Undergraduate Corner: "Who Told You That?"

On this blog, the first and third Tuesday of each month are dedicated to presenting discussion geared toward undergraduate students, in a series called, "Undergraduate Corner."

I think one of the most underutilized verses in the Bible is right at the beginning: "Who told you you were naked?"

I had a similar question arise last week in my Quantum Mechanics class.

One of my students was growing frustrated with his halting success and many intellectual roadblocks to completing the first round of homework problems. "How can I calculate this thing [the expectation value of x]?" he asked. "I've never even seen this kind of formula!"

I spent the better part of this week thinking over how to help him overcome his frustrations. It is, at first glance, an intimidating formula

but there was something odd about his frustration.

Then, I realized what it was: He was expecting to be able to complete this course using only concepts he already knew.

"Who told him that?" I asked myself. "Who told him he needed to know everything before taking a course?"

I realized, then, that this was a cognitive hurdle that many of my students were troubled by, at all levels of physics.

I brought this up with the student during class on Friday, as the students began to work another set of problems. "Somewhere along the way," I said, "someone told you---and many of your classmates---that you had to know everything before coming into a course. I don't know who did, or when or why, but that's what keeps you from succeeding."

His jaw hit the floor. He realized that it was true---and went on to best a rather lengthy Quantum Mechanics problem, involving many formulas more scary than that for <x> quoted above.

Where did these students get this idea? Who told them they did not---and could not ever---have what it takes?