I have been waffling for over a month on how to start the first day of my “teaching of physics” course. My first inclination was to start by doing some science together. However, I have really decided to better capitalize on certain aspects of place and time.  See, in the course, we are going to be examining a lot of artifacts and events of student thinking. This will involve analyzing student data from diagnostic instruments, analyzing students’ written work to problems, observing student discussions, facilitating student discussions, watching video of students’ working on physics, and watching me interviewing students, analyzing video of my interview students, interviewing students, etc. The course is really an inquiry into student thinking. Along the way, we’ll be reading and writing a lot.

So I have decided to jump right into this kind of work, but tied spatially and temporally to what’s going on else where in our department. See, this Thursday is the first day of my teaching physics course. On Friday, however, I have to give out the FCI to students in my algebra-based physics course. So here’s what we’re going to do the “teaching of physics course”

Part I: FCI answers and predictions

On Thursday, I’m having students in my teaching physics course take the FCI three ways:

• By indicating what they think the right answer is
• By trying to predict the most commonly chosen wrong answer (from my class)
• By trying to predict the percentage correct (maybe even with upper and lower bounds that would be surprising if the actual value fell outside)

As a class, we’ll look over our choices of answer and try to reach an agreement on the right answers, noting places where we are not able to. All of our data goes in a googledoc.

Part II: FCI explanations

For homework, they have to pick four (?) problems to discuss more thoroughly. For those four questions they must,

Explain why they chose their answer, including a discussion of any changes to their thinking that might have happened while taking the FCI, while discussing it in class, or while thinking about it afterwards.

Discuss why a student would pick the predicted wrong answer: What might they have been thinking? What reasoning would lead someone to this answer? What experiences might a person have in the everyday world that support this answer? Why is the right answer not appealing?

Explain why they chose the percentage they did: How did you decide whether this would be an easy or hard question? What about the question? What about the content? What about students? impacted your decision.

Part III: FCI Comparisons

They have the weekend to complete the part II, just before I send out the data from the FCI for my class, also in google doc. Here is the new assignment due following Thursday based on data:

For each question, determine what the most common wrong answer was. In places, where you did not correctly predict the most common wrong answer, discuss why you now think students might have chosen this other answer so frequently and not the one you predicted they would.

For each question, determine the percentage of students getting the answer correct. Make a plot “Predicted percentage vs. Actual Percentage”. Explain the meaning of plot, making sure to discuss the meaning of points that fall far above, far below, or near to the diagonal. Pick your two worst predictions and discuss the discrepancy between what you thought would happen and what actually happen.

At this point, they should be sufficiently exhausted.

Below is data from my teaching evaluations last semester, presented in terms of the 7 factors that the University derives out of student responses to this form.

Obviously, I faired better with respect to evaluations in my algebra-based physics course than my inquiry-based physical science course. This is not a huge surprise. Over the semester, I talked about student discontent in my inquiry course here, here, and here. I also talked about the need in the future to better frame this course in terms of their careers as future teachers, as I recognized that I was doing a poor job. Based on those discussion with students, it is also not that surprising that students in my inquiry course evaluated me fairly strong in terms of interactions and motivation with students, but poorly on both grading and value/effectiveness of course. This breakdown is also consistent with my previous self-assessments that I need to improve in areas of both organization and course architecture. In my physics course, I have to do little course design. In my inquiry course, I am completely over-hauling course design.  This semester in inquiry, there are a lot of changes, including a changes to grading policies and course organization. This semester in physics, there are a lot of changes, mostly pertaining to how quizzes are administered and graded.

Anyway, here’s the breakdown, with +/- given with respect to department averages.

Presentation Ability: 

Physics: 4.9  (+0.9)

Inquiry: 4.4  (+0.4)

Organization /Clarity:

Physics: 4.8  (+0.9)

Inquiry: 3.9   (0.0)

Assignments / Grading:

Physics: 4.8  (+0.5)

Inquiry: 3.9  (-0.4) 

Scholarly Approach:

Physics: 4.7  (+0.7)

Inquiry: 4.0  (+0.0)

Student Interactions:

Physics: 4.9  (+1.1)

Inquiry: 4.5  (+0.7)

 Motivating Students:

Physics: 4.7   (+1.1)

Inquiry: 4.2   (+0.4)

Effectiveness / Worth

Physics: 4.5  (+0.8)

Inquiry: 3.0  (-0.7) ouch!

