We Need To Talk About Calculators
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- Опубліковано 29 чер 2024
- My Courses: www.freemathvids.com/ || Whether or not calculators can be used in certain math classes is an endless debate that will probably never end:) In this video I discuss this, and I also talk about what the most popular calculators are for Calculus. Both of these are awesome! What are your thoughts on Calculators? Please leave any comments below.
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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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Thank you:)
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.
I agree that there's no point in chugging your way through 20 pages of algebra when that has nothing to do with your understanding of a problem and doing long calculations with pen and paper when you don't need to does just increase the likelihood you'll make a mistake. Using a calculator is also often thought of as a way of avoiding doing calculations by hand but when it comes to engineering I don't think that's necessarily a fair take. Modeling and simulation are important skills for students to develop and learning to use the tools they have available in their approach to problems is a part of that.
At the same time though it is also important to understand the models you're using and how different systems interact mathematically. Working through calculations and knowing how to derive different mathematical tools is a part of that especially because at the end of the day the old aphorism holds true, "all models are wrong, some are useful." When you do the work yourself you know what simplifications you're making, you can see what parameters of a system are well behaved or can be isolated and which are sensitive or highly nonlinear and you get a feel for where a model of a system breaks down and what isn't being considered within it. I can't tell you the number of EEs I've run into who have created problems for themselves because their system with perfectly matched transistors and ideal components that worked great in simulation doesn't work at all in practice. Now nobody should be expected to do Gummel-Poon in their head, but I think having to grind through some of the more tedious parts of problem solving can actually be pretty valuable sometimes.
@@esven9263A calculator isn't the right tool for any model more sophisticated than a least-squares regression, a computer is.
@@costakeith9048 Any mathematical representation of a system is a model. A transfer function is a model, the Shockley diode equation is a model, hybrid-pi is a model, a line of best fit can be a model. And all of them can be done just fine on a calculator.
For the abstract Mathmatician or student doing a proof based course a calculator is generally unneeded. For the engineer the calculator today is what the slide rule was to the engineer of yesterday. The slide rule is an ingenious device requiring no power but it can't match the convenience of the calculator.
"Any manual work must be checked by a machine."
Maybe, we should learn the opposite: results from one machine should checked with manual calculation or calculation with another different machine ...
😁
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.
You are very lucky. I took one year to study Precalculus. I failed calculus 1 three times…
@@yangzhen2889 Interesting, what do think led to the failure? Not long enough in Precalc or not enough pen and paper practice or conceptual issues?
I teach Calc 1 and 2. And I taught it online as well during Covid. And I allowed my students all technology because I couldn't check it anyway. And I severely WARNED them of the consequences if they "cheat" by not doing the actual work. And once we went back to in-class, more than half of these online students had to retake both calc courses precisely for the reasons you state. They though they saved time (and money) but it backfired big time.
I read precalculus book for at least 5times. Than, I am taking calculus 2 now. And I feel many questions seem so hard, but I can deal with them. I also feel my brain has much more power than several year ago.
I wasn't allowed to use anything more than a TI-30 until after Calc 3, and it made a HUGE difference. calculators are a crutch and a detriment to learning.
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.
Yeah basically you did what you where supposed to get out of the class.
Yes! Back in '83 I was doing Actuarial courses. I was failing miserably. I then got an HP41CX and started to implement the functions and logic.... in the final exam I must have got 100%, not by using the 41CX, but because I had that light-bulb from implementing those equations/logic/thought process. These calcs are learning tools, not necessarily solution tools.
I have the hp15c app on my work iPhone. An actual vintage hp15c is around $100 if you can find one.
This same thing happened when I programmed my calculator too. programing a calculator to do a given math computation is a good way to learn how to do the computation. To program it correctly, you need to learn the computation at a relatively deeper level.
It is kind of like learning the proof for the computation. At least for me, learning the proof makes doing the computation much easier
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.
I'm probably a decade younger and got a HP-48G+ in 2002, calling it a calculator is an understatement, it's really a pocket computer. I lost count how many times I've written User RPL code to make my life easier with it while away from a desktop computer. The TI-89 may have had a better CAS, but for me RPL felt a lot more intuitive and natural to use than TI-BASIC.
During college I've had to use a number of different software to solve different problems in different classes, even if cost and convenience weren't issues, I'd still prefer my 48G+ over a laptop for most of college stuff back then. Some software were just too clunky to use, even though it was vastly more powerful and ran much quicker than my 48G+.
I have an HP-48GX right here on my desk.
Preach it! I have a 48SX that still gets used all the time.
I had the HP-48SX. Excellent calculator. Unfortunately it died when a student spilled his drink on it, so I got an HP-48G to replace it. The SX and G are VERY similar. I think the only real difference is that the G has some pop-up menus that the SX doesn't.
@@Skank_and_Gutterboy That is true. I think they used the same CPU (Saturn?).
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 XXXXX 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.
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.
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.
