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2016 April 10

Transfer of learning

Filed under: Circuits course — gasstationwithoutpumps @ 09:58
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In a recent e-mail list discussion, being a math major was justified by the transferability of problem-solving skills from one domain (math) to others (banking, sales, and other jobs).  This justification for studying math is a popular one with mathematicians and math teachers.  One of the primary justifications for requiring geometry, for example, is that it teaches students how to prove things rigorously.​  The same case for transferable problem solving can be (and has been) made, perhaps even more strongly, for computer science and for engineering fields that do a lot of design work.
I was a math major (through and MS) and I got my PhD in computer science, and I certainly believed that the constant practice at problem solving made me better at solving certain classes of problems—ones with clear rules, not social problems or biological ones.
Education researchers have tried to measure this transfer effect, but so far have come up empty, with almost no indication of transfer except between very, very close domains.  I don’t know whether the problem is with the measurement techniques that the education researchers use, or whether (as they claim) transferability is mainly an illusion.  Perhaps it is just because I’m good at problem solving of a certain sort that I went into math and computer science, and that the learning I did there had no effect on my problem-solving skill, other than tuning it to particular domains (that is, perhaps the transferable skill was innate, at the learning reduced transfer, by focusing the skills in a specialized domain).
Two of the popular memes of education researchers, “transferability is an illusion” and “the growth mindset”, are almost in direct opposition, and I don’t know how to reconcile them.
One possibility is that few students actually attempt to learn the general problem-solving skills that math, CS, and engineering design are rich domains for.  Most are content to learn one tiny skill at a time, in complete isolation from other skills and ideas. Students who are particularly good at memory work often choose this route, memorizing pages of trigonometric identities, for example, rather than learning how to derive them at need from a few basics. If students don’t make an attempt to learn transferable skills, then they probably won’t.  This is roughly equivalent to claiming that most students have a fixed mindset with respect to transferable skills, and suggests that transferability is possible, even if it is not currently being learned.
Teaching and testing techniques are often designed to foster an isolation of ideas, focusing on one idea at a time to reduce student confusion. Unfortunately, transferable learning comes not from practice of ideas in isolation, but from learning to retrieve and combine ideas—from doing multi-step problems that are not scaffolded by the teacher.
“Scaffolding” is the process of providing the outline of a multi-step solution, on which students fill in the details—the theory is that showing them the big picture helps them find out how to do multi-step solutions themselves.  The big problem with this approach is that students can provide what looks like excellent work, without ever having done anything other than single-step work.  De-scaffolding is essential, so that students have to do multi-step work themselves, but often gets omitted (either by the teacher, or by students cheating a little on the assignments that remove the scaffolding and getting “hints”).
I find myself gradually increasing the scaffolding of the material in my textbook, so that a greater proportion of the students can do the work, but I worry that in doing so I’m not really helping them learn—just providing a crutch that keeps them from learning what I really want them to learn.  I don’t think I’ve gone too far in that direction yet, but it is a constant risk.
I’ve already seen students copying material from this blog as an “answer” to one of the problems, without understanding what they are doing—not being able to identify what the variables mean, for example. (I used different notation in class than I used in the corresponding blog post—a trivial change in the name of one variable.)  I’m trying to wean students off of “answer-getting” to finding methods of solution—the entire process of breaking problems into subproblems, defining the interfaces between subproblems, and solving the subproblems while respecting the interfaces.
I do require that the students put together a description of the entire solution to their main assignments—a design report that not only describes the final design, but how the various design decisions were made (what optimizations were done, what constraints dictated what part choices, and so forth).  This synthesis of the multi-step solution at least has the student aware of the scaffold, unlike the fill-in-the-blank sorts of lab report which makes the scaffold as invisible as possible to the student.
I also try very hard for each design problem to have multiple “correct” solutions, though some solutions are aesthetically more appealing than others.  This reduces the focus on “the right answer” and redirects students to finding out how to test their designs and justify their design decisions.
I have been encouraged by signs of problem-solving skills in several students in the course (both this year and in previous classes).  Often it is in areas where I had not set up the problem for the students.  One year, a student came up with a good method for keeping his resistor assortment organized and quickly accessible, for example.  This year, one pair of students used their wire strippers and blue tape as an impromptu lab stand for their thermometer and thermistor, to save the trouble of holding them.
The problems students set themselves often lead to more creative solutions than the ones set for the class as a whole—but how do you set up situations in which students are routinely identifying and solving problems that no one has presented to them?  I believe that the students who identify problems that no one has pointed out to them are the ones who become good engineers, but that attempts to teach others to have this skill are doomed by the very attempt to teach.  Capstone engineering classes are one attempt to get students the desired experience, but I think that in many cases they are too little, too late.

