More thoughts on calculators

[Jane in NC]

Hello all.

 

Use of and restrictions on the use of calculators are perennial themes here. Jean has a thread going on the College Board regarding restrictions on calculator use in her son's College Math course. Regularly parents ask about which calculators are allowed on standardized tests. Etc.

 

I wanted to weigh in with some new thoughts that I have had regarding the use of graphing calculators of the TI-83 or 84 vintage. I have not fiddled with the new TI-nspire (a name which annoys me) nor do I have personal experience with the more sophisticated calculators that have symbolic manipulators.

 

My son's math work since 8th grade (when he did Algebra) used calculators sparingly. For example, I allowed him to check the graphs he drew by hand with a calculator. I have always allowed a calculator for word problems or science applications where answers are rarely given in exact form but are rounded. Further, we have used "antique" math texts, old Dolcianis, that did not contain calculator applications as the modern books do.

 

Since my son is now studying Calculus using one of the suggested texts for AP courses (Larson), the time seemed right to integrate the use of the calculator into his work. I have ulterior motives as well: prior to this time, my son has used my old TI-85 calculator, something that I bought when he was a baby. The old 85s function a bit differently than the 84 which seems to be a fairly standard educational model these days. The transition is not automatic.

 

I wanted to share our recent experience. The material on limits and continuity in Larson was covered in Dolciani's Analysis book last year. We are revisiting it (always a good idea to look at epsilon/delta proofs more than once) but adding a calculator component. My son is using the graphing calculator and its table function to estimate limits and discover the limitations of technology. Further, one does not find every feature and application of the calculator overnight. I purposely assign problems that give him the opportunity to explore certain calculator features. Larson does a good job of labeling problems that are to be done with a graphing utility. I should note that the calculator applications do not form a majority of his homework problems--most of the Larson problems do not require any technological aids.

 

Warning: calculator instruction manuals are rarely user friendly. In fact, my son just went out for a long walk after a rather frustrating experience with his device. An application was accidentally turned on by his mother (oops) and it took a bit of work to figure out how to turn it off. I am left with instructions not to touch his calculator again. Snort!

 

Jane

Edited September 14, 2009 by jane.kulesza

[HSHS]

My DD's a complete calculator-phobic. She only likes using them for basic +-x/ for quickness but doesn't use them for anything else. Is this going to be a big problem when we get further into her high school years?

[sarahli]

I remember that calculators were allowed for our classes even in elementary school. Thankfully I am absent-minded and always forgot mine. I realized in high school that I could do mental math or "pencil arithmetic" easier and quicker than my classmates, who had always used calculators.

[Janet in WA]

Warning: calculator instruction manuals are rarely user friendly.

Ain't that the truth? We used a fairly user friendly tutorial we found online. That was many years ago, but I'd imagine similar things are still available.

[Jane in NC]

My DD's a complete calculator-phobic. She only likes using them for basic +-x/ for quickness but doesn't use them for anything else. Is this going to be a big problem when we get further into her high school years?

 

Not initially. There is always a question of when graphing calculators should be introduced. Personally I believe that students do not need them for basic algebra courses. Back in my day, math texts had log, trig and root tables in the back of the books. Modern day texts assume that students are using at least a scientific calculator.

[HSHS]

DD has a scientific calculator since the school she went to has required them since she was 11 but I'd never even heard of a scientific calculator & I don't know what the difference between a scientific & graphing calculator either. ;D

 

So anything past Algebra needs a calculator, do you think? That could cause some trouble xD

[Tullia]

I've wavered on this question a lot over the years so it's probably a good thing that sometime after Algebra I dh and ds bypassed me and bought a graphing calculator which gave them several weeks of fun. Owner's manual? THEY couldn't be bothered--it was a lot more fun to just "hack about". Dh calls it intelligent, informed hacking.

 

I am, big sigh, old enough to remember when slide rules were allowed in high school in upper level classes and then only when absolutely necessary. Dh's first calculator (HP from the early '70's) cost over $600 dollars, and was a major purchase. Our second, a Sharp bought in 1980, cost $25 and does more than the HP. We still have and use both, but I prefer mental math with pencil and paper backup if needed.

