Friday’s lecture went fairly well.

There were a few questions at the beginning of class, one of which lent itself well to my talking about choosing different models for the same phenomenon and using the simplest model that worked for the design being done. In this case it was about the relaxation oscillator using a 74HC14N Schmitt trigger and where the constraints on the feedback resistor came from. I told them about some more detailed models we could do of the Schmitt trigger, including input capacitance (max value on the data sheet), input leakage current (not specified, but probably fairly small, under 1µA), and output resistance (which would get added to the feedback resistance). I’ll have to incorporate some of those ideas into the book, when I rewrite those chapters this summer—the hysteresis lab needs the most rework of anything so far this quarter.

After the questions I mainly talked about polarizable and non-polarizable electrodes developing the R + (R||C) + half-cell model of an electrode that they will be fitting (without the half cell) in labs this week.

This weekend’s grading was a bit painful, and I’m probably going to have to spend all of Monday’s lecture filling in gaps in their prior education that I had not anticipated. Some holes also became apparent from e-mail questions I got from students over the weekend.

I’ll try to gather the common problems here, so that I can use the list as lecture notes tomorrow.

- There were a lot of REDO grades for errors on schematics. I hate giving REDO (since it doubles my grading load), but I told students at the beginning of the quarter that any error on the schematics was an automatic REDO. I plan to stick to that, despite the pain for both me and the students, because they have to develop the habit of double and triple checking their non-redundant documents (schematics, PCR primers, …). Sloppy documentation is a serious problem in engineering and too many faculty and graders have been perpetuating the myth that the almost right idea is good enough. I’m particularly harsh on students who change kHz into Hz or pF into nF. Off-by-a-factor-of-1000 is not good enough! The most extreme case so far is someone who specified a capacitor as being in the gigafarads (they’d typed 10
^{9}instead of 10^{-9}). A factor of 1,000,000,000,000,000,000 off is not the sort of thing one can ignore. I also get annoyed by students who randomly pick a unit (H when they need Ω, or Ω when they need Hz), as if all units were just decorations to please a teacher, with no real meaning to them - Frequency is 1/period. For the relaxation oscillator, they do two charge/discharge calculations to get the period as a multiple of RC (though many blindly copied one of the formulas for just the charge time without understanding it, and assumed it was the period). But even after computing the charging time students blindly used 2πf = 1/(RC) as a magic incantation. That formula was relevant for the corner frequency of RC filters, but has nothing to do with the oscillation frequency of the relaxation oscillator.
- The capacitance calculation being done in the prelab was for the capacitance of a finger touch to the touch plate, but a lot of students claimed that it was the calculation to determine the size of the ceramic capacitor. Only a couple of groups bothered to explain the connection between the two capacitances. I think I need to rewrite the prompts in the book to force the values to be more different, so that students have to think which capacitance they are talking about.
- I find that students often talk about “the voltage” or “the capacitance” as if there was only one in their circuit, and when asked which one they are talking about are completely mystified—to them invoking the magic word is all that can be expected of them—actually knowing what it refers to is unreasonable.
- Students in general were doing too much ritual magic. They would put down a formula they thought was relevant (often copying it incorrectly), then claim that from that formula they got some number for their design. Often the formula was not relevant, or additional assumptions needed to be made (like choosing arbitrary values for some variables). At the very least, there was some substantial algebra to be done to convert the formula into a usable form. Some students claimed that Wolfram alpha gave them the solution (when there was not enough information to solve for the variable they wanted a value for). Basically, I’m a bit angry at the students for trying to bullshit their way through the assignment. One pair of students said quite honestly that they did not know how to do a computation and got the value they used from the students at the next bench. I gave them bonus points, and I’ll help them figure out how to do the computation they were having trouble with—I have no problems with students not knowing how to do something new and somewhat tricky, but I do have trouble with students deliberately looking dishonest and stupid by writing bullshit.
