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2018 September 23

Learning outcomes for my electronics course

Filed under: Circuits course — gasstationwithoutpumps @ 17:15
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Faculty at UCSC are required to write “learning outcomes” for any new course they want to teach, and these outcomes are vetted by the Committee on Courses of Instruction, as part of the approval process for new or revised courses. I was on that committee for a couple of years, and most of the learning outcomes I saw were vague, generic statements about students understanding the content of the course—a rather useless expression, as “understanding” is not a measurable concept.  For memorize-and-regurgitate courses, there may not be any learning outcome beyond “knowing” a set of facts, but I would not want to teach such a course, nor am I aware of good ways to determine what students know.

Another common set of learning outcomes were very vague statements about reading, writing, or thinking that could be applied to almost any course at the university—general statements of desired outcomes of a university education, with no specific relationship to the course.

A good learning outcome should be something observable, not something internal to the student, even if what we are attempting to achieve is indeed an internal change of state, and a good learning outcome should be specific to a particular course (and perhaps even to a handful of assignments in the course). The hard part is coming up with good, observable proxies for the real learning we want students to acquire.

For my applied electronics course, I have a lot of different goals for students: to think like engineers, to work together effectively, to meet deadlines, to write well, to design and debug, … .  But listing these broader goals as learning outcomes would be too vague, as they do not define what this particular course is doing, nor do they provide ways to measure whether they have been achieved.

The course is split into two halves (51A and 51B), with the following (cumulative) goals for the second half:

Students will be able to

  • draw useful block diagrams for amplifier design.
  • use simple hand tools (screwdriver, flush cutters, wire strippers, multimeter, micrometer, calipers, … ).
  • hand solder through-hole parts and SOT-23 surface-mount parts.
  • use USB-controlled oscilloscope, function generator, and power supply.
  • use python, gnuplot, PteroDAQ data acquisition system, and Waveforms on own computer.
  • do computations involving impedance using complex numbers.
  • design single-stage high-pass, band-pass, and low-pass RC filters.
  • measure impedance as function of frequency.
  • design, build, and debug simple op-amp-based amplifiers.
  • draw schematics using computer-aided design tools.
  • write design reports using LaTeX and BibTeX.
  • plot data and theoretical models using gnuplot.
  • fit models to data using gnuplot.

Note that these outcomes ask for observable skills, not internal states of the student’s mind—I ask that students draw schematics, not that they understand schematics, I ask that they design, build, and debug amplifiers, not that they know how to.

These learning outcomes are very specific for this course—indeed, for just the most recent offering of the course, as we did not use SOT-23 components or USB-based instruments until 2017–18.  They are also all evaluated repeatedly during the quarter (though some tools, such as the calipers, are only used once).  In order to pass the course, students have to have done all these things, at least at a minimal level, and the student’s portfolio of work for the course shows ample evidence of their skills.

I’m also convinced that students who show that they can do all these things in the course as it is structured have also met the vaguer goals of thinking like engineers, working together, and meeting deadlines.

For my readers who design courses: what have you come up with for listing learning outcomes?  Are there ways that I could improve the list I have?

2014 April 11

Arthur Benjamin: Teach statistics before calculus!

I rarely have the patience to sit through a video of a TED talk—like advertisements, I rarely find them worth the time they consume. I can read a transcript of the talk in 1/4 the time, and not be distracted by the facial tics and awkward gestures of the speaker. I was pointed to one TED talk (with about 1.3 million views since Feb 2009) recently that has a message I agree with: Arthur Benjamin: Teach statistics before calculus!

The message is a simple one, though it takes him 3 minutes to make:calculus is the wrong summit for k–12 math to be aiming at.

Calculus is a great subject for scientists, engineers, and economists—one of the most fundamental branches of mathematics—but most people never use it. It would be far more valuable to have universal literacy in probability and statistics, and leave calculus to the 20% of the population who might actually use it someday.  I agree with Arthur Benjamin completely—and this is spoken as someone who was a math major and who learned calculus about 30 years before learning statistics.

Of course, to do probability and statistics well at an advanced level, one does need integral calculus, even measure theory, but the basics of probability and statistics can be taught with counting and summing in discrete spaces, and that is the level at which statistics should be taught in high schools.  (Arthur Benjamin alludes to this continuous vs. discrete math distinction in his talk, but he misleadingly implies that probability and statistics is a branch of discrete math, rather than that it can be learned in either discrete or continuous contexts.)

