Will it rot my students' brains if they use Mathematica?

This is a sensitive subject for me. I was in a Linear Algebra class where I was asked on an exam to do, among lots of other things, a (nonzero) determinant of a 6x6 matrix by hand. I got no credit for making an arithmetic mistake.<p>I'm a CS major. I will never in my life (outside of school) be asked to solve a difficult math problem without having a ridiculously overpowered tool like Mathematica in front of me.<p>I'm all for teaching hard math to students. But we need to be teaching them how to do things their calculator can't (or better yet) teaching them how to build the calculator. Not teaching them how to add 600 numbers by hand.

Using a programming language is perfectly reasonable. The thing I have a problem with is the scam of graphing calculators in high school calculus classes: basically in the interest of guaranteeing a revenue stream for Texas Instruments, curriculum has been filled with obtuse impossible-to-symbolically-reason-about equations, which have little relevance to any of the important concepts being taught. Only a trivially small percentage of the students will ever be placed in a situation where they need to regularly use that graphing calculator or similar tools in the future (basically just engineers). The Soviet high-school-age math curriculum of a few decades ago is in my opinion (and admittedly quite limited personal experience) vastly superior to what we do in the US. Much better to aim for understanding of underlying mechanisms, and make people do real proofs (and not the bullshit proofs of “geometry” courses), instead of just punching (effectively) arithmetic into calculators.<p>I think banning calculators from all elementary/secondary math education would be a tremendous benefit because (a) it would improve familiarity with basic number relationships, and (b) it would force problem authors to keep the numbers reasonable, and push problems toward higher levels of abstraction, rather than simply tacking on extra digits after the decimal point. Most importantly, anyone who understands the mathematical structures and relationships involved can learn how to compute with a calculator or similar tool in about a week. Someone who only knows how to punch things into a calculator but doesn’t have a solid grasp of what it means is in a very tough spot as soon as anything slightly out-of-the-ordinary pops up.

This reminds me of a story from all the way back in high school algebra. I had just got a ti-83 calculator that year and was having fun writing basic programs for it. One of the class topics towards the end of the semester was the normal distribution and we were expected to memorize the percentages up to 3 standard deviations. I hated having to remember fixed quantities, so I wrote a program to calculate what I later learned were Riemann sums on the equation for the normal distribution I saw tucked away in the textbook.<p>I wrote a lot of programs like that one throughout high school and into college, and for me it was far more educational to solve a problem once and for through automation than to memorize constants, formulas, or to solve particular instances over and over.

If it helps with exploring concepts without distracting from what the course is trying to teach, sure. But I think high school math is generally too basic to warrant using Mathematica as anything but a plotting tool. Doing math problems by hand slows you down and gives you more space to think about the problem in your head, versus having a computer simulate a bunch of outcomes for you.<p>Every college STEM major, however, should know how to use it. It is an incredibly powerful tool.

"Life is not 'easy to use'" such a great statement, in reference to software that panders to the impatience of most consumers, and their desire for constant stimulation. It reminded me of the programs I use which were _not_ initially easy: Emacs, gnuplot and LaTeX, but after investing some time to learn them, I realized that they're some of the most productive and well designed programs I've ever used. Great article, or dialogue rather.