Learning Critical Thinking Through Astronomy, Week 3

This week, we dived into Activity0102, which introduces two huge concepts.

The first is that there are different types of knowledge and therefore also different types of questions. Students are presented with a group of questions, let’s call them Group 1 Questions, and are asked to decide what they have in common. I’ve used this activity for so long that I can perfectly predict what they will say about this, and it is that these questions all have definite answers that are all fact-based. Unfortunately, this is not what I intend for students to land on. I won’t say here what I want them to land on, but it’s something else. Students are then presented with another group of questions, let’s call them Group 2 Questions, and are again asked to decide what these questions have in common. Once again, I can predict exactly down to the word what students will say about these questions. They always say that these questions have no definite answers and the answers they do have are all matter of personal opinion.

For theatrics, I set this up at a mind reading stunt. While I’m describing this part of the activity to the class, I tell them that I can predict what they will say about each group of questions with astonishing accuracy. I write my predictions on a sheet of paper, fold it, and seal it with tape and hand it to “the most honest looking student in the class” for safe keeping until I ask that student to open it and read it to the class. They then do their thing with the two groups of questions, and then I have them come to the room’s center for a checkpoint to discuss their decisions. After they go precisely where I predicted they would go (but not where I wanted them to go), I reveal my predictions.

I describe how my accurate predictions are troubling for me because it indicates to me that questions requiring more than regurgitation of facts are considered questions for which there is no objectively correct answer (don’t worry…I didn’t reveal anything there). This leads to one of the first really deep conversations of the semester.

After this semester, I will restructure this activity to make it more streamlined and to put the parts about what each list of questions has in common adjacent to each other, separate from the questions about tracing one’s knowledge back to…well…back to something (can’t reveal that here of course).

The second huge concept in this activity is that of operational definition. I was introduced to operational definitions by Arnold Arons and use them extensively in this course. Basically, an operational definition of a sequential list of step one must carry out in order to define a concept or a measurement. I use the obligatory silly example of the steps one must go through in order to define the concept of “peanut butter sandwich.” It’s astonishing how many people forget to open the peanut butter jar before putting peanut butter on the bread! I give each student a set of four, five, or six wooden sticks. I usually use barbeque skewers from a local grocery store, but toothpicks work just as well. The important thing is that each student’s sticks must be essentially identical. The activity then asks for students to formulate operational definitions for the concepts of “parallel” and “perpendicular.” I chose these concepts becuase students think they are already familiar with them, but quickly find there is more to these concepts than they realized (which is one of my goals of course). We will use geometry later in describing the behavior of shadows and in the geometry of the sky so students will definitely see these ideas again and again in the course. If I sense students are struggling with this, and they always do, I interrupt and offer a slightly more familar example. I give each table (there are six in my classroom) a cup and a handful of glass beads. I ask them to formulate an operational definition for “adding two small positive integers each of which is less then ten.” The use of small integers less than ten is entirely arbitrary on my part, but I don’t want to deal with fractions, large numbers, or negative numbers.

It’s very interesting to watch students realize that they’ve probably never really thought deeply about simple arithmetic (it’s not so simple) but eventually they land on what I need them to land on. If time permits and they need more practice, we do similar operational definitions of subtraction, multiplication, and division. It’s very eye opening for both students and me. As a bonus, they see how these operations are related to each other and how they really work. Of course, they ultimate goal is to construct good operational definitions.

After practicing with operational definitions of basic arithmetic operations, we then move to the actual activity in which students must formulate operational definitions of “parallel” and “perpendicular” using the sticks I gave them. The instructions list words students are not supposed to use (mainly because my experience is that these words represent partially understood concepts in most cases). For theatrics, I move around the room attemptning to break the operational definitions students formulate. They make it a competition to see whose operational definition can survive “The Joe.” It’s fun!

Incidentally, one interesting aspect of operational definitions must be culturally independent. For example, if a students write a step in his/her operational definition calling for the reader to “make a letter H” this won’t work becuase in, for example, Japanese there is no H. Therefore, the operational definition must not rely on something not shared by all cultures.

Given that most students have simply memorized trivial definitions of “parallel” and “perpendicular” and that when they try to use these previously memorized definitions operationally, they find that I can always break them. Therefore one of my goals is to get them to abandon those old, mostly meaningless definitions and find new ones. As a hint, I tell them that Nature sometimes uses geometry to talk to us. Most then go on to where I need to be and are happy about it.

I welcome questions, comments, feedback, and constructive criticism.


