As someone who taught math and physics for about 20 years, I've given this some thought, and I'm convinced that the whole idea of what and how we teach these in high school is upwhacked. One of the common complaints from kids, "what is this good for". And you, know, they are right. I've had careers as a school teacher, expedition leader, photographer, house renovator, and tree farmer. I have used 2 equations, 2 unknowns twice. I've determined a few cliff heights by dropping rocks, used eyeballed centre of mass felling trees. But overall, the high school curriculum is not well used by people in their every day life. What would I teach? Critical thinking. This is a current buzzword, but I don't see much effort to actually teach it. Formal Logic Logical fallacies How logic goes wrong. Cognitive biases What are they, broad categories, why are they useful, recognizing when to use, and not use them. Advertising & Propaganda How does advertising work? The appeal of sex, youth, vitality, being special, an insider. Types of advertising. . Propaganda: Demonizing the opponent. Use of connotations in making biased sentences. Selective editing. (A video class was given 3 minutes of film of a protest march, with aobut 2 mintues of “man on the street” interviews. Each editing team was assigned a different spin. Was hard to tell that the 4 stories were of the same event.) Lying with graphs and statistics How to be deceptive, and how to detect deceptive practices. *** Math::Estimating Approximate any series of calculations to 1 significant digit rapidly. Fermi problems. These are problems to teach the use of common sense in estimating. You could hold your head up if you got within a factor of 10 of the right answer, and were entitled to take a bow if you could get within a factor of 3 One of the most frequently used bits of my physics education is the ability to to BOTEs quickly. Math::Geometry Formal Euclidian geometry -- as an adjunct to the formal logic course. Showing how long chains of logic can be put together. While I don't use theorems (other that dear Pythagorus's famous one) much, I end up 'thinking geometrically' a lot. Math::Statistics High school grads should understand at least average and standard deviation well. They should also know and understand how to lie with statistics. Physics::Vectors This one I use a lot, from canoeing (Intuitive vector sums of of current and paddling speed) to tree felling, to whipping together a roof on a shed, to which way a knot will try to slide. What would I take out? Most of high school algebra. Keep it as an elective for the science majors.