To have a strong understanding of fundamentals is in some ways becoming independent — independent of guides and hefty notes and calculators, to a degree. I can read over my Linear Algebra textbook ad nauseam, but that doesn’t mean I truly understand the material within the book. If I can’t clearly explain to someone what matrices can represent and how matrix operations cause the matrices to interact, it’s very unlikely that I’ll be able to understand where they apply to the greater engineering problem I’m trying to solve.
Sure, I can just type my matrices into a calculator and hit “multiply,” but if I don’t understand what that represents in the real world then that’s not all that useful.
If we talk about a more simple math like algebra, of course we can have calculators solve most of our math problems. Great for a test, where I could probably earn a perfect score relying solely on my calculator to do “plug-and-chug” problems. However, that does not mean I understand the concepts driving the calculation. I’ve seen plenty of kids try to get through math class just by pure reliance on the calculator; I tutored middle school children in math. They always, always, always tried to jump right to the calculator before really thinking about the problem at hand, even for something so simple as finding the area of a shape.
For that reason I disagree that “An average engineer with a calculator will always be ‘stronger’ than an expert without one.” An expert engineer will understand the concepts driving the problem enough to at least estimate the outcome of a calculation — sure he won’t be able to obtain those ten decimal places like the average engineer with a calculator would, but if he should use the wrong concepts in his calculations then those ten decimal places are useless.
But once again, I will say I agree with you to some extent. “Handicapping” students for an entire exam is silly, since real world calculations demand precision; most students can’t mentally calculate an equation’s result when the equation includes pi (3.14159…) or e (2.71828…) because it’s simply not possible — even calculators “estimate” those calculations.
I think that the AP Physics B exam (now the AP Physics 1 and 2 exams — not sure how much these differ from Physics B, the one I have experience with) is a good example of how to possibly approach a compromise between “handicap” and testing concepts. The first portion of the exam is entirely multiple choice, and is no calculator. This seems threatening at first, but the numbers are usually easy to work with for students who have truly mastered the concepts presented in class. The exam even goes so far as to demand you use a value of 10 m/s² for Earth’s gravity instead of 9.81 m/s² for the sake of easing calculations.
The second half of the exam introduces problems that more closely approximate real world situations (as much as an AP exam can anyway — there are a lot of simplifications in introductory physics) and allow you to use a calculator due to the presence of lengthy numbers. However, even with the calculator, a test taker cannot expect to score well if he or she doesn’t know the science concepts and how the math applies.
In regards to your statement that the SAT should suggest what schools would teach, I feel that it’s a sort of “chicken and egg” situation — which changes first? I don’t know if the SAT has the power to reform an entire education system, given that the changes put in place are following the current system’s demands.
So to conclude, I do agree the SAT still needs some work. The entire education system from pre-school to undergraduate school still needs some work. Other characteristics and skills should definitely be brought into play, and it certainly isn’t fair that everyone’s intellectual worth is determined by how well they can crunch numbers. But that certainly does not mean that the ability to work without a calculator is worthless, rather I’d still argue its priceless.