Gas station without pumps

2015 May 31

Confidence and not opting out

Filed under: Circuits course — gasstationwithoutpumps @ 09:06
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In the Geeky Mom blog, Laura Blanken, Computer Science Chair at The Baldwin School, a K-12 all-girls’ school in the Philadelphia suburbs wrote about The Confidence Code by Katty Kay and Claire Shipman (full article at Women and Confidence).

They found one study where men and women were given a test on 3D shapes. The men outperformed the women significantly, which some might think revealed a deficit in women’s spatial reasoning ability. A closer look at the results, however, showed that the women didn’t even answer a significant number of the questions and that’s where the difference in performance lay. They gave the test again, and this time, they told everyone they couldn’t leave an answer blank. When the results were tallied this time, the women performed as well as the men. When women try at most things, they do just as well. This result says to me that making things that people are afraid of mandatory might help eliminate the gap in performance between women and men. And yes, I’m thinking about Computer Science, but there are other things as well.

In my courses, I have not noticed a difference in achievement between men and women, but I have noticed some differences in confidence, though the sample sizes are small enough and the observations informal enough that it could all be biased observation.

I wonder whether the difference in willingness to put down answers that are not confident is part of the reason that the SAT removed their correction for guessing and effectively put in a penalty for leaving answers blank instead.  The effect would initially be to provide a boost for boys (who apparently are more willing to guess), but might eventually lead to more guessing by everyone as students got test-taking training telling them not to leave any answers blank.

The suggested intervention in the Geeky Mom blog is akin to one of the techniques in Teach Like a Champion by Doug Lemov: No Opt Out (Technique 1 in the first book, but 11 in Teach Like a Champion 2.0). While that might work on exams, I don’t think it is enough in the classroom, as it presupposes that you can get the students to participate in the first place. I think that it needs to be combined with Cold Call (technique 22 or 33, depending which edition of Teach Like a Champion you have).

I started this quarter doing a fair amount of cold calling, but by the end of the quarter I am doing very little—there were too many students who were not even willing to guess, and applying No opt out after cold calling was taking up a lot of time without having discernible good results for any of the students. I still do a little cold calling, but only on very easy questions (half the questions in the electronics class are answered with a voltage divider).

It bothers me that at the end of the quarter, I still have students unable to do the simplest design problem (sizing a DC bias resistor for a microphone, because they can’t apply Ohm’s Law coherently: they pick a random voltage in the system, rather than the voltage across the resistor). It isn’t even a matter of transference or dealing with unfamiliar problems, as we’ve done the same problem in labs and in class several times, but some students are still forgetting that there is a voltage across the microphone. It is as if they wipe their minds every week, and start fresh with no memory of anything they have done before.  I don’t know how to reach these students.

I suppose I could give them hundreds of almost identical problems so that they could, eventually, do that problem by rote, but there is no value in that. What I want them to learn is to figure out how to solve simple problems, not how to invoke rote procedures or ritual magic.  But if they can’t solve even the simplest problems after attempting the problem and being helped through the solution a dozen times, I don’t know what to do.

I do have a lot of students still who seem to believe that science and engineering are ritual magic: they hope to give the right incantation (“By Ohm’s Law” is a popular one, and “we calculated” is another), put down a random number copied from another student, and get full credit. I think that some of their other classes have trained them in this—biology classes are full of vocabulary tests where getting the right phrase is all that counts (understanding it is entirely optional) and physics and chemistry classes are full of homework and tests that are graded on “the right answer” with little attention paid to how they student got it (copying works well in those situations). I want to see their reasoning—what assumptions they made and how they applied Ohm’s Law (or whatever other principle is involved) to get their answer.

Copying does not work well in my electronics class, because the correct answers are not unique, and somewhat arbitrary design choices affect the correctness of other choices. For example, the correct size of the DC bias resistor for the microphone depends on the power supply voltage and on the operating point chosen for the microphone, both of which may be somewhat arbitrary. There are reasonable justifications for almost any size resistor from 2kΩ to 33kΩ, so there isn’t a “correct answer” that can be checked off—the reasoning behind the choice is the entire point of the exercise.  But I’ve had students try to size the resistor without choosing the power supply voltage (a sure sign of copying) or behaving as if the voltage across the microphone was 0V (inconsistent with the current they assumed through the microphone). They spent a full lab day measuring the current-vs-voltage characteristics of the microphone, so it can’t be that they have no idea that the current and voltage are related. Or wait—they already turned in that lab, so it is something to be flushed from memory and never thought of again!

