Midterm quiz doesn’t tell me much new

I don’t usually give exams in my courses any more, because I’m more interested in what students can do when they have time and resources than what they can do on toy problems under resource limitations.  But if students don’t do the homework, then they don’t learn the material, so I threaten each class that if too many students don’t turn in the homework, I’ll have to add a quiz (worth as much as one of the lab reports, each of which is equal to all the homework) to the course.

This quarter I had to follow through on that threat, because 12% of the class had turned in half or less of the homework (and by that, I don’t mean answered half the questions—I mean turned in nothing at all for half the assignments).  A quarter of the class had not turned in 25% or more of the assignments.

I gave the quiz yesterday, with 6 easy questions that only tested the very basic material: single-pole RC filters (passive and active) and negative-feedback amplifiers.  I told students ahead of time (and on the exam) that they could use the Bode approximations (the straight-line approximations to the gain of the RC filters) and we even reviewed them in class last week.  There were 60 points possible on the test, and none of the questions were design questions—they were almost all of the form “what is the corner frequency?” or “what is the gain of this circuit?”.

There are a small number of students in the class whose probity I have reason to question, so I took steps to reduce cheating that I would not normally bother with: I made up two versions of the test (same schematics, but different component values) and alternated them in the piles passed along each row.  I also had the students sit in different rows from usual, reversing front and back of the room, with the front row reserved for latecomers. I’ve noticed a high correlation between good homework grades and people being on-time and in the first two rows, so I had those students sit in the back row, where no one would be able to copy from them.

I normally figure that a test is appropriately long if an expert can do it in about a quarter of the time allotted.  So I made up the keys for the test while the students were taking it.  Working through one form with the Bode approximations took about 5 minutes.  Doing exact computation with the formulas for series and parallel impedances and complex numbers using only real-number arithmetic on my calculator extended that by another 15 minutes.  The students had 63 minutes, so the exam was too easy if the students used the Bode approximations (as they were told) but a little too hard if they worked just from the fundamentals of complex impedance and negative-feedback amplifiers.  As a consequence, I decided to give bonus points for exact computations of the gains that didn’t use the Bode approximations, though the class was not informed of this bonus, because I didn’t want them to waste time on the tiny bonus.  (The differences in answers were small, because I had deliberately asked for gains only at points well away from the corner frequency, so that the Bode approximations would be good.)

Even if students really didn’t understand complex impedance or RC filters, 39 of the 60 points could be earned with just DC analysis of the negative-feedback amplifiers and knowing that capacitors don’t conduct DC.   So I was hoping that students would do better on these very easy questions than they did on the harder design questions of the homework.  As a confirmed pessimist, though, I expected that students would show almost exactly the same distribution on the test that they showed on the homework, with the middle of the class being around 20 out of 60 points and showing serious misunderstandings of almost everything, with a long tail out to one or two students who would get almost everything right.  I also expected that the correlation between the homework scores and the quiz scores would be high.

So what happened?  First, I saw no evidence of any cheating (not that I had expected any), so that is one worry removed.  Second, my pessimistic assumption that students really were not learning stuff that they had done many times in homework and in lab was confirmed:

Here is a stem-and-leaf plot of the scores:

OO: 3
05: 6889
10: 011112444444
15: 555667777899
20: 00111112223344
25: 677999
30: 12224
35: 5678
40: 00444
45: 67
50: 01
55: 
60: 2

The median is indeed 21 out of 60, as I feared. At least no one got a zero, though the scores at bottom indicated complete failure to apply the basics of the course.

Most students could compute a corner frequency from a resistor and capacitor, but few had any idea what to do with that corner frequency. Many students could compute the DC gain of a non-inverting amplifier, though many could not then apply this knowledge to the DC gain of an active filter (which only requires replacing the capacitors with open circuits). A lot of students forgot the “+1” in the formula of the gain for the non-inverting amplifier.

Inverting amplifiers were even less understood than non-inverting ones, with students forgetting the minus sign or trying to use the formula for non-inverting amplifiers.

A lot of student answers failed simple sanity checks (students were having passive RC filters with gain greater than 1, for example).

Very few students used the Bode approximations correctly, and many tried the exact solution but either couldn’t set up the formulas correctly or couldn’t figure out how to use their calculators, often getting numbers that were way, way off.  Others seem to have ignored the complex numbers and treat as if it were .

