Learning Critical Thinking Through Astronomy, Week 10

This week was all about observing. Students were assigned Activity0301, which consists of two main parts. The activity, both parts, is to be done from the same location each night. Students are expected to have previously established the four cardinal directions at their respective observing sites.

The first part is observing Moon. This can be simple, or it can be not simple and I designed this part of the activity with both simplicity and subtlety in mind. The main idea is to go out AT THE SAME TIME ON FIVE SUCCESSIVE EVENINGS and look for Moon in the sky. If it’s visible, draw its visual appearance and record the date, time, and general sky conditions. When I introduced the activity in class, I pointed out that choosing a time during daylight is perfectly legitimate. This, of course, generated many surprised stares because “everybody knows” Moon is never visible during daylight. It’s astounding how widespread this misconception is despite it being trivially contradicted. The catch is that where we are in the synodic cycle (phase cycle) determines whether Moon is visible during daylight or not. Each student can pick his/her own time for going outside. (I’ve considered assigning each student a pareticular time to go outside, but I don’t think I could get by with that given their varied work schedules and other external obligations. There’s already too much resistance to doing anything outside of class so I dare not assign specific times for things.)  If enough people go out at different times, we can come back to class next week and piece together a timeline for when Moon was visible (and more educationally, when it was NOT visible!) and its corresponding visual appearance. The timing of this activity this semester was excellent because it formally began near full Moon so Moon would be visible all night, which means students could go outside before or after midnight and “find” it. More than likely, most student will try to go outside between sunset and midnight rationalizing that they can’t get up early to go out between midnight and sunrise (but they can certainly do other things between midnight and sunrise, things more important than their education). If they go outside at the same time  between sunset and midnight, they will eventually not be able to find Moon and I’ve told them that not finding it counts as data. Remember that at this point, they know nothing about what terms like “full Moon” mean. They’re simply being asked to make observations and record those observations. As usual, they strongly resist, but I point out that this is the type of thing they were previously complaining about NOT doing earlier in the course.

The second part of the activity consists of observing four stars close to the horizon, one in each of the four cardinal directions, for thirty minutes each. For each case, draw a simple diagram consisting of the horizion, a small vertical tick mark on the horizon labeled with the direction the diagram faces, a representative star close to the horizon, and an arrow showing the star’s approximate motion from the beginning to the end of the thirty minute observation.

The total minimum time committement for this activity is thirty minutes for each of the four stars, five lunar observations each of which takes only as much time as needed to look for and find (or not) Moon and draw it on a blank template I provide to them. Then add in the time necessary to record most of their work (sans drawings) in WebAassign. I estimate two and a half to three hours max. As you see when I reveal the results next week, based on previous years most student will not even attempt the activity. I hope I’m wrong this time, but I have yet to see more than about 25% participation.

In class this week, we focused on a WebAssign assignment that reinforces modeling shadow behavior with the celestial spheres. Ironically, one student walked in Friday morning asking for help in assembling the sphere, which we had already done over a week ago. This is what I’m up against.

As always, feedback is welcome.

Matter & Interactions I, Week 10

This week we moved into chapter 4, which contains A LOT of interesting physics! Among other things, students see the importance of simple spring systems and how they can be used to model certain quantum mechanical phenomena like chemical bonds. The Einstein solid model is introduced, and will play a central role in chapter 12 (if we get that far). Here are some things I find especially noteworthy about chapter 4.

Tension is introduced in a pretty cool way, which was never the case in my undergraduate experience. In this framework, tension is the magnitude and direction of each part of the third law pair at any point where a rope, spring, cable, etc. is cut and separated into two pieces. The direction is always parallel to the axis of the thing that is cut.  I always thought of tension as a force, but it’s not. Tension is a tensor quantity. I can imagine an introductory framework in which the stress tensor is introduced, after an appropriate introduction to tensors earlier, for a particular material and geometry and students see how to let it operate on a direction (unit vector) to get the stress, and force if the appropriate area is known, for a specific geometry. The traditional introductory approach is really one for which certain directions are parallel (or antiparallel) so the full geometric beauty goes unnoticed. Other than general relativity, elasticity is the only area of introductory physics where fourth rank tensors are needed but I may be mistaken and ignorant of other situations. Anyway, this would be an excellent place to bring tensors and geometry into the course. In his blue book (Teaching Introductory Physics), Arons has some fantastic problems on tension and how it must be nonuniform when the rope (or rod, or cable, or whatever) accelerates parallel to its long axis.