[Brenda in MA]

of calculator usage as well. My older son (now a freshman in college) used Saxon Math up through most of Advanced Math. The Saxon books have a few lessons on the graphing calculator, but it is not their emphasis. He really wasn't getting the upper math concepts with Saxon, though, so we switched to Chalkdust for PreCalc & Calc.

 

Chalkdust uses the graphing calculator fairly heavily in PreCalc & Calc, and my son's conceptual understanding of the math was greatly improved by the more visual approach. However, over the two years he used the Chalkdust programs, he became very dependent upon the calculator, even for simple calculations. I definitely see this as a downside of heavy calculator use. When he got to college this fall and the no calculator rule, he really had a hard time re-learning the old paper & pencil method of basic math calculations with things like simple trig functions, logs, exponents, etc.

 

I still don't know why 2 years of heavy calculator use had the effect on him of making him forget the paper & pencil method. Maybe he never really understood the basics well? Maybe it's just this particular kid and his learning style? I'm mulling this issue over because I have his brother (8th grade) to school for the next few years, and I'd like a better outcome this time.

 

Last year for Algebra I, I got the brother a basic scientific calculator that also happened to have a fraction manipulator. You can directly enter a mixed number and get it converted to a fraction. The thing will also directly add, subtract, etc. fractions with unlike denominators. Over the course of the last school year, I saw the brother forgetting how to do basic fraction manipulations with paper & pencil. That scared me a bit, so I've gotten him a very basic 4-function calculator to use and put the scientific model away. We'll see how things go this year.

 

I still want to know at what point the basic paper & pencil calculations are ingrained enough that one can use a calculator without forgetting the old methods. I had a scientific calculator in high school and college, but we were not allowed to use them on tests in high school because not everyone in the class had one. I definitely remember looking up trig & log values in tables in the back of my math books. Does the manual nature of looking things up and the manual calculations aid understanding? I wish I knew.

 

Fluency with the graphing calculator is definitely important, though, especially for the SAT/ACT exams, so I think teaching the dc to use one well is important, too. So many approaches, so little time...

 

Brenda

[Jane in NC]

DD has a scientific calculator since the school she went to has required them since she was 11 but I'd never even heard of a scientific calculator & I don't know what the difference between a scientific & graphing calculator either. ;D

 

So anything past Algebra needs a calculator, do you think? That could cause some trouble xD

 

Need? Probably not. I for one earned a BS in mathematics without a calculator! I will admit, though, that I borrowed a programmable calculator in grad school. It was required in a numerical analysis course that I took. Today, calculators may be required in precalc or calculus--or may not be allowed as some posters have noted. It all depends on the course, the school and the instructor.

 

Here is the deal with calculators: there is the minimal function one that Sears use to give away when you opened a credit card. They do minimal arithmetic.

 

A scientific calculator has trig, logarithmic and exponential functions. If a student in Algebra II does not have one of these, he will have to use tables with trig and log values. Old texts have these in the back of the book; modern texts do not.

 

Graphing calculators do just that. Enter a function and you see the graph on a screen. There is an argument that a graphing calculator does all the work, but that is not quite true. The operator may have to know how to find the domain of the function or that image that is appearing or not appearing on the screen could be misleading.

 

There is a more advanced generation of calculators that manipulate variables. They take derivatives, compute integrals--the stuff of calculus. These are the machines (and they are small computers) which are banned on various standardized tests or in many math courses. Most students do not need this advanced type of calculator, although I suspect that engineers probably love them.

 

My argument is that students are not going to master the functions of a graphing calculator overnight. If your student is going to need to use one of these calculators, I would give him the opportunity to fiddle with it as Martha in NM mentioned.

 

Be forewarned that TI seems to own the market on graphing calculators in schools. There is a generation of older engineers who love their HPs. Are Sharps and Casios still available? They use to be less expensive than the TIs but it seems that text books exclusively have examples with a TI screen. Anyway, TIs run about $100 for the basic graphing calculator. More for the new TI-Nspire.

[Gwen in VA]

There is a generation of older engineers who love their HPs.

 

HP's are still being used by certain nerdy wonkish teens. There are even facebook flair for HP's!

 

When time came for my son to get a graphing calculator, he actually got a HP-50g. He had used dh and my old HP's in algebra 2, so he was comfortable using reverse Polish, and he couldn't imagine going with a TI.

 

He loves his HP.

It hasn't been a problem in his classes -- his profs haven't required a specific brand of calculator.

