher said about order of operations, he remained sceptical: "if it was on telly, it must be true". We had an argument which I wasn't easily winning. He produced his 4banger and demonstrated how the producers got the result. Up to that point I didn't realise that someone must have doublechecked the question using a 4banger!
Half an hour and a whole collection of scientific calculators and pocket computers later (plus Excel, plus a few maths books), he was "kind of convinced" that telly is sometimes not right, and a bit embarrassed that he so easily got it wrong forgetting the precedence. At least he will never forget how he learned once and for all about it.
As when it comes to his 4banger, it was promptly replaced by a Texet scientific from Tesco (Â£2.49) which doesn't say "0" as the answer to 5 + 3 x 0.
▼
Posts: 3,283
Threads: 104
Joined: Jul 2005
Operator precedence isn't a question of right or wrong. It's all about convention.
A mathematician or an engineer will answer 5, because for him/her operator precedence holds. But what about a business man? It depends. HP's chain calculation mode (HP10b and others) will give 0 as the result, on TI's BA II Plus, the mode can be selected between chain mode and AOS.
And on the 12C? I think RPN is the best answer because it delegates the decision to the operator in the most predictable way.
▼
Posts: 1,092
Threads: 57
Joined: May 2007
Quote:
Operator precedence isn't a question of right or wrong. It's all about convention.
A mathematician or an engineer will answer 5, because for him/her operator precedence holds.
The question itself is ambiguous because it assumes the reader knows the precedence rules intended. If taken literally, as it should be unless you have predetermined the precedence rules with the author of the question or by some other means, the "correct" answer must be 0.
If the question was written by an engineer (like me) there would be no ambiguity. It would have been written as 5+(3*0)
Dave.
▼
Posts: 335
Threads: 12
Joined: Dec 2007
Quote:
unless you have predetermined the precedence rules
When you ask someone to solve a math problem, all rules are predetermined, the precedence rule as well as what 3, 5, 0, + an x mean. The only question is if the someone knows this.
Taken "literally" as you suggest, 5+3x0 would be read as "strange snake form" followed by two perpendicular lines followed by a curly thing followed again by two lines that look different from the first ones and then something that looks like an egg. ;)
▼
Posts: 1,092
Threads: 57
Joined: May 2007
Quote:
When you ask someone to solve a math problem, all rules are predetermined, the precedence rule as well as what 3, 5, 0, + an x mean. The only question is if the someone knows this.
The precedence rule may be known, but how do you know if it applies? Not everyone (or all calculators for that matter) agree on whether precedence is actually used.
One may also be able to argue that the answer is what the majority of calculators say it is. I don't know the figures, but I hazard a guess that 4 bangers (with no precedence) outnumber scientific models (with precedence).
Quote:
Taken "literally" as you suggest, 5+3x0 would be read as "strange snake form" followed by two perpendicular lines followed by a curly thing followed again by two lines that look different from the first ones and then something that looks like an egg. ;)
What does it mean in Klingon I wonder? :>
Dave.
▼
Posts: 335
Threads: 12
Joined: Dec 2007
Quote:
A mathematician or an engineer will answer 5, because for him/her operator precedence holds. But what about a business man?
Quote: the precedence rule may be known, but how do you know if it applies? Not everyone (or all calculators for that matter) agree on whether precedence is actually used.
From these two quotes I derive that this is an actual question: does it apply or not? I wasn't aware of that. I thought it always applies.
Still curious though: can someone confirm that in business mathematics, the precedence rule is NOT applied?!?
Edited: 22 Jan 2009, 6:48 a.m.
▼
Posts: 4,587
Threads: 105
Joined: Jul 2005
Quote:
Still curious though: can someone confirm that in business mathematics, the precedence rule is NOT applied?!?
And if true, may this be one cause of the financial crisis? d;)
▼
Posts: 54
Threads: 2
Joined: Jul 2008
Good one :)
Anyway, to be on the safe/serious side, knowing that a good proportion of the readers of this forum are engineers, and that engineers traditionally show a slight mistrust towards business people, the precedence does apply in business world.
I work in a world of "business math", and precedence just applies, just as it ever has. It is always implied, in verbal communication, in papers written by quants and analysts, in Excel, SQL, Clike languages... it is taken into account, full stop.
