Logic (or lack thereof)

I keep forgetting that high school sophomores not only know nothing, but are averse to figuring things out.

Today's example: I gave all four classes a Quizlet asking them to find out the centripetal force on a theoretical person in a rotor ride and "the number of complete circles the rider completes in one second." They were given the radius of the ride, the linear speed of the rim of the ride, and the mass of the rider. They have the formula for centripetal force, and just about all of them managed that part of the question, but three out of the four classes completely balked at the second part. They didn't have a formula for "number of complete circles"! They couldn't possibly even take a stab at the problem without an explicit formula, nevermind that they have a definition of frequency as "the number of circles completed in one second" and they all know the formula for circumference and the formula for the time it takes to travel a certain distance as a given speed and the formula for linear speed as "circumference/period". I had not explicitly given the the definition of period as "1/frequency", but I had given them the definition of period as "the amount of time taken to complete one circle." Given this, I suggested that if they could not solve for the frequency, they could solve for the period. This also baffled the vast majority. Critical, conceptual thinking is dead, at least among my students.

What's even worse is that the college prep (middle track kids who think they're going to college in two years) could not follow the algebra required to get from v=C/T to T=C/v.