2016 February 20

On not using kits for a design class

Filed under: freshman design seminar — gasstationwithoutpumps @ 10:07
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A question came up in e-mail from a student in my freshman design seminar that I had planned to discuss in class, but I ran out of time before getting to it:

Upon determining the actual parts and part numbers for our design, its become increasingly apparent that the DIY kits neatly contain all of the parts we require. Considering this, we wanted to recap with you regarding the DIY kits from our projects. Are we allowed to purchase a kit and build our pulse monitor from it, or are we only allowed to use some parts but not the entire kit?

I answered the student after class, but I wanted to share my thinking more widely.

I like kits in many ways—I learned a lot from building Heathkits as a kid (see Thanks, Dad), but there are limits to what a kit can do for learning, particularly if people just assemble the kit with little or no attempt to understand what each part is for and how the whole thing works.

In a freshman design course, where students know very little or no electronics or programming when they start, the projects that they can reasonably tackle have to be quite simple. Most of the problems that they can solve have been solved before, and solutions by experienced engineers are easily found. Furthermore, commercial solutions are often available for less money than the parts needed to build them, due to the high cost of stocking, distributing, and shipping low-volume parts.

So students who see their role as answer getting are easily convinced to grab one of the good designs so readily available on the Internet and present it as the solution—very little work on their part and a good design, so what could be better?

The problem, of course, is that it is not the goal of the course to have a pulse monitor, an LED cube, or an ultrasonic rangefinder—none of those were part of the syllabus.  I can buy a pulse monitor for a few bucks, and for under $2 an ultrasonic rangefinder module that works better than anything the students are likely to come up. A finished RGB cube is a bit more expensive, but kits are still pretty cheap. One can buy the products the students could produce for far less time and effort than designing and making them. So the product is not the goal of the course.

The goal of the course is for students to (begin to) learn to design things.  This means doing things like writing specifications, drawing schematics, building prototypes, debugging prototypes, writing design reports, and doing iterative prototyping. It means learning a lot about how things work—not everything, but the specific details they need for the projects they have selected. The process of design is the core of the course, not the product of the design.

Buying a kit and assembling it short circuits a lot of that design learning.  You can build a kit and get it working with little or no understanding of how it works, and with no ability to modify the design. Of course, it is not the bundling of parts into a a kit that is the problem—copying a design off the Internet and buying the parts separately also does little to help students learn design. If you just copy other people’s work, then little learning takes place, and there is not much point to doing the class. Perhaps there is a little skill learning—how to use a soldering iron or an oscilloscope and how to order parts from a distributor, but not much how-to-design learning, which is the main point of the course.

That is not to say that students shouldn’t be looking at designs on the web!  Indeed, the freshmen do not have enough of the basic building blocks of electronics and programming to come up with their own designs de novo (though by their senior year they should be able to, if they continue into the bioelectronics or assistive technology: motor concentrations). So they need to look at solutions others have come up with, in order to know where to start on the design. But they should not just pick one design and implement it—they should be looking at several designs and trying to find common elements, figuring out what tradeoffs the different designers have made. Some of the designs come with good explanations of how they work—they should be reading those very carefully, so that they can follow the design decisions and reproduce the design from understanding.

