Part of the problem is the way math and science is taught as if they
were obscure theoretical subjects with little application to real life
and this is because most teachers do not understand the subjects. This
is even the case in college where the profs are great at theory but
have no understanding of how it all applies in real life. I have a
turn-of-the-century (1912) college physics text written by Millikan
(yes, that Millikan, you know, the electron charge measurement) and
it's tone is entirely different from the texts I learned from. My
texts were very strong on abstract theory and short on explaining the
real world. Millikans text is a great read explaining in detail how
steam engines work and the detailed thermodynamics behind them. He
explains EM waves and even explains how the spark-gap radio
transmitters of the time worked in great detail.
Today, Math and Physics are taught as if they are entirely theory
neglecting everyday real world problems. How many people have ever
gone around looking at their home appliances looking at the power
rating and figuring out how much it costs to run each one. This
excercise teaches the relation between power and energy and some
practical economics. How many kids have ever figured out how many
calories they burn by running up some stairs? Why doesnt this compare
correctly to the caloric content of food (one of the calorie units is
1000x the other is why).
Last year, I took my 15 yr old son on a long sailing trip during the
school year and had him plotting position, figuring out how leeway
would change our DR position, and doing coastal navigation. These real
world examples give a "feel" for trig relationships that you cannot get
just from books.
A person who know science, math and engineering can read a
psuedo-techie article in the paper and realize when the writer is full
of crap.