- The computation that the honest students had trouble with is one that many students had trouble with, so I’ll go over it in class. I gave the students a derivation of a formula for the charging time of the capacitor in the relaxation oscillator, but I didn’t have time to step them through the derivation. It seems like most of the class can’t read math, since many just copied the final formula without reading the text that said it was the time to charge the capacitor. There was an exercise immediately afterwards asking students to compute the time to discharge the capacitor, but this exercise was added to the book after the students had done their prelab exercises, so they didn’t bother to look at the exercise. What they needed to do for the lab was to add the charge and discharge times (which are not quite the same) to get the period.
- I need to remind the students that they are turning in
*design*reports, not*lab*reports. I’m not looking for fill-in-the-blank worksheets, but descriptions of how they designed and tested their circuits. Omitting the design steps is omitting the most important part of the report! - I gave the students three models to fit to the data, and showed them how to do the fits for two of the models in Wednesday’s lecture. There wasn’t time to get to the third model, so I just told them to use the same technique as the second model, but with the different formula. Most of the class never bothered to fit the third model (the only one that really fits the data well)—if I didn’t do all the work for them in lecture, then they weren’t going to generalize even a tiny bit to do it themselves.
- A lot of students did not do a good job of fitting the models, because they fit the data with linear scaling, rather than with log scaling as I had shown them. This is a fairly subtle point (errors on a linear y axis are differences, but on a log y axis are ratios), so I’ll review it in class.
- I think that some students don’t have any idea when one would use a log-log plot, a log-linear plot, a linear-log plot, or a linear-linear plot. I thought that was covered in precalculus, but I guess not. So tomorrow I’ll present the idea that the only curve most people understand visually is a straight line, so one wants to choose axis scaling so that the expected relationship is a straight line. Linear plots are for linear (or affine) models, log-log plots are for power laws, log-linear are for exponentials, and linear-log are for logarithmic relationships. I’ll put a general straight line on each and derive the form of the function that matches that straight line.
- The purpose of the Tuesday lab was to collect data and model the loudspeaker with a few parameters. But many students neglected to report those parameters in their design reports! They produced a plot and fitted models to it, but nowhere on the plot, in the figure caption, or in the main body (in decreasing order of usefulness) did they report what the parameter values were that the fit produced. For students who are so focussed on answer getting that they neglect to explain how they came up with their answers, this seems like a strange omission.
- For the Thursday lab, no one did back calculations from their observed frequencies to estimate the capacitance of the 74HC14N input, of the untouched touch plate, or even of the touch itself, to see whether their observations were consistent with their design predictions. One group of students claimed to have done sanity checks, but I don’t believe them, as they also reported oscillations around 20Hz, instead of 20kHz.
- For the prelab, it seems that a lot of students computed instead of , though most got it right in the gnuplot scripts for the lab itself. I have to remind students that .
- On the typesetting front, I’m making some progress on getting students to put their plots in as figures with captions, though way too many are still referring to “the plot below” rather than to “Figure 3”. I’m also having some difficulty getting them to be sure to refer to all the figures in the main body text. A lot of times they’ll toss in a handful of plots with no reference to them at all.
- On the opposite side of the coin, I have to teach them that equations are properly part of a sentence, generally as a noun phrase, and are not standalone sentences. When there is an explanation of variables after a formula (“where A is this, and B is that”), the where-clauses are still part of the same sentence.
- Some other little things to tell them:
- The word “significant” should be reserved for its technical meaning of “statistical significance”—very unlikely to have occurred by chance according to the specified null model. It should not be used in the normal English way to mean “big”, “important”, or “something I like”.
- To get gnuplot to produce smooth curves when there are sharp changes in function, it is necessary to do
`set samples 3000`to compute the function at more points than the small default number. - Students have been misusing the word “shunt” for any resistor. Properly, it is a low resistance used to divert current from some other part of the circuit—in our designs, it is the resistor being used to sense current and change it into voltage. I wonder if I should switch terms and talk about a “sense” resistor, though “shunt” is the standard term for ammeters.
- A minor pet peeve of mine: I hate the word “utilize”. I have yet to see a context in which “use” does not do the same job better.