Understanding designs well enough to explain each part, how it functions, and what the effects would be of changing the part may be enough at this stage of their design learning. Part of the point of the freshman design course is to inspire them to want to learn the foundations in other courses, many of which seem to students to be irrelevant gatekeeper classes to survive by cram-and-forget techniques. If they have some idea why complex numbers are important for filter design, or why capacitors are useful, they are more likely to pay attention in those parts of math and physics classes and to retain the knowledge later on.  Of course, it would be best if the math and physics classes included more of the inspiration themselves, but there are many different applications for the material, and it is difficult to find universally inspiring applications—what excites a math major, a computer science major, a physics student, or a bioelectronics student may be quite different, but the same course has to serve all of them.

My role in the classroom is to provide explanations for those things that the students have trouble figuring out on their own, give them generic guidance in the design process, anticipate things they will need to know, and try to hurry them up (in the past most waited far too long before starting their projects, with the result that they get very little done). Having three different projects going on at once means that there is not enough class time for students to get everything they need from me—they must be reading on their own and trying to understand their project thoroughly, but based on the time logs they have been submitting, few in the class have been doing that—they mostly seem to be waiting for me to tell them what to do, which is not going to work for them. I had hoped that having students pick their own projects would inspire them to investigate the projects more deeply without my having to keep kicking them with assignments, but that only seems to be working for a few of the students.

Some aspects of the design they can do—for example, everyone in the class should now be able to size a current-limiting resistor for an LED, and those who need amplifiers should be able to make a simple non-inverting amplifier out of an op amp.  (Hmm, I should probably give a quiz on those ideas next week—maybe the students have absorbed less than I expect.) By this point, the students should be asking about those parts of the design that they don’t understand, but I’m not getting very many questions, despite starting each class asking for questions and covering student-requested material before anything that I have queued up as things students might need.

A big chunk of what the class is trying to do is to nudge students away from regurgitating factoids that have been spoonfed into learning for the sake of understanding deeply enough to do things themselves—that means generating a lot of the questions themselves and seeking solutions by trying things out, and not just by looking up “the answer” or waiting for a teacher to tell them what to do and what to think.  That is a hard transition for many students to make, as they have been steeped in “answer-getting” culture for the past 13 years.


2014 May 14

Mixed topics in lecture

Filed under: Circuits course — gasstationwithoutpumps @ 21:27
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Today’s lecture was a mish-mash of different topics.