If I could overhaul math education at the high school level, I would make it go something like

  1. algebra
  2. logic, proofs, and combinatorics (as in applied discrete math)
  3. statistics
  4. geometry, trigonometry, and complex numbers
  5. calculus

The STEM students would get all 5 subjects, at least by the freshman year of college, and the non-STEM students would top with statistics or trigonometry, depending on their level of interest in math.  I could even see an argument for putting statistics before logic and proof, though I think it is easier to reason about uncertainty after you have a firm foundation in reasoning without uncertainty.

I made a comment along these lines in response to the blog post by Jason Dyer that pointed me to the TED talk. In response, Robert Hansen suggested a different, more conventional order:

  1. algebra
  2. combinatorics and statistics
  3. logic, proofs and geometry
  4. advanced algebra, trigonometry
  5. calculus

It is common to put combinatorics and statistics together, but that results in confusion on students’ part, because too many of the probability examples are then uniform distribution counting problems. It is useful to have some combinatorics before statistics (so that counting problems are possible examples), but mixing the two makes it less likely that non-uniform probability (which is what the real world mainly has) will be properly developed. We don’t need more people thinking that if there are only two possibilities that they must be equally likely!

I’ve also always felt that putting proofs together with geometry does damage to both. Analytic geometry is much more useful nowadays than Euclidean-style proofs, so I’d rather put geometry with trigonometry and complex numbers, and leave proof techniques and logic to an algebraic domain.

2013 December 23

Different levels of the “same” course

Filed under: Uncategorized — gasstationwithoutpumps @ 12:46
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In thinking about the redesign of the bioengineering curriculum, I’ve had to pay a lot of attention to what level of courses the engineers would be required to take.  Our campus offers physics at three different levels (one algebra-based, the other two calculus-based) and calculus at 4 levels (honors for math majors, for physicists and engineers, for life scientists, and for economists). Do I allow the students to take either of the calculus-based physics courses? Do I allow any of the three calculus classes (excluding the one for economics majors)?  I’ve wrestled with this problem for a while (see for example, my post Physics for life-sciences majors from last June).

In favor of allowing the lower level courses:

Usually there is the most scheduling flexibility for the second-lowest level—the level aimed at biology majors—because that is where the largest numbers of students are, so the courses get offered repeatedly during the year, while the more advanced courses get offered only once.  So from a scheduling standpoint, it would be best if students were able to take those courses.

In bioengineering, we also get a lot of students who start out in biology, but who later realize that other majors are more interesting (freshman year everyone thinks they want to go to med school—most have given no thought at all to engineering).  Because the biology majors are advised to take the calculus and physics courses intended for biologists, the students have taken only those and not the higher level calculus and physics courses intended for engineers.  So a change of major is easier if students are allowed to take the biology-level calculus and physics.

One thing I’m trying hard to avoid in the bioengineering curriculum redesign is “creeping prerequitism”—the tendency for most courses to gradually increase the prerequisites in order to have better prepared students in the course.  In many cases the prerequisites are irrelevant to the material of the course (like multi-variable calculus for a data structures course or genetics for a cell biology course), but are just filter prereqs, to make sure the students have more “maturity” by having passed a gantlet of other course.  Because of these prerequisites (both real ones and filter ones) being added independently by each of the 8 or 9 departments that teach courses required for bioengineers, we end up with a program grossly overloaded with lower-division “preparation” courses, and not enough upper-division “application” courses.

Against allowing the lower-level courses:

In exit interviews with seniors last spring and this fall, we asked them about their experiences in calculus and physics.  Those who had taken the lower level of calculus-based physics course felt that it had been a waster of their time—neither their classmates nor their professors seemed to care much about whether the material was learned, and everything was covered rather superficially.  (We didn’t get the same info about calculus, because most had been forced to retake the higher-level calculus class if they had only taken the biology-level one.)  So from a pedagogic standpoint the students get a better course if they take the higher level with students who expect to use the material and with professors who expect their own majors to be taking the course.

Some upper-division courses do rely on math and physics skills of the more advanced courses.  For example, the upper-division probability and statistical inference classes do rely on students being adept at integration, the statics and dynamics course relies on students knowing Newtonian mechanics well and being able to handle differential equations, and the electronics courses require some skill with calculus and differential equations.

Concluding thoughts

I read an blog post today by a high-school physics teacher addressing a similar question at the high-school level: Jacobs Physics: How do you tell the difference between AP and “regular” physics?.  He doesn’t have to face what courses students are required to take, but only which ones they should be advised to take, but the underlying questions are the same. In the post, Greg Jacobs writes

If an AP and a Regular course cover the same “standards,” how are the two classes different?