The concept of mass density as a connection between the microscopic and macroscopic never ceases to amaze me! The fact that we can calculate, even if only roughly, the “size” of an atom by treating it as a classical particle and combine that result with an estimate of Young’s modulus found by “piling weights on the end of a wire” as Bruce Sherwood loves to call it to get an effective interatomic spring stiffness that can be used to predict and model some real physics is astounding! I think that’s probably the biggest “thing” in chapter 4.

Analytical solutions to simple harmonic motion are introduced. In this context, students see some of the basics of solving differential equations, which they will learn formally in their ODE course next semester. I think that sometimes we should introduce formal solutions in intro physics, but I waiver on that quite a bit. Numerical solutions always work, so maybe we should introduce those computationally and leave it at that. I don’t know.

We did a more or less traditional spring lab in which students measured stretches and calculated spring constants and experimented with springs in parallel and series. We also did a formal Young’s modulus lab in which students measured Y for two different wires. We only have one apparatus so I did a runthrough as a demo and then the students (there are only eight in the class) did their two experimental trials the next day.

In all, this is a very meaty chapter with lots of good physics, computation, and stuff to talk and think about.


Matter & Interactions I, Week 9

Monday, Tuesday, and Wednesday of this week constituted our fall break so this class only met once this week. I had extended all of the past WebAssign problems set deadline to Thursday of this week (the one day we met) and yet some students still haven’t not done them. Guilt. Whatever.

Since we only had one class day, I didn’t move into chapter 4. Instead, I gave the class another opportunity to raise questions from the first three chapters and associated WebAssign problem sets. I was met with mostly silence, knowing there was some who are struggling quite a bit.

One student raised the issue of some problems being “tricky.” I asked him if he could elaborate on precisely how he defined “tricky” and to my surprise, he did (most student evade that questions, thinking I don’t really care about their response but I do). He said that a “tricky” problem looks simple to begin with, but is then made harder by the presence of numbers and associated calculations. Aha! This is helpful! He’s really telling me, I think, that the requirement for “attention to details” is what he equates to “tricky.” He confirmed this! Wow! I pointed out that this is a false equivalence and should be thoughtfully abandoned.

Another student raised his diffuculties with another problem that asked for a comparison of the gravitational and electric forces shared by a proton and an electron. Okay, so we tackled that one, again by me modeling the process on the board. I drew a system schema. They chose the system; I drew the system boundary. We saw two interactions crossing the system boundary, one gravitational and one electric. They knew how to calculate both as evidenced by their ability to cite the relevant equations. I really didn’t see where they were having any substantial difficulties so I took the opportunity to emphasize order of magnitude estimation without a calulator. So we estimated the pertinent quantities in this problem. I reminded the class of Cliff Swartz’s advice about solving problems, namely to never do so without first knowing the answer (looking for citation…will add it later).

So we got the gravitational and electric force magnitudes…ho hum. The real physics comes in comparing these two numbers, and in doing so we find that the latter overwhelms the former by some 10^39. That’s why we call gravitation a weak force. It’s weak, but because the Universe is essentially electrically neutral, gravitation’s weakness dominates our Universe’s largescale structure.

So if nothing else, we ended the week with a good discussion of some fundamental physics that goes beyond textbook problem solving, at least I hope we did. We’ll begin chapter 4 next week and also do more with LaTeX and VPython.


Matter & Interactions I, Week 8

This post was written one week late.

This week was devoted to chatper 3 of Matter & Interactions. The fundamental physics still centers almost exclusively on the momentum principle. Student are seeing more ways to apply it.

I’m asking quite a lot of my students. I expect them to read an entire chapter, doing the checkpoints in situ as they read, and work a parallel set of WebAssign problems in a single week (I define a week as beginning on Monday and ending on the following Sunday). That’s a lot. Sometimes I’m ridden with guilt knowing that most of my students won’t follow this schedule because they have other classes, jobs, families, or some combination of these and other obstacles (recall one student this semester is not fluent in English and is struggling because of that). However, I am expected to make my courses at least as rigorous as those in a four year institution and I like to think I set goals that are somewhat higher, at least for my students. By that I mean that sometimes my goals are different, and not necessarily harder to achieve, from the goals in a corresponding class at a four year school. Working textbook problems isn’t the be-all-end-all to learning introductory physics. Unfortunately, though, it’s how too many introductory physics are judged and I think that is quite unfair. I want my students to be able to talk about the underlying physics. I want them to think in terms of systems, system boundaries, and interactions crossing system boundaries. I want them to eventually recognize why we speak of a system’s momentum, energy, and angular momentum in particular. In addition the reading, I expect them to bring questions caused by the reading to class with them for discussion. I begin every class meeting with something like, “So what questions have been raised as you read through this chapter?” and I’m almost always met with total silence. I jokngly tell them that I treat silence as either total comprehension or total cluelessness knowing that it’s usually the latter. It gets a laugh, but I’m serious. I then morph the lead into something like, “What particular problems gave you trouble so far?” and this usually get a more concrete response. The trouble is almost always one of two things: not knowing where to begin or not getting “the answer” that WebAssign expects.

