Today’s class was not content-rich, but a low-key decompression after yesterday’s too-long lab.
I started out taking some questions from the class, which were mainly about what to do in the design report.
I then discussed my ideas about what had gone wrong with yesterday’s lab that made it take so long, and both how I planned to fix the problem next year, and what we could do as a class to keep it from happening again this year. I particularly stressed the importance of doing the pre-lab work early, so that they could ask questions in the lecture portion of the class, rather than taking up valuable lab time. I also suggested that they do the writeups for the Tuesday lab before Wednesday’s class, so that they would have much less to write up after the Thursday lab—making the Friday deadline for the writeup feasible.
I asked the students for their ideas about what were problems with the lab, and they agreed that the soldering and installing PteroDAQ software took up almost 2 hours, so it would be best to separate that into its own lab period. They also brought up their frustration with the design problems I had given them: not so much the optimization for the lab, but the design exercise I had added: Design a circuit to convert a 1kΩ–3.3kΩ variable resistance sensor to a 1v–2v voltage output, with 1v for the 1kΩ resistance and 2v for the 3.3kΩ resistance. Use standard resistor values that you have in your kit. They were frustrated because they did not know how they were supposed to approach the problem.
This gave me an opportunity to explain what I was trying to do with problems like that. It was indeed entirely appropriate that they should have been uncomfortable with the problem, because I was trying to push them to think in new ways—to handle problems that were not completely laid out for them ahead of time, but where they had to struggle a bit to figure out how to formulate the problem. This is precisely what engineers have to do—to take problem statements that may be unclear or not precisely solvable, figure out how to formulate them more precisely, set up equations, solve them, check that the design they come up with makes sense, and (often) adjust the problem statement to reflect what is actually doable. (I didn’t say it, but in this case you have to accept a few percent error in the output voltage or the resistances in order to use standard values.) I promised them more uncomfortable problems in future, in an attempt to stretch them. They seemed a little more at ease with the difficulty they’d been having, once they realized that this was expected—I think some had been afraid that they were in over their heads and were panicking.
Another student mentioned having heard of an analogy between programming and engineering. I pointed out that programming was a form of engineering, and that all engineering required identifying problems, breaking them into subproblems, and solving the subproblems. Programming tends to involve many, many subproblems, with formal interfaces between them, but even the simple hardware we’d do in this course involves breaking problems into subproblems, using block diagrams (which I promised to talk more about later in the course).
Somewhere in the discussion of what engineers do, I brought up the example of the student who had presorted his resistors and taped them into a booklet. What the student had done was to identify a problem (that it would be hard to find the resistors he needed), come up with a solution, and implemented it. I pointed out that the technology he used (scotch tape) was available to them all, as was the notion of sorting. The engineering thinking comes in looking at something unpleasant (finding a sheet of resistors in a pile of 64 different sizes) as a design problem to solve, rather than something to get irked about or try to avoid. I’m hoping to get them thinking more like engineers during the course of the quarter—anticipating problems and looking for ways to solve them.
I took more questions from the class—there were a few about voltage dividers, which I explained again in a different way, using analogies to similar triangles and giving them the voltage divider formula in the form . I did not give the voltage divider in the “ground-reference” format shown to the left, but drew lines out horizontally from the nodes, and had the voltages indicated as distances between the lines (like in a mechanical drawing), to give them a more visual representation of voltages as differences. I also had them figure out what the voltage across R2 would be and how it would relate to the other voltages.
The more different ways they work with voltage dividers, the better they will internalize the concepts and be able to use them in designs.
A question also came up about what it meant to have 2 input voltages with no ground shown in a circuit (as I had given them as an exercise in the first lab handout). That is an excellent question—one that uncovered an assumption I had been making that I had never explained to them! I explained that what an “input voltage” meant was shorthand way of drawing two voltage sources.
I’ll have to fix the handout next year to include this explicit explanation of a common shorthand—I’ve used it for so many decades that it simply hadn’t occurred to me that it wasn’t obvious. I apologized to the class for having skipped the explanation, and pointed out the importance of them asking questions, because otherwise I would never know where some omission like this was confusing them unnecessarily.
When they ran out of questions, I got in some new material, explaining the difference between “precision”, “repeatability”, and “accuracy”. The digital thermometers they used in lab were a good example—they had a precision of 0.1°C, were repeatable within a single thermometer to about ±0.2°C, but between thermometers were repeatable only to about ±2°C. The accuracy is unknown, since we did not have anything traceable to a temperature standard, but the ice water baths should have been close to 0°C, so the thermometers we used on Thursday were probably less than 1°C off, but the larger set we used on Tuesday included some that were 3°C or 4°C off. In the repeatability part of the talk, I managed to bring in the biologists’ notion of technical replicates (different measurements of the same sample) and biological replicates (different cultures or tissue samples), and why biological replicates show less repeatability.
I also used this as a chance to talk about the uselessness of ±0.1°C or error bars without an explanation of what the range means (standard deviation, 90% confidence interval, 3σ, 5σ, observed range, …), and the even greater uselessness of “significant figures” as a way of expressing uncertainty. I told them that I’d rather see 1.031±0.2 than 1.0 as a way of expressing the uncertainty in a measurement.
Towards the end of the 70-minute period, I got in a little discussion of AC voltages as time-varying voltages, and that we usually did analysis in terms of simple sinusoids, rather than the complex waveforms that we’d actually be measuring. I did assure them that, though there was a lot of mathematical machinery (Fourier analysis) that justified this way of doing things, the math was outside the scope of the class and I’d only be giving them intuitive ways of working with AC. I only got as far as giving them amplitude—telling them that I’d start with RMS voltage next time. (I’d originally hoped to explain RMS voltage today, but that would have taken another five minutes, and we were already 3 minutes over.)
Overall, I was fairly pleased with how today’s class went—the students are getting more comfortable asking questions and I’m getting a better sense of what they already know and what they need explained. Undoubtedly I’ll make more mistakes like not explaining the “hidden voltage source at inputs” convention, but I think we’ll recover from such mistakes a little quicker each time, as the students get more confident in asking for clarification.