As I reported last week, students did poorly on the first quiz, which came as no surprise to me. I had the students redo the quizzes as homework, allowing collaborative work (as long as they acknowledged the collaboration in writing). They turned in the homework on Monday, a week after the quiz, and I returned them today. No one aced the redo, with the top score being still only 25/33 (which would have been an A on the first pass, on a redo maybe a B+).
A lot of the students still seem to be having trouble with complex numbers—they got the formulas right when working symbolically, but then the exact same question with numbers instead of letters (which could be done by just plugging into the formulas) came out with real numbers when complex impedances were asked for. Also, a lot of sanity checked were skipped (several people reported a battery as doubling in voltage when hooked up to a resistor, for example).
These students are not major mathphobes (they’ve all passed a couple of calculus classes and most have done more math past that), but they don’t seem to have any sense for reasoning with or about math—they just want to plug in and grind, even on simple problems like ratios in voltage dividers. This class has almost no memory work (I gave them a one-page handout at the beginning of the year with all the math and physics I was expecting them to memorize), but relies heavily on their being able to recognize how to apply those few facts. This often requires subdividing a problem, like recognizing that a Wheatstone bridge is the difference between two voltage dividers, or that a 10× oscilloscope probe is a voltage divider with R||C circuits for each of the two impedances.
I spent the entire class today working through each problem in the quiz, to make sure that everyone in the class could understand the solution, and (more importantly) see that they did actually have enough knowledge and math skill to do the questions. Some of the students were feeling overwhelmed on the quiz, because they are not used to doing anything more than 1-step pattern matching for problems, and some of the quiz problems required two steps. None of the quiz problems were as hard as the prelab they had to do this week, which involved 8 or more steps to get the resistor values to set the gain of the amplifier:
- Determine the pressure level of 60dB sound in Pa.
- Determine the sensitivity of the microphone in A/Pa:
- Convert -44dB from spec sheet to a ratio
- Get V/Pa sensitivity for microphone for circuit on spec sheet
- Convert to A/Pa given resistance of I-to-V conversion resistor on spec sheet.
- Determine voltages needed for op amp power supply.
- Determine I-to-V resistor needed to bias microphone in saturation region.
- Convert A/Pa sensitivity, RMS pressure level, and I-to-V resistor to RMS voltage out of microphone.
- Determine corner frequency and R, C values for DC-blocking filter.
- Determine maximum output voltage range of the amplifier as the most limiting of
- Voltage range of op amp outputs
- Power limits of loudspeaker (10W)
- Current limit of op amp (which is a function of the power-supply voltage) into 8Ω loudspeaker
- Determine max gain as ratio of RMS voltage into op amp and RMS voltage out of op amp (I’m allowing them to be a bit sloppy about RMS voltage vs amplitude, since we are not looking just at sine waves—the amplitude of a symmetric square wave is the same as the RMS voltage.)
- Choose resistor values to give the desired gain.
I’m hoping that pushing them go through these multi-step designs in the lab will give them more practice at decomposing problems into smaller pieces, so that two-step problems on a quiz no longer seem daunting, but routine.
I’m going to be giving them another quiz in about a week, covering op-amp basics and the amplitude response of RC filters. I’ve got to figure out the best time to do this—possibly a week from Friday, after they’ve done another op-amp lab (using a phototransistor to make a pulse monitor, using this handout). I think I’ll reorder the labs after that, doing the pressure sensor instrumentation amp lab, then the class D power amp, then the EKG.