[eric_h]

A friend of mine who does math tutoring for high school seniors and college freshman told me that many of her students who did well on their AP Calculus exams did not actually understand what a derivative/integral was. They could procedurally find the derivative/integral for a given function, but they didn't know what it meant.

Admittedly, this is anecdotal, but it does seem to support the argument/rant in the article.

I feel that I, personally, was very lucky in my high school mathematical education in that my teachers exposed us to the concepts/meanings of all of the operations we were doing long before they exposed us to the procedural trivia of finding integrals/derivatives and the like. It is unfortunate that not all schools are like this.

[tunap]

Just another anecdote... when I passed Calc 225 my 1st semester my counselor informed me my math prerequisites were fulfilled(counting college prep in HS). She did not encourage me to consider pursuing further, just that I didn't need to take any more and focus on "business". Working PT/3rd shift & taking 19+ credits a semester I figured my path was paved in business so I took her advice...Until 2nd year, taking motherload of hard classes, I was informed she was incorrect & I had to take probability. I missed first the first week of class, assuming cakewalk, and never caught up. The dominoes fell from there, my GPA suffered & after 2 years of midnight merchandising I realized I did NOT want to work sales or anything remotely retail. After grad, I washed out of corp sales job & Merrill job in under 8 months. Went back to construction and the picture hasn't been especially rosy ever since. Cest la vie.

TLDR: Take the maths for the sake of knowledge, even if you don't 'have to'. It can't hurt.

[mtourne]

I recently read the book Calculus Made Easy. The way it teaches the material is very intuitive and if you understand the premises you should be able to re-derive all of the formulas yourself. I would highly recommend it to high school students and teachers alike.

I remember being taught about derivatives with the formal limit formula, then all the tricks for finding them (power rule etc), and finally finding function extrema using derivatives; all before developing much intuition about the concept.