+1000 for RPN
@@stultuses 1000+, surely?
don't call him shirley.
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
We need to talk about slide rules
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.
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.
This is why I never had an issue with a calculator. Use it check your work not do your work.
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.
in 1975, this guy had this slide rule which sat on four feet, it had TWO sliding bits, we looked at him in awe. Then he bought a HP45 which was hugely expensive.
HP12C is what got me through all the actuarial exams. I still keep one on my desk just so I can see it everyday.
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.
Interesting, my university in the USA never allowed us to use calculators for our math exams. We were always encouraged by our math department to not do so during our lectures and discussions. Needless to say, they made sure the math was doable by hand.
Well, that is funny. In my college, I used the TI-84 plus CE from calc 1-3 and diff eq and linear algebra. However, I do have the TI-36X Pro which is scientific and non-programmable and non-graphing. It is the only calculator I use now.
@@tmann986 The TI-36X pro is the calculator I used for calc 3, diff eq, and most of my math classes in University. It's a very good calculator for the price and can also do numeric derivatives and definite integrals. Finding concavity and extrema can be done on the TI 84.
Zero calculator restrictions at my US uni. You simply had to show and prove your work.
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...
"You get to see numbers as positions" I think you made another argument to bring back the slide rule!
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.
I don't know about other countries, but in the UK you cannot use a calculator with CAS it's forbidden by all the exam boards I've come across. Even when I did my Engineering degree, the recommended calculator was a very basic Casio FX 82 - it cost roughly $10.
@@blaser80 For some certified exam, you can't use a CAS calculator, and I'm guessing probably no graphing calculators at all. The only certified exam I've taken was the GRE (for grad school) and the probability actuary exam, and I think I just had a regular scientific calculator for both, like a TI-30 or some 30 series
Agreed. And in my experience at least, I used my Nspire to get the final answer, just to make sure I got at least some points. But then I would actually solve it by hand.
It is also nice knowing that for homework problems I got the answer right and am not just screwing it all up and don’t know it
Back in the day, you couldn't use calculators at all on SAT/ACT/etc. You can today, but only on certain sections, and only with approved calculators. Like slide rules before, calculators are tools that only work if you are able to set up the problems correctly first.
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.
How many games do you have on it 😏
In school (back in the 80s of the last century), we used a TI 30, because no programmable calculators were allowed ... I now learned to use an "RPN" calculator, because i saw the advantages of the app "free42" on my mobile phone.This app simulates an advanced version of the HP 42s calculator, and it is really amazing.
@@inspectorvoid Oh, many, haha. You geezer. 🤣😆 Making me laugh when we’re dealing with the topic of math.
The TI-83/84 are the worst things that have happened to high school and college math education in the past 40 years.
I was a physics undergrad and can't recall many situations where a calculator would have helped in physics.
That said, I did use a calculator in my Chemistry class. Until the calculator ran out of power during a final. The only thing that saved me was that I had been carrying an old slide rule around (because slide rules give serious geek cred) and I knew how to use it. I ended up using most of the time in that final, but got an A in the class.
In my 1976 high school calculus class there was a little arms race of red LED calculators. The rich kids had HPs and the rest of us TIs, Bowmars, NSs, or others. I upgraded 3 times, from basic 4 function, to Bowmar MX 140 scientific, then to TI SR51, and finally to TI SR56 programmable. Next, in college, to the TI-59 magnetic card programmable. I think some tests allowed them and some did not. I still have that 59 and have re-collected the others. Good times!
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!
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.
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.
Still have several TI-84 Plus. The one class I remember best where the professor was adamant that no calculators be used was linear algebra. After the class struggled through row reduction, determinants and a bunch of other stuff, the professor said that now, since we had a "first hand" understanding of the techniques - and the sheer drudgery - of doing this on, oh say, 3x3 and larger matrices, we could now use the TI which had some cracker-jack matrix functions. The professor also had a multi-page guide on how to use the TI and some programming tips for the thing to boot. Made life a heck of a lot easier. The first few weeks burned the basics of linear algebra into lasting memory, but I guess that was his point.
My DE professor said we could use calculators but remember that the thing could not understand the problem or set up the appropriate structure which was needed before any calculations were done. She was right of course. And then there are the CAS systems which can give unpredictable results if you do not understand the problems and how to proceed to solve them.
I add that when I was in these classes mentioned, I was a "non-traditional" student: Retired and taking them for fun. The first time around physics and mathematics problems were worked out on paper and calculations were done by hand, literally, with the help of a log-log duplex slide rule. Still have a couple of those around here too, but, I'd rather use a calculator. For obvious reasons. . .
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.
Same here. The 15c had all you really needed.
Same. I just picked the HP 15c Collector's Edition in case my original ever dies on me.
I agree, the HP-15c is the best calculator for math and physics. Anything beyond its capabilities should be done on a computer.
The HP-41 series was also quite good.
@@aaronbredon2948 I had the HP-41CX also and it was a fascinating calculator for the time but there were things the 15C had built in that I wished had been in the 41 series as well.