I’ll address the second one first. It is almost always my experience that the error can be traced to a calculator. I want students to completely abandon traditional calculators but that’s proving to be quite difficult to do. We’re all so used to carrying them around with us, even on our phones, and such habits are hard to break. It’s annoying, but this problem isn’t my main concern.

The bigger problem is when students perceive that they don’t know where to begin with a new physics problem (I don’t like the work “problem” and I really want to replace it with something more like “situation” or “vignette” or…I don’t know). In one instance this week, a student cited a problem he found particularly difficult. The problem asked to calculuate the vector gravitational force on a planet due to a nearby asteroid. Numerical masses and the objects’ mutual separation were given. The student was completely stymied. I mean he REALLY didn’t know where to begin. I was quite disturbed because this particular problem didn’t even use the momentum principle. It represents what I call a “sideline skill” type of problem. It’s something of a routine nature that is necessary for doing other things, except in this case the problem didn’t go that far. It’s just calculating a gravitational force. After more attempts on my part to lead the student to a starting point, he was still utterly lost (hopefully I didn’t cause that). So, I began a slow in situ analysis, modeling what I wanted him to do. I wrote on the board how a vector can be factored into a magnitude and a direction, and that at least for gravitational forces, Newton gave us a simple expression for the magnitude; the direction must come from simple geometrical reasoning. To me, the hardest part of this problem was calculating the relative position of one object from the other to get the correct direction vector. I don’t consider substituting numbers and units into the expression for the magnitude to be physics…it’s numerical substitution. So I worked the problem on the whiteboard and the student was quite satisfied afterwards (of course I did all the work, but whatever). Still, I’m not so naive to think that this student is where he needs to be; he clearly isn’t, and that bothers me. It REALLY bothers me, to the point where I almost blame myself for his being lost. Sometimes I care too much, but I can’t help it. Other students in the class weren’t stymied by this problem the way he was. That’s at least some reassurance to me that I probably didn’t cause his confusion. But oooooooh the guilt.

I remind student daily to not wait till the weekend to begin the WebAssign sets, but they almost always ignore this advice. Again, this causes me guilt but I realize that ultimately, they have a choice whether or not to take my advice.

But oooooooooooooh the guilt.

Let me know if you have suggestions for dealing with the guilt.

Learning Critical Thinking Through Astronomy, Week 9

Monday, Tuesday, and Wednesday of this week constituted our fall break. Unfortunately, that means the evening section, which meets MW, did not meet at all and the two daytime sections (one of which meets MWF and the other meets TuTh) only had one full class period each.

This “week” was devoted entirely to what I call “celestial anatomy.” By that I mean learning the various parts of the Earth/sky system. Here is the list of anatomical terms students should be familiar with and should be able to operationally define:

  1. horizon
  2. north-south line
  3. east-west line
  4. celestial meridian
  5. prime vertical
  6. zenith
  7. celestial equator
  8. north celestial pole
  9. south celestial pole
  10. ecliptic
  11. equinoxes (named for the months in which Sun sits there, not seasons)
  12. solstices (named for the months in which Sun sits there, not seasons)
  13. time bumps

Allow me to elaborate on some of these. Note that items 1-6 have something very important in common, namely that they are conceptually attached to the ground. None of them make any sense otherwise. The cardinal directions (north, south, east, and west) have been previously operationally defined in terms of a shadow’s behavior, which also is “attached” to the ground. Once you leave the ground, this way of defining directions has no real meaning. Okay, you need to be very far above the ground, like in low Earth orbit. There is a way of operationally defining cardinal directions on the plane of the sky, but it obviously can’t be done with shadows. That’s an important and often overlooked conceptual point. Items 7-12 are inherently attached to the sky and have sensible meanings without referring to the ground or anything attached to the ground. Students frequently lift their celestial spheres out of their cradles (the cradle is the cardboard box the kit was shipped in) and attempt to point to the zenith or the celestial meridian without realize that those things have no meaning without the horizon or ground.