Don’t use standards to define courses; use tests and exams, preferably as written by someone external to the course, to define courses.  Once you’re clear on the level, topics, and depth of question that your students will be expected to answer, then you can make up a concordance with any state standards you need to.

The AP Physics 1 exam covers much of the same material as regular/Regents. The major difference is the depth of that coverage, as evidenced in the test questions.

A regular question can generally be categorized in a single topic area, and can be answered in one step, or two brief steps, or a one-two sentence explanation with reference to a single fact of physics.

An AP question generally requires cross-categorization across two or three topic areas. Most require multi-step reasoning, or a two-three sentence explanation with reference to more than just one fact of physics. AP questions, for the most part, require students to make connections across skills and topics.

As an additional comparison, you might consider a conceptual class. Conceptual Physics can cover many of the same topics as “regular” physics, but without using a calculator.  …  A conceptual approach provides a greater contrast between AP and non-AP physics.

The key idea here is that the difference between levels is not in what subjects are covered, but in the expected skills of the students after taking the course. That holds true at the college level as well—I can’t decide based just on catalog copy what level of course students need, because the catalog copy only lists topics, not the complexity of the problems that students who pass will be able to solve.

In the interest of minimizing filter prereqs, but making sure that all genuine prereqs are met, I’m suggesting requiring the higher level for the bioelectronics and assistive technology: motor tracks, but allowing the lower calculus-based physics for the biomolecular and assistive technology: cognitive/perceptual tracks.  I am suggesting requiring the physicist/engineer track for calculus in all tracks, since it is needed for a higher-level course in all of them. It’s not the same course in each track, but electronics, statics and dynamics, and statistical inference all require greater facility with calculus than the calculus-for-biologists track provides.

2013 October 10

xkcd: Null Hypothesis

Filed under: Uncategorized — gasstationwithoutpumps @ 22:10
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I have a number of my favorite xkcd comics on the bulletin board outside my office, including this one:

(Click on the image to go to the website to get the mouseover—I don’t have it on my bulletin board, but it is worth the effort of clicking.)

Today I had a student ask me to explain the joke—more precisely, to explain what “the null hypothesis” was.  I did so, of course, explaining how the p-values that calculate how likely something is “by chance” need a  formal definition of “chance”—the null model or null hypothesis.  I even explained that all statistical tests do is to allow you to reject (or not reject) the null hypothesis—that they tell you nothing about the hypothesis you are actually testing.

Given the casual nature of the question, I did not go into detail about how important it is to choose or construct good null models—ones that contain all the explanations other than hypothesis you hope to test.  I normally spend a full lecture on that in my bioinformatics course, as well as one of the weekly homework assignments, having the students program different null models for an open reading frame that result in very different p-values for a protein-coding gene detector.

Normally, I enjoy this sort of conversation with students—I like students who are curious and who are unafraid to ask questions to clear up things that confuse them.  Today I was a little disturbed by the question, as the student had been in my office to get a signature on an approval form for a senior thesis in bioengineering.  How had the student gotten that far in our program without having learned what a null hypothesis is?  Where is the hole in our curriculum that allows that, and how can we fix it in the curriculum redesign this year?

I realize that no curriculum design can completely cure the cram-and-forget disease that infects many college students, but I did not get the impression that this was a student who had known it once but forgotten.  Rather, I had the impression that the concept was a new one, though the name might have appeared before.

On looking over the bioengineering curriculum I see that students can take a probability course without any statistics course—perhaps that is what happened here.  Unfortunately, biomolecular experimentalists have to be very familiar with null hypotheses and statistical tests, so I think we have patch the curriculum to make sure that all the students get statistics.

2013 October 5

Balancing fun and fundamentals

In Computing is a Liberal Art » Automatons and Entertainers, Keith O’Hara writes

One oft-cited axiom in the MOOC debate is that Math and CS are easier to MOOC-itize than other fields. This is one fact that crosses the intellectual aisle. MOOC-leaning scientists and anti-MOOC humanists both take for granted that the teaching of math and programming should be the first to be automated. As you might have guessed, I whole-heartedly disagree. If you can’t automate the teaching of writing you can’t automate the teaching of math. You can automate multiplication drills, but you can also automate spelling drills. Humanists don’t consider spelling writing, Mathematicians don’t consider multiplying math. And for the record, computer scientists don’t consider programming language syntax computer science. Spelling is necessary to write. Multiplication is necessary to do math. Writing grammatically correct programs is necessary to study algorithms. But those aren’t the interesting parts of those disciplines, for exactly that reason, they can be automated. Academics are concerned with new knowledge, and that necessarily lives on the boundary of what is known and what is unknown. And if we can automate something, we know it very well.