During uni I've had classes with two types of calculator requirements, either free (but you're expected to use the recommended one) or from a strict feature set.
The former was using in my EE related classes and we were informed to get the HP50g, but since they had gone out of production it fell back on what most students already had from highschool the Casio FX-9860II or similar. The only real big comfort for the calculations we did was being able to easily work with complex numbers.
The latter choice was what we used in pure maths classes, and we were insturcted to get a Casio FX-82 or similar.
I don't mind this at all, as long as the curriculum and exams are designed with your available resources in mind, it shouldn't matter
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.
I was about to say the same thing. Americans think when something is popular in their country it's also popular worldwide
France starts shifting to Numworks calculators
You would have been better off simply saying that CAS calculators would calculate derivs and integrals EXPLICITLY, thereby allowing student to write down the correct answer WITHOUT actually knowing how to do calculus. The non-CAS versions computed numerical derivs & integrals, i.e. the calculator would compute the derivative or integral INTERNALLY and would wait for the user to input 1 value for a num. derivative and 2 inputs for a num. integral and then spit out a specific numerical value for the derivative at that input or for the integral between the 2 given inputs. For non-experts: A) the derivative of x^3 = 3x^2 But the non-CAS calc wouldn't yield that specific answer. It required the user to input an x-value, say x=4, and then it would calculate internally 3(4^2) and spit out 48. That is you'd get 48 instead of 3x^2. Same for the integral. As an aside, in 1997 I had a student show up for the AP Calculus exam with a TI-200 which provided Explicit answers. This thing made dinner! Too bad he couldn't use it on the exam.
I still have a casio fx992s. It is approaching 30yrs and still working. It is fast, there is no nonsense and i really liked it during school, university and now, sometimes at work.
Hey Wiz. Love your content/channel. I've been thinking about the similarities between calculator functionality - as a learning tool (when we were coming up) and the perceived challenges emerging AI tools represent to the next generation of teachers and professors. It seems like a good analog.
I'd be interested in how you see AI tools from a teaching perspective and as professional tools much as we might use a calculator with CAS functionality to quickly dispatch workloads.
Bit of an aside, but I continue to use my Ti-83+ since I got it for maths class in high school, back in about 2003. I have this calculator and a high school friend to thank for introducing me to programming.
I owned a Sinclair scientific calculator in the 70's and since then i have always used Casio calculators, currently using a casio fx991-EX, an excellent calculator.
In avionics, the qualification testing mandates the TI-30xa. This is due to (as you said) all the things it *can't* do.
This means I have to teach my younger students to unlearn the V.P.A.M. input method they were raised on and learn how to employ the algebraic entry system that was in common use from the '70s through the '90s. This is a surprisingly difficult hurdle for them, so I keep a supply of these calculators on hand, sell one to anyone who doesn't own one, and insist that they *only use that one* in day to day operation until the day of the test.
I demonstrate solving a resonance problem using a Pickett microline slide rule, then the calculators I used in school (the Commodore SR4120D, the Casio FX120, and the Casio FX82) to show that the process is the same for all of them.
I also drill them heavily on linear to deciBel conversions and back (necessary in our field), and show them how to use that to calculate close approximations of products, quotients, powers, roots, and reciprocals without the use of a calculator.
I went to school and university in the days when we all carried log tables and a slide rule. At that time the abacus was still popular in China and Japan. There were competitions for school children, in which the fastest students did not actually touch the "beads" during a calculation, they just waved their fingers a little above the device. That allowed them to hold more digits in mind in intermediate stages of a calculation than would normally be possible. What they were doing was extending their brain's working memory by borrowing some visual memory for the purpose of doing calculations. I believe when computer memory was very expensive, some PCs did the same thing, by using memory reserved for one purpose for something else.
Joke about the log tables, but when I took a statistics class and the prof put an example problem for students to do in class, I was done first without using a calculator.
Still got my HP-48SX. It was a must have for getting a degree in mechanical engineering.
I have perspective both as an electrical engineer with 45+ years of experience and as a parent with two kids having gone through math programs upto various levels. When I went through high school in the mid '70s no calculators were allowed, but we could and did use slide rules. As I continued my education the use of calculators were increasingly allowed, but none of the calculators of the day had the ability to do algebraic or calculus functions. I had a TI-58, then TI-59, then HP41CX, then HP48SX, then HP48GX which I still have but mainly now use the emulator app for the 48GX on my iPhone. Having had the 48GX for 30+ years I have many programs that are really handy to have in my pocket, not to mention the unit library and unit conversion functions and more.
When my oldest daughter started taking her math classes I bought her the TI-84 Plus CE and that was fine. She did take some AP math classes but didn't go on to calculus. For my younger daughter I bought the TI Nspire CX II CAS. The calculator does have a test mode that turns off certain features so it can be used on exams where the advanced features aren't allowed. The problem with the Nspire calculator was that the HS math teachers were more used to the TI-84 calculators and many of the examples taught in class used that. The programs and steps weren't usable on the Nspire calculator. So I purchased one for myself and started using it and writing or converting some of the programs for her and also converting some of my old HP48 programs for use on my Nspire at work. It's nice that it has a companion software package to emulate the calculator on the PC and transfer programs, etc.