Log-log and log-linear plotting:

Student not knowing about log-log and log-linear plotting is no surprise. None of my American students heard of it, and one international student did hear of it but didn’t know it.

A great missed opportunity in data structures and algorithms courses is assignments to put simple time measuring functions into code, run it for over a wide range of input sizes, and plot the results in different specified ways.

Comment by chaikens — 2015 April 27 @ 05:45 |

Is there a good source for teaching log versus linear plots, a textbook or website? I fear I don’t have a good grasp on it either.

Comment by V John — 2015 April 27 @ 15:59 |

Try Wikipedia: log-log plot and semi-log plot

Or try http://www.intmath.com/exponential-logarithmic-functions/7-graphs-log-semilog.php

Comment by gasstationwithoutpumps — 2015 April 27 @ 18:03 |

Ahhhhh yeeeeeeeeesssss… I’m glad it’s not just me (and my students).

Re: filter critical frequency vs. oscillation frequency and capacitance calculations: I’ve had some good results in similar situations using TIPERS-style practise problems as troubleshooting exercise. I’m thinking particularly of the “Meaningful/Meaningless Calculations Tasks” — asking students to justify why a calculation does or doesn’t mean anything. Of course this sort of thing takes up a lot of time. In some situations I require practise problems to accompany resubmissions — might be worth considering. In other words, in order for me to accept their resubmission, they have to show that they understand the problem with their previous submission.

Re: rewarding honesty over meaningless answer-getting: I deal with that by allowing resubmissions *without practise problems* from people who honestly (and accurately) tell me what they don’t understand. It helps convince students that I am serious about the value of saying “I don’t know” when that’s the truth. Otherwise, they tend to assume that encouraging students to be honest about what they don’t know is something profs say but don’t mean. Any thoughts about making that systematic in the grading structure?

Re: design reports vs lab reports… I encourage students to write a commentary about *what the electrons are doing*. It takes a lot of practise for them to separate “what causes me to think what I think” (the current was 20uA because IB = IE-IC) from “what causes the electrons to do what they do,” (the current was 20uA because the base of the transistor is so lightly doped that very few electrons are able to exit through that lead). but it dramatically improves their ability to think causally, back up their assertions with *meaningful* (rather than vague, unrelated, or hand-wavey) data, and connect old ideas to new ideas. I am willing to sacrifice formal style for causal thinking, so I encourage a fairly informal, conversational sort of “note to self” style — with the “why I made these assumptions” next to their predictions, and “why the physical quantities are what they are” next to the measurements that back up their points. It evolves into a presentable form over the course of the semester, and results in me being much less angry, as well as giving me much better data about what they do and don’t understand.

Re: log vs linear scaling… I agree 100% with your rationale. Unfortunately, my students often tell me that the reason you use a semi-log plot, for example, is because “it’s hard to represent such a wide range of data on a linear scale.” As if a linear scale somehow couldn’t reach 1MHz. And they’re not alone; I’ve seen it in textbooks too. I can’t help feeling dejected when people repeat things that so blatantly fly in the face of their own experience, but I’ve found that it’s more helpful simply to get them to plot it both ways. Then we can talk about readability and ease of mental calculation, as well as helping them see what the ratios on the semilog plot actually represent — it improves their number sense about logs. Maybe. A little anyway.

If you manage to get people to stop using “utilize”, I hope you’ll share how you accomplished it!

Good luck.

Comment by Mylène — 2015 April 27 @ 20:19 |

I’ve been guilty of the “wide range” explanation for log scales myself. What I mean is that ratios are what matter, not differences, and I want 10% errors to look the same everywhere, not get bigger on the right of the graph. I’ve been trying to use ratios and % change as the justification for log scales more explicitly this year.

Some students were mystified in class by my assertion that straight lines were all that people understood visually, and that the point of changing the axis scales was to make other functions into (nearly) straight lines. I then showed them the “straight line” for linear, log-log, and both semi-log plots. I don’t know if that will take hold, but at least a seed has been planted.

