We Need To Talk About Calculators

***********THE CALCULATORS AND OTHER STUFF**************
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0:00 The TI-84 Calculator
1:23 It Does Not Have a CAS
2:07 Should You Allow Calculators?
3:23 Ramanujan Era Mathematician Was Hardcore

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[SenorGato]

In engineering school we embrace the hell out of our calculators. I've had a number of exams that could not be completed on time with manual calculation. They allow us to perform much more complicated work that can reasonably be done manually. My higher math courses embraced this philosophy as well. If you've passed calc 1-3 you have shown you know the underlying maths, the calculator is for advanced application.

That said, it's a tool like any other. You have to know what your tool does to use it properly.

Another facet is, at work (I do stress and reliability testing for a semiconductor manufacturer) we never trust manual calculations. Any manual work must be checked by a machine.
You can take my Ti-89 from my cold dead hands.

[Aaron-lpzt]

I took calculus 1 and 2 in the first year of university during COVID. My prof said we could use ANY technology we wanted since he couldn't enforce the restrictions fairly due to online. I got good grades in those classes, but I often relied on wolfram and calculators as a crutch. Let me just tell you... when I took calc 3 in 2nd year and we couldn't use any calculators at all, I hated myself for not learning things properly that whole semester. I just find that math is the subject that will haunt you for not learning things properly, and it was more painful to relearn those things manually when further classes assumed the knowledge.

[dopplerdog]

So my Linear Algebra class allowed the programmable HP15C in the exam (I'm now showing my age). I thought I'd be clever and implement all sorts of algorithms on the calculator (eg triangularization, diagonalization, etc, etc) so I'd have an edge in the exam. I did really well in the class, but afterwards I realized that the time I spent learning the algorithms in order to implement them was what got me through, not the fact that I used a calculator in the exam. True story.

[fudgenuggets]

Maybe not the most popular because of its price at the time, but the hands down best calculator had to be the HP-48SX. I still have mine that I bought in 1992. This thing is amazing and holds up well 30 years later. RPN notation rules.

[markcrites]

When I was in engineering school in the '80s, calculators were absolutely forbidden from math classes. However they were regularly allowed in physics, chemistry, and engineering classes. Back then we used variations on the HP 41, which used reverse polish notation. It was much faster than an algebraic calculator for doing computations.

[Skank_and_Gutterboy]

In an engineering class, my calculator proved that a table in an engineering textbook had errors. When doing a problem in acoustics, there was a table of results for a commonly used differential equation. I didn't mess with the table lookup, I just programmed the differential equation into my HP-48 so that I could enter the couple of parameters required and the answer would pop up. I just wanted to eliminate table look-up error. On a test, I got a problem "wrong". Instructor wrote, "You looked on the wrong column of Table and that error carried forward." I got most of the credit but docked a few points because my final answer was "wrong". Funny, I didn't do the table lookup, I had my calculator calculate that diff. eq. value. I pointed this out to the prof. He went and did some calculations with his HP calculator and MathCAD. As it turns out, the table was screwed up, it had a column of junk results inserted and that column shifted several other columns to the right so that about 1/4th of the table was just wrong. I got full credit and he sent a letter to the author telling him that his table is jacked-up.

[JeffRyman]

I took a graduate level thermodynamics class in the mechanical engineering department sometime around 1973 or 1974. I had an HP 45 calculator purchased after its introduction in 1973 that cost $395.00. There were about 10 students in the class and everyone except one poor fellow had a calculator. The professor decreed that we had to use slide rules on exams because not everyone had a calculator. I knew how to use a slide rule from my undergraduate days (1965 to 1969) but was pretty rusty, as were many others. If I had it to do over again, I would have grabbed all the other students who had calculators by the collar and told them "We are all going to contribute enough money to buy poor Joe a calculator so that we can all use them on the exams."

Sometime in 1974 I dropped my HP 45 on the pavement getting out of my car and it quit working. I sent it to HP for repair and got it back with a completely new or refurbished set of interior parts with about a three week turnaround time. The charge was about $40 plus shipping. That tells me that the manufacturing cost for the HP 45 was about $50 to $60 for everything. The remainder of the original $395.00 cost allowed HP to recoup its development costs plus make some profit.

[paulfrank]

I like your approach to student calculator use. I took a Linear Algebra course many years ago and had a calculator that could perform matrix functions (very unusual at the time). Because we had to show our work, I still had to do all the steps by hand. But, I could also solve it on my calculator. If the answers didn't match, I would go back and check my work to find my error. I'm convinced I learned the topic much more efficiently and easily by using that calculator.

[Crw]

I never really embraced the graphing calculators and my favorite calculator of all time (which I still have and use) is the Hewlett-Packard HP-15c which I got in June 1985. To me, it was perfection and I have an emulator for it on my iPhone and use it as my phone calculator.