 

I also thought it was interesting to just look at the highs and low for each course.

Inquiry Class

5.0 Encourages Class Discussion

4.8 Is enthusiastic about his/her subject.

4.6 Gives examinations requiring creative, original thinking

…

3.6 Assigns grades fairly

3.5 Presents the origins of ideas and concepts

3.2 Explains the grading system fairly

Physics Course

5.0 Seems to Enjoy Teaching

5.0 Enthusiastic about his/her subject

5.0 Relates to student as individuals  (this one I’m particularly happy about, every student rated this as a high as possible)

…

4.5   Presents origins of ideas and concepts.

4.5   Gives assignments and exams that are reasonable in length and difficulty.  (I don’t assign anything or write exams; all done by a third party)

4.4   Discusses recent developments in the field.

In our algebra-based physics course, students have had to complete two independent projects that are carried out in groups. Each independent project involves the group of students writing a proposal, the group giving an oral presentation, and each individual student submitting a formal written report. The independent projects have to be related to course content and must involve data collection and the use of analytical skills developed in lab (linearizing data so that equations of best-fit give physically relevant quantities, and managing and reporting uncertainties ). Typical projects have been students investigating terminal velocity, spring constants, the independence of horizontal and vertical motions, coefficients of friction.

In December, the fall-semester instructors met to debrief about how the semester went, and student projects were a large part of the discussion. There was a strong consensus-view among the instructors for reducing the projects from two down to one, mostly for reasons that, in their current implementation, we could not see much realized educational value.  Although they are grading intensive, this did not seem to be a driving concern of anyone. Now, the issue is going to be discussed at our department meeting next week, but the decisions has already been made to keep two projects for this spring semester.

Here are my experiences and thoughts about doing the projects, at least as they are structured now:

• Despite being given extensive guidelines for grading the projects, there have been no clear learning goals communicated to the instructors regarding the projects. If the grading guidelines are any indication of any tacit learning goals, it is to make sure that students can follow directions by using appropriate formats, figures, headings, citations, etc. This contributes, I believe, in flaky assessment practices and poor communication to students about the purpose and value of these projects.

• Group projects have been tough to manage on social level. Last semester, I had cases where I suspected minority students were being denied access as full participants in their groups, and then later identified as not carrying their weight (in peer-evaluations).  I had another case, where an older and  returning student (with a job, family, and child on the way), became immensely frustrated at the lack of initiative and commitment from a bunch of eighteen-year olds who declined to show up twice for agreed-upon meetings. In another class, two students got into a screaming match over the project, nearly resulting in a fight during class.

• In an already over-crammed schedule, we lose 2 full days of class to students giving presentations (8% of our time together). The presentations are mostly boring and somewhat horrendous with a few gems here and there. They are  also peer-graded, which contributes to making them fairly meaningless, as most students will not really give a bad grade out.

But I don’t want to talk about any of that on Wednesday. I worry that those above concerns contribute to a very unproductive conversation in which everyone gets to weigh in on whether or not they like projects, what they do and don’t like about projects, how projects have gone well and not well in the past, etc. “Me, too” conversations are better suited for lunch talk, not for meetings. What I most fear about our meetings is that there is no structure in place for constructing arguments about course reform.

Instead, what I want to talk about on Wednesday is this:

What educational goals or values are these projects intended to support? Why are these goals important to us?

How would we know if the projects are, in fact, helping us to meet these goals? What would be convincing evidence? What would not? What would we do differently if we found that the projects were not? Would we be more likely to tweak the implementation, drop the goals, or seek out other avenues for meeting these goals? Why?

What are other avenues for meeting these goals? Have these been considered, used, or discussed in the past? What are the advantages and disadvantages?

Even if we are meeting our goals, are there any undesirable / unintended consequences that deserve our attention? Are these issues of implementation? Do these merit considering alternatives?

I’d really love to throw this one in, but I fear it would be too much: Are we assessing student work in a way that is consistent with our learning goals?… If not, why not? If so, do we think we could be doing a better job?

From Editorial in Journal of Teacher Education

We bemoan the fact that many  content-area education researchers, researchers who engage in teacher education in their own universities, almost exclusively submit their research that could potentially benefit teacher education to specialized content journals—journals that may or may not be read by teacher educators. Clearly, faculty who walk in two university worlds—for example, both science education and teacher education—have choices to make about their identities as researchers. Could we benefit from encouraging content-area education researchers to frame their work from the “inside” teacher education perspective discussed previously and viewing the JTE as an outlet for that work?