I Need to Work Where Teaching is Not Valued

Yes, you read that right. I’ve been looking around for a new work environment for at least a year now, and I have come to an unexpected conclusion. Until now, I have only applied to places where I thought, at least initially, teaching might be valued. It seems logical, but to my surprise there are problems with that line of thought. It seems that the places that claim to value teaching are, at least in my recent experience, also the places where faculty are treated more or less as children who must be overseen to the point of nanomagement (a term I just invented on the fly) on a daily basis. They must be told how to walk, talk, dress, and conduct class. They must be told what email software to use, what textbook to use, what facial expressions to use, and what word processing software to use. In short, faculty at these places apparently cannot be expected to do their jobs. As one recently retired dean put it, “We can’t expect people to just do the right thing.” Yes, professionals cannot be expected to do what they’re expected to do. They must be supervised, as I said above, like children.

So I’ve decided to try a different approach. I will now focus on applying to places where I think teaching will NOT be valued. If I get hired, I may be allowed to teach courses that no one else wants to teach, which is a good because it means I will probably not have anyone looking over my shoulder waiting for me to make a mistake and punish me for it. I will have the freedom that I’ve enjoyed over the years, until recently, to do what is best for my students as opposed to what is best for lawyers, students’ parents, or accreditors. I probably won’t have someone from another discipline telling me what my discipline is all about and what topics are appropriate for my courses. Hell, I may even be allowed to create new courses for my students without the local university system’s permission

A school that doesn’t value teaching may be a refreshing environment in which to work.

Learning Critical Thinking Through Astronomy, Week 2

I’m a few days late with this post. It applies to last week.

We began the activities in earnest this week. Activities are named as ActivityCCNN where CC is a two digit chapter number (there are five chapters in the course) and NN is a two digit activity number. Chapter 01 is critical thinking and reasoning. The first activity, Activity0100i, is intended to get students to buy into group work and collaboration. The i indicates a particular version of this activity; I currently have ten different versions, each of which presents a different puzzle or question for students to consider first individually, and then in collaboration with other students. The questions are the same in all versions. Students also see their first standard in this activity.

As you might expect, students usually don’t see the connections between this activity and astronomy. I take great pains to explain that astronomy is a science, and this is a science course, and we must therefore start at the very beginning with detailed discussions on how the process of science works. I don’t think any introductory science course can genuinely leave this out and yet, most do. It really bothers me. It also bothers me that we traditionally treat subject content as though it were more important in these courses. I have come to realize that it is not, at least within the supposed mission and purposes of such courses. If we force subject content too soon, we are reinforcing the notion that both science and this course are about ingesting facts and not about reasoning. Think about it. Music teachers never start introductory instrumentalists out by playing concert selections and yet, that is precisely the analogy to what is typically done in introductory science course.

Students also did Activity0101 this week. I wish I knew how to make this activity more engaging. I’m certainly open to suggestions. It’s partly intended to generate good class discussion and it usually does so. It’s important for students to understand that they will never be asked to simply regurgitate definitions. My expectation is that they will learn correct terminology by context. For example, they will, hopefully, recognize that when they hear “only a theory” they recognize it as a misuse of the word “theory” and immediately recognize two legitimate ways (which I won’t divulge here beucase students could find them) to respond to this commonly heard antiscience trope. That’s relevant science literacy and awareness, and no numerical facts need to be memorized in order to understand it.

One section had the guts to admit that they were still confused about the standards-based grading approach. They said they didn’t entirely understand the differences among standards, assessments, and proficiency indicators. This is valuable stuff to know. So to address this, we did a formative assessment of the standard associated with Activity0100i. I asked for three advantages to working in groups and three disadvantages to working in groups, each of which should be articulated in a complete sentence (for a total of six sentences). Most did fine. They even commented that they didn’t expect something so straightforward. Some expected a “trick question” of some sort. Given that the other two sections probably had similar concerns, I did the same formative assessment in those sections too. Everyone now says they feel more comfortable with this new approach and that they actually feel relaxed and ready to learn. This is precisely what I wanted to instill. Learning shouldn’t be stressful.

As always, I welcome comments, questions, and other feedback.


Matter & Interactions I, Week 2

This week we began readings from chapter 36 (24MB) of Arnold Arons’ 1965 calculus-based textbook Development of Concepts of Physics (rare, but occasionally found on the used market…I have two copies and I hope to get Dover to reissue the book in paperback). This is the chapter on special relativity, and in my opinion forms the best foundation for relativity for any introductory physics course regardless of whether it’s calculus-based or algebra-based. Using mainly words and delightfully simple prose, Arons begins with Newton’s conceptualizations of space and time and then moves through a detailed discussion of clock syncoronization.