One disturbing result was how many students failed to recognize or understand a circuit that they have designed in three different labs: a voltage divider and unity-gain buffer to generate Vref, combined with a non-inverting amplifier. I asked for the output voltage as a function of the input voltage (both clearly labeled on the schematic). This was intended to be almost free points for them, since they had used that circuit so many times, and the formula they needed was one of the few formulas on the study sheet: . The frequent failure to be able to fill in the blanks of this formula for a circuit that they have used several times in design makes me question whether the students are actually learning anything in the course, or if they are simply copying designs from other students without understanding a thing. (Note: the extremely poor performance and group-think duplication of ludicrously wrong answers on pre-lab homework this year has also lead me to the same question.)

Did the quiz tell me anything that the homework had not already told me? Here is the scatter diagram:

Pearson’s r correlation is 0.539 and Kendall’s tau is 0.306, so the homework and quiz scores are highly correlated. There are a few outliers: a diligent student who bombed the quiz and a student who has turned in few of the homeworks who actually understands at least the easy material. The points have a small amount of noise added, so that duplicate points are visible.

The high correlation between the quiz and the homework mostly confirmed my prior belief that the quiz would not tell me much that is new, and that the homework grades were pretty reflective of what students had learned. I will want to talk with a few of the most extreme outliers, to find out what happened (why were students who mostly understood the material blowing off the homework? and why did diligent students who had been doing moderately well on the homework bomb the quiz—is there undiagnosed test anxiety that should be getting accommodations, for example?).

Most of the points that were earned were from students randomly plugging numbers into a memorized formula and (perhaps accidentally) having chosen the right formula and the right numbers. Only a few students showed real understanding of what they were doing, and only one student saw the quiz as the trivial exercise it was intended to be.

It seems that the hands-on active learning that I have been so enthusiastic about is not working any better at getting students to learn the basics than the traditional (and much cheaper) droning lecture that EE uses. I’m not in complete despair about the course, as there is some evidence that students have picked up some lab skills (using oscilloscopes, multimeters, soldering irons, …) and some writing skills (though many are still not writing at a college level). But I’m trying to teach the students to be engineers, not technicians, so I was aiming at them understanding how to design and debug things, not just implementing other people’s designs. Picking up lab skills is not enough for the course.

I need help. How do I reach the lower half of the class? How do I get them to think about simple electronics instead of randomly applying half-remembered formulas? We’ve only got 3 weeks left—I don’t know how much I can salvage for this cohort, but I certainly would like better outcomes next year.

More writing advice from the electronics course

I spent the entire long Presidents’ Day weekend grading and still did not clear my backlog (the cold I’ve had for the past two weeks has really reduced my ability to work long hours).  I did get a homework set graded and a design report set graded during the 3-day weekend, but I was left with a set of 18 redone lab reports that I still hadn’t gotten to.  Wednesday produced another set of redone reports (so I now have about 35), and Friday produced another homework set (which I just finished grading after spending all Saturday—I haven’t even gotten dressed yet and it is almost 8pm). Tomorrow I’ll tackle the first set of redone reports, assuming my cold lets me do anything tomorrow.

In Disappointment with chain stores, I commented on no longer wanting to grade in the Peet’s coffee shop I used to grade in, and commenter “Mike” wanted to know what solution I came up with. This winter, I’ve mainly been grading in my breakfast room at home, using a tiny laptop (an 11″ MacBook Air, which we bought for travel and for lecturing) when needed to look things up (data sheets, my solution sets, the exact wording in the book, …).  This has worked out ok this year, though I do tend to wander into the kitchen for snacks a bit too often.  Still, the snacks at home are healthier than in a coffee shop!

Here are some general comments that I shared with the whole class, based on the most recent design reports:

Content:

Many students reported using a 3.3V power supply without measuring it, resulting in inconsistent information, such as V_OH > 3.3V.  PteroDAQ reports the power-supply voltage on the GUI and in the metadata for the data file, so the data was available, even if the students hadn’t thought to measure it while in lab.