My younger daughter ended up being awarded the calculus student of the year at her school so she was able to make the Nspire work OK. That said, she is now in her second year at UCSD in the EE program and she wasn't allowed to use the Nspire in some of her classes so she bought a fairly inexpensive non-programmable one that I don't think even does graphing, or if it does it's fairly limited in its capabilities. That is her daily driver and she said she rarely uses the Nspire now. That may change when she gets deeper into the EE program.
In my day job, we of course don't have any test restrictions, so I'll use whatever computing functionality gets the job done. Computer simulation often times, increasingly the Nspire mainly because I'm forcing myself to, but the HP48GX emulator on my iPhone in my pocket is till the #1 goto because I always have my phone, and I have decades of familiarity with it and the library of programs I've written over the years - that and it is lightning fast compared to the original HP48 :)
I'm still torn about the use of calculators before a certain age or grade level. I never saw, touched, or used any calculator until I was forced to purchase and use a basic scientific calculator for high school chemistry class (10th grade) and then physics class. Never used a calculator in any high school math class including trigonometry (pre-calc) and calculus. When I got to college, the scientific calculators were instrumental, especially in the engineering classes. I went on to get an undergrad degree in Electrical Engineering and a graduate degree in Computer Design Engineering. I've never used any graphing calculator or anything like the TI-83, 84, and so on. I do have issue with students using calculators for any reason before they absolutely need to (e.g., perhaps high school chemistry & physics and I guess, nowadays, trig/pre-calc and calculus, since I don't believe today's textbooks contain printed trig tables). It absolutely blows my mind that kids in 4th and 5th grade are allowed to use calculators. I taught high school Algebra and Geometry for a few years and those students couldn't add 2 simple numbers together at 15 and 16 years old. Pathetic. I've heard teachers and administrators claim that, because students need the calculators for the SAT, they have to be taught early to used them. I refuse to believe that irrational and illogical line of thinking.
I agree with you. I never quite memorized multiplying certain numbers, but I used my fingers and managed to have success throughout college. I still use a calculator for everything in life that’s complicated. If I had never used a calculator, I would have forced myself to learn correctly to pass. That probably would have lead me to become a electronics engineer. I love circuit boards and tinkering with stuff. My lowly IT career didn’t stand a chance with everyone and their mom learning how computers work and centralized cloud computing becoming so common. I’m happy now working as a specialized mechanic. I can really understand what’s happening and use my tools that are far more complex than anything else in the shop. Life is good.
Even in high school chemistry and physics classes, the use of calculators is somewhat gratuitous. Number sense is the enemy of learning math or science.
The story from The Man Who Knew Infinity is true. The academic was Percy Macmahon who was into combinatorics, not only did he quiz Ramanujan as soon as he saw him, but also continually whenever their paths crossed.
I use either the computer or phone's calculator app, Excel, or Jupyter depending on what I need to do.
The sort of calculations we do at work would take days to do by hand, but can be done in less than a second on a computer. And what is important isn't knowing how to do a calculation, because computers can do that much quicker and much more accurately. It is knowing what numbers to use, and which calculations to perform on them to get the answer to the question.
I bought a hp 48gx in the late nineties as a civil engineer student and im still using it now. It works better than a Swiss watch. I love it especially because of 1 enter 1 + functionality and the units conversion and it matrices functions etc etc.
I used SymPy for the Linear Algebra class, mainly to check my manual calculations (Matrix inversion, eigenproblems etc.)
TI calculators where also popular because Texas Instrument had an incentive program. If a teacher or school required the students to get a TI calculator then the school could get free calculators and other materials from Texas Instruments based on the number of students were required to get the TI calculators.
I first learned algebra with logarithms in a night-school college course while I was in high school in 1968. Half the work was looking up and copying the right logs from the massive catalog of tables. My TI84+CE stores all that, trig functions, and a lot more in such a small, easy-to-access device -- PLUS it removes the decimal and reading errors I could make with my beautiful K+E slide rule -- which I still have. I think calculators make it easier to learn more math in shorter time. 😎🖖
In my elementary algebra class, we were required to have a ti-83 (can't remember if plus or not), but I almost never used it. In my engineering math class, which was basically pre-calculus with tons of application exercises, we were required to have ti-86 (can't remember if plus or not), and I used it all the time. After I graduated, I bought a nspire cas. Great calculator. For on the go, and for super cheap, I just got a Casio fx-115ESPLUS2 2nd Edition. It was $17, and it's the best money I've ever spent. I LOVE the thing. Recommend everyone gets one. There's another, newer version with a significantly better screen, but they buried some of the useful functions in the menu which, otherwise, have their own, dedicated buttons.