The first bit of physics is the concept of a frame of reference. This week I discovered that this Wikipedia entry now uses the term observational frame of reference to mean what I have always previously defined as a frame of reference. The first sentence of the article now conflates the concepts of reference frame and coordinate system, and I think this is a significant conceptual error. One can refer to a reference frame without referring to a coordinate system, and the converse is probably true (I need to think more about that…).

Next we addressed how to name and draw reference frames. We largely follow historical convention here: O or S is the name of a frame, primes indicate a frame moving relative to another frame, axes in standard configuration favoring the righthand direction. It occurred to me that in every textbook I can think of, we’re used to seeing two frames of reference in introductory relativity, a stationary S (or O) frame and a moving S’ (or O’) frame, which neglects one important frame, namely that of the reader! Yes, I understand that the reader is assumed to be in either of the two given frames, but that certainly is not how the diagrams are always, or even usually, drawn. Therefore, I also introduce the S” (or O”) frame and call it your frame. So in all, we have the S frame, the S’ frame, and your frame.

This image shows the naming conventions. Many, if not most, textbooks erroneously dictate that the S’ (or O’) label must apply to “the” moving frame. Aside from the use of “the” there is something else troubling about this edict, namely that if adhered to it requires changing that frames label during the reasoning for the current situation. Remember that labels are just that, arbitrary labels, but the important thing is to be consistent within the scope of a particular situation (I am trying to avoid the word “problem” becuase I think it’s, well, problematic.). Once a set of labels has been chosen and assigned, keep it intact for the duration of that situation and everything should be fine.


Naming conventions and notations for reference frames.

I have one huge concern with my drawings, and it is that by drawing a visual representation of a frame in standard configuration in this conventional way, I have committed the error of conflating the concepts of reference frame and coordinate system. I need a way out of this so I don’t feel guilty about it! I’m open to suggestions! Must we draw coordinate axes? Given that there is always a relative velocity involved, perhaps some coordinate-free geometry could be somehow employed…I don’t know, but this issue bothers me. As I write this, another option occurs to me. Perhaps we could just draw the physical entities involved and label them with their velocities and let the drawing as a whole represent the frame of reference, with no need to to draw or otherwise visualize coordinate axes. What do you think? This really bothers me.

While I’m on the issue of drawing, here’s an example we formulated in class.

LCTTA_2016-Aug-24 1

Drawing for an object moving to the left relative to you.

The situation is “an object moves to the left relative to you.” Note that I drew the S” frame so as to suggest that it includes or encompasses the other frames. This, I think, is more in keeping with how the S and S’ frames are shown in textbooks from the reader’s perspective.

Note that I’m setting the stage for proper vector notation here too by using velocity magnitude, and I’m careful avoid the word “speed”. Familiar though it is, “speed” sticks out like a sore thumb because it’s the only term I know of that is a special name for a particular vector’s magnitude. We don’t do it with momentum, acceleration, force, etc. Pedantic? Okay pedantic.

I’m thinking a good assessment of understanding at this point might be to state the situation and have students draw the appropriate diagrams for all relevant observers.

We also use manipulatives to help visualize these ideas. Students are given homemade (by me) kits with reference frames and other assorted objects. These can be used to act out the scenarios describes in the Arons reading.


Simple manipulatives to help understand reference frames.

I used a short assessment in class that asked students to act out a scenario for which an observer in the right hand frame reports the ball bearing is moving to the left. Of course there are many such scenarios that will work, and sure enough different students came up with different, and equally valid, scenarios. For example, the ball bearing might be stationary in the left hand frame while the right hand frame moves to the right. The right hand frame may be stationary while the left hand frame moves to the left carrying the ball bearing with it. Try asking students to demonstrate different scenarios making the ball bearing move to the right, move to the left, and not move at all relative to them (the S” frame).

No discussion of reference frames is complete with out showing the famous 1960 Frames of Reference video featuring Patterson Hume and Donald Ivey. There are several links to it on YouTube; I tried to find one with no ads becuase I don’t like shoving ads in students’ faces. Apologies in advance if the one linked below displays ads or if the link rots. Notify me and I’ll fix it.