[doughoffman]

As an engineering student in the 1971-1975 era I feel like I have seen it all. We began with slide rules, and slide rules require you to estimate straight math which I think became a lost skill once pocket calculators (and now notebook computers) came on the scene. I remember knocking 1-2 hours per night off the time it took to do my homework when I bought my HP-35. Wow. Of course the question of allowing calculators on tests was an immediate issue. That was solved by the realization, that you have alluded to, that the real knowledge was in knowing how to set up the problem. So all test questions became designed such that the hardest math was dividing 4 by 2 and so forth.

[FiatLuxSayRelax]

I still have my TI-84 Plus after all these years in EE. Used it to the point my batteries actually ran out after years of constant use through high school to university. They truly are exceptional in what they do and I agree they should be used as a tool despite the fact that my university has always discouraged us from relying on them. We couldn’t use them in our math exams for example.

[joshhallam]

I used a TI-89 for my math degree. I had some teachers that wouldn't let us use calculators at all, but I never had a teacher say I needed a calculator without a CAS. I always showed my work, and usually did problems by hand first and then checked with the calculator. I loved that calculator. Luckily, in the upper division classes we were able to skip some remedial work, like putting a matrix into rref, so being able to just draw an arrow with rref and let the calculator do the work was such a time saver. I would not have enjoyed my classes nearly as much without it. I even wrote some programs for my number theory class to cut down on repetitive modular arithmetic.

[lidsolbarnes]

The TI 84 can do numeric derivatives and definite integrals. It can also graph the functions. Only scientific calculators, non-programable and non-graphing, are allowed for Calculus in most universities in the United States.

[DannerPlace]

I still use my HP 15C, bought it new in 1982 for engineering school, and have used it all my life. It's in from of me right now.

[arunray]

Thank you for making this video. I prompted you to make a special video on calculators as I was struggling to buy a new one and you said you would very soon come up with a video. This video was an eye opener and helped me immensely in making a wise decision. Thanks once again.

[shanemcinally]

I remember getting an exercise sheet from a chemistry teacher on doing conversions or something... I was also taking a math course and I think I just felt inspired to try with all my might to do the calculations in my head. I spent most of the class just doing the calculations and from that point on I just tried to do it more and more. I've kind of lost the habit of doing things that way but I would definitely say it helped me process things better. it's like you get more used to seeing numbers as positions, I remember seeing the numbers like this in my head. lol trippy...

[barmherzigsein]

Thank You for making this video. Although my formal training has been in Chemistry and Medicine (which required Calculus), I found myself (in 2006) disabled after severe trauma to my spine and accepted a temporary job teaching Calculus and Chemistry to preparatory High School students (Gymnasium).
As I myself had been taught in undergraduate and graduate schools, I permitted my students the use of a calculator (of their own choosing) and insisted they demonstrate their work in detail. Like you, my conclusions were that calculators can greatly enhance the learning, as well as the enjoyment, of Calculus. Of equal importance to achieving cognisance was the daily use of real world problems requiring Calculus to obtain solutions as well as making each student teach one 30 minute lesson in problem solving to our class (and myself).
PS - By 2007 I was walking again and had become a better teacher, professor, student, and Human Being because of the immensely significant lessons I had to master and the immense support received from my Calculus students.
Salomè, und leb wohl!
Mögest Du in das Licht, der Wahrheit, und dem SEIN der Schöpfung leben.

[christoskettenis]

As a part-time lecturer, I teach many Math-heavy courses and I make open-books exams so that the responsibility of success lies exclusively on the student. They can have any notes they want and they will get full marks if they show their working. There is no way of cheating this way and also I hate it when people are made to remember formulae

[TitoSpadini]

Very interesting points. In Brazil, the calculators most commonly used by students used to be Casio FX-82MS (general), HP 50G (engineering, physics, chemistry and mathematics) and HP 12C (economics and business). I am not sure about how it is nowadays.

[gmcenroe]

Since I am an old timer, I can tell you that we simply did not have advanced features on calculators in the mid to late 1970s. Even programmable calculators were quite expensive but none had graphing capabilities. When I took calculus and physics, we never were given exam questions that could be solved on our calculators, and we had to show our work. Even in physics only first semester physics that covered basic mechanics involved calculations, after that it was all theoretical when I took Physics. Since we could not graph on calculators, we learned the methods to graph 2D functions, find asymptotes, etc. My kids all used TI calculators in school. I don't see why any objection to advanced CAS calculators should be in place. My favorite calculators are the HP-41 and HP Prime calculator because I became hooked on RPN, HP Prime can even do 3d graphing. For more complex math I will throw it on Mathematica on my computer, even though I have found that the solutions obtained there can find you deep in the woods with much more complex solutions than one would expect to find by other methods. I know that HP-Prime can turn off CAS for predetermined time periods for exams that can be checked by professors in exams. I think that even now SAT exams allow calculators. A good professor can write exams that make a calculator almost useless if they want to. For learning it is up to the student to not use a calculator as a crutch and learn the math!