In some countries, Casio is the default in education.
Part of the reason could be is that PE exams require specific calculators. You want to learn on the one that the exam requires.
@@metatechnologist TI is the default in some schools too. There must be some long-standing agreements with the schools. One could argue they keep prices high but they also pay for development of excellent calculators at scale. And it is easier if all the students are on the same platform. Casio, TI, and HP make excellent calculators.
@@dosgos So does Sharp. How did they get excluded?
@@metatechnologist I didn't know Sharp was also a required brand for some countries / exams.
@@dosgos No. It's not a question of mandates, it's a question of being "allowed." Sharp, which has made a capable calculator since the early days, is not allowed for the P.E. exam. There may be a very technical reason, but I doubt it.
I bought the new $150 Ti84-CE but ultimately went back to the good old $20 Ti30-Xi. Also invested in a really nice slide rule, thought I would be cool busting out a 1950's slide ruler in my algebra class, but those things are actually really complicated. So good old Ti30-Xi, fast, cheap and uncomplicated.
A teacher in high-school wouldn't let us use calculators on a particular test. I asked about slide rules. He thought I was joking and said said ok. I crushed that test.
Calculators are a tool just like what tools a contractor uses to build a home. My opinion is a student should know how to do the calculations on paper first then once they know how to do the calculations then use a calculator. This is a side note. I go to a store and hand an associate a $20 bill for a purchase for example $9.10 cents. Back in the day when we had the old fashioned cash registers you would take the $20 and count how much change to give back to the customer. Now we have cash registers that will display the total amount we need to give to a customer. I have in many instances helped the associate how to count the amount of money. I know it's elementary math but my point is if you don't know how to do the calculations then learn this first on paper then after you mastered this use a calculator. Sorry for the long winded example.
I finished my BSEE in 1972. We used slide rules to perform our calculations for homework and exams.I still have my slide rules but have forgotten how to use them. The first hand calculators came out in 1974 and I was eventually able to purchase one for use in grad school.
It’s all about stating expectations in the class ahead of time. Had a professor state at the beginning of a semester that no calculators were allowed and if you couldn’t do a lot in your head quickly you’d run out of time on exams. Fair enough.
I recommend the TI-36X Pro for people in my statistics class as it's under $25 and can do some really nice stuff like normal distribution calculations most others in that price range can't touch. the functions like !, Permutations, and combinations are also easily accessed with thier own dedicated key instead of having to hunt through menus. It's also just a lot better laid out for data entry and other functions requiring fewer keystrokes to get the job done.
Its also the most powerful calculator allowed for the FE exam 😂
It’s a great calculator. Four line display, MathPrint, and as you say easy access to things that the graphing calculators hide in menus. Definitely my favorite calculator ever.
In my high school algebra I class I always loved typing in
MALFUNCTION on the Ti84 calculator then turning it off at the end of class to trick the next class into thinking it was broken
I've taught several physics courses as a TA. When we deny calculators, either 1) the exam will either be without numbers so that the answer will be a formula or 2) the numbers will have been selected to be friendly and other rounding will happen like gravity will 10 m/s^2 instead of 9.8 m/s^2.
The reason TI-84's are so popular is because high-school (and some college) math curriculum is designed around the use of this calculator. In the age of laptop and netbook computers, graphing calculators are obsolete and ridiculously overpriced toys. I think a much better approach is to require the use of cheap $10 basic scientific calculators on exams, and train students to use software (Mathematica, Maple, Matlab, Excel, Python, etc) that is used in the real world (transferable skills).
HP calculators are the BEST in the world. I started with TI calculators, but they failed after just a few months. I use HP 50g, HP Prime, and HP 35s calculators now. In the past, I used HP 41C, HP 18, HP 28, and HP 48g calculators. I think calculator use is good to a point, but they should only be allowed for one section of a test, the section with the truly difficult calculations. My last year in engineeriing school was when the HP 35 calculator came out. It cost $395, well out of my range. I used a slide rule through to graduation. One of our professors made us put whether we used calculator or slide rule at the top of the first page of the test. The slide rule students performed better than the calculator students.
Hp Prime G2 is the KING🔥❤️
@@crazychaba9816 Did they fix the RPN so it acts like older models? I got an HP Prime (the original) when it came out and the RPN was a mess, I ended up buying a used HP 48GX off ebay instead.
When I was in school we had no electronic "calculators". We did have slide rules, trig tables and sq root tables. By the time I was halfway through high school calculators were just starting out. In 12th grade in 1975 I had a Texas Instruments SR-50. It was well over 100 bucks and state of the art for its time. It could do trig functions exponents, roots, natural.and base 10 logarithms and a 10 digit red LED display. Most calculators of that era had at most 8 digits .