It’s important to remember that textbook astronomy has an inherent northern hemisphere bias. December is almost always called a winter month, but our friends in Australia (and everywhere else on the southern hemisphere) would certainly disagree. However, both our Aussie friends and us would agree about Sun’s postion along the ecliptic during December. One of my goals is to eliminate the northern hemisphere bias in all of my activities so they can be used anywhere in the world. At an AAPT conference, I once asked a representative from a prominent physics textbook publisher how they handle the northern hemisphere bias for their users in South America. That representative’s response was that they “just translate the books into Spanish.” I smiled politely and walked away.

Item 12, time bumps, stands by itself at this point becuase there are obviously no time bumps on the real sky. These are small dimples around the celestial equator on the kit students construct that mark hourly increments in right ascension (RA). I have students count the intervals between consecutive dimples and they correctly count twenty-four of them, and almost immediately make the connection with the concept of twenty-four hours in a day. Why twenty-four instead of some other number? It’s probably because twenty-four is divisible by 2, 3, 4, 6, 8, and 12. You’d be hard pressed to find another reasonable number with so many divisors. The next chapter is devoted entirely to the measurement of time but for now, we simply use the time bumps as a way to estimate time intervals when the sky changes. This would probably make more sense if you had one of the kits in front of you.

After I present this guided anatomy lesson, I let students go back over it and quiz each other in their groups. Then we have an assessment in class, for which the standard is

I can correctly identify parts of the Earth/sky system.

Students come to me individually with their kits and I randomly pick four of the above items (omitting time bumps) and ask each student to identify it on his/her model. Most do well, but many need further practice and will need to reassess.

In today’s (Friday’s) class, I noted at least three students who either didn’t have their kits with them or had them and had not yet complete construction of their kits. I guess I can’t win ’em all.

As usual, I’m happy to field questions and comments.

Learning Critical Thinking Through Astronomy, Week 8

This post is being written one week late. That seems to be a pattern and I need to stop it.

The first class day of this week was devoted to finishing up some WebAssign assignments related to the shadow activities. There are STILL some students who have not completed these activities but I have given up on motivating them at this point. There’s only so much I can do, and only so much I can be expected to do, to help them.

The remainder of the week was devoted to constructing the celestial sphere kits. If you’re not familiar with these kits (developed at Harvard as part of Project STAR) most of this point probably won’t make much sense to you. The kits actually contain parts for a celestial sphere, a working telescope, and a working spectrometer. The second and third items are used in second semester astronomy.

These celestial spheres take about ninety minutes to construct from start to finish. One time consuming part is cutting out the star charts that must be traced onto the inner surfaces of the plastic hemispheres. I’ve eliminated this step by having a supply of pre cut star charts available in the classroom. Students use these and “dontate” the new charts from their kits to me, ensuring that I have a perpetual supply of them for future clases. With that problem solved, the most time consuming part is now the actual tracing.

There are many places where construction can go wrong:

  • Students can trace the same star chart (half of the sky) onto both hemispheres.
  • Students can not align the end points of the ecliptic (they don’t know that name yet…we just call it “the arc” at this point) with the end points of one of the ridges on a hemisphere.
  • Students can trace the star charts onto the outsides of the hemispheres instead of the insides.
  • The paper strips representing the calibrated ecliptic (calibrated with dates and constellation names) can be installed backwards or upside down.
  • The paper strips can be installed with too little tape to securely hold them.

I’ve seen all of these before, but this semester everyone seemed to do quite well with the assembly. The MWF section only meets for one hour on Wednesdays so they obviously didn’t have time to complete the assembly so they did so on Friday. Both the evening section (MW) and the TuTh section completed assembly in one class period with some time to spare.

Now that everyone has a working celestial sphere, we can spend next week (a short week due to fall break) learning the parts of the Earth/sky system or as I call it, the anatomy of the sky.

What computer skills do my students need?

It never fails. Every semester, I stymied by how many of my students don’t know how to do the simplest of things with their fancy notebook computers. I know that when it comes to computers, “simple” is relative but there are some things that I expect everyone who owns a computer to be able to do, and that expectation is even higher with students who have ostensibly placed out of any developmental (our word for remedial) computer proficiency courses. While I’m at it, let me emphasize that I don’t care whether or not students can use Microsoft Office for anything. Using Office, or any other individual piece of software for that matter, doesn’t equate to computer proficiency by my standards.