Formatting:

• Equations are parts of sentences, not figures and not objects dropped randomly on the page. Treat them grammatically as noun phrases.
• Explicit figure credit is needed any time a figure is copied or adapted. The caption must say something like “figure adapted from …” or “figure copied from …”. Failure to do so is plagiarism, and I’ll have to start academic integrity proceedings if students fail to do proper figure credits in future.
• Don’t bury the lede. Start with the design goal, not with generic background. A lot of students still wanted to give me a bunch of B.S. about what hysteresis was, before telling me that they were designing a capacitive touch sensor using a relaxation oscillator built around a Schmitt trigger.

Grammar:

• The subjunctive mood marked by the auxiliary verb “would” is used for many things in English, but technical writing primarily uses just one: contrary-to-fact statement. “The inverter that we would be using” says that you didn’t use that inverter and are about to say why. A lot of students seem to think that “would be” is some formal form of past tense—they’ve seen it in writing, but never understood what it means.  I fault their middle-school English teachers for not stressing the importance of more advanced grammar than the bare minimum, but the fault could have been corrected in high school or in college composition classes, but still persists.
• Students are still using way too much passive: “It was decided …” should be replaced with “We decided …”.  Part of the problem here is that much of the writing they are exposed to overuses passive also—excessive passive is a common writing error for scientists and engineers, not just students.

Wording:

• “Firstly”, “secondly”, “lastly” ⇒ “first”, “second”, “last”. These are already adverbs and don’t need an “-ly” ending.  Strangely, I never see the corresponding problem with “next”, though it is in the same class of words that are simultaneously adjectives and adverbs.
• There are a lot of words that are compound words as nouns, but separable verb+particle pairs as verbs. For example, “setup” is a noun, but “set up” is a verb. Other examples include layout, turnaround, pickup, putdown, stowaway, flyover, and setback.
• Avoid the unit abbreviation mm², as it is too hard to tell whether you mean m(m²) or (mm)². Most often, the (mm)² interpretation will be made, but a lot of students used it for m(m²).  (Same for cm².)
• Many students are using “proportional” wrong, for any increasing function. The phrase “f proportional to d” means f=kd for some k, not just that f increases with d. Similarly, “T inversely proportional to d” means T=k/d for some k, not just that C decreases with d.

Punctuation:

• Capitalize at beginning of sentence and proper names only: “Schmitt trigger” not “Schmitt Trigger”, “Figure 3” but “many figures”. Figure names, table names, and equation names are proper nouns, so should be capitalized: “There are three figures on the last page: Figures 4, 5, and 7”.
• Unit names are not capitalized (hertz, volts, amps, …), but symbols for units from people’s names are (Hz, V, A)
• Hyphenate a noun phrase used as a modifier for another noun: “Schmitt-trigger inverter” but “Schmitt trigger”.

Units matter

I was a little surprised by how many students had trouble with the following homework question, which was intended to be an easy point for them:

Estimate C2(touching) − C2(not touching), the capacitance of a finger touch on the packing-tape and foil sensor, by estimating the area of your finger that comes in contact with the tape, and assume that the tape is 2mil tape (0.002” thick) made of polypropylene (look up the dielectric constant of polypropylene on line). Warning: an inch is not a meter, and the area of your finger tip touching a plate is not a square meter—watch your units in your calculations!

Remember that capacitance can be computed with the formula
where is the dielectric constant,  8.854187817E-12 F/m is the permittivity of free space, A is the area, and d is the distance between the plates.

The problem is part of their preparation for making a capacitance touch sensor in lab—estimating about how much capacitance they are trying to sense.

There is a fairly wide range of different correct answers to this question, depending on how large an area is estimated for a finger touch. I considered any area from 0.5 (cm)² to 4 (cm)² reasonable, and might have accepted numbers outside that range with written justification from the students.  Some students have no notion of area, apparently, trying to use something like the length of their finger times the thickness of the tape for A.

People did not have trouble looking up the relative dielectric constant of polypropylene (about 2.2)—it might have helped that I mentioned that plastics were generally around 2.2 when we discussed capacitors a week or so ago.

What people had trouble with was the arithmetic with units, a subject that is supposed to have been covered repeatedly since pre-algebra in 7th grade. Students wanted to give me area in meters or cm (not square meters), or thought that inches, cm, and m could all be mixed in the same formula without any conversions.  Many students didn’t bother writing down the units in their formula, and just used raw numbers—this was a good way to forget to do the conversions into consistent units.  This despite the warning in the question to watch out for units!

