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The American elementary and high school education system would do young students a huge favour by abandoning the use of electronic calculators. I have no doubt
by n00b101 10y ago
The American elementary and high school education system would do young students a huge favour by abandoning the use of electronic calculators. I have no doubt that the abacus is a superb pedagogical tool but simple pencil and paper calculation would be a huge improvement over the calculator culture in early mathematical education.
I majored in Applied Mathematics in university and did not use a calculator in a single class or exam - it was explicitly forbidden to use them.
But I was also educated in the American elementary and high school curriculum. I am thoroughly convinced that the use of calculators in the American system does a huge disservice to students. The calculator culture begins at an astonishingly young age, in elementary school, when kids are first introduced to the Texas Instruments TI-108 calculator [1]. This bright blue and red, solar-powered gadget is very exciting for children in a classroom, but it is poison. At the very age that students should be drilling mental math, they are instead given this huge crutch. It's like never taking the training wheels off a child's bicycle, robbing them of the opportunity to actually learn to ride a bicycle.
The same story is repeated in middle school (with the same TI-108). And then you reach high school. You would think that at least now the the training wheels would come off. But instead, you are "upgraded" from bicycle with training wheels to an adult-sized tricycle. I am, of course, speaking of the Texas Instruments "graphing calculator" [2]. This abomination is a full-fledged programmable computer with CAS software. You are encouraged (even required) to use this machine all the way through Advanced Placement Calculus. If you are not distracted in class playing video games on your "graphing calculator," then you may use it to automatically solve algebraic and trigonometric equations and evaluate derivatives and integrals. Why bother memorizing identities when you can just program them into a computer? If you have been programming from an early age, then you may be in the worst place possible because you are predisposed to wasting your time trying to program your way out of math homework instead of focusing on learning math. When students complain about why they have to learn Calculus, your American math teachers tell you that nobody "in the real world" actually solves integrals by hand and it's all done on computers, but you have to learn it anyway for obscure pedagogical reasons. An aspiring future Comp Sci student is likely to take this as a clear signal that it's all a waste of time, and soon high school will be over and you'll never need to worry about this antiquated Calculus thing again - your computer will do it all for you.
There are other ways in which American mathematics education is extremely flawed, but the calculator culture is the worst offence by far. I suspect that the bureaucrats who decide on such things rationalize this by calibrating the curriculum to what they see as the "lowest common denominator" student who will never need to learn anything beyond basic algebra and arithmetic. The goal of the system is to train this student to be a productive, low-wage worker, with just enough mathematical training to be able to mindlessly punch numbers into a cash register or simple spreadsheet on the rare occasion that the need for numerical computation may arise in their "careers."
I have a three year old and I have no idea what I could do to save him from this insane system, short of moving to a different continent.
[1] https://en.wikipedia.org/wiki/TI-108 https://en.wikipedia.org/wiki/TI-108
[2] https://en.wikipedia.org/wiki/Comparison_of_Texas_Instruments_graphing_calculators https://en.wikipedia.org/wiki/Comparison_of_Texas_Instrument...
- partycoder 10y agoIn addition, the choice of algorithms in use for arithmetics are a bit counterproductive. Then, notation in some cases is inconsistent and weird. https://www.youtube.com/watch?v=sULa9Lc4pck https://www.youtube.com/watch?v=sULa9Lc4pck
- zeveb 10y agoI think there's a lot to be said for the abacus, jettons, slide rules and other pre-electronic mathematical aids, as well as simple pen-and-paper calculation. Those mathematical aids tend to help one see how numbers and functions move and change over a space so that one develops an intuition for a range of problems, rather than just get an answer to a specific question.
- jlos 10y agoCalculators are tools and just need to be used in an appropriate context. Engineering programs in Canada allow no calculators for math classes (Calculus, Linear Algebra, etc) but they are an absolute necessity for for Engineering classes (e.g. dynamics). It's a very nice balance because the math classes hone your abilities to think and reason mathematically unaided by the engineering classes hone your ability to apply those skills without getting bogged down in details about calculations.
- n00b101 10y agoI don't disagree that computers/electronic calculators are appropriate tools for engineering, science and business classes, even at the secondary or primary school levels. Those are contexts where numerical computation with "messy" numbers are necessary. Insisting on manual calculation in such a context would be tedious and of no pedagogical value. I was only talking about math classes, where exam questions can be made up with "clean" numbers so that there is never any need for using a calculator. Although, given that we are in 2017, I really don't think that the traditional pocket calculator is a good tool in any educational context. In any context where using a pocket calculator makes sense, a full-fledged computer makes much more sense (except perhaps elementary school science classes). If you are numerically solving equations in an engineering class (e.g. dynamics), then you should really be using something like MATLAB or Python (or Julia!). Similarly, if you are analyzing a financial statement in an accounting class, it would make far more sense to use a spreadsheet rather than an HP 12C calculator. Using a computer would be much more convenient and have far greater pedagogical value for "real-world" training in such contexts. I think the only reason that pocket calculators are prevalent in higher education contexts (such as your dynamics course) is that it is more difficult to cheat on an exam using a calculator (e.g. smuggling in notes) than it is with a full-fledged computer. But that is really a computer security issue and there ways to solve that problem which don't involve a throwback to antiquated, 1960s desktop computing technology.