I had a prof last semester limit our calculators to just a scientific for a vibrations and controls class. So stupid, doing math at that level it's done by software in real life and unless you do these types of calculations by hand on a daily or wkly basis, you quickly forget all the rules and steps to do em. Profs should just teach fundamentals and let ppl use technology the way ppl do in the jobs they'll be going into. I agree with how you teach, you were a great prof. Had you a 2+ yrs ago for calc 3 and DE. Keep up the good work!
The technology evolves. The prof is trying to teach the material in a way that will adapt with the technological changes. Or if the person is involved in making the tech changes...
Taking an intro to statistics my Casio fx-9750GII has been clutch. But we are also able to use StatCrunch during the exams.
A decade ago, I used an HP50g (the most capable calculator on the market at the time, before the HP Prime came out) for Calculus. My prof's rules were the same as yours.
Rules varied for other classes. For my circuit analysis classes, I had to have a cheaper TI model (a variant of the 30, if memory serves) because it had no storage or programmability, but could still solve systems of linear equations with complex numbers. Solving the linear equations by hand would have forced the professor to write tests that focused more on solving the equations than on the actual circuit analysis itself.
I still have and use the TI-83 along with the instruction book and an Open University book about using it in various STEM uses. I first got it in 1997 and it was a steep learning curve at the time.
I've found it very useful over the years.
I got my first calculator as a very expensive Christmas present in about 1975/6. Unfortunately at school we still had to use slide rules and the new calculators weren't allowed in maths classes. The first thing every boy did back then was type in the numbers that made rude words when turned upside down and they've probably been doing it every generation since.
I had poor maths teachers who would only explain things you couldn't understand a couple of times then gave up on you. If it hadn't been for calculators and the new computers back then I would have been in real trouble as they gave me a leg up and a career.
I think that your position is the best one. I personally only use a calculator if it’s for a numerical answer that would be impossible to compute by hand in a reasonable timeframe. Or if I have done a numerical method to solve something like a DE and want to check my work afterwards. Because it’s easy to make small arithmetic errors here and there when dealing with very complicated numericals. Other than that I don’t touch a calculator.
I got a TI-85 in the early 90s when I was in high school. I did not have a computer, so this WAS my computer. I learned the calculator inside and out, and as a result of my fascination with the calculator, I learned more about math. I later discovered HP calculators, and enjoy them more, but I still have my old 85 (and 86, and 89, 92, etc, etc)
I think I was the rare student who improved my math skills by having the calculator, even when only given a pencil and paper I was better that before I got the calculator.
The crazy fact about these calculators though is that they still can be used to do certain mathematical tasks even without a CAS, due to the extensive macro and programming capabilities of them. Especially the 84 Plus CE with its extended memory and easier access to computer connection. I definitely used this feature responsibly in school 😅
The popularity of the TI calculator is mostly due to the requirements of the AP exams. It's the most powerful device allowed by the rules of the tests (Calculus, Physics, Chemistry).
The UK version of that calculator is the Casio CG50.
I strongly believe that the hardcore mathematicians in the pre-electronics days could do mental math similar to what was shown in that movie.
I know the scene you're talking about. With the mental square root calculations. Back then the square root algorithm was probably taught to (advanced) students. But it's not taught to anyone anymore because we have calculators and the algorithm itself is too extreme to worry about. Gotta google it to learn it. For those who do not know, it's basically long-division on steroids. Students have a hard enough time doing simple long division, and memorizing the quadratic formula. Heh.
It would be nice some videos about using ti-84 plus!
I have that exact same calculator. 20 years old now.
The best calculator I have used is the TI-36X Pro. It is what I grab for Statics, Dynamics, Mechanics of Materials, and Circuits. You do not need to graph functions after the math classes for engineers. If you do, it was elementary, like shear-moment diagrams in statics and mechanics of materials. But I loved my TI-84 Plus CE, especially when I downloaded Pac-Man. My TI-84 was lost, unfortunately.
Also, the TI-36X Pro is around 20 US dollars. Excellent for people who have restrictions on calculator use in the class.
Best value calculator for sure...
I'd say use them for results checking etc. but with the _big_ caveat that most maths/physics exams i've taken (up to undergraduate level) _don't_ allow CAS calculators so don't get too reliant - you still need to be able to do the operations yourself in exams so it's best to get the practice beforehand.
I once gave an Algebra II test and did not allow graphing or scientific calculators. I allowed the students to use a printed 12x12 multiplication chart and a chart of perfect squares. They did just as well with these pieces of paper as they did with their expensive calculators.
My calc teachers lets us use any calculator we want for the classwork (I use the TI-92), but for tests there is no calculator section and then a calculator section, on which we are only aloud to use the non-cas nSpire calculators. I think its a fair system, it lets me cut through some of the monotony of homework yet still requires learning to occur.
I remember once, I was monitoring an exam (I think it was statistical physics) and one student did 1+1 on the calculator LOL
Ok to be fair, during exams I also double-checked super simple math... mostly because of the pressure during the exam, which might trigger some "OCD" like state where you compulsively need to double check everything, even super simple stuff, you would not use a calculator for otherwise.