Some days I despair of the future of engineering in the US—way too many of the students passing engineering classes are still incompetent as engineers. And I’m at a highly rated R1 university—I hate to imagine what it must be like at less selective schools. At least I get a few good students each year, and the pleasure of teaching and inspiring them can compensate for a lot of the frustration of not getting through to the students at the bottom of the class.

It is a good thing that we get away with only a small fraction of our workforce being competent, because that is the reality we live in.

2015 April 4

Third lecture: resistance and voltage dividers

Filed under: Circuits course — gasstationwithoutpumps @ 20:13
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Yesterday’s lecture was pure chalk talk, with no projector.  I took a number of somewhat random questions from students, then started on getting the class to try to define resistance. I got a number of fairly vague statements, until someone dredged up Ohm’s Law from their high school physics classes (or perhaps the reading they were supposed to have done before class), and suggested voltage divided by current, which is a good answer for this course.  I then explained to them the difference between resistance (V/I) and dynamic resistance (dV/dI) for non-linear devices, but I think that confused people more than helped them.  I should probably wait on the concept of dynamic resistance until they actually need it (perhaps with the electret mic?).

A question came up about how resistors were made, which I hadn’t planned to talk about, but was a reasonable digression, so I described wire-wound, metal-film, and carbon resistors.  We won’t use wire-wound resistors in this class, but half the class will have 1% metal-film resistors (bought last year) and half will have 5% carbon resistors (what the staff bought this year).  Maybe I’ll bring in a wire-wound power resistor to show them what they look like—the cooling fins on a 100W resistor are fairly impressive. I did tell them that they could experiment with carbon resistors by using pencil leads of different lengths, diameters, and compositions (the hardness of a pencil lead is dependent on the graphite/clay ratio, and the graphite is the carbon part of a carbon resistor).

I had the students do a simple Ohm’s Law exercise (3.3V across 1kΩ), then introduced a voltage divider with 5V across 2 1kΩ resistors in series. I had the students work out the current (after first getting them to realize that we needed to add a constraint that the current through the output is known to be 0A), and then the voltage output of the voltage divider.  I also had them work out what the effect would be if we tied the Vout node to ground, instead of having no current through it.

Throughout the class I relied on dice-assisted cold calling, so that students had to keep paying attention, lest they get called on without having thought about the question. As suggested in Teach Like a Champion, I asked the question before rolling the dice and choosing who would answer, so that (almost) all students were engaged with the question for at least a little while. I had 32 students registered in the class, so I was using D100 divided by 3 (round up) to get numbers on the class list, which is a bit slow.  I think I’ll switch to rolling a D8 and a D4, and computing 4*(D8-1)+D4 to get the numbers.

I did not get quite as far as I wanted to—we did not get to the general form of voltage dividers with all symbolic values (and I suspect that half the students are still having trouble switching from arithmetic to algebra, despite having had a couple of calculus classes and possibly more math). The material is in the book, which the students were supposed to have read before class (and probably didn’t), so they should be able to do the homework exercises for Monday’s class.

On Monday I’ll take questions about voltage dividers (I suspect that there will be some) and do a quick derivation of the Vout/Vin = R1 / (R1+R2) formula, perhaps in the form Vout/R1 = Vin/(R1+R2), since that corresponds directly to the notion of the currents being the same.  The rest of Monday’s lecture will be about temperature measurement using thermistors, RTDs, thermocouples, and diode junctions. I probably won’t have time for all of those, so I’ll concentrate on thermistors (which we’ll use in next week’s lab) and RTDs  (which are used for high-precision measurements in biological temperature ranges).  I don’t really care if we don’t cover thermocouples and diode-based temperature sensors, as neither are particularly important for bioengineers, and I have some material on them in the reading they are supposed to do by Monday..


2014 November 12

Autodidacts (against and for)

Filed under: Uncategorized — gasstationwithoutpumps @ 22:05
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Lately I’ve seen a lot of blog posts talking about autodidacts (people who learn things without teachers) as if they were some strange breed of alien being. For example, there is the post Ed tech promoters need to understand how most of us learn | The Hechinger Report, which includes the following paragraphs:

This is a very particular take on learning: the autodidact’s take. We shouldn’t mistake it for most people’s reality. Productive learning without guidance and support from others is rare. A pair of eminent researchers has gone so far as to call the very notion of self-directed learning “an urban legend in education.”