Just why 4bangers still work in the "chain" mode, is totally beyond me. Retro things are nice, but that particular 70ism should have been left behind in the 70s, like... let me think... like mens' flares ;) Best forgotten.
Posts: 1,545
Threads: 168
Joined: Jul 2005
Long before I was a business person, I was taught in the fourth grade that "multiplication and division come before addition and subtraction".
No engineer, scientist, business person, doctor, nurse about it.
If a calculator does not have precedence builtinto it, it is up to the user to use the calculator in a way that handles precedence.
Grade school teaches you the way things are supposed to be. :)
And, shame on HP for making their algebraic calculators use chain logic aka no precedence for so long... until the arrival of the HP 20b.
The correct result should always e 5 as written. Take it up with Mr. Hodges from the 4th grade if you disagree. :D
▼
Posts: 335
Threads: 12
Joined: Dec 2007
Thanks Dusan and Gene!
So, I can safely discard my newly won (dis)information, that business math is somehow different from math in general.
*wipssweatfromforehead*
Posts: 4,587
Threads: 105
Joined: Jul 2005
Quote:
A mathematician or an engineer will answer 5, because for him/her operator precedence holds. But what about a business man? It depends. HP's chain calculation mode (HP10b and others) will give 0 as the result, ...
So called chain calculation mode (CCM) is a relict of the early days of computing, when memory was too small to take care of operator precedence. Remember even parentheses were not available in very early electronic calculators. BTW, this was the golden era of RPN. But nowadays there is no need for CCM anymore. As seen above, CCM fosters confusion in thinking, and thus must be regarded "dangerous". So CCM ought to be overwritten by the worldwide accepted rules of math very soon.
▼
Posts: 1,278
Threads: 44
Joined: Jul 2007
Except in finance where professors have been screaming for it from HP for years. . . hence the inclusion in the 20b.
TW
Posts: 121
Threads: 21
Joined: Jun 2008
It occurs to me that the debate about how precedence rules are handled in answering a question such as 5 + 3 x 0 need to take into account how the question is being asked.
If I'm looking at a formula: 5 + 3 x 0 = ?, then the answer will always have to be 5. This is important because success in algebra (and beyond) depends on knowing the precedence of operators in order to understand the relationship between terms.
On the other hand, if a friend posing a mathematical puzzle says to me, "Five plus three times zero", then the answer is zero. In this case, rather than looking ahead, I'm calculating "serially". It's more of a program than a formula.
Now, of course, if my friend wants to insure I'll answer five, he needs to consider how he poses his procedure to me. If he wants to make sure he gets five, he should say, "add three times zero to five" or "add five to three times zero".
This is the crux of the confusion. Some people are thinking in terms of a sequence of operations, others are thinking in terms of the relationship, or formula, being expressed.
MikeO
▼
Posts: 2,448
Threads: 90
Joined: Jul 2005
You're right.
I remember my algebra teacher saying things like, "Ecks times the quantity four ecks + 1."
Edited: 22 Jan 2009, 1:35 p.m.
Posts: 149
Threads: 7
Joined: Dec 2006
I have to agree with Mike O. and Marcus. Mathematical notation is a convention used to overcome ambiguity in a written mathematical expression. When the format is the written word or an oral statement, the convention may not apply.
Posts: 40
Threads: 5
Joined: Oct 2008
It's all in how the question is presented, the pauses/inflections of the speaker. "What is five plus threetimeszero"  obviously 5. "What is fiveplusthree times zero"  arguably zero. A visual inspection of the problem adds perspective to the verbal understanding and processing of the question. To compartmentalize the responses into right and wrong requires more subtlety than a simple formula, which by all accounts to someone with math skills, yields the correct answer of 5.
Calculators are for people who know how to do arithmetic and more complex mathematical operations. Just like spell checkers in word processing programs  they are only good for people who know how to spell already otherwise they may be lead [sic] down the wrong road!
▼
Posts: 2,448
Threads: 90
Joined: Jul 2005
Quote:
are only good for people who know how to spell already otherwise they may be lead [sic] down the wrong road!
or even:
are only good for people who know how to spell already otherwise they may be graphite [sic] down the wrong road!
