It's just a grade...

So far this year my regular-level physics classes have had three lab assignments.  Those are Inelastic Collisions in One Dimension, Elastic Collisions in One Dimension, and Explosions in One Dimension.  Each of these involved placing Vernier Motion Detectors at opposite ends of a Vernier Dynamics Track and graphing the motion of a pair of carts as they are put through the various situations described by the lab titles.  (To be clear, I have done the same lab just as well with Pasco.  I don't advocate Vernier in particular.)

In our labs, students took multiple data runs with varying amounts of mass added to the two carts.  The whole goal of this is for students to see that momentum is a useful concept in physics, and that its conservation holds true in many different situations.  Hopefully they will then believe it when I tell them that this holds true in any situation where there is no outside force acting on a system.

In each of these labs, the students obviously have to calculate the momentum (mass times velocity) of both carts, both before and after the collision (or explosion, but let's just say "collision" to make it simpler).  Students therefore had to have a way to find the velocity of each cart.  Earlier this year students learned that the slope of a position vs time graph actually is the velocity of the object being graphed, so that's what I expected they would do.  Sure enough, each lab group graphed x vs t for the carts and used the software to determine the linear fit for the time before the collision, and for the time after the collision.  They printed out these graphs and stapled them into their notebooks, with the slope clearly labelled.

And then they wrote that the momentum is conserved.

There are no calculations in many of the notebooks.  No equations to show whether or not momentum had been conserved in these collisions, and to what degree.  There is simply the statement that momentum is conserved.  Clearly we've got a disconnect here between my expectations and student performance.  It's amazing how exhausting it is to continually stay on top of these things.  Students by and large do not want to do this kind of work--it's just a grade.  It's very hard to stay excited as an educator when students so clearly see no connection between the work they are asked to do and conclusions they are asked to make, let alone questions on an assessment.  To actually connect this with what they think their futures will be?

Today I assigned a step-by-step exercise  for the classes in question. For each of the three labs, students were asked to calculate the initial momentum of cart A, and then of cart B, and then the sum of these.  And then the final momentum of cart A, and then of cart B, and then the sum of those.  And then the percent difference.  And then the question: does your data demonstrate that momentum was conserved?  It may not have been fun, but it clarified things.  Many times students showed me that the data in their notebooks was not sufficient to calculate these values, which means that they could not conclude one way or another about the conservation of momentum.  What should we do?  Well, frankly, the fact that you realized that you documented the wrong data is more important than the number crunching.

I hope this serves us well in our next lab: Impulse.

The Order of Concepts and Chapters

After a decade teaching high school physics, I'm still working on what order the material should come in.  At this point I am pretty happy with the order for my regular-level course, where I start with momentum and collisions.  Those classes will have their second test of the year later this week and after that we will use impulse to transition to our first mention of Newton's Laws and acceleration.  I think it works really well in developing a strong student knowledge of a very important fundamental concept in physics: Conservation of Linear Momentum.  It really bothers me that so many textbooks seem to just tuck that topic as an afterthought in a chapter somewhere after energy.

The course where I am really unhappy is AP Physics B.  Perhaps it is only natural, since College Board themselves are unhappy with AP Physics B, so much so that they are splitting the course apart soon (some excellent details here).  In training with VASS and NMSI I have been encouraged not to start with Mechanics, specifically to avoid introducing students to the physics course with some of the most complicated math and concepts (vectors and acceleration are traditional problem areas).

I have tried to start the year with Thermodynamics and Fluids before, and I think that went well.  Most of the students remember their chemistry, so PV=nRT and some of the other topics actually make Thermo a good place to start.  But there is a lot of hand-waving when talking about work, as in the work on or by a contained gas.  And I admit I struggled to explain fluid physics to students who hadn't yet learned about kinematics, forces, or energy.

This year I started the AP course with geometric optics, and I think it went swimmingly.  Reflection, refraction, lenses and mirrors are mathematically easy and conceptually clear.  The lab equipment is uncomplicated.  And to be honest, lenses and mirrors are fun.  I should write a followup at some point about the fun we have with those labs.

What did not go well was the obvious followup chapter in waves, interference, and diffraction.  Student learning was much weaker, the material less intuitive, the labs less clear and helpful.  Student confidence was damaged and I don't want to repeat that next year.  As this year's class moves on to kinematics, part of my thoughts will still be with how to better teach waves (in a very limited period of time) next year.

"Next Year I Will..."

