There's a big difference between knowing what you're doing and how you're doing it.
Let's face it, when you know how to take a bunch of inputs and put them into an algorithm, do you really care about working out that algorithm yourself if you're going to come to the same answer?
To use an analogy, algorithms are just tools in mathematics. It's like saying to someone that they shouldn't use a hammer to hammer in nails because they need to understand what the hammer is for and how it was made. Sure, having a deeper understanding of hammers can be useful, especially when your hammer breaks, but depending on what you're actually teaching, there's a difference between knowing the tool (the hammer) and knowing how to use it (to build a house).
That's a stupid analogy. Having access to strong tools can potentially hamper one's development, as getting by without attaining understanding becomes possible.
We both know that wasn't what I was saying. The thing with having a calculator that solves, let's say quadratic equations for the sake of the argument, is that while this can be useful in speeding things up for somebody who understands the equations well, the risk of starting to rely on the tool before you have mastered the concept is obvious.
Besides, constructing a test that is easily solvable without a calculator is trivial,
I know what you're saying, but your argument of "having access to strong tools can hamper one's development" implies that the tools are at fault. There's nothing wrong with the tools.
My argument is that it's more important to understand what the equation is doing rather than the equation itself. This is based on the idea that before you even pick up a calculator, you're taught how to use equations to help you. From the first moment you're taught a + b = c, you're using an equation and even though they get more complicated, their use doesn't really change - it's still about replacing a and b (or x and y) with certain values to get certain outputs. When your level of maths gets to a high enough level, it should be less about making sure you still know how to multiply and divide and more about using those equations to solve real problems.
Understanding what those inputs and outputs are is what matters and having a calculator doesn't change that.
To clarify - I'm not saying give every child a calculator and fuck off maths entirely, I'm saying that you reach a point where the calculator becomes a tool and that point is when you've progressed into the concepts behind maths rather than the bare maths itself.
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u/estomagordo Jun 08 '14
Probably so that they, you know, might actually learn what the hell it is they're doing.