A lot of students thought that 1 (cm)² was 0.01 m², rather than 1E-4 m². Others made conversion errors from inches to meters (getting the thickness of the tape wrong by factors of 10 to 1000).

A number of students either left units entirely off their answer (no credit) or had the units way off (some students reported capacitances in the farad range, rather than a few tens of picofarads).

A couple of students forgot what the floating-point notation 8.854187817E-12 meant, even though we had covered that earlier in the quarter, and they could easily have looked up the constant on the web to figure out the meaning if they forgot.  I wish high-school teachers would cover this standard way of writing numbers, as most engineering and science faculty assume students already know how to read floating-point notation.

Many students left their answers in “scientific” notation (numbers like 3.3 10^-11 F) instead of using more readable engineering notation (33pF). I didn’t take off anything for that, if the answer was correct, but I think that many students need a lot more practice with metric prefixes, so that they get in the habit of using them.

On the plus side, it seems that about a third of the class did get this question right, so there is some hope that students helping each other will spread the understanding to more students.  (Unfortunately, the collaborations that are naturally forming seem to be good students together and clueless students together, which doesn’t help the bottom half of the class much.)

Broken bike seat

Yesterday was not a good day for me.

First, I spent most of the day struggling with the homework for the control-theory class I’m sitting in on. The course is dual listed as an undergrad and grad course, with shared lectures but different homework and projects. The undergrad part of the homework was straight-forward, and I finished it Monday night, but the two additional problems for the grad students were tough.  One of them had a simple “engineering” solution that I got quickly by formal manipulation of the formulæ, but I could not justify some of the steps, since they involved a integral that was not finite.  The other problem was not difficult, but involved a rather tedious amount of algebra to linearize the system—the professor had done the linearization in lecture notes,  and we were just supposed to check it for the homework, but he’d made an error in algebra, so I had to redo the whole thing.

Late in the afternoon, I decided to take a break and replace the sump pump that had failed sometime in the past couple of weeks.  Originally I was going to disassemble the pump and see if the problem was repairable (I think that the switch for the float is not turning on reliably, possibly from corroded contacts), but I decided that I could do that later to have a spare pump, meanwhile getting a working sump pump.  (My house is built over a seep where an aquifer comes to the surface, and the water table is about 3 inches below the surface—during wet years, the water table is sometimes right at the surface.)

I put the old pump in my panniers and headed down to hardware store, when my bike seat suddenly failed.  I tried riding for a block with the failed seat and gave up and returned home.  The failure was right at edge of the block that holds the horizontal crossbar at the front of the seat:

Here is a view from the front showing the tubing displaced vertically from where it belongs.

A closer view shows a very clean break right at the surface of the block that clamps around the tube.

I probably should have had some warning about the imminent failure, as the bike has been creaking a bit more than usual when I pedal for the past several months, but I was never able to track down the creaking. I’m not sure I could have seen the crack that was probably propagating, since it was flush with clamp block.

The seat on my Longbikes Vanguard is not a standard, off-the-shelf component, so I’m probably going to have to custom order a new seat from the manufacturer (who no longer make the Vanguard model, so probably has no spare seats built) and wait weeks or months for one to be built.

I got my old upright bike down from the garage wall, inflated the tires, adjusted one of my panniers to fit the different rack, and headed off to the hardware store, carrying the old pump in the pannier. At the hardware store, I could not find a sump pump with the same outlet size as the old one (they all had bigger outlets). I needed to match, in order to hook the sump pump up to the existing plumbing. Luckily, they did have a reducer that would adjust for the difference.

After buying the pump, I went out to my bike and realized that I couldn’t fit both pumps into one pannier—in fact the new boxed sump pump wouldn’t fit into the pannier even by itself. Normally I carry a bungee cord or two for strapping stuff onto my rear rack, but those were left on the other bike. So I had to go back into the hardware store to buy some new bungee cords—not a big deal, but an irritation.

The bike was a bit wobbly on the way home—I’d forgotten how much difference a high center of gravity makes on an upright bike—and the bike has much twitchier steering than my recumbent anyway—but I got home without incident.