This one stirred up many interesting and varied arguments at lunch, even spilling over to email throughout the day:

How much of the variation in earths’ temperature across the seasons is accounted for in terms of (1) the changing daylight hours (resulting in either shorter or longer exposure times) vs (2) changing altitude of the sun (resulting in more or less incident flux)? Does your answer depend on where you live? More importantly, how do you know and why do you believe?

As usual, guesses, intuition, wild speculation, careful theory, contrived experiments, and natural data are welcome.

** My bigger point in bringing this up was more to these questions: What does it mean to explain the seasons? How do we want students to approach and attempt to make sense of the seasons? **

Oh my god. Am I really doing this? Am I really, one week before classes, going to totally uproot what I thought I was going to do in my inquiry course, and do something totally different.

Am I really going to make the entire course about the sun?

When I reflect back on the value of going to college, I come up with a solid list of things that occurred outside classrooms.

An opportunity to wrestle in a Division III athletics program

An opportunity to teach kindergarteners in inner-city Baltimore

An opportunity to apprentice in a scientific instrumentation development group

More and more, I am coming to think that one really shouldn’t go to college because classes are offered.  Just maybe you should go because the courses that are offered are mostly a joke; and if you are sufficiently prepared, you can probably just spend a few hours a week studying, focusing the rest of your time taking advantage of the abundant opportunities around college to find out about the limits of your physicality, humanity, and reason.

Surely, if you do happen to find an instructor that challenges you deeply as a human, by all means engage with those challenges, too  A fiction and poetry instructor troubled me deeply with two lines atop of a page: “Russell Edson covets your twisted brain. Ditch physics.” I had no idea who Russell Edson was, nor why I should ditch physics, but this led me to dig deep into poetry and writing, and think about why I was studying physics. In a very different way, a professor of mathematics who taught a course I wanted to take challenged me, by allowing me to take his course without a prerequisite course. In allowing this, he plopped down a book on differential geometry and said “Do all the problems in chapters 1-12 in the first five weeks and you’ll be caught up enough to understand the last ten weeks of the course.” Little did I know that everyone else in the course was doing the same thing. As the class unfolded, I learned that all he wanted was for us to learn how to learn from a textbook on our own.

In graduate school, because of prerequisites, I had to take some rather basic educational statistics course before taking some more advanced one that I wanted to take. About a third of the way into the semester, the professor wanted to meet with me after class. At that meeting he had a point to make: that it was a disgusting waste of my waking hours to come to his class. Then he handed me the final exam to take. I never attended his class nor talked to him again. Looking back on this moment, I feel like this professor knew something that I am just beginning to fully recognize, but yet I still can’t articulate what it is.

I do, however, tell people this all the time: I took very few courses in college every semester. I took 12-13 credits, whereas many student I encounter are taking 16-20 credits. See, in my mind, if you can come in with 24 credits from AP or community college classes, you could try to graduate from your university in 3 years. Or, you could just take 12 credits each semester, and free up your time to wrestle, teach kindergarten, and work in a research group. Your courses will mean more anyway, because you’ll have the mental space and time to immerse yourself in the course that, every now-and-then, springs up meaningful. Instead, I see college students either over-whelmed with superficial engagement, or slyly admitting that most of their courses are a joke.

I’m not sure how I feel about anything that I’ve just written. My thoughts are muddled, conflicted, and unstable. Should students seek out challenging courses, or should they just take the courses they are supposed to, and find ways to challenge themselves outside of courses? Maybe I just want to remind myself of these thoughts before I embark on another semester.

Arnold Arons, in teaching introductory physics, asks us to consider the quantity dv/ds as an alternative possible concept for acceleration. Arons claims that Galileo considered both dv/dt and dv/ds. He also suggests that Galileo gave some less-than-compelling arguments against dv/ds, favoring dv/dt because of his hunch that it better described free-fall. Arons invites us to explore the meaning of dv/ds as a concept for changing speed, so here are some of my explorations.

Constant Alternative Acceleration

I started by considering the case of 1D constant alternative acceleration, and worked to rewrite it in terms of the more familiar time-parametrized trajectories.