That said when I was in college we could only use non-graphical calculators. So just very basic ones that can do the four basic operations, exponents, logarithms, trig fuction and not much more.
Thanks for this get discussion.
In some times, calculators are essential. To calculate faster. That is what they are basically made for. Each have times that they fit to be used; calculator computation, and brain computation.
I am old, 61. My undergrad was electrical engineering, worked until 2012, and 'retired' at 50. A year later, I am part time in a HS tutoring kids in math.
I am more than surprised that so many students haven't mastered the multiplication table, not to mention it seems to have shrunk from 12x12 to 10x10.
It seems to me that students are losing math fluency for multiple reasons, one of which may be the early introduction of calculators. Student is working on a quiz question, a gravity problem. Drop a rock from 1200 ft, how long to hit the ground? "866 seconds". I ask if she checked her work. Yes. Hmm. I ask how long 900 seconds is. 15 minutes. So just under. So you see your friend drop the rock, go to the coffee shop, order the coffee, talk to a friend, and come back before it hits the ground? She took the quiz back, and finally saw where the mistake happened.
I've seen students use their calculator for adding, as you commented on. Yesterday a student struggled to subtract, something like 15-7. I encouraged tapping her fingers to count down. She thought this was embarrassing. Why is using your own fingers more embarrassing than using a calculator for this?
We are at the point that we have a mix, some tests are no-calc, some allow it depending on the topic.
TI Graphic Calculators were really useful because they had a lot of features for university, the deal is to write and confirm the process, smartphones could have replaced the use of calculators but are more focused on CPU and Camera improvements and Google Play Apps math focused sometimes don't update too much as they want.
They allow scientific calculators because power numbers and analitcal methods are more used IRL.
Nothing wrong with using a calculator to check your answers on the test after you complete it. Especially most math test is timed and you only have a limited time to do it.
I always used HP's with RPN. Always! Ever since 1973. I still use an HP10, 41CX, and 48GX.
I have had 2 interesting math experiences where having the calculator during the exam somewhat adds to the difficulty.
The first is the ACT , a standardized test for US colleges. Unlike the SAT act does not have distinct "calculator" and "non-calculator" math sections. It's not difficult math but there's a harsh time constraint around solving 60 math MCQs in 60 minutes (you generally cannot afford to spend one minute on each question since some are harder than others ). So the expectation is that you should be able to quickly when a question is solved faster using a calculator Vs when it's solved faster using some high school math intuition.Clumsily trying to compute everything using your calculator can cost valuable time.
The other experience is IB math (the curriculum has changed quite a bit since I took it so I'm not sure how muc of this is still the same ). You have alreast 2 different equally weighted final exams , one with a graphing calculator and one without. Rather than having the calculator paper be easier than the non-calculator one , having a calculator allows them to test you on some material you wouldn't be able to solve without graphing calculator. Even there time management wise some key decisions have to be made between doing parts of long calculations by hands and other parts by calculator, while showing sufficient working to alreast get partial credit if you get the final answer wrong.
In Calculus II currently, computer science and data science majors. Our calculus sequence did not allow calculators, our statistics sequence does. (or you can use R on the test)
Calculus I really shouldn't allow calculators because it is basic Calculus concepts where as Calculus II I think could. It is so easy to screw up a sign when using higher level integration techniques that it would help to verify. Even with a CAS in the calculator, if I had to show my work, I would feel more confident in my answers. Without a calculator sometimes the solution isn't always clear so you can spend a lot of time integrating the wrong way, a calculator in the class could help and you could "prove" your answer. I dont know at this point especially in my field, I can write a function for most of the maths I'm doing, but proving it is what matters.
I've had my TI84 for 10 years and hope to give it to my kid as something sort of cool
As a 30 year teacher, I have watched students become so dependent on technology, they can't think for themselves. So, when an incorrect answer comes up (due in part by human error) they cannot see the problem. So, for example, when I told my class (as an experiment) to use their calculator to change 1/4 to a decimal, too many of them had an answer of 4.00. They didn't understand the mistake they made.
I use a PC running python3 programming language and the python3 sympy , numpy , and scipy library modules. Then for fun, I implemented some college algebra routines to better understand the calculations and computer algebra. But I studied Calculus in 1980s , for now , I do my calculations with the PC, back then on paper .
Thank you math sorcerer I used james stewart calculus book to figure out cal 1 deals only lines and curves now I jump to cal 3 and learning vectors all by reading each section
I agree with you. Enjoy your videos. Best regards.
I live in Australia.
(I find it very self-explanatory at this point 😂)
At higher math levels called Mathematical Methods and Specialist Mathematics, our Paper 2 exam (VCE; State Exams) require CAS calculators. And because you are not required to delete its history, you can download programs and use it to your full advantage. In a specialised science school in Victoria (John Monash Science School), I think they even use laptops with the CAS program downloaded in the proper exam.
So I think that the use of CAS in Australian high school mathematics is not because they want to teach us maths properly, but to weed out students who can’t use calculators quickly.
