Curving Grades: Gordon Tullock’s Solution Ideally a grade in a course one professor teaches represents the same level of accomplishment as the same grade in a course someone else teaches. Often it doesn’t, since different professors have different standards. The usual solution to that problem is to impose a grade curve on the professors, a fixed distribution of grades, sometimes with some flexibility in the details. That makes it hard to get an A in a class that only the best students take, easy in one populated mostly by the worst students.
I agree with your point on economics, and other applied sciences.
But for students studying uni math (and perhaps physics also), rigor is essential, not even so much as a tool for their future profession (which might very well not be math anyway), but as a way to absorb the essence of what mathematics is.
Hardy famously said that all good mathematics is useless.
I'm also fairly certain that at least 75% of my former fellow students in the bachelor math program would be able to provide the intuition behind the fundamental theorem of calculus.
Related to the scavenger hunt, Iowa State's student radio has an annual 26 hour trivia contest called Kaleidoquiz. Some examples of questions include:
For how many years was there a banana for a head?
In over ten languages, a certain sea animal is named after a certain mythological monster. What animal is this?
How much taller is the tallest man in the world than the tallest man on earth, in barleycorns?
‘How not to Teach Math — or Economics’ really hit home for me. As an engineer, I couldn’t agree with you more.
I took calculus 1 and 2, and definitely don't know that proof
I agree with your point on economics, and other applied sciences.
But for students studying uni math (and perhaps physics also), rigor is essential, not even so much as a tool for their future profession (which might very well not be math anyway), but as a way to absorb the essence of what mathematics is.
Hardy famously said that all good mathematics is useless.
I'm also fairly certain that at least 75% of my former fellow students in the bachelor math program would be able to provide the intuition behind the fundamental theorem of calculus.
I got a great second hand story about cookbook mathematics.
A top student in highschool is solving a question that boils down to x^2 = 16.
The student solves everything correctly and in the last step writes x = 4.
The teacher is noticing this and asks gently if that's the only solution, to which the student replies by writing x = 4 + C.
The teacher's eyes open in amazement. The student notices and modifies the solution again, this time to x = 4 + 2*n*pi.
(This is a true story as far as I know, although I only heard it from someone).
Could you explain the last solution (for n any real integer)?
In trigonometry you often end up with equations like sin(x)=0.
Due to the cyclic nature of the functions there's an infinite number of solutions expressed using n (where n takes the value of any integral).
For example the solution to sin (x) = 0 is
x=n*pi.
I agree that is certainty the case for trig functions, but f(x)=x^2-16=(x+4)*(x-4) isn’t periodic. It’s just a quadratic with only two zeros.
That's the point of the story. The student was blindly applying cookbook receipts and betraying their misunderstanding.