I was educated in the U.K. so a lot of this is quite alien to me. I never had to use a graphing calculator and indeed never owned one. I used a scientific calculator (perhaps $20-30) for (high) school and for some exams but university entrance exams and all my exams at university proscribed calculators of any kind. (I used gnu Calc in emacs for some number theory homework but I don’t think this was beneficial to my education).
I’m curious as to people’s opinions of the usefulness of graphing calculators. I feel like most of what they produce is a sketch and it’s typically more useful to learn how to sketch a function than to learn how to ask a calculator to sketch it. I think the hardest function I had to sketch in high school was exp(-1/x^2) and that was in a university interview rather than in school itself (and I feel like the reason for the choice was partly for the follow up of asking for the McLaurin series).
Was I missing out on some fundamental understanding that one gets from using a graphing calculator? Perhaps I didn’t miss out because I was just about able to plot arbitraryish functions using a computer anyway. Perhaps I was ok but other students would have benefitted from a full graphing calculator (perhaps benefitting from a graphing calculator is something more common amongst hn readers than the general public/high-school maths students).
In my university it felt like the common opinion was that calculators harm one’s understanding of mathematics and that exams ought to forbid them. I intuitively want to agree with this. A graphing calculator wouldn’t be very useful in the courses I studied at university but those courses were, I think, hardly representative of what matters in the real world. But asking for data also feels like an easy way to ignore good arguments.
Even if graphing calculators are very useful, it nevertheless feels deeply unfair to me that they are so expensive. One might ask what the solution is. More general and ubiquitous smartphones seem too general and capable to be allowed. It feels to me like graphing calculators ought to not be necessary but maybe this is coming from my own biased position. Perhaps another solution would be having more competition in the market. HP (at least in the past) produced high quality scientific and graphing calculators and I think I would prefer an HP48 to a TI83 but it seems like they failed. Were their volumes too small? Or their margins unsustainable? Or were they removed from the set of exam-allowed graphing calculators by TI lobbying? Or did people just not like RPN? I think the question of why manufactures other than HP didn’t really produce graphing calculators is easier: TI sold most of the calculator chips and they were able to sell a calculator for less than they sold the chip to their competitors for. Maybe exam standards mean there is no longer innovation in the pocket calculator market and therefore there is much less incentive for competition or price decreases amongst the incumbent manufacturers.
I’m curious as to people’s opinions of the usefulness of graphing calculators. I feel like most of what they produce is a sketch and it’s typically more useful to learn how to sketch a function than to learn how to ask a calculator to sketch it. I think the hardest function I had to sketch in high school was exp(-1/x^2) and that was in a university interview rather than in school itself (and I feel like the reason for the choice was partly for the follow up of asking for the McLaurin series).
Was I missing out on some fundamental understanding that one gets from using a graphing calculator? Perhaps I didn’t miss out because I was just about able to plot arbitraryish functions using a computer anyway. Perhaps I was ok but other students would have benefitted from a full graphing calculator (perhaps benefitting from a graphing calculator is something more common amongst hn readers than the general public/high-school maths students).
In my university it felt like the common opinion was that calculators harm one’s understanding of mathematics and that exams ought to forbid them. I intuitively want to agree with this. A graphing calculator wouldn’t be very useful in the courses I studied at university but those courses were, I think, hardly representative of what matters in the real world. But asking for data also feels like an easy way to ignore good arguments.
Even if graphing calculators are very useful, it nevertheless feels deeply unfair to me that they are so expensive. One might ask what the solution is. More general and ubiquitous smartphones seem too general and capable to be allowed. It feels to me like graphing calculators ought to not be necessary but maybe this is coming from my own biased position. Perhaps another solution would be having more competition in the market. HP (at least in the past) produced high quality scientific and graphing calculators and I think I would prefer an HP48 to a TI83 but it seems like they failed. Were their volumes too small? Or their margins unsustainable? Or were they removed from the set of exam-allowed graphing calculators by TI lobbying? Or did people just not like RPN? I think the question of why manufactures other than HP didn’t really produce graphing calculators is easier: TI sold most of the calculator chips and they were able to sell a calculator for less than they sold the chip to their competitors for. Maybe exam standards mean there is no longer innovation in the pocket calculator market and therefore there is much less incentive for competition or price decreases amongst the incumbent manufacturers.