Our school kind of requires us to have TI Nspire CXII. However, for all of us this affects our basic math thinking. I remember when some students couldn’t solve things like (k^3=27/125), it seems like a problem to be solved by Calculator, but you can solve it by hand too 3/5
I saw the solution within a second. I ammnot shure, if that would be the case, if i would have used a calculator for all calculations ...
I took what was essentially calculus I and II my senior year in HS. No calculators, period. The following year in college, I took calculus I and II again. Again, no calculators, period. This was over 25 years ago. I am proud to say that to this day as I type, my math skills are still really good. I can do differential and integral calculus by hand like a hot knife through butter. In many ways, my calculus skills are better now than they were in college. So much so, I am considering taking some online courses in higher math for the first time. My secret? My calculus book (Thomas/Finney) had answer to the odd problems and during college I did them all. Sometimes twice to get really fast.
I have texas instrument 84 ce plus and casio cg50 however cg50 is way ahead, high speed, more options and more friendly with 20 equations in one screen. Simply the best.
My calculator of choice is still the HP 48G from the mid-90s. I have not found another calcular that I would want to trade it for yet. That said, most of the calculations I do now are all on PCs without much need for a classroom calcular.
Prior to this in junior high I vaguely recall having a Sharp calculator. I do not recall the model anymore, but I do remember writing a program for it to solve multi-variable linear systems. As far as the teacher was concerned the calculator did not have this functionality as I created it.
HP48GX for me. RPN changes everything. Now use the HP RPN emulators on my iPhone.
My first ever calculator was a plastic abicus my parents got me when I was a child and I never used it properly until I was 5-6, I just liked the noise. It's still in the attic I think.
The calculator I use now and have done since my Civil Engineering class' is the fx-83GT X Casio. Cost around £10 😅
I the TI 85 and the TI-89. The TI Inspire does a little to much for me. The advanced calculators are better for classes outside of the Calculus sequence.
In EE the Ti89 came in handy for matrices and could even help with Laplace transforms. The main thing to consider is the deadline. Doing a multiple page length tedious equation manipulation by hand an hour out from a deadline isn’t fun.
still got my ti-92 from 96. Works like a champ.
Retired engineer wanting to get into a graphing-calculator but want RPN since I started with an original HP-35 back then.
I’ve been considering the HP-Prime G2 but not sure if it is the way to go…
Here in the UK, Casio are probably the most familiar brand, I use the Casio fx85. I bought it in 1999 and it's still going strong. It's pretty basic in its features though.
All the engineering college courses I attended in the UK recommend a Casio calculator, I'm currently using the fx99-1EX which is a brilliant calculator, very sadly this model has now been superseded.
At my University (engineering) math course, they had the exam split in 2 parts.
One part where we were only allowed to use pen and paper, nothing else, not even notes (so not even a simply calculator).
Second part where we would use our laptops with Math Software, and all software and notes were allowed.
In this way we got tested both on our basic math skills in the first part, but also on our skills in more advanced problems using computer software.
I personally think this was a fair way of balancing it.
Sidenote: The part of the exam where we could use a laptop was "math problems on steroids", making it the hardest part of the exam.
I remember a fellow student passing out when an exam proctor took away their 'illegal' calculator.
They had to call for an emt to carry him out.
My feeling is that if you're a student in a calculus class, you're there to learn how to do calculus, not to test your arithmetic skills. It would be a shame to have a student who is very strong in understanding of calculus concepts (or statistics, linear algebra, etc) be hindered because they struggle or are slow with arithmetic, a skill which is borderline unrelated to the content of the class.
That being said, STEM students should of course be able to do basic arithmetic. I've tutored calculus students who were completely unable to do things like 1/6 + 2/9 without using a calculator, which is a result of previous teachers being arguably too lenient about the use of calculators. I think an ideal situation would be to allow calculators in general (something equivalent to a TI-84, anyway, not a CAS), but maybe have a small section of each exam where a calculator is not allowed, forcing students to keep their arithmetic skills sharp.
I had a math teacher like that for college algebra we use a ti30 x and no other calculator everything done by hand
At my engineering school all math exams are divided into 2 parts :
- first half of the exam no calculators are allowed. This ensure you know the formulas, know how to compute by hand;
- second half you NEED the calculator to solve the problems as they are a lot more complex and in-depth. They require a deep understanding of the concepts so knowing only how to compute the stuff and what to plug into the formulas is not enough. It often requires a lot of theorizing, proofs and trial and error, so it's litteraly impossible to finish on time without the calculator to test a lot of hypothesises.
For every other course such as chemistry and physics the calculator is always allowed as the math is not the point of the course.
Every student has the same calculator, the TI-Nspire CX CAS II which is amazing. Spreadsheets, programming, graphing in 2D and 3D, LUA and Python support, and just so much more useful stuff that we actually get to use in practice.
I love my calculator. It can be a useful tool for teaching more than just basic computation.