Oh, and I’ve grown tired of the old “I don’t know how to use a Mac” trope. It’s utter nonsense, because both Macs and PC’s running Windows use the exact same metaphors for file managements: icons represent files and folders and these can be organized according to the user’s needs. Sorry, but if you can drive Windows then you can drive macOS (previously called OS X).

So, here’s a working list of things that I assume all my students know how to do unless they specifically tell me otherwise, in which case they’re assignment is to get up to speed with them preferably without my help.

  1. Power on the computer and log into a user account if necessary. Most contemporary operating systems allow for single users but using an account is always best.
  2. Log out of a user account and power off the computer, and know the differences between these two things.
  3. Update your operating system when it is necessary and when YOU want to do it, not when your computer wants you to do it.
  4. Know how to restart your computer in the event of a hard crash that locks everything up.
  5. Know how to connect to wifi networks both with and without a password.
  6. Organize files into some semblence of logical order or structure so that you can find anything when you need it without wasting time searching randomly for it. Do not clutter your desktop with files and other folders. Proper file organization means removing unnecessary files (e.g. application installers) after they have served their purpose so they don’t take up valuable disk space.
  7. Use your operating system’s search facility, for those times when you need it, to find a particular file.
  8. Transfer files to a USB drive so you can reliably transport them from one computer to another.
  9. Install and remove user software by the preferred means for your operating system. Windows usually installs applications with executable installers. macOS usually installs applications with disk images or packages. Linux usually installs applications by package managers. Software applications should be stored in the proper place (e.g. the /Applications folder on macOS for example).
  10. Use a mouse to launch an application when you need it.
  11. Know the different between quitting an application and merely closing its window(s) and keeping it running in the background.
  12. Navigate a menu driven, clickable user interface. These have been around for many, many years and all work essentially identically. If you can use any one of them, you can use all of them.
  13. Print a document from inside an application using your operating system’s standard printing facility.
  14. Create, view, and annotate a PDF files or forms using the builtin capabilities of your operating system or a free third party app that provides this functionality. Both Windows and macOS let you save pretty much any document as a PDF file. Note that Windows requires special software to do this while macOS does not.
  15. Use ANY modern web browser. Once again, if you can drive any one of them you can drive all of them. The external differences are negligible from one to another. At present, you should be able to use Firefox, Safari, and Chrome. There are many alternative browsers around.
  16. Use a search engine to find resources helpful to you.
  17. Use an ASCII text editor to create and save plain text documents. In this context, “using” means creating, editing, saving, and printing files.
  18. Use a simple word processor to create formatted documents.In this context, “using” means creating, editing, saving, and printing files. Note that the overwhelming majority of science and mathematical publishing uses LaTeX, but I don’t expect everyone to be familiar with that…at least not yet. You need not be restricted to Microsoft Word. There are many free alternatives.
  19. Use a simple spreadsheet to create simple tables and data plots. In this context, “using” means creating, editing, saving, and printing files. You need not be restricted to Microsoft Excel. There are many free alternatives.
  20. Know the difference between a computer’s memory and a computer’s disk space. This is a perpetual pet peeve of mine. For the most part, disk space doesn’t constitute storage. One can add memory to one’s computer, and one can add disk space to one’s computer. However, adding one has no effect on the other.

Note that keyboarding or typing are not mentioned here. That’s because it’s not always necessary. Typing on a keyboard is only one way to interact with a modern computer. Being able to type quickly is a big advantage, but doesn’t even make the list of required skills I assume students have so let’s stop pretending it’s more important than it really is.

Note that almost all of these things are agnostic to operating system and hardware platform. Any genuine computer proficiency course should let students learn these things on THEIR harware and operating system of choice. Students should NOT be forced to learn everything on Windows because quite honestly, the world doesn’t run on Windows despite the marketing to the contrary. And no, I don’t honestly think everyone should be required to use a Mac. For the overwhelming majority of us, any computer will do what we need it to do.

At some point, I want to add an additional expectation:

  • Use a programming language of your choice to perform numerical calculations.

I don’t think we’re to the point where that’s a reasonable expection just yet, but we’re definitely getting there. After any introductory physics course, it should definitely be added to the list becuase we need to deprecate calculators and the evils they perpetuate.

Did I leave anything out? Leave a comment and let me know. The list can certainly grow! Thanks for reading!