First let’s just consider what a constant dv/ds means qualitatively. This means that you gain the same amount of speed in an equal amount of distance covered. This makes sense from the units, which are (m/s)/m or  1/s.

Mathematically, we can approach this the following way:

dv/ds = constant (we’ll just call it b), from which is follows that

dv = b ds

From which, we’ll integrate, and for now assume some positive initial velocity vo, giving us

v = b (s-so) + vo

Let’s just set so = 0. Now, we want to integrate one more time to get us an expression for position vs time, so we’ll rewrite v as ds/dt

ds/dt = bs + vo

And then we’ll separate variables and integrate again, from s = 0 to s = s’, and t =0 to t=t’ (and of course rewrite t’ as t and s’ as s)

ds / (bs + vo) = dt

1/b log(bs+vo) – 1/b log(vo) = t

Then it’s just a rearrange game:

log [ bs/vo +1] = bt

b/vo s + 1 = Exp[bt]

s * b/ vo = Exp[bt] -1

s = vo/b (Exp[bt]-1)

Taking a derivative to get v as an expression in terms of t, we get  v = vo Exp(bt), which shows that for positive values of b the speed exponentially grows a, and for negative values of b, the speed exponentially decays. What is interesting is that constant alternative acceleration has no turn around. It’s either run-a-away speeding up or taking forever to slow down. Well, of course is b=0, then velocity is constant.

There is another interesting feature of constant alternative acceleration. Consider the case that vo = 0. For that case we’ll can back up in our derivation, and not assume s0 = 0.

ds/dt = b(s-so)  + 0

This says that if you are located where you start, then you have no velocity. And then, the only way to can get somewhere not where you started, is to have some velocity. So I think this means that if you start with a velocity = 0, then no matter how much alternative acceleration you have, you will never get anywhere. This is strange: Any finite alternative acceleration cannot get an object moving.

Constant Normal Acceleration viewed from the Alternative Acceleration

Now, what if we look at it backwards, how do we describe normal constant acceleration in terms of our alternative constant acceleration. Let’s do that.

dv/dt = a

(dv/ds) (ds/dt) = a

(dv/ds) * v = a

dv/ds = a/v

This says that the “alternative acceleration”, which is obviously not constant, decreases as velocity gets big. This makes sense, because as you move fast, you cover a lot of distance in a lot of time, so you don’t change speed very much over that distance. What’s interesting is that we now have a “zero” in the denominator to contend with, where the alternative acceleration is not-defined where the velocity is zero. But we know this must be the case (from my previous exploration):  If v=0, any finite amount of acceleration cannot get an object moving.

Another interesting feature is that the alternative acceleration changes sign as velocity changes sign. For a tossed ball, on the way up, the alternative acceleration I think would be negative and approaching infinity, then it’s undefined, then it becomes positive moving away from positive infinity approaching zero asymptotically. Oddly enough, I think this connects somehow to the puzzle described here.

A physical situation where alternative acceleration is simple

One more case I’d like to consider, because it’s simple is the case of linear drag force. From Newton’s Second Law, we get.

m dv/dt = -cv

using the same trick above, we write this as

v dv/ds = -c/m v

As long as v isn’t equal to zero, we get

dv/ds = -c/m

Which shows that linear drag has constant alternative acceleration… which makes sense from my exploration above, where we round that for negative values of alternative acceleration, the speed approaches zero asymptotically, taking forever to slow down completely.

Other commentary, thoughts, and explorations…

dv/ds as a definition of acceleration is inertial-frame dependent, which tells us something important about how it can relate to a Newtonian perspective.

It’s interesting to think about what the next derivative should be to describe how alternative acceleration changes: d(dv/ds)/dv?  or d(dv/ds)/ds ? or d(dv/ds)/dt or something else?

dv/ds is, of course, directly related to slope of the phase space. Plotting the phase space for various motions helps you get a feel for why dv/ds behaves as it does and especially why it approaches infinity when it does.

Some related and interesting alternative definitions to consider are the quantities  d|v|/ds  and d|v|/d|s| . One way of approaching thinking about these is through reflections of the phase space… Other odd ones to consider are both d(v²)/dt  and d(v²)/ds, wherein we are trying to describe the motion of objects that lose kinetic energy either at a constant time-rate or a constant position-rate. The constant position-rate one is easy… as we’ve actually already explored it.