So I set up this blog years ago to help me keep track of what I do well and (more importantly) what I do poorly as a science teacher.  I haven't made much use of it, because I just don't feel as though I have the time.  Clearly, time management is something that I do poorly.  I have got to find the time to reflect on how each lesson goes, or else I simply won't be able to improve my teaching in the way that I should be able to.

The one issue that is prompting me to finally write is lab notebooks.  I don't know how many science courses require lab notebooks at the high school or college level, and I am a bit agnostic on their value.  Lab assignments themselves are of paramount importance, but I am open to the argument that the composition notebook is not the best format for documenting the purpose, procedure, data, and conclusions of the students during the assignment.  If somebody would make a compelling argument to that end, I would stop using composition books as lab notebooks and I would move on to some other format (digital or otherwise).

Until then I will continue using the composition book.  This brings me to the title of this post.  Next year I will have a composition notebook from each student by the end of the first week of school.  That simply has to happen.  I will have them securely locked in the cabinet in my room and they will not leave the classroom--that part I already manage to do most of the time.  But in grading some of the notebooks I am finding all kinds of notes from the students in first couple of weeks of this school year, and many assignments are missing altogether.  Too many notebooks simply start at the second lab of the year.  Between my falling behind in grading the lab notebooks and my trusting that students would bring note books just because they needed them, I have left a gap where nobody was properly responsible, and the result is that assignments were not properly completed and documented.  That simply isn't an acceptable practice.

Resurrection

This blog has lain fallow for too long.  It's a new school year, and I'm at a new school, so I'm going to resurrect this blog to document my progress in my physics classes.  Hopefully I can get myself in the practice of actually taking the time to record some Reflections of Physics on a very regular basis.

For the record, I am now teaching at Glen Allen High School in Glen Allen, VA, which is the newest school in Henrico County Public Schools.  I currently have one section of honors physics and one section of college-prep physics (otherwise known as "regular" physics).  I am treating each of these as a pre-AP physics class, with the assumption that every student will be taking either AP Physics B or AP Physics C Mechanics next year (their senior year).  (I am also teaching three sections of college-prep chemistry, but it is not my intention to write about these classes here.)

Making standing waves

Newton's Law of Motion

Contrary to popular belief, we can teach students that Newton had only a single law of motion. That law is F=ma. When these four simple symbols are properly defined, that's all a physicist needs to know about Newton's laws of motion.

Textbook after textbook, website after website fails to cut to the chase and sum up Newton's three laws of motion into one simpler statement, and as a teacher I find it very frustrating. It bothers me that millions of students around the world are expected to have word-for-word understanding perfect memorization of Newton's three laws of motion as spelled out by the publisher of their school's physics textbook. The reason this bothers me is that science in general (and physics in particular) is generally about finding the simplest expression for the underlying principles involved in any phenomenon. Sure, there are details, and we do care about them. I am not arguing otherwise. But the fact is that Newton's laws can be summed up in four simple symbols, and I can't see any reason not to do so for our students.

For those physics historians who really want to memorize the words, let's look at what Isaac Newton actually wrote. According to my notes (cribbed from the book On the Shoulders of Giants, in which Stephen Hawking both transcribes and interprets several great works of science, including Newton's Principia), Newton's choice of words was:

1. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
2. The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
3. To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

If a teacher is going to insist that students memorize all three laws and regurgitate them on command, I'd at least recommend historical accuracy. But if you want to simplify, then I'll tell you how to do it.

First, we recognize that #2 above means F=ma, where "F" stands for the net force acting on an object (and both "m" and "a" are defined below). A force is often defined as simply a push or a pull, and that works for most conversations, but when teaching this topic at middle school or above I think we should define a force as an interaction between two objects that would tend to accelerate the objects. The term "net force" simply means that forces can combine, add together, and/or cancel one another out. The forces acting on an object need to be summed with vector addition before F=ma is used.

To continue, "m" stands for mass, which is a way to quantify inertia. Inertia is an object's tendency not to change it's state of motion. Things don't speed up, slow down, or change direction without something making them do so. Some things are more obstinate than others in this regard, and mass gives us a way to measure this quality in any object.

Lastly we note that "a" stands for acceleration, which is the rate of change of velocity. Acceleration is how quickly an object is speeding up, slowing down, or changing direction. Like force, acceleration is a vector quantity, which means that the quantity has a direction. Specifically, the acceleration of an object is in the exact same direction as the net force acting on the object. "F" and "a" are in bold font because that's shorthand to note that they are vectors.

