You can easily store notes on a TI calculator. I had a TI-85 in college, and was occasionally guilty of writing TI-BASIC programs to make tests easier (for example, I had one which computed Euler's method).
I also wrote a basic stock portfolio manager - this was the only chance I had to program during my 5 years there.
Of course, you could always use a paper one-time pad, and if you can get the pad distributed without interception, there's no way they can ever break that.
Trashy is sort of a slur on the poor. Not trying to call you out or anything, maybe there's a better word that trashy aka saying a person is like trash.
https://duckduckgo.com/?q=expensive+designer+fashion+runway&...
https://file.wikileaks.org/file/anakata/13.1_GSW_09042013_AP...
You're thinking in the wrong direction—testing companies don't really care if you can access notes that you wrote, they don't want you to be able to quickly type up new notes as you take the test. Specifically, they don't want you to be able to copy down the test questions, because they charge money to get old test questions. They don't want the test itself to get out.
Maybe kids have gotten better at it since I was in school, but text entry on the TI-8x was a laborious process, and calculators with qwerty keyboards (like the TI-92) were quickly banned.
To this day I don't consider myself to have understood something until I can code it.
One time before a calc test I dropped my graphing calculator. The battery door popped off and the batteries popped out. The unit was otherwise unharmed... but my cheat sheet in the notes app was gone!
I nearly crapped my pants.
Luckily though... as most cheaters know... to make a decent cheat sheet you actually have to comprehend the material first. Half the time you wind up not even using your cheat sheet. Luckily for me that was the case. I still did well on the test.
There was definitely something about miniaturizing notes that reinforced learning
Worked a charm. Next time, noone had bothered to hide notes as they didn't want to spend time helping some random sod out.
Solidarity is dead.
(You could, of course, try to counter this by having the entire class install the same cheat - but that would be unlikely to succeed...)
Of course, I’d probably not be in as much trouble as whatever poor sod got stuck with my HP.
Problem solved. Except if you happened to prefer RPN; I had a HP-48 which I had bought prior to the edict naming The One True Calculator - the day I enrolled at university, I started using it again, only to be met with a similar edict in my second term, naming the Ti-89 the only kosher graphing calculator.
Since I graduated, the HP-48 has been in daily use.
Oddly enough in a computer science class we had an old professor. He accused me of cheating. He was right. However, he physically inspected my calculator like under the cover and where batteries are lol but did not check the programs. He apologized. I did well on the test.
The attention to detail really got to me however over time - the normal reset message was in lower case, but all the custom programs could print was in UPPER case. I was always "its sooo obvious - they'll find me out", when I saw RESET, but nobody ever clocked.
I never did use these notes or solvers in an exam - once I knew I had them, I would remember them anyway.
The funny thing is to an extent, the performance of the student seems to be inversely proportional to the density of the cheat-sheet.
The worse thing you can request of a professor is to make it an "open book" test. Those tests are always damm hard.
Now the math department? They were a different story. No calculators. Period. Ever. Made higher-level calculus... interesting. Thankfully I'd already had it in high school in a tools-based curriculum, so repeating it with just fundamentals was less of a headache than it might've been.
And I agree - the simpler the cheat sheet the better of an understanding of the subject the pupil is likely to have.
When I took calculus the professor made sure that every arithmetic problem could be solved quickly. The trick he used was to carefully track factors when setting up the problem, so that the numbers never got very big, and also so that things had a way of cancelling (I can't tell you how many problems had one or zero as an answer.) Calculators weren't necessary and in fact would have been slower.
Usually the same rule applied in physics exams too...
Good exam questions can be approached in multiple ways and are not a mental math test.
Bad math exam questions are usually those that can only be solved using one specific technique or lemma (ideally one that was only mentioned in passing once or twice) or require a lot of error-prone calculation.
We had one professor who was rather infamous for being really sloppy when writing exam questions. On more than one occasion did he accidentally transpose a couple of numbers in a problem, turning an equation that should have easily reduced to a trivial linear problem into a 4th degree polynomial with complex roots.
There is no reason for any math course at any level to ever need a calculator, period.
The point of math courses is learning to think, not learning to avoid fat-fingering tiny buttons or learning the specific crappy interface of some anachronistic antique machine.
