Rote Correctness vs Mechanistic Incorrectness
I asked the following question in lecture in today:
Besides A, the other popular choice was C. During peer discussion I walked around and asked a few students to explain to me how they came to their answer. I noticed an interesting difference between the explanations from students who picked A and from students who picked C*.
Students who picked A were happy to explain why i4 > i2 in terms of Ohm’s law or in terms of resistance and the speed of charges in the different branches. However, when I asked them why they thought i2 = i3 they would simply reply “Because they’re in series.” When I pushed them and asked why being in series meant the currents were equal they would look at me blankly and repeat “They’re in series.” While correct, this was clearly a definition for these students. They did not seem to understand that a mechanistic explanation to this question was even possible.
Students who picked C were happy to explain both why they thought i4 = i2 and why they thought i2 > i3. These students thought that i3 had gone through two resistors while i2 and i4 had both only gone through one resistor. Their reasoning was that resistors slow down charges so charges at i3 should be slower than charges at i2 and i4. While incorrect, these students had a logical, consistent mechanism underlying their answer.
For the class discussion I started by saying that A was the correct ranking but said I wanted to talk about C because I think there are a lot of good ideas and reasoning that go into picking that answer. I summarized what I heard as the student argument in favor of C and pointed out that they are absolutely correct that the second light bulb slows down the current even more. I said I wanted to add one more idea to this argument – the idea that charges cannot bunch up because they’re all electrons and they repel one another. I asked what would happen if charges in i2 moved faster than charges in i3 and students quickly concluded that bunching would occur. From this we decided that the second light bulb slows down not only i3 but also i2. Hence, A must be the correct answer.
I should have pointed out the bunching argument is the sort of mechanistic explanation that I was pushing for from students stated that i2 and i3 are the same “because they’re in series.” Unfortunately, I was a little too excited about building productively from answer C and didn’t think to connect back to students who chose A until I was reflecting after class.
*The sort of contrast that I’m describing was the focus of Brian Frank’s presentation to the Global Physics Department. I recently viewed Brian’s presentation which is likely why this contrast caught my attention.