These three paragraphs to describe the equation F=ma are covered by every physics teacher and physical science teacher around the world. That's certainly not my complaint. My point is that Newton's First Law is unnecessary if you actually understand the equation for Newton's Second Law. The First Law is just telling us that when the left side of F=ma is zero, so is the right. In Newton's day, this was a major insight--he was basically pointing out to people that Galileo was correct about inertia, and Aristotle was not. I find that my students are unfamiliar enough with Aristotle that I don't need to address the misconception as a separate lesson--it's just part of the Second Law lesson.

Having done away with the need for the First Law as a separate lesson, allow me to point out that the Third Law doesn't need a separate lesson, either. It is covered by our definitions. Since a force is an interaction between two objects that would tend to accelerate the objects, I need only remind students that the Second Law will apply to both objects experiencing the force in question. Done. Again, in Newton's day it was necessary to state this as a separate concept, because action at a distance (without contact, as in gravitational forces or electromagnetic forces) was not well understood. As with the First Law, the Third addresses a misconception that my students simply don't have.

To summarize, Isaac Newton gave us a single law of motion that works helps us to predict the motion of any object we might study in AP Physics and equivalent college courses. This Law does fail to explain quantum mechanics and relativity, but it has us covered up until those topics, both of which are beyond the scope of our course and our everyday lives. For any problem we have, F=ma, and that's all there is to memorize.

Differentiated Lab Instruction

An excellent way for any science teacher to practice differentiated instruction is by tailoring how we give (and grade) lab assignments. Labs can be inquiry-based or not, open-ended or not, even mandatory or not, and each of these is a method of differentiating in the classroom. I'd like to point out a few practices I've been using that qualify as differentiated instruction in the physics classroom, particularly in lab assignments.

(A good primer on differentiated instruction in general can be found at the website for the National Center on Accessible Instruction Materials at CAST, Inc.)

1. Lab directions on PowerPoint
A major problem for students who are less than meticulous is that they are easily distracted. Especially if they feel rushed, they tend to skip large sections of the directions. To address these students, I have been putting our lab instructions in PowerPoint slide shows, which students can then retrieve to their school-issued laptop. It's harder to accidentally skip 4 slides than it is to skip 4 lines in a paragraph.

Of course, it's also easy for me to delete 4 slides from the procedure for advanced classes. In fact, there are several labs for which I give no procedure at all with AP physics students--a practice that simply doesn't work in my Conceptual Physics classes.

Another nice benefit to using PowerPoint is that I can easily embed photographs or videos of our lab setup if I want to aid students in understanding exactly what to put where. As they say, a picture is worth a thousand words.

Of course, this is within the context of labs in actual lab notebooks, and not as worksheets. I have students use composition notebooks that do not leave the classroom. This leads me to the next practice I want to share:

2. Labs do not have to fit into class time.
Particularly in my AP physics classes, I am an advocate of requiring students to come in on their own time. I assign them at least one lab per marking period for which absolutely no class time is allotted. Before school, after school, during lunch... students will have to find a time to come in with a lab partner or two (I don't assign these lab partners and I don't think teachers should even try in this situation). I am comfortable taking the equipment to a colleague's room if students request to work during study hall... provided that teacher agrees, of course. I've only ever had one colleague decline.

By the second marking period, students understand that lab work is not constrained to scheduled class time. Consider the impact this has on the labs we do during class time; I can tell students that if they didn't finish, they're welcome to come in whenever they have time and complete their measurements. They don't protest, because they already have had to do that before. In fact, for many students it removes the stress that comes with any timed assignment. This allows these students to perform better on the assignment, and to learn the material at a pace that encourages retention. And it gets students to feel comfortable coming in to my classroom outside of class. There is no way to overstate how important that last point is.

3. Don't help.
I have a tendency not to answer students' questions during lab. There are exceptions, but usually what they are really asking is for the teacher to do or explain something that they are supposed to be figuring out themselves. So I repeat the question back to them, or I tell them I don't know the answer but I'm hoping they'll figure it out so I can publish it. It's amazing how quickly students start turning to other lab groups for ideas and clarification.

The "don't help" practice dovetails nicely with not giving a procedure for the lab.

These are three practices that I've introduced over the years in order to make lab assignments more enjoyable for me and more educational for my students. At the time I started each, I hadn't even heard of differentiated instruction. But I had heard of playing to a student's strengths, remediating their weaknesses, and working individually with students on their specific difficulties. And I'm pretty sure that's all differentiated instruction really is.