On this question, they were (in general) in the weeds:
" Two radio towers 30 km apart transmit synchronized 240 kHz signals. If a car equipped with a radio receiver tuned to the transmission frequency drives directly from one tower to the other, what will the receiver hear? Explain; a diagram would help! Radio signals are light waves that travel 300,000,000 meters per second.
What would the signal be like at a point along the drive that is 8750 meters from the first tower
How would the driving experience change if the radios’ frequencies were changed to 300 kHz?"
We've done some work with 2-source interference, from looking at the "overlapping ripples" diagrams to doing some predictions of frequency from two interfering sound waves given the locations of some points of constructive and destructive interference in the room.
This is the same concept, but a different-looking context, and that's where kids that haven't quite figured out the whole axiomatic reasoning thing have difficulty - yes it looks different, but we can still use the same principles to make predictions about what happens.
In particular, the big message for 2-source interference is that, even though both waves start in phase, they may not be in phase when they reach you, if you're different distances from the two sources. The difference in travel distance determines the phases of the waves and whether they'll interfere constructively or destructively. [This type of relationship is familiar: rates (relatives of differences) are famously difficult for students to intuitively grasp - see calculus!]
Back to the story, though:
I collected the assessments at the beginning of class and then posted this problem via projector. I set the online stopwatch to five minutes and told them to come up with something coherent in their whiteboarding groups. There was a good discussion after that, and we made a lot of good connections.
...before that, though, there was an audible groan when I posted the problem.
Why? It's a hard problem! They've already wrestled with it for some period of time, felt anxiety that they were adrift about (da-dum!) an assessment problem, and here I was bringing it up again.
Here's the thing, though: you don't learn anything by running away from those difficult problems - you have to figure them out so that you can use that understanding in the future. Denial is death in problem-solving.
Soldiers and police officers are incredible because they run towards gunfire, while the rest of us run away. There's an anxiety-filled and dangerous situation, but they do the harder thing and confront it directly.
In physics (or learning in general), we have to run towards the gunfire too - you have to seek out and fix those misconceptions and misunderstandings. It's anxiety-filled, too, but one student yesterday noticed a crucial difference between the two situations, when SBG is used: for us, the wounds aren't permanent.
Not Proficient? No problem - wrestle with the problem, come back, and then you'll be whole again. Using traditional grading that students are accustomed to, I totally understand why they get gunshy, even at the level of course selection. Reminding them that this is a safer space for making mistakes has to be a constant occurrence because of that ingrained anxiety, but it's well worth the effort.