On getting home, I immediately attached the pluming to the new sump pump and lowered it into the sump. Let me correct that—I tried to lower it into the sump, but it wouldn’t fit. The pump was a couple of inches wider than the old pump and though the hole at the top was more than wide enough, it narrowed significantly where the bottom of the foundation for the house spread out, and the remaining hole was simply too small for the new pump. This was particularly frustrating for me, as I was meeting my wife downtown for dinner in less than an hour, and I was going to have to walk rather than bike, so I only had about 10 minutes to come up with a fix.

I then remembered something that should have occurred to me much earlier—I had another one of the small sump pumps in a different sump in the back garden. Quickly pulling it out and attaching the plumbing got the main sump working again (though I still need to recheck the plumbing for leaks). And it turned out that the garden sump was wide enough to accept the new pump—problem solved!

I cleaned up, grabbed a backpack so I could do some shopping after dinner, and walked down to the library to meet my wife. After the stresses of the day, I felt the need for comfort food, so we went to Betty’s Noodles, a hole-in-the-wall Chinese restaurant in the bus station. This restaurant has taken over the niche that Little Shanghai used to fill of providing cheap, tasty Chinese fast food (noodles and rice bowls).  I had ma-po tofu over Chow Fun noodles, which went a long way to de-stress me.  Going to Mission Hill Creamery for a plum sorbet cone afterwards helped also.

On the walk home, a couple blocks before we got home, I realized that I had not done my shopping! I decided not to go back downtown, but to do without my chocolate soymilk for a couple of days, until I can go shopping again.

This morning I finished the homework and submitted it. I’m still a bit bothered about the inverse Laplace transform problem that  can be formally solved but that ends up with a function that doesn’t have a Laplace transform, but I’m pretty sure I did what was expected. After turning in the homework, I realized that there was a possible different interpretation of part of the linearization question than what I did, so I queried the professor about what he really meant.  (The homework isn’t due for a week, so if there is a clarification needed, he can get it to the grad students before the homework is due.)

The TA does not grade my homework, since I’m just auditing, but I’m doing the homework using Python instead of Matlab, so I’m sharing it with the TA and professor anyway, so they can see whether it would be worth switching to free tools.

Currently, the scipy.signal package and matplotlib seem as easy to use at Matlab, but there is no equivalent of SIMULINK, which the professor is relying on for students doing simulations.  I can do the simulations in Python, but setting them up is all text-based, and requires thinking explicitly about the state vector, rather than having a GUI that does all the setup for you.

I bicycled up to campus today on my old upright, after adjusting my other pannier to fit the rack.  I had forgotten how uncomfortable an upright bike is.  This evening my neck and shoulders are sore, and I have chafing on the inside of my thigh.  I really hope I can get the recumbent seat replaced quickly, so that I can go back to riding comfortably!  It might even be worth taking the seat to a local frame-builder and finding out whether they could replace the tube, even if only for a temporary fix. (Although most of the bike is chrome-moly steel, the seat appears to be all aluminum tubing.)

Too much prelab homework for microphone lab

In putting together the book for this quarter, I added exercises to some of the chapters, and I assigned a chunk of them due today as the pre-lab exercise for the microphone lab.  I just spent over 3 hours grading the set, just marking questions right or wrong. There were too many questions, and even the best in the class got only 8/11, with the bottom of the class getting 3/11. I think that the class is doing better this year than previous years’ classes, but some of them got discouraged by how much and how difficult the homework was.  The amount was certainly more than I had intended, but next week’s homework should be substantially less.  I’ll have to figure out how to distribute the load more evenly next year.

I spent most of today’s lecture going over two of the questions (in response to student request), and I’ll have to do some of the other ones on Wednesday, in addition to showing them how to model DC behavior of the FET in the electret microphone. I may also ask the group tutor for the class to have an extra help session this week.  The two questions that got asked about were the modeling of the oscilloscope probe and computing the sensitivity of the electret microphone circuit with a different load resistor.

Some of the problems students had were ones that can be easily fixed (like that 1/10000 is 0 in gnuplot, because it looks like integer arithmetic—1/10E3 does the right computation, as does 1./10000).  Other problems were fundamental misunderstandings of complex numbers or complex impedance, which may be harder to address.