In a paper published in Educational Psychologist last year, Paul A. Kirschner of the Open University of the Netherlands and Jeroen J.G. van Merriënboer of Maastricht University challenge the popular assumption “that it is the learner who knows best and that she or he should be the controlling force in her or his learning.”

There are three problems with this premise, Kirschner and van Merriënboer write. The first is that novices, by definition, don’t yet know much about the subject they’re learning, and so are ill equipped to make effective choices about what and how to learn next. The second problem is that learners “often choose what they prefer, but what they prefer is not always what is best for them;” that is, they practice tasks that they enjoy or are already proficient at, instead of tackling the more difficult tasks that would actually enhance their expertise. And third, although learners like having some options, unlimited choices quickly become frustrating—as well as mentally taxing, constraining the very learning such freedom was supposed to liberate.

And yet, to paraphrase the economist Larry Summers: There are autodidacts. Look around. We all know at least one successfully self-taught expert, and the tech world is teeming with them. How’d they get that way?

While I do see a benefit to teaching (or I wouldn’t spend so much of my time teaching), I don’t think that the autodidacticism should be dismissed as “an urban legend in education”. In fact, the end goal of all my teaching is to turn out students who can continue to learn on their own, without needing the continuing crutch of having a teacher lead them. I’m not sure how successful I’ve been in a lot of cases—I see students for a 10-week class and then they disappear, giving me no clue whether they have developed new ways of learning that stay with them or they have just managed to fake it through my course and relapsed to expecting to be spoonfed immediately afterwards.

I think that Annie Murphy Paul has it wrong when she claims that few people can be autodidacts—she seems to be assuming that it is some sort of innate gift that one is born with (Carol Dweck’s hated “fixed mindset”). I am convinced that becoming an autodidact is something that most people are capable of. I recently read an account of one student who turned herself into an autodidact, and what prompted her to do it—How to become a programmer, or the art of Googling well | okepi:

He was the very picture of the competent hacker I held in my head, that I nursed a secret crush for. But most extraordinary, he threw something together using tools that he’d never used before. Yes, he did spend more time on Google than he did coding, but through sheer force of googling and a prior, general picture knowledge of how these things worked, he’d roped together a pretty sophisticated and working app. He knew where Twilio belonged in the grand hierarchy of things, knew exactly where to apply it, and so, even without knowledge prior, was able to figure things out.

And I despaired. How do you get so good that you can build something out of nothing?

The rest of the semester passed glumly, and without incident. Come winter, I began to panic again. Driven by the need to become employable, I tried my hand at a couple Code Academy website tutorials. Hm. Not bad. I made an attempt at my first website—pretty terrible, just one, static page full of boxes and awful colors, but it was something. Something I realized. Just like my code-god compatriot, when I didn’t understand something, all I needed to do … was google it.

To a large extent, the difference between the autodidact and the ordinary student is not one of competence, but of confidence. It is Carol Dweck’s “growth mindset”—the conviction that you can learn the material and are not doomed forever to learn only what someone predigests for you.  There are tremendous resources now available to everyone that can turn them into autodidacts: Wikipedia, for example, has thousands of excellent articles in all sorts of sciences (and the science articles suffer much less from point-of-view problems and vandalism than pop culture articles).  And, as “okepi” says, Google can find all sorts of answers for you (she goes on to much larger accomplishments later in her post).

I learn a lot of stuff on my own by reading Wikipedia articles, reading survey articles, reading research papers, googling stuff in StackExchange, going to weekly research seminars, even (sometimes) taking classes.  [The astute reader will have noticed that I did not include MOOCs or videos in that list—despite the claim that MOOCs are a godsend for autodidacts, I have found them profoundly unmotivating, and videos as a learning tool are just too bloody slow for my taste—I fall asleep before anything has been conveyed.]