I agree with him whole-heartedly.  The Java syntax courses that pass for first programming classes are a lot like spelling, grammar, or arithmetic drills.  They are essential skills, but boring as hell. Details matter, but details are not the whole picture.

One approach that gets used a lot in K–12 education is to drop the drills and concentrate on the “fun” parts.  This has dominated English teaching at the elementary and secondary school levels for a while now, so that many students entering college cannot spell and have only the vaguest notions of what a grammatical sentence is.  They’ve also only written self-reflections and literary analysis—styles of writing that have little existence outside English classrooms. Some math curricula have gone the same way, and students are entering college unable to multiply or add fractions and with only vague ideas about algebra, trigonometry, or complex numbers.  I can’t support a system in which fundamental concepts are ignored in this way.

Another approach is not to allow kids to do the fun stuff until they have mastered the fundamentals (the finish-your-spinach-or-no-dessert approach).  Unfortunately, the result is that many students never get to the fun stuff, and end up believing that huge swaths of knowledge are inaccessible and uninteresting.  Note: this approach dominates many engineering schools, which do a bottom-up approach teaching years of math, physics, and “fundamentals” before getting to engineering design, which is the heart of the field—the result is often a very high attrition rate and “engineers” produced who can’t actually do any engineering.

I think that a balanced approach, that mixes fun stuff in from the beginning but continues to teach the boring details, is essential to effective teaching in any field.

I am trying to create such courses for the bioengineering majors at UCSC: the applied circuits course, for example, and a new freshman design seminar. The bioengineering major at UCSC probably has the least engineering design of any of the majors in the School of Engineering (except for Technology and Information Management, which I don’t think belongs in the School of Engineering).  I want to fix that flaw in the curriculum, but it is hard to overcome the “you have to know all this before you can do anything” attitude of both students and faculty.  Fitting in all the prerequisite chains for math, physics, chemistry, biology, programming, and statistics makes it very difficult to schedule courses for freshman—students need to get prereqs done early enough that they can finish in 4 years.

I think that the computer engineering department at UCSC does a good job of mixing in engineering design down to at least the 2nd year courses (I’ve not looked at their freshman courses lately—they may be doing well there also).  I’m less impressed with what computer science has done, though the large sizes of their courses make good teaching and design content harder to incorporate.  Their game-design major does get into design much sooner than the standard CS course sequence, I believe. I’m decidedly unimpressed with EE, where there is no design content at all until the 3rd or 4th year, even where it could have been easily incorporated.

Note that engineering design is damn hard to MOOCify.  The essence of design is that the answers are not known in advance—there are many ways to achieve desired design goals.  There are also many different tradeoffs to make in setting the design goals.  Students not only have to come up with designs, but have to build and test them—the real world is very important in engineering, and simulation is rarely an adequate substitute. (Note, I’m not saying that engineering students should not use simulations. Learning how to use simulators properly and what their strengths and limitations are is an important part of engineering education—but simulation-only education is not sufficient.)

One problem I am facing in trying to improve the bioengineering curriculum is that most of our bioengineering students are in the biomolecular engineering track.  Molecular engineering is decidedly slower and needs more science background than most other fields of engineering (which is why it is mainly a graduate field elsewhere). It is particularly hard to provide freshman with design experience in molecular engineering.

UCSC has one honors course that attempts to provide this experience to freshmen, but the capacity in the course is only about 20 (shortage of wet-lab space and teaching resources), and probably only 3 or 4 bioengineering students qualify for the honors course—what do we do with the other 50–100 bioengineering freshmen?

The freshman design course I’ll be creating this winter will be able to handle maybe half of them, but it will be focusing on designing low-cost do-it-yourself instrumentation, not molecular engineering.  (I’m hoping that we can entice more students into the bioelectronics and rehabilitation tracks, and reduce the load on the biomolecular track.) The course is just 2 units, not 5, so that students can add it to a nominally full schedule, without delaying any of their required courses. That was all I thought I could get students to take with the current curriculum.

I’d like to have a required 5-unit course with substantial engineering design in the freshman year, and not just a 2-unit optional course, but I don’t currently see how to fit that in even with a revised curriculum—it would require reducing the chemistry requirements for the degree substantially, and the Chem department is unlikely to create a faster route to biochem.


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