;)
Posts: 54
Threads: 2
Joined: Jul 2008
To clarify, the question was displayed on a big flashy screen as "5 + 3 x 0" for the contestants  no ambiguity.
Posts: 122
Threads: 9
Joined: Jul 2007
I teach physics in a high school in Luxembourg. So my students are approx. 13 to 19 years old. Here is what I noticed in the last years:
 Most students don't really care about a calculator. If they need a new one, they buy whatever calculator which fits their budget.
 Most students are not interesetd in "how" their calculator works. That's why most of their calculations are wrong. They don't know whether they must type sin 25°, or 25° sin, or sin(25°). They don't know how to switch between radians and degrees, they dont know how to make use of the E, EXP, 10^ button etc. And above all they don't care. It always gets interesting when they lend a calculator from a fellow. Most of the time they are completely lost.
 In the lower classes, my school forces all the students to use the TI30 ECO RS. For those students it certainly has all the needed functions. But later, when they switch to a more sophisticated model, problems arise.
 In those classes, where students specialise in maths and sciences, the TIVoyage is the imposed calculator. It is nice to see that many students use a second, ordinary calculator for doing most calculations, because the Voyage is too big and complicated. Sometimes the voyage is even prohibited in those classes during tests ... nonsense. But they like it to play games.
 Concerning my upper classes, I recommend the Casio fx991ES. It is cheap, well built, and has many useful functions for those students, like regressions, the capability of solving quadratic equations, simple systems of equations and it can do simple calculations with complex numbers. Maybe 20% of my students use it. In my exam class (those who can attend university next year) we are at 90%. Most have understood that this calculator can save them some precious minutes.
 Concerning the teacher, he uses the HP32sii daily and sometimes the 48GX and 49G.
 It would be great, if RPN could be IMPOSED. In my view, someone who manages to use RPN knows how to calculate. When the student uses algebraic, you never know whether he has understood what he is calculating.
Edited: 22 Jan 2009, 4:59 a.m.
▼
Posts: 335
Threads: 12
Joined: Dec 2007
Quote: It would be great, if RPN could be IMPOSED. In my view, someone who manages to use RPN knows how to calculate.
The question here, to that I don't know the answer, could be: might it be the other way round? Only someone who has a "math brain" in the first place will manage to use RPN on a level of understanding?
▼
Posts: 4,587
Threads: 105
Joined: Jul 2005
Quote:
Only someone who has a "math brain" in the first place will manage to use RPN on a level of understanding
I second this statement fullheartedly. RPN leaves the math rules (operator precedence, parentheses etc.) to the educated user, while algebraic calcs carry and apply these rules.
Posts: 540
Threads: 22
Joined: Jan 2005
Quote:
Most students are not interesetd in "how" their calculator works. That's why most of their calculations are wrong. They don't know whether they must type sin 25°, or 25° sin, or sin(25°). They don't know how to switch between radians and degrees, they dont know how to make use of the E, EXP, 10^ button etc. And above all they don't care.
Unfortunately, I have the same problem  and I am interested and I do care. But whenever I pick up a Casio  or any other lowend Japanese calculator  I get confused by their inconsistent interface. That's why I like RPN  it's generally consistent (if we overlook things like STO being a prefix operator  RPL uses STO postfix but takes it to the point of pain).
Even with the manuals  which usually consist of one simple worked example for each function  I am usually unable to build an abstract conceptual model of how the calculator functions. Again, this is not a problem with RPN.
So I don't blame the kids  there are just too many rules and sequences to remember on those (imho) poorlydesigned calculators.
Best,
 Les
[http://www.lesbell.com.au]
▼
Posts: 2,448
Threads: 90
Joined: Jul 2005
The variation in logic between calculators is no less than infinity minus one it seems! And it is troublesome.
Being an rpn user primarily, I found that whenever I borrowed a machine I had to be very thoughtful about how to use italways aproximating the answer in my head or on paper. The other thing I tend to do with unfamiliar machines is to avoid any chain or parenthesis workrather keep finding intermediate results and continuing on. This is the most surefire way to muddle through with even the most recalcitrant calculator logic!
