A recent item written up on the phys.org site points to a worrying trend. A researcher at the U. of Pittsburgh did a limited study on the use of calculators by undergrad engineering students. To quote the phys.org piece,
"(U. of Pitt. post doc student Samuel) King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. .....The students were given a number of mathematical questions related to sine waves....and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem. 'Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct,' said King. 'It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values.' "
Second-year engineering students who don't understand sine waves???!! Yike! I hope this finding causes a lot of soul searching among engineering educators.
As one suggestion, I'd humbly encourage engineering schools go back to the use of slide rules in engineering classes. Tedious and slow, yes, but I can't count the number of times I looked at how a calculation would trend on my sliderule and realize there was something wrong with my logic.
At least a few of the 18 people commenting on the phys.org piece seem to agree with me:
http://phys.org/news/2012-11-students-bypass-holistic-mathematics.html#nwlt