I don’t have a semester to get students up to speed. I’ve got 10 weeks to get them from knowing essentially no electronics to being able to design amplifiers and simple RC filters for EKGs and pressure sensors. I’ve done it twice before, but it is a bit of a stress test for both the students and me.

Comment by gasstationwithoutpumps — 2015 April 27 @ 22:26 |

This looks good but on the intmath.com website you cited it reads: “The idea here is we use semilog or log-log graph paper so that we can more easily see details for small values of y as well as large values of y.” Is this innacurate?

Comment by V John — 2015 April 29 @ 08:03 |

Using a log scale allows one to see details in the small values that would be too tiny to see in a linear scale, at the expense of making large differences in the big values appear smaller. If differences are what matter, then a linear scale is appropriate, if ratios (or growth rates) are what matter, then a log scale should be used.

Watching an investment over time, for example, should be a semi-log scale (linear time, log $), because we want to see %/year growth. Using a linear scale shows us only the most recent behavior, where the numbers are largest.

Comment by gasstationwithoutpumps — 2015 April 29 @ 09:16 |

semi-log plots are used when you want to emphasize the small numbers and hide the big ones. Linear plots do the opposite. (I’m thinking of data that span 3 or more orders of magnitude.)

If number sense about logs is important to you, have them calculate the logs and then plot it on a linear scale rather than use a program.

Comment by CCPhysicist — 2015 April 30 @ 21:25 |

I don’t think that having students do the calculations increases their number sense about logs at all. It just increases the tedium and gets them into “ritual magic” mode, pressing buttons on a calculator without thinking. Thinking about Bode plots and what the slopes of the lines would be for resistors, capacitors, and inductors does more for number sense than any amount of calculator button pressing.

Comment by gasstationwithoutpumps — 2015 May 1 @ 12:14 |

[…] lecture went fairly well—I used my post Comments for class after grading as lecture notes, and pretty much covered everything, though not necessarily in the order presented […]

Pingback by First half of electrode lab a bit long | Gas station without pumps — 2015 April 28 @ 20:47 |

I’m not sure I can tag the bullet points properly, but will try.

#1: I became a fan of the “redo” concept when I had a class where there was no partial credit for homework. It had to be perfect or you had to redo it. Apart from the issue you mention, it had the side effect of ensuring that the last solution you wrote out was perfect, fixing it in your mind. There is pedagogical value in that. Random units is a symptom of classes where exams were multiple choice (so they didn’t have to know the units) or where the penalty for wrong units wasn’t a zero.

#2: Equation grabbing is a horrible problem. This might be the first time that they have had problems where there have more than one equation containing frequency or period. I suggest having a few beers with the folks teaching physics and find out what the kids are being tested on.

#5: This is a symptom of classes where the algebra between the start and end is not graded, or even looked at. There are algebra classes where the test is taken on a computer or where the answer goes in a box and that is the only thing that anyone looks at. I have had reliable informants tell me about calc 3 (vector calculus) classes where the exams were all on a computer and the results were curved. No human ever looked at their work. This enables a great deal of cheating, as you noted.

#10: I don’t think students make graphs any more in math classes. It’s all graphing calculators, following some ritual (I liked the way you used that term) they only remember for a week for a specific problem. No concepts at all.

#16: They are unlikely to have heard the word “shunt” before, so they have no cognate to associate it with. If they do, it might include any sort of rare alternate route (a shunt in british auto racing lingo) or in medical use (where the low resistance of the bypass is relevant but not obviously the main meaning). Even the old meaning from railroading, to get a train out of the way of another, has been sharpened when borrowed for electrical work. They wouldn’t have seen it used at all in a trig-based physics for biologists class because they don’t explore how a meter is designed.

Comment by CCPhysicist — 2015 April 30 @ 21:53 |

The misunderstanding of “shunt” is not a reflection on the students—it was a new term for them and I expected it to be a new term. What I had not realized is that I hadn’t carefully enough defined when it was and wasn’t appropriate to use the term. So that was more a reminder to myself to clear it up in the book and in lectures, so that future students wouldn’t be so confused.

Comment by gasstationwithoutpumps — 2015 May 1 @ 12:16 |