We wrapped up class time this week with a discussion of the breakdown of simultaneity as a result of the invariance of the magnitude of light’s velocity. This was basically a group demonstration using a “skateboard” and an apparatus consisting of a small stick (about 1 light-nanosecond long) and two plastic square mirrors. We imagined what would happen if a light at the stick’s center suddenly turned on, sending a pulses toward either end of the stick. Which mirror would catch its light first? Well, of course the answer depends on whether or not one is in the frame for which the stick is at rest. Students are to read the details in Aarons for next week.

Matter & Interactions I, Week 1

This is the first post of a series of sixteen in which I will attempt to describe the weekly goings on in my introductory calculus-based physics course. You probably already know that I use Matter & Interactions for this course, and I have since 1999. In fact, I was the first instructor in North Carolina to adopt M&I back when it was still considered to be in “beta testing” outside of Carnegie-Mellon University, where Chabay and Sherwood were working at the time. To my knowledge, my institution was the first community college to adopt M&I, and I’m told by Sherwood that our adoption of M&I influenced NCSU‘s decision to adopt it for their intro course.

My intro calculus-based physics course meets four days per week for a total of six contact hours each week. This year, as last year, it meets M-Th 10:00-11:20. This time has proven to be very convenient…not too early and not too late in the day. This semester’s enrollment is eight students, which is down from the past two years. It is also the first all male class in approximately three years. All eight current students plan to go into some form of engineering.

As in the past, the first week was dedicated to tech setup. Students set up their WebAssign accounts, and created accounts at both GlowScript.org and Overleaf. That’s a lot of online stuff to keep track of, but we will use it all in this course. The big innovation this year is teaching LaTeX, and Overleaf is the best solution I have come across. It works online, so it requires nothing to be installed locally (which is good because I can’t update my iMacs in my classroom). It also works on tablets as well as notebooks and desktops so as far as I can tell it’s completely platform agnostic. We spent most of the first week learning the basics of LaTeX. Specifically, we saw how to use the most common math commands and constructs (exponents, subscripts, fractions, roots, inline math mode, display math mode, parentheses, trig functions, and Greek letters).  The remaining time was spend demonstrating, as opposed to learning, GlowScript and VPython. We will, of course, come back to VPython and GlowScript later. I felt that LaTeX took precedent this time because my expectation is that all homework will be done in LaTeX via Overleaf and I wanted students to get used to it. I gave students a ZIP file containing everything they need to get started creating LaTeX documents with my mandi package. Note that the version my students get is usually a small increment ahead of the CTAN version. They give me feedback on new features before I push an update.

Next week, we begin with special relativity.

I welcome comments, feedback, and constructive criticism.

Learning Critical Thinking Through Astronomy, Week 1

This is the first post of a series of sixteen in which I will attempt to describe the weekly goings on in my introductory astronomy course. As many of you already know, I don’t use a traditional textbook and, instead, use my own activities based on the critical thinking model of Richard Paul and Linda Elder. In 2007 when I first announced this project at the summer AAPT meeting in Greensboro, I anticipated completing the activities and having them in publishable form by 2012. Four years after that expected deadline, I have learned that this was a far more involved undertaking that I imagined. I found I spent a lot of time refining the activities and most of that refining came, and continues to come, directly from student feedback. Of the five broad chapters in the LCTTA Project, I have activities for the first three. I have ideas or draft activities in mind for the remaining two chapters, but nothing that I’m willing to share just yet.

My course typically has three sections in the fall and two in the spring. I generally think of my weekly teaching schedule has being three “cycles” each week: a Monday/Wednesday cycle, a Tuesday/Thursday cycle, and a Friday cycle. With the exception of the evening section (section 200), which meets on Monday and Wednesday evenings, each of the other two sections meets once during each cycle. In the past, the MW and TuTh cycles have been identical for the two day sections, but this semester the second day section (section 101) only meets on Tu and Th whereas the first day section (section 100) has a schedule that is inverted compared to past years. In case this makes no sense, here is each section’s schedule. Note that all sections meet for five contact hours per week.

  • Section 100: MF 12:00-13:50, W 13:00-13:50
  • Section 101: TuTh 12:30-14:50
  • Section 200: MW 18:00-20:20

I try very hard to keep all three sections synchronized, but the nature of evening class is that they are sometimes behind or ahead of their day counterparts.

Week 1 was, this semester, devoted to tech setup and an introduction to the Elder/Paul critical thinking framework. Students purchase The Miniature Guide to Critical Thinking: Concepts and Tools and the College Astronomoy Kit (which had its origin in the old Harvard Project STAR materials) from the bookstore. Students will not need the kit until we get to the third unit, and that usually takes three or four weeks. I remind them that they should purchase it immediately because the bookstore always runs out for some reason.