There are some things for which teachers are essential—it is very hard to learn a foreign language well on your own, without a native (or near-native) speaker to help you hear the differences between what you say and how a native speaker would say it.  Theater is hard to do on your own (though a group of autodidacts could get together to learn to act).  Feedback on writing is very valuable, as is having an audience for public speaking. And there are times when it is useful to have the structure of a scheduled course to help with time management—to keep you on task to meet an external deadline when there are dozens of other things to do. But in a lot of cases, a textbook is all the structure that is needed, or an on-line tutorial document, or even just a particular problem that needs to be solved shaping what needs to be learned.  I learned those skills decades ago, and I think that my son learned them well by the time he was halfway through high school.

So I know how to be an autodidact, but how do I teach it to others?  That is a question I have no easy answers for. I try giving open-ended assignments, I try scaffolding by having students search for answers to specific questions, I try deliberately leaving material out of a lecture or a lab handout and telling students to go read about it in Wikipedia, and I try whatever else I can think of that will get students to learn on their own.  For some students something clicks, and they start doing more learning on their own—sometimes a lot more. For others, I’ve not found a secret sauce.

I particularly despair of those students who take copious notes in class and want to record my lectures (I have two of them this quarter)—they seem to have developed the attitude that I am the sole source of knowledge, and that if they just cram everything I say into their memories, they’re golden. But I’m not interested in hearing my words echo back to me—if I wanted that, I’d lecture to an empty classroom.  I’d much rather the students wrote down two or three keywords from my lecture, so that they could find what others had to say on the topic using Google and Wikipedia—or even looked up the topics I’m covering in the textbook (which does have an index). I’d rather that they thought about how to derive the algorithms we are learning in class, rather than trying to memorize what are really fairly arbitrary recursive definitions (and ones that are more easily derived than memorized).

Does anyone have any good techniques for converting note-takers into autodidacts?  Those are the techniques I need to learn (and I didn’t really see anything in Teach like a Champion that would help).


2012 November 28

Faculty discussion of online courses at UCSC

This afternoon I attended a Faculty Senate panel discussion on the future of on-line courses at UCSC.  A couple of the panelists had already taught on-line courses, and their presentations were particularly interesting.

One had taught a hybrid course where half the students attended live lectures and the other half watched videos of the lectures.  Both halves had required weekly hands-on discussion sections, so the course wouldn’t scale to MOOC sizes.  The bottom line was that there was no significant difference in performance between the on-line and live-class halves of the class, and that students spent a lot less time looking at the videos than predicted.  (The class has been offered 4 times to about 300 students each time, so this was not a small sample.)

The other professor is currently teaching a tiny boutique class (14 students, I think he said), using software that lets him lecture from his office, with a whiteboard window, a little web-cam video feed, and a chat window.  I’ve used similar software in conversations with the Global Physics Department (whose meeting tonight I missed, because of the panel discussion, but they were just discussing the College Board’s plan to split AP Physics B into two courses, which I’m not all that interested in).  When I gave a presentation to the GPD, I found it very difficult to present material on the whiteboard, talk, and watch the chat box all at the same time.  I asked the professor about this problem at the reception afterwards, and he said that with a small, quiet class, he can usually keep up, but if everyone chats at once, stuff scrolls off screen before he can read it.  He thinks that the technology might scale up to 60 students with a very non-interactive lecture style and sleeping students (I exaggerate his description), but not beyond that.

Another professor presented a course that is going to be offered soon that takes the form of a self-paced e-book (on calculus).  He showed a couple of features of the e-book, and I think that it has many of the bells and whistles that math bloggers have expressed an interest in seeing in math e-books.  Personally, I did not find the examples he showed very appealing, but I’m not part of the target audience. (He also loves math history, which I have always found to be a tedious addition to math books, so I’m really not part of the target audience.)

Some of the panelists just raised questions for us to think about, though they went by so fast that I don’t think anyone in the audience will remember more than one or two of them—the questions they were thinking about before coming to the meeting.  I hope that the Committee on Teaching or the Committee on Educational Policy will send out the list of questions as e-mail.

One thing that disturbed me about this meeting was the average age of the attendees. I think I was well below the median age there, and I’m turning 58 this week.  If we are talking about the future of online education at the university, then we absolutely need to be talking with the people who will be the faculty in that future.  It can’t be only us old farts who will retire in the next decade (and the professors emeriti, who have already retired)—where were the assistant and associate professors?  I’d be very surprised if there were more than 4 assistant or 6 associate professors there.