He used it in the PSAT, SAT, and the relevant SAT-II's and AP exams without a problem.

 

And -- best thing of all -- he doesn't worry about having it stolen. At a LAC, nobody else even knows how to use it! :D

Edited September 15, 2009 by Gwen in VA

[Tullia]

Ds was able to use his HP graphing calculator for the SAT, but ACT specifically forbids graphing calculators (at least that was true last fall). Not true-- it was only certain models including ds' particular HP; please see Jane's correction below! Ds works fairly slowly, was used to "polish notation", and therefore found that using our old Sharp scientific slowed him down on practice tests. Believe me, he needs every second of the time available on standardized math tests! Ds was able to borrow a friend's HP scientific version for the ACT.

 

We've also seen the TI dominance this fall at the CC. The course catalog specifies TC 83 or 84 for most classes with instructor permission required for other models. Ds has discovered that all this really means is that if you use something else you can't expect the instructor's help with how to use the calculator. However, one other thing he's found is that graphing calculators are allowed for use during chemistry lectures/homework, but not on exams.

 

When dh and ds bought the HP graphing calculator they assumed that it would be the one model that would take care of every need, but it hasn't been that simple.

Edited September 15, 2009 by Martha in NM
to correct wrong information

[Colleen in NS]

just bookmarking this thread for future reference. Thank you, Jane once again!

[Tullia]

HP's are still being used by certain nerdy wonkish teens. There are even facebook flair for HP's!...And -- best thing of all -- he doesn't worry about having it stolen. At a LAC, nobody else even knows how to use it! :D

 

I am ROFLOL! One of the things dh told me when we first met that he never, ever, ever carried his precious HP in a belt "holster" like some folks did. I guess that would have been too nerdy. :D

 

Martha

[Jane in NC]

HP's are still being used by certain nerdy wonkish teens.

 

Well I married an HP guy. Since I haven't been in an engineering classroom for a few years, I wasn't sure if there was still that adorable wonkish subset around. ;)

[Jane in NC]

Ds was able to use his HP graphing calculator for the SAT, but ACT specifically forbids graphing calculators (at least that was true last fall). Ds works fairly slowly, was used to "polish notation", and therefore found that using our old Sharp scientific slowed him down on practice tests. Believe me, he needs every second of the time available on standardized math tests! Ds was able to borrow a friend's HP scientific version for the ACT.

 

We've also seen the TI dominance this fall at the CC. The course catalog specifies TC 83 or 84 for most classes with instructor permission required for other models. Ds has discovered that all this really means is that if you use something else you can't expect the instructor's help with how to use the calculator. However, one other thing he's found is that graphing calculators are allowed for use during chemistry lectures/homework, but not on exams.

 

When dh and ds bought the HP graphing calculator they assumed that it would be the one model that would take care of every need, but it hasn't been that simple.

 

The ACT does allow graphing calculators to be used. As is always the case, test takers should verify which models are allowed.

 

When I taught calculus, I could usually help students with assorted TIs, sometimes help those with Sharps or Casios, and rarely could help the HP crowd, although the HP crowd rarely needed help. I guess that says it all!

[Tullia]

I'd forgotten what actually happened; it was ds' particular HP model (along with a few others) that was on the "forbidden" list NOT graphing calculators in general. One thing I do know is that the list does change from time to time as new calculators come on the market, so it's a good idea to check again if you repeat a test.

[Jane in NC]

I am ROFLOL! One of the things dh told me when we first met that he never, ever, ever carried his precious HP in a belt "holster" like some folks did. I guess that would have been too nerdy. :D

 

Martha

 

Must say that I have been giggling over your post for the last hour. What a fashion statement--the calculator "holster" and the pocket protector!

[Gwen in VA]

Are pocket protectors still sold? My ds (an hp geek) wants to buy my dd1 (the chem major) one as a gag gift for Christmas!

[Tullia]

Are pocket protectors still sold? My ds (an hp geek) wants to buy my dd1 (the chem major) one as a gag gift for Christmas!

 

How could I have forgotten the other sure sign of geekdom??!! Wouldn't you know they're still available...and here is the intro from the site linked below:

 

"You're bold, practical, self-confident, and you don't give a hoot what other people think about you... you wear a pocket protector!"

http://www.pocketprotectors.com/