# Analyzing Mistakes: Results so far

I wrote recently about creating a rubric to help students analyze their mistakes.  Here are some examples of what students wrote — a big improvement over “I get it now” and “It was just a stupid mistake.”

The challenge now will be helping them get in the habit of doing this consistently.  I’m thinking of requiring this on reassessment applications.  The downside would be a lot more applications being returned for a second draft, since most students don’t seem able to do this kind of analysis in a single draft.

### Understand What’s Strong

• “I thought it was a parallel circuit, and my answer would have been right if that was true.”

• “I got this question wrong but I used the idea from the model that more resistance causes less current and less current causes less power to be dissipated by the light bulbs.”

• “The process of elimination was a good choice to eliminate circuits that didn’t work.”

• “A good thing about my answer is that I was thinking if the circuit was in series, the current would be the same throughout the circuit.”

### Diagnose What’s Wrong

• “The line between two components makes this circuit look like a parallel circuit.”

• “What I don’t know is, why don’t electrons take the shorter way to the most positive side of the circuit?”

• “I made the mistake that removing parallel branches would increase the remaining branches’ voltage.”

• “What I didn’t realize was that in circuit 2, C is the only element in the circuit so the voltage across the light bulb will be the battery voltage, just like light bulb A.”

• “I looked at the current in the circuit as if the resistor would decrease the current from that point on.”

• “I think I was thinking of the A bulb as being able to move along the wire and then it would be in parallel too.”

• “What I missed was that this circuit is a series-parallel with the B bulb in parallel with a wire, effectively shorting it out.”

• “What I did not realize at first about Circuit C was that it was a complete circuit because the base of the light bulb is in fact metal.”

• “I thought there would need to be a wire from the centre of the bulb to be a complete circuit.”

• “I wasn’t recognizing that in Branch 2, each electron only goes through one resistor or the other.  In Branch 1, electrons must flow through each resistor.”

• “I was comparing the resistance of the wire and not realizing the amount of distance electrons flowed doesn’t matter because wire has such low resistance either way.”

• “My problem was I wasn’t seeing myself as the electrons passing through the circuit from negative to positive.”

### Improve

• “In this circuit, lightbulb B is shorted so now all the voltage is across light bulb A.”

• “When there is an increase in resistance, and as long as the voltage stays constant, the current flowing through the entire circuit decreases.”

• “After looking into the answer, I can see that the electrons can make their way from the bottom of the battery to the middle of the bulb, then through the filament, and back to the battery, because of metal conducting electrons.”

• “To improve my answer, I could explain why they are in parallel, and also why the other circuits are not parallel.”

• “I can generalize this by saying in series circuits, the current will stay the same, but in parallel circuits, the current may differ.”

• “From our model, less resistance causes more current to flow.  This is a general idea that will work for all circuits.”

1. These are terrific. On this,

> most students don’t seem able to do this kind of analysis in a single draft

Yet. My precalc students, halfway through the year, are getting about 60-70% of their first submitted drafts accepted as-is. At the beginning of the year it was more like 2-5%. With practice they begin to do it right the first time and they are motivated because they don’t want to have to redo it. So if you can handle the transient, steady state might be manageable…

• Good point, Dan! It’s very encouraging to hear of the dramatic increase in your first draft acceptances. Yes, I think this is possible. I’m always amazed at how much the students benefit from getting narrative feedback on multiple drafts… of anything. I’m starting to think that that’s most of my job description.

The downside is introducing this 2/3 of the way through the year, at the time when they are most overwhelmed. I think this will be easier to introduce next year at the beginning, so that by the time we get to really tough concepts, they don’t have to learn this new thing at the same time.