My personal feeling is that UCSC should not invest large amounts of money in online education.  It does not seem to be much cheaper than conventional teaching methods, and UC does not have a good track record for providing infrastructure cheaply, nor for running businesses.  I think that UCSC should be concentrating its shrinking resources on the things where there is enormous value added by being a UC: on lab courses and small seminar courses where students get direct hands-on experience and interact with faculty.  If this means outsourcing the teaching of the 1000 students a year taking precalculus,  well, that’s too bad, but high schools and community colleges can teach those courses ok.  I don’t believe that UC should be teaching precalc—certainly not to a quarter of each incoming cohort!

Unfortunately, the budgetary pressure in recent years has been towards eliminating small grad courses and expensive-to-teach lab courses, and creating more and more mega-lecture courses.  These mega-lecture courses are relatively easy to replace with MOOCs, since the teaching in mega-lectures has already been degraded almost to the level of video lectures, with no interaction for most students. Once you start moving to a factory model of education, it starts becoming “obvious” to outsource the production to cheaper labor elsewhere, or to look for “economies of scale” that allow you to mass-produce a course.  I’m not convinced that there are economies of scale in education—I don’t think that it is really more cost-effective to teach 1000 students at once than 20 students at once.  You can make the course cheaper per student, but the cost in quality is pretty high.

The calculus e-book looks like a promising alternative to big lecture courses, though I suspect that not that many students will slog through it without someone holding their hands and cheering them on.  Even my son, who is very interested in math and quite good at it, finds it much easier to learn in the context of a class with regular meetings and feedback from the teachers than in a self-paced course with the same content—lack of time-management skills ruins self-paced courses for most students.  Of course, there is no reason that e-book has to be used in a self-paced course, but adding math coaches or teaching assistants to the course raises the cost of offering it to nearly the levels of a conventional  course. Furthermore, the time, money,  and effort involved in creating such an e-book means it is unlikely that UCSC will create many such resources.

The chair of the Committee on Educational Policy suggested that there would be a market for on-line courses in bioinformatics from UCSC, since UCSC is an acknowledged world leader in bioinformatics.  And it is true that there might be a market, but as the teacher for our core graduate bioinformatics course, I don’t think that our quality of education would survive a transfer to on-line format.

My “lectures” are very interactive—I try to get students to derive things like the Smith-Waterman algorithm and the forward-backward algorithm for HMMs from reasoning about how to break problems into sub-problems for dynamic programing.  I could present the algorithms in a textbook-like way in a quarter the time, eliminating the long waits for students to digest and idea and suggest a next step, eliminating the cold calls, eliminating the checks for understanding at every key point, … .  I can teach a group of 20 students in the same room with me, but I’d lose most of the useful feedback in an online setting.  I’d also lose the chats with students between classes—e-mail and forums do not bring up the same issues that come up when I stop by the grad office to get more hot water for my tea. Even recording my extemporaneous presentations would flatten them—I’m likely to be just enough nervous about making mistakes on camera that I’d play it safer, doing pre-canned examples, rather than riskier live-action math and algorithms that show how I think about problems, rather than just showing “the solution”.

Just Monday, when I was presenting a numeric example of computing HMM probabilities, I made a serious mistake that amounted to multiplying by two transition probabilities instead of just one in the first step.  It was caught by one of the students, and I could correct it and go on.  Today, after we together derived the more general recurrence relation for the forward algorithm, one student suggested an optimization that wouldn’t quite work, and I could point out that it was exactly the same as the mistake I had made near the end of Monday’s lecture.  With an online course, either the mistake wouldn’t have happened in the first place (if I polished my examples before presenting them, following a script rather than extemporizing), or the students would not have had the involvement to correct me or to propose optimizations that didn’t quite work.  Having a small class that has been encouraged to present ideas, to challenge me when I may be making a mistake, and to ask questions when they don’t understand is crucial to my teaching style, and having a record of the class is likely to ruin that.

I sometimes deliberately make mistakes and hope for the students to catch them—if they don’t, I have to spend more time stepping them through the pitfall, so that they can see it and avoid making the same mistake themselves.  At the beginning of the quarter, the students were pretty shy about saying anything, but I now have over half the class participating on a regular basis,  and even the weaker students are willing to ask about potential errors, though they ask more timidly than the stronger students, since there is a bigger chance that they are misunderstanding something, rather than pointing out my error.  Encouraging the students to correct my mistakes does get me more feedback about misunderstandings, when their attempts to correct something that is actually already correct highlights where they did not quite grasp a concept.