Without an electronic calculator students can’t be expected to do as much mindless number crunching, so instead the problems can be made much more interesting, unique, and conceptually challenging.
Frankly the same goes for science courses. If people need to process data resulting from physical experiments they should use a machine with a full-sized keyboard and a real programming language. If you want something portable a slide rule is entirely sufficient for anything that might come up in high school or intro undergrad level science courses. The students might even learn something about significant figures.
I could plausibly believe that upper-division engineering courses benefit from handheld calculators – I have no experience with those – but foisting $100 calculators on every high school student is a tremendous scam.
In theory that means that you could use your graphing calculator to verify your answer. But in practice, people ended up spending too long trying to fiddle with their calculator, not knowing how to use it properly, and getting the wrong answer in their calculator but the right answer when they did it by hand, getting flustered that they didn't match, and crossing out their correct answer.
Even in engineering and physics courses, you had better show all your work. If a numerical calculation was made in error, and you should all your work, you could still get a good amount of partial credit.
30 years later, I still just use a basic RPN calculator.
Try doing matrix multiplications for hidden markov chains without a calculator. I dare ya.
Making students do nontrivial matrix calculations on a timed in-class exam just tests their calculator skills. There are a wide variety of alternative types of problems which will better probe their understanding of the course.
If your students are trying to learn about numerical linear algebra, consider getting them implementing the relevant algorithms in computer code.
> consider getting them implementing the relevant algorithms in computer code.
Cool, so we went from a statistics exam with no programming experience required, to a programming language exam with a theme of statistics. Because what? Because calculators are bad mmkay?
Yeah I'm not sure this idea has been thought through.
Seems to me like the concern is “what someone decided should be in the curriculum 30 years ago and nobody ever bothered to change even though it is now an anachronism”.
But anyway, I am suggesting writing programs could potentially be part of the homework, not part of exams. (At least, writing computer models was far more useful for learning about statistics than any textbook problem I ever did. YMMV.)
On timed in-class exams, there are many relevant pen and paper exercises that could be posed. Posing problems requiring a handheld calculator is a generally poor way to track whether students understand the content of a course. Then again, personally I think timed in-class exams are terrible. YMMV; some teachers seem to love them.
But numbers are a big part of some mathematics too. And getting some help with them can be useful.
Lots of our past mathematical geniuses were great at calculating by hand. And some of them even invented some mechanical calculators (or electronic ones, too).
Numerical methods courses need calculators for questions about practice rather than theory. Basic (non-graphing) cheap ones are usually sufficient, though.
I think slide rules are thoroughly obsolete in almost every context. There's no point in wasting students' time when better tools are available.
The point of learning a slide rule is not that it is a particularly important practical tool, but that understanding how it works has independent pedagogical value.
If someone built their own electronic calculator from discrete components, programmed one on an FPGA, or even implemented a bunch of mathematical functions on an existing computer, that would be similarly educational (though teaching different things than the slide rule), but just knowing how to navigate the interface of an electronic calculator doesn’t teach anything.
The point of using a calculator is to skip over the tedious unimportant details when learning other things e.g. Newton's method or Euler's method. The calculator itself is a tool, not an educational destination.
Learning a slide rule as you say makes sense in a history of maths course, and implementing one's own calculator makes sense in an electronics or computer science course.
There’s really not much pedagogical value in using a handheld calculator to apply Newton’s method to some root-finding problem or apply Euler’s method (forward differences) to model a differential equation. Both of these are very simple and students can learn enough of some simple programming language to implement them both in a very short amount of time. That time is much better spent than doing 4 or 5 examples of each with a handheld calculator. If a general-purpose programming language seems too much, get them implementing these simple tools in desmos or geogebra.
On a timed in-class exam in an introductory calculus course, there are much better ways of judging someone’s understanding than making them perform a bunch of tedious and error-prone number crunching. (For example you could give the students rulers and printed graphs of a function – without any symbolic expression written down – and ask them to sketch approximately what a solution using Newton’s method would look like).
If you want a nice introductory calculus book organized along more computer-focused and conceptual lines, take a look at http://www.math.smith.edu/~callahan/intromine.html
In a post-introductory-calculus “numerical analysis” course, the exams should consist of writing proofs, not performing algorithms.