Pre-lab assignments not getting done.
I asked the students for advice on how to get them (or next year’s class) to do the pre-lab assignments before coming to lab, rather than wasting lab hours doing homework that doesn’t need the fancy lab equipment. I told them some ideas I had had, and how everything I’d tried so far had not worked. The only idea they thought might work was requiring that pre-lab assignments be turned in the day before the lab, so that they would prioritize the work. I’ll have to look to see if that is feasible for any of the labs left this year.
Answer getting
I talked again about the “answer-getting” mindset, and how it wasn’t an appropriate one for engineers. The problems they’ll face in industry are open-ended ones, where there isn’t a single unique answer—no one is going to be giving them multiple-choice tests. They’ll have to come up with designs, justify their design choices, and document them well enough that someone else can maintain things after they get hit by a beer truck.
Subdividing problems
I told them that I was deliberately giving them long multi-step design problems so that they could get used to subdividing problems and tackling them a little a time. I had noticed that some of them were stopping as soon as they got to a subproblem they didn’t know how to handle, rather than leaving a symbolic value for the result and solving the other subproblems. It is a lot easier to fill in one hole in a long computation than to have to do the whole thing from scratch each time.
Engineering by design or by tinkering
There are two different styles of engineering: one which uses careful modeling and calculation to try to get a design that works correctly first time, and one that consists of making quick reasonable guesses, trying them out, and adjusting the design to correct problems. I confessed that as a hobbyist, I generally prefer design by tinkering, but most modern electronics does not lend itself to tinkering, because the parts are too small for hand soldering, so one needs to go through a more expensive PC board design and pick-and-place assembly to build a prototype. I did, accidentally, tell them a lie—I said that the MCP6004 quad op-amp chip they are using is available in a 2mm by 3mm package, but that package is for the 8-pin MCP6002 dual op-amp chip, and the smallest for the MCP6004 is 4mm by 6.4mm (substantially larger than 2 MCP6002 chips!). This week’s lab was intended to be a compromise between the two design styles, with Tuesday being engineering by design for the first stage and today and Thursday being tinkering to correct the problems of the first stage, but only one group got to the point on Tuesday of having a partly functional design that could be tweaked.
Results from stage 1
I had a student whose group had gotten stage 1 working in lab yesterday talk about what he and his partner had seen on the scope. He mentioned the voltage going very high when there was no finger blocking the light (and we talked a bit about saturation, pointing out the similarity to the loudspeaker lab, where they observed clipping from either voltage or current saturation—I even managed to tie in the chemical concept of saturated solutions). He talked about how the voltage dropped to Vref+100mV with a finger blocking the light. He mentioned the large 60Hz noise on top of this DC signal, and the tiny voltage that may have been from the pulse. I gave the students some ballpark figures for the sorts of currents that they might see from their phototransistor (based on both what the first group saw and what I had seen at home): about 90–150nA DC and about 2–10nA for the pulse.
Gain of first stage
We talked about ways to increase the gain of the first stage and the desirability of making it as big as possible without saturating at the top rail. One subject that came up (in response to a student question) was increasing the headroom by dropping the reference voltage for the transimpedance amplifier. That brought up the other constraint on that voltage—biasing the phototransistor. The spec sheet gave a VCE saturation voltage of 0.8v, and I suggested that they stay above that voltage (though I suspect that the design might work down to 0.7v since their currents are so small—something I should probably experiment with).
Need for filtering
I asked the students how to get rid of the DC bias, and by this point they all know that a high-pass filter was needed. We then discussed what sort of frequency range a heart rate might be (several were pretty clueless about this), but we eventually got to 30bm–240pbm, or 0.5Hz to 4Hz. I suggested that they might want a wider bandwidth, particularly on high end, to see the shape of the pulse as well. I talked about the need for a low-pass filter to reduce the 60Hz signal.
Synchronous sampling
With a little too much prompting, I managed to get them to come up with the idea of sampling at 60Hz, so that the 60Hz noise would be sampled at the same point on the waveform on each cycle and so be less of a problem. I also showed them that 30Hz or 20Hz would work just as well.
Active filters
Finally we got to what I had intended as today’s topic: modifying the transimpedance amplifier to include a low-pass filter. I showed them the transimpedance amplifier circuit again, and reminded them that the feedback did not need to be a simple resistor but could be a complex impedance. We drew the Bode plot for the desired gain of the amplifier using a 1/f (6dB/octave) rolloff, and I asked them how to design a complex impedance with that magnitude. They fairly quickly came up with the idea of using a resistor and capacitor, but at first they wanted to put them in series. We computed what the plot for that would be, and they decided to try parallel instead. Success! But almost out of time for the day, without talking about multi-stage filters or putting complex impedance in both arms of a voltage divider in the feedback loop for a bandpass filter.
Gnuplot boilerplate
I did give them a quick look at the boilerplate gnuplot script I wrote for them, that allows them to create models and test them out quickly with gnuplot, but I did not have time to work through an extended example of modifying the script for more complicated circuits, and I doubt that any of them will take the trouble to try it on their own.

I did not get a chance to tell them about the pressure on the finger being optimally between the systolic and diastolic blood pressure, but there should be time in lab for that tomorrow. By grasping the edge of a table lightly and gradually increasing the grip force, one can slowly increase the pressure until the finger throbs with the pulse—that is the amount of pressure you want to put on the fingertip.

I expect that I’ll be in the lab quite late with the students tomorrow, getting them to build their stage 1, tweak the feedback resistor (and capacitor) until the circuit has reasonable gain, then design and build their second stage. I’m betting that no one will have thought about what they need for the second stage, and most still won’t have a schematic even for the first stage.

On Friday, I’ll introduce instrumentation amps and strain gauges, for next week’s instrumentation amp lab. Monday will have to be class D amplifier design concepts, because Wed will be the quiz, and there is no Monday the week after next (Memorial Day), so we’ll have to develop class-D block diagram on Friday next week.