Even if we could somehow magically provide online all the visual cues and social interaction of the face-to-face classroom, I don’t think that we could scale up other aspects of the course: I’m already spending almost all my weekends providing detailed feedback on programs and papers for a class of around 16 students.  If we scaled the class up by even a factor of 2, we’d lose that detailed feedback, which I see as an essential part of the homework.  For many of the seniors and grad students, my reading of their programs and papers is the first time any professor has read any of their work closely—and they desperately need to hear how to fix their in-program documentation or how to reorganize their sentences to avoid flow problems.

Incidentally, in my other class (which includes many of the same first-year grad students), the students just finished doing 10-minute presentations on techniques from Teach Like a Champion.  Tomorrow, before we start reviewing the video recordings of their presentations, I think I’ll have them try to think about which of the techniques they presented that they have seen me use in the bioinformatics core course.  This year they presented Circulate, Ratio, Cold Call, the Hook, Pepper, Warm/Strict, Wait Time, No Warnings, Check for Understanding, Stretch It, Positive Framing, No Opt Out, Board=Paper, Call and Response, and Begin at the End.  I think that they’ll find that I use about half of those on a regular basis. (I leave it to my readers to guess which of these I don’t use much—those who had me as an instructor a decade or more ago might make different guesses than those who’ve had me recently, as I’ve gotten better about some things.) Note that most of the teaching techniques in Teach Like a Champion are difficult to apply in an online course.

I’m not planning to teach any on-line courses in the near future, and I’ll be putting my efforts into creating more of the interactive, lab-style courses that are difficult to replicate on-line (like the Applied Circuits course I’ve been designing for the past 5 months).  I think that the future of the university is in these high-interaction-level courses—artisanal education, not mass-produced factory education.  There will undoubtedly be a huge market for the Wal-marts of education, but that’s not where I want to work, nor where I want my son to be a student.


2010 November 6

Teach like a Champion in grad school

Filed under: Uncategorized — gasstationwithoutpumps @ 00:06
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I have previously posted on Doug Lemov’s Teach Like a Champion (and a critique of his “Name the Steps” as applied to math). But the book seems practical enough to be worth exposing students to.

I teach a how-to-be-a-graduate-student class to first-year grad students in my bioinformatics department, with the intent of preparing them for careers in research and teaching. New faculty members in many fields complain that they were never taught anything about how to teach, and so I thought it would be worthwhile to have the students learn something about teaching. This course is also the only training they get for being TAs, and we have students TA in several courses that require real teaching skills (for example, the Bioinformatics Tools course, which is taken by biologists with no understanding of computers, and the Bioethics class, where TAs have to run discussion sections in which students discuss difficult ethical questions).

This year I have instituted a new assignment, which takes up one of our nine 105-minute class periods:  each student is required to select one technique from the book and present it to the class.  I recorded the presentations with a video camera and will review them with the students individually.  This serves two purposes: getting the students to do some reading and thinking about teaching techniques and giving the students practice and feedback on presentation skills.

I bought a new video camera specifically for this assignment, an Everio HD620BU, a fairly low-cost HD camera that supposedly has good low-light performance.  Low-light performance was important to me, because I also want to use this camera for recording my son’s plays.  What I had not realized is how long it takes to download and process HD video.  The download from the camera to my laptop ran at about half real time (45 minutes for 90 minutes of movie), and exporting the video from iMovie into a low-resolution (640 × 360) format that can be shared takes about real time.  The movie took up 10 Gbytes on the camera, expanded to 47.7 Gbytes in iMovie, and exports in low-resolution format to about 1Gbyte. After verifying that the low-resolution movie is watchable, I’ll have to delete the HD version—47.7 Gbytes is too much disk space on my laptop for me to be comfortable keeping.

I found the user interface for iMovie rather unintuitive—nothing like other Mac tools I’ve used.  You can’t click and shift-click to select a region, the precision editor doesn’t scroll, everything has to be dragged (a pain with a touchpad), … .  I did finally manage to get titles in the upper left corner for the first 30 seconds of each clip, but it was much harder than I had expected.  I decided not to try to trim any of the clips, although there were a few seconds at the beginning and end of each clip that should have been cut.

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