The important thing for numerical analysts about different root-finding methods (etc.) is their convergence speed, numerical stability, computational complexity, and so on. In the 1960s and before it might have made sense to get students performing the role of human computer, but nowadays it is anachronistic.
> Learning a slide rule as you say makes sense in a history of maths course
No, learning how to use a slide rule makes sense in an algebra course for ~15-year-old secondary math students who are learning about logarithms, and for 15–17-year-old secondary science students. They’ll end up with a better intuitive understanding of logarithms and significant digits and error bounds after regularly using a slide rule for even a few weeks than any amount of reading about it or doing formal algebraic manipulation.
Electronic calculators give students a very misleading impression that all of the digits printed on its display are meaningful. But in high school chemistry, physics, etc. courses there is pretty much no experiment ever done with better than about 2 digits of precision.
As long as you showed the working and the closest you could get without a calculator you'd get full marks (e.g. you could leave the answer as a fraction like 543/42, or as a power like 26^12).
They were quite good at my university for mathematics exams though. You were usually allowed a handwritten cheat sheet in the exam, and if you couldn't get the answer to a question that had follow-on questions they'd still give you marks for the follow-on question if you just made up an answer for the earlier question. If only the lectures weren't usually at 8 AM I might have gotten good grades.
This brings back the memory of the circuit theory exam. You could bring a cheatsheet but it was mostly useless. The test had very simple numbers (1, -1, 2, 1/2, -i or things like that) because the professor didn't want to be bothered checking complex formulas and the difficulty was mostly in keeping all of the subject in your head and applying all of the procedures without messing up the signs.
Needless to say, that exam by that professor had a reasonable passing rate and there was prettu much no way around it: you had to study.
They were by far the hardest tests I took in college.
I think it is standardized tests where the "clear your memory" would come up, but again, it was never done. I also don't think they asked any questions where the programs would have been an advantage, either. (The thing that's stuck most in my mind is the quadratic formula. The SAT could ask you "find the roots of this equation", but you don't need to know the quadratic formula to do that... the test is multiple choice so you can just multiply their answers and pick the one that matches the question. For that reason, I don't think they ask that kind of question, but I could be wrong. It has been a while.)
That said, I don't recall my teachers ever getting too fussy about having us clear our memory; in fact, iirc one of them actually told us to write programs to handle some of the nastier formulas.
Anyway, in my opinion, a good mathematics course should focus less on regurgitation of formulas, and more on problems solving---recognizing which theorems or strategies might apply to a problem and applying them to come up with a result.
If the rules say 'no computer assistance', and you break those rules in a way the test monitors didn't expect, the only people you are cheating are other students.
I think the bigger "loophole" is the ability to quickly solve simultaneous and and quadratic equations very easily using built-in functions on the calculators. This saves real time on tests like the SAT, because all you have to do is reorganize the equation to be in the right order, then tap in the coefficients to get the answer.
Get off my lawn.
Anyway I used an HP48GX throughout high school (carrying a TI83 only if absolutely necessary). The HP had a pretty much universal following in France.
Really depends on the goal of the course. I agree a lot of courses I took focused too much on memorizing equations, but if you haven't committed something to memory, odds are you won't recognize new problems it can be used to solve. So, yea, 99% of everything you memorize will be worthless, but the problem is predicting which 1% will be useful in the future.
I’ve never seen a professor that knew about archived programs.
The professor still got me, I wound up memorizing it because the effort it to write and debug the program.
Casio FX-82/Sharp EL-W531/Texas TI-30. These go for ~20$.
Fancier ones like the TI-84 etc were only allowed during lectures, where you can already use your phone or whatever.
I think the market is under change for sure. Apart from less distractions and more native interface, there's no edge in having a TI-84+ anymore.
This also would align with driving costs down since schools will not want to pay $100 per calculator for their student body.
Lol, I don't think I've seen that argument made before. They already pay near college prices for the text books.
1. Ability to identify the right methodology;
2. Memorisation of all steps of that methodology;
3. Ability to execute the methodology correctly;
Parts 1 and 3 are important to demonstrate learning, whereas in the real world 2 is not. Denying books and notes only penalises children who have difficulty with 2, which is stupid.
Oh well, maybe someone will write a magnus opus EM book using differential forms to rival Jackson's book, and the next generation of students can learn it.