Gas station without pumps

2017 May 18

Midterm quiz doesn’t tell me much new

Filed under: Circuits course — gasstationwithoutpumps @ 09:53
Tags: , ,

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
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 x+jy as if it were x+y.

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: \frac{V_{out}-V_{ref}}{V_{in}-V_{ref}} = 1 + Z_{f}/Z_{i} . 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.


  1. I run into the same problem teaching troubleshooting. Unfortunately you can teach them knowledge but you can’t make them think. I despair…

    Comment by rich — 2017 May 18 @ 13:24 | Reply

  2. Maybe this course needs a stiff prerequisite class?

    Comment by V John — 2017 May 18 @ 14:25 | Reply

    • All prerequisites to the course were removed except differential calculus, as students appeared to have retained nothing from the Physics E&M course and I had to reteach the parts students needed anyway. The intent of this class was to be the first electronic course for the students (and, for many, the only electronics course), so there are no other suitable prerequisites. I’m trying to get some of them ready for the EE circuits course and for the Mechatronics course (though neither has my course as a prereq), and I’m trying to get others just to think like engineers—to be able to do easy amplifier designs and to be able to recognize things they have done before!

      Comment by gasstationwithoutpumps — 2017 May 18 @ 20:00 | Reply

      • My experience is that they appear to forget everything (sometimes quite actively) from a previous semester but still retain the framework that makes re-learning it quite easy. My experience is that my students have no experience with even the concept of “circuit” prior to taking Physics 2. Although my students are, in principle, quite different from yours, a colleague at a fairly selective university has the same problem with students taking a “constructivist” version of physics 2. They cannot use a battery and wires to light up a light bulb as a day 1 exercise. So it could be the prereq had more effect than you thought.

        Can you plot your current data based on whether they have passed the physics E&M class?

        Comment by CCPhysicist — 2017 May 23 @ 06:22 | Reply

  3. Do they think they cannot fail this class? That you will curve the quiz grades? That a mere technician with an engineering degree will never be replaced by an engineer from another school or another country that can think?

    For the better students (quiz grade) that have not done the homework, you need to show (with a midterm grade) how not doing the homework is hurting them. For the ones who copied homework, evidenced by a much lower quiz grade than the person who also got 30/50 or even 20/50 on the homework, this should be a wakeup call that this approach leads to an F. I see that all the time, by the way: perfect homework and negligible scores on the first test. There is a cargo cult view about high homework scores that confuses learning with points.

    I don’t really have the time right now to provide feedback on classroom methods, but one colleague swears by weekly quizes that are open (uncollected) HW notes. More to the point might be attendance. Active learning doesn’t work if they are not present. Maybe you should correlate attendance with quiz scores and see if being in class and active did matter.

    Comment by CCPhysicist — 2017 May 23 @ 06:16 | Reply

    • I’m not seeing many “high homework-low quiz” scores. I’ve talked to the most extreme outlier in that direction and found out a little about the causes, which are not related to the class itself, but to outside problems, which caused taking the quiz after over 24 hours without sleep. This was definitely not a case of a student copying for high homework scores, but a diligent student with outside problems.

      I think that some students feel they can’t fail (and the failure rate in the course has been only about 2% over the past several years), but there are a few this year in danger of failing, and the rate may go up. I’ve talked individually to several (though not all) students at the bottom of the class who have been freeloading on their partners in labs (different partners on every lab, so it becomes pretty obvious who the freeloaders are). They are now aware that they are in danger of failing if they flake out on their lab partners again.

      Perhaps a bigger problem is that senioritis has struck a number of the students. I’ve not done a careful check, but I was looking at the top 10 quiz grades looking for possible group tutors for next year, and I think that none (or only one) of them were graduating this quarter, while many in the lower half of the class were planning to. (That partially addresses the “did they pass the Physics E&M course” question also—almost all the people at the bottom of the class probably took Physics a year or more ago. Unfortunately, faculty have no access to data for answering questions about how students did in other courses, except by a very slow one-student-at-a-time process, or by asking staff to fetch the data and waiting a week or more.)

      Several of my students have made suggestions about ways that they think would help their learning:
      more drill-like homework on the basics (like the quiz questions)
      miniquiz (one question) at the beginning of each lab
      actually doing a somewhat facetious suggestion I made in class, of handing out schematics and having students circle different subcircuits (voltage divider, unity-gain buffer, …)

      I’ll try some of these next year, particularly having some exercises on reading schematics, because this year’s class seems to have more trouble understanding schematics than previous years’. Maybe I’m just more aware of the problem, because of the bigger class size producing more students showing the difficulty, or maybe students are getting less one-on-one help early on because of the bigger class size, and so a bigger fraction are falling behind.

      Comment by gasstationwithoutpumps — 2017 May 23 @ 07:43 | Reply

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