Friday, December 3, 2010

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.

Thursday, December 2, 2010

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.

Wednesday, October 27, 2010

Opening Pitch

Why blog about teaching physics?

I've got several reasons that I want to start this blog. The first is simply to document what I am doing on a regular basis, both for my sake and for the sake of anybody who cares to note what I am doing (peers, parents, supervisors, and perhaps even students). This may help others to understand the pacing and order of my courses, but primarily it's just to make it easier for me to plan and improve in the future.

I've been teaching for a few years now, and I've gotten to the point where I feel that I am competent. Now I would like to elevate beyond simple competence. I want to be a better physicist and a better teacher. I repeatedly tell students to document their purpose, procedure, results, and conclusions in their lab notebooks in real time, but I haven't been doing this myself. I think it's time to change that, so this will serve as my lab notebook for class, with the aim that I learn from my experiences and deliver each lesson better next year than I did last year.

I'd like to thank Greg Jacobs for being the impetus for this move. I've blogged before in many different places on many different topics, but I had refrained from wedding this practice to my profession for some reason. Reading Greg's blog Jacobs Physics got me thinking that I could be ready to use a blog as a tool for communicating with many people. If you are interested enough to have read this far into the post and you have any questions or requests, please share them.

A quick blurb about me: I teach at JR Tucker High School in Henrico, Virginia since 2003. I currently teach AP Physics B as a first-year physics course and AP Physics C Mechanics as a second-year physics course (visit our class website). I also teach Conceptual Physics and in years past I have taught Regular-level high school physics and chemistry. I am a Nanotechnology Fellow for the Math Science Innovation Center in Richmond, and I teach a course on nanotechnology at the Center for Virginia's Summer Regional Governor's School. And I think it's a blast.