2014 May 12

Answer getting

Filed under: Circuits course — gasstationwithoutpumps @ 21:16
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I read a post last week by “Mathy McMatherson”, talking about students in his math “intervention” classes (which is the current euphemism for remedial math):

A Student with an Answer-Getting Mentality will:

Blurt Out 1-2 Word Answers because eventually I’ll say the right thing and the teacher will acknowledge it and then move on with the lesson and I can stop paying attention. If the teacher asks me why, I can just say “I don’t know” and they’ll explain it or just call on someone else. It’s easy for me to give a quick answer and be wrong. It’s hard for me to admit I struggle with this and need time to work it through knowing that it’ll probably be wrong anyway.

Assignments are Turned In On-Time but are Incomplete or Incorrect because I just want to be done with the problems as soon as I can so we can move on to the next thing. Once it’s done, it’s done and I don’t want to think about it again. I’ll get it back tomorrow with a grade so my teacher knows I did it, but I already forgot what the problems were about anyway.

Take notes and do problems with the teacher, but becomes disruptive during those ‘investigations’ they make us do every once in a while. When we take notes, I know what I need to write down. When we do problems, I know what the answer looks like—I just look at the examples we just did. But when we do investigations, I never know what they want us to do. Most of the time we don’t even finish—what’s the point? And the next day they just tell us what we were supposed to do anyway. Just tell me how to do it so I can move on.

Avoid Showing Work because the answer keys just have the answers on them, so I guess I should just do as much as I can in my head. This makes it easier for me to copy too, since I don’t have to worry about all that scratch work. But, deep down, I know I don’t show my work because I’m not confident in all of the steps that lead up to the answer and I don’t want to admit that by trying to put it down on paper and letting other people see my mistakes. Mistakes are bad, right?

“I’ll do it because the teacher told me” mentality. All I want is for the teacher to not bother me and let me sit here and think about other things. If I turn in my work, they’ll leave me alone.

These behaviors are not, of course, unique to remedial students.  I see versions of the behaviors even in quite good college students, continuing into grad school. Disruptive behavior is rare (college students just don’t bother showing up if they don’t want to participate), but avoiding showing work, forgetting a problem as soon as it is “done”, doing things only because the teacher requires it, turning in incomplete or incorrect work, blurting out random guesses—those I certainly see.

Of course, recognizing the ubiquity of a problem, or even its cause, does not necessarily lead to a solution. I still don’t know how to budge the students off their answer-getting mindset. Unfortunately the blog post does not furnish much in the way of suggestions, ending with

One of the things I’ve realized is that any intervention strategy has to address both this Answer-Getting mindset (which, as I write this post, I guess I could also call a Failure-Avoidance mindset) as well as any missing mathematical skills. This Answer-Getting mindset acts as a wall between my classroom and any long-term understanding—before any real learning can occur, I need to break these habits. As long as a student lives in fear of failure, they’ll never be able to learn as effectively as they could be. My very first goal in any intervention needs to be breaking down this wall and creating some kind of intrinsic motivation and self-worth.

So breaking down the answer-getting mindset is important, but how does one do that?

I try to combat the answer-getting mentality by requiring students to write up design reports that describe how they arrived at the design they came up with, and grading them primarily on the accuracy of their description and process, rather than the quality of the final design (though serious errors in the design or any errors in the schematic will result in a “REDO”). Most of my design problems don’t have a single “correct” answer, and the only way I can tell whether the design is any good is by following their chain of reasoning in creating it. As I mentioned in my previous post, some students are beginning to do a careful job of describing their design methods, while others appear to be just pulling numbers out of the air (there may be method in their designs, but they keep it well hidden).

To reduce “failure avoidance”, I try to keep any one assignment from having huge weight (I don’t have exams, for example, but only quizzes with the same weight as for weekly design reports, and with the same redo policy).

To reduce dawdling until the problem goes away, I commit to staying in the lab until every group has completed a working project.

None of these measures are enough, by themselves or together, to eliminate answer-getting mindset, but I think I’m making a little progress.  Does anyone have suggestions for other strategies I can try?


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