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Cheat-sheets are also far more "real world" than the fake environment many schools cling to. I don't know a single practicing engineer that doesn't have a note

Cheat-sheets are also far more "real world" than the fake environment many schools cling to. I don't know a single practicing engineer that doesn't have a note scribbled somewhere. My engineering school recognized this decades ago and adjusted accordingly. 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.

whatshisface 7y ago
>Now the math department? They were a different story. No calculators. Period. Ever. Made higher-level calculus... interesting. 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.
- spookthesunset 7y ago
  Yup. One clue you were going off course on a test in a high level math class was when all your numbers were getting rather crazy and unwieldy... Usually the same rule applied in physics exams too...
  - blattimwind 7y ago
    Except some professors / PhDs deliberately set up exercise in a way that they involve large-ish (3-5 digits) or stupidly large (9+ digits) numbers to turn otherwise trivial exercises mostly into a mental math test. (Another all-time favourite of mine was the guy who always included an exercise in his exams that required you to determine the non-trivial prime factorization of a four digit number). 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.
  - dagw 7y ago
    One clue you were going off course on a test in a high level math class was when all your numbers were getting rather crazy and unwieldy... 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.
jimktrains2 7y ago
I don't remember a math course I college anything but a ti89 or one of the other few capable of handling symbolic expressions would have even remotely helped with. The arithmetic was usually small or just non-existent.
jacobolus 7y ago
> Now the math department? They were a different story. No calculators. Period. Ever. Made higher-level calculus... interesting. 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.
- toomanybeersies 7y ago
  The odd thing about my exams at high school (in New Zealand) is that although you were allowed to use a graphing calculator, you still had to show your working. So you'd plug the numbers into your trusty Casio graphing calculator, get the answer, then still have to work out the answer anyway. 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.
- madengr 7y ago
  Couldn’t agree more. Though this was 1990, the professor for the calc classes could care less if you had a calculator, as it “won’t be of any use”. 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.
toomanybeersies 7y ago
I only did 100-level mathematics at university (except for discrete mathematics), but for all my tests and exams, the lecturer made sure that all the problems could be solved (or reduced) without a calculator. 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.

whatshisface 7y ago

>Now the math department? They were a different story. No calculators. Period. Ever. Made higher-level calculus... interesting. 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.

spookthesunset 7y ago
Yup. One clue you were going off course on a test in a high level math class was when all your numbers were getting rather crazy and unwieldy... Usually the same rule applied in physics exams too...
- blattimwind 7y ago
  Except some professors / PhDs deliberately set up exercise in a way that they involve large-ish (3-5 digits) or stupidly large (9+ digits) numbers to turn otherwise trivial exercises mostly into a mental math test. (Another all-time favourite of mine was the guy who always included an exercise in his exams that required you to determine the non-trivial prime factorization of a four digit number). 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.
- dagw 7y ago
  One clue you were going off course on a test in a high level math class was when all your numbers were getting rather crazy and unwieldy... 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.

jimktrains2 7y ago

I don't remember a math course I college anything but a ti89 or one of the other few capable of handling symbolic expressions would have even remotely helped with. The arithmetic was usually small or just non-existent.

jacobolus 7y ago

> Now the math department? They were a different story. No calculators. Period. Ever. Made higher-level calculus... interesting. 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.

toomanybeersies 7y ago
The odd thing about my exams at high school (in New Zealand) is that although you were allowed to use a graphing calculator, you still had to show your working. So you'd plug the numbers into your trusty Casio graphing calculator, get the answer, then still have to work out the answer anyway. 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.
madengr 7y ago
Couldn’t agree more. Though this was 1990, the professor for the calc classes could care less if you had a calculator, as it “won’t be of any use”. 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.

toomanybeersies 7y ago

I only did 100-level mathematics at university (except for discrete mathematics), but for all my tests and exams, the lecturer made sure that all the problems could be solved (or reduced) without a calculator. 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.