I also find this a sensitive subject. I always thought that the learning process was held up by the need to constantly reinforce things I learned a long time a

I also find this a sensitive subject. I always thought that the learning process was held up by the need to constantly reinforce things I learned a long time ago. For example, electrical circuits classes at Purdue do not allow you to use calculators and must therefore make numbers that work out nicely to keep the math manageable. However, this means that your problems are not particularly realistic; 4.7 uF capacitors, 33 mH inductors, and 2.2 kohm resistors are far more common than 1/2 F, 1 H, and 1 ohm resistors. When I taught senior design, I was stunned to find students looking for super-huge capacitors, but that's all they had seen on their exams up until that point. Likewise, complicated FET sizing problems may require a complex system of equations. Students are short-changed by having to design circuits with only one or two unknowns so the math can be done by hand. On the other hand, mathematics courses are supposed to teach you how to solve these problems by hand. A TI-89 or Mathematica renders my first three semesters of calculus useless. However, those skills are necessary for understanding probability, electromagnetics, and all sorts of advanced material. Calculators with symbolic manipulation cannot possibly be allowed in those classes. Otherwise, students will have superficial understanding of all the dependent courses. IMHO, the only answer to this question is "it depends." We can explore much deeper levels of mathematics, science, and engineering if students aren't burdened with basic arithmetic, but we must ensure that students are only able to take shortcuts after they have demonstrated mastery of the material using manual computation.