So, on the first class day, I let students set up their WebAssign accounts. This is usually painless, although there are always a few students who have difficultiies that stem from having to use WebAssign in a math class, in which case they access it through Blackboard. I avoid Blackboard like the plague that it is, and we eventually get everything sorted out. While I used to “go over” the course syllabus in excruciating detail, I no longer do so becuase it takes too much time and is mostly institutional policy anyway. I do, however, emphasize the attendance policy and the importance of regular attendance.

I tell students that one of my goals is to establish the classroom as a barrier-free learning environment where they are free, perhaps for the first time in their academic careers, to fully engage in their education and to immerse themselves in intellectual development within the contect of an introductory science course. I don’t want them coming into the room with anything that might distract them. They need not be afraid of intimidation from me or from classmates (although their definition of “intimidation” is frequently different from mine in that being held accountable for engaging in their work is, to some of them, a form of intimidation) and they need not be afraid of being wrong.

Rather than bore with a bunch of school policies that they can (or cannot) read for themselves, I instead present for discussion the definitions of teaching, learning, and taking a class that will be used in the course. I emphasize that these are the operational definitions I will use and model for them, and that at the end of the semester or at any other time if they lodge a complaint that “Joe isn’t teaching us anything” I will present them and any other administrators (our policy states that administrators are not to get involved unless the student has first addressed the issue with the instructor, but alas this is rarely enforced in this day of students as paying customers) who have been brought into the non-situation these very same definitions and ask for the precise sentence(s) I have failed to uphold. We discuss these operational definition in detail. I have found that most students readily accept them despite having been exposed mostly to traditional lecture-based instruction before. Perhaps they are hungry for something better. I hope that’s the case anyway.

I spent the remainder of the time this week discussing standards-based grading and the growth mindset concept. Many students seem confused by standards-based grading at first and this prompts much excellent discussion.

On the second class day, we begin a detailed discussion of the Elder/Paul critical thinking framework and the elements of thought. I begin by discussing the simplest (ostensibly) of the eight elements, namely the element of purpose. What is the purpose of _________, where most anything can be put into the blank. We specifically discuss the purpose of this class, astronomy, science in general, and education in general. The idea is to demonstrate that the elements of thought can be used very broadly and very narrowly. Then I ask students to discuss, in groups of four (my class seats twenty-four student organized into six pods of four students each), the remaining seven elements and to write the one they find the most difficult to understand on their whiteboards (one per group). I then ask students to photograph the boards with their smartphone cameras (may as well put them to good use, right?) and then to circulate around the room and discuss each group’s whiteboard. I tell them this is close to what professional scientists call a “poster session” at a conference and is a frequently used format for professionals to talk with each other. They like this and buy into it immediately. This lasts until I sense no productive discussion, which usually means about twenty minutes or so. I give everyone a chance to revise their boards based on the feedback they got from each other.

They then discuss the findings in what I call “checkpoint format.” This means the entire class forms a circle around the room’s center and everyone takes a turn speaking. The current speaker holds a large, red stuffed Angry Bird and then “gives the bird” to someone else of their choice. This continues for as long as the discussion is productive, which can be as long as a half hour or so. This almost always takes the rest of the class time this day.

For the third class day, students apply the elements of thought to an article. This semester, I used the article Too Smart to Fail? from the Inside Higher Ed website. I assign a random element to each of the six groups. I try to focus on the more difficult ones in the hopes that during the “poster session” a lot of meaningful discussion will ensue, and it always does. Once again, students photograph the whiteboards, revise them based on feedback and discussion, and photograph them once again.

So this is what we did in the first week. Next week, we begin the LCTTA activities proper and thus the first chapter of the course, critical thinking and reasoning.

I welcome comments, feedback, and constructive criticism.

Conceptual Understanding in Introductory Physics XXV

This question emphasizes geometry and should be done without use of a coordinate system. It should also be done using only symbolic manipulation of vectors. Here it is.

Consider a particle moving with a constant, non-relativistic velocity. Starting with a general expression for kinetic energy in terms of either velocity or momentum, prove that the particle need not be under the influence of a non-zero net force. Do not refer to a coordinate system. Your argument must be stated in words as well as mathematically.

I’m not entirely happy with the way I articulated the question. I’m open to suggestions for improvement, but I want the question to have an air of vagueness about it.