Teaching Physics To My Mom: February 2017

Tuesday, February 28, 2017

Homework Interlude 1: Please Excuse My Dear Aunt Sally

I had a big problem with my homework, but I figured it out.

Oh? What was it?

I knew I had to use those equations you gave me to fill out the tables, but it turned out I was reading them wrong.

How so?

Well, you wrote $x_{\text{new}} = x_{\text{current}}+v_{\text{current}} \times 0.1$ , so I took the velocity 0.3 and the position 0 and I added them to get 0.3, then multiplied by 0.1, giving me $0.03$ , which is my new position. Then I did it again, 0.3+0.3 times 0.1 is 0.06. And then I get 0.036, and then 0.0096, and that started to look crazy, because the position is getting smaller each time.

Yeah, it does look crazy. What did you figure out?

I asked your dad and he reminded me of PEMDAS, Please Excuse My Dear Aunt Sally.

And what is that?

It’s the order of operations. Parentheses, Exponentiation, Multiplication, Division, Addition, Subtraction. So when you wrote $a = b + c\times d$ it means to multiply $c\times d$ first, then add $b$ . I was doing things in the wrong order, and that’s why my answers came out crazy.

That’s right, and I guess it’s my fault for not explaining that! I’m glad you figured it out.

It’s alright. What’s funny is that once he said “Please Excuse My Dear Aunt Sally” a vague memory of it came back. I remembered the phrase but had always assumed it was a line from some forgotten song from my childhood.

Ha ha. I guess since you figured that out we can review the homework. You were supposed to repeat the exercise that we did last week and generate your own tables of position and velocity using whatever rule you wanted for acceleration. And then you were supposed to plot some position versus time graphs. Let’s see what you’ve got.

Mom's table of values for a constant acceleration

Tell me how you generated the values in this table here.

Okay, I started with this position and this velocity at the top. Then I used the formula you gave me. So I take the velocity and I multiplied it by 0.1, then I add that to the position, and that gives me the new position, 0.6. Then I used $a=15$ , and I multiply that by 0.1, and add it to the velocity, which gives me the new velocity, 3.5. And then I repeated that. Is that right?

It’s exactly right. Good job. Now can we look at the plots? You have two, it looks like; one with constant velocity and one with constant acceleration.


Mom's plots of time versus position. The one that makes a straight line has a constant velocity. The others have		acceleration

The constant velocity one looks good. But the one with constant acceleration is looking strange. Shouldn’t the accelerating curve cross the constant velocity curve because it’s going faster and will have a bigger position? See, in your table here —- Oh wait! I see what happened.

The plots viewed the conventional way, with time on the horizontal axis and position on the vertical axis.

You put time on the horizontal axis, so I was looking at it backwards, but if I flip it around like this, it looks just right. You see how it’s curving up, getting further and further away from the constant velocity one? That’s just what we want. Good job on your homework.

Thank you.

Friday, February 17, 2017

Lesson One: In which Mom pretends to be a particle

The coordinate system

Welcome to physics!

I thought we would start with a game, which I’ll explain after we get set up. The first thing we need to do is to mark out a ruled measuring line on the floor. I used pieces of masking tape placed 50 centimeters apart on our living room floor, which Mom then labelled with a marker.

We need a range of 2 or 3 meters. We’ll choose one of the pieces in the middle to label 0, and then the piece to the right of that will be labelled 0.5 meters, then 1 meter, and so on like a ruler.

Mom: Wait, but what do I do with the ones to the left?

We’ll use negative numbers. So 1 meter to the left of 0 is labelled -1m and 1 meter to the right is labelled +1m.

So it’s like a number line.

Mom marking out out coordinate system on the floor.

Exactly. Positive or negative just points out different directions. Here, let’s try it out with the first stage of the game: You’re a particle, and I’m The Laws of Nature. You move around on the number line according to the rules I give you. We’ll take it in steps. For right now, we’ll just practice; I’ll tell you a position and you move to the corresponding spot on the floor. Ready?

I guess so.

First, start at zero. Here? Good. Now move to 1 meter. Now move to 0.5 meters. [Good again.] Now move to -1 meter.

That means I move over here, to the left of zero?

Yep, you got it. Now move to -1.5 meters. [Mom moves to the right spot.] Now pay close attention. You moved from -1 to -1.5 Did you get closer or further from zero? Further. And which direction did you move? Left. Okay, let’s try one more thing. Increase your position by 2 meters.

Oh, hmm. Okay, 0.5, 0.5, 0.5, 0.5. That makes 2 meters. Now I’m at 0.5 meters.

Correct. Now change your position by -1 meters.

Uh, I guess I go left? 0.5, 0.5, now I’m at -0.5 meters.

Mom at 0.5 meters, doing what she called a “particle dance.”

Yes! Good job. You can change your position by positive or negative numbers, and all it means is what direction you’re moving.

If you’re wondering why we’re doing this, it’s because this is the most fundamental task in physics. The job of physics is to explain why objects move the way they do. But objects do all sorts of interesting things, so the first thing we need is a way to describe their motion precisely. The solution is a coordinate system, which is where we assign every possible location a number, called its position. At every point in time, every particle has a position that we can keep track of, at least in principle. At a certain level, this game of “move around on the number line” is all physicists do.

The Physics Simulator

Okay, now the game is going to get a little more complicated. Here are the rules. You’re going to start at a point on the coordinate system that I tell you, and you’re going to take this pad of paper and keep a table of two things, your position, and something new called your velocity. At every step you’re going to tell me, The Laws of Nature, your position and velocity. Then I will tell you to move to a new position and give you a new velocity, and we’ll start over at the next step.

But here’s the trick, I’m not going to tell you random numbers for your new positions and velocities, I’m going to be following a rule myself. The rules use two formulas. So every step you’ll give me your current position $x_{\text{current}}$ and current velocity $v_{\text{current}}$ , and I’ll give your $x_{\text{new}}$ with the formula

$x_{\text{new}} = x_{\text{current}} + v_{\text{current}}\times \Delta t$

and then—-

Hold on, what’s that little triangle thing?

Ah, well we’re pretending that you’re a particle moving along and we’re taking a snapshot of your position at regular intervals. The length of that imaginary interval is $\Delta t$ . Today I’m going to use $\Delta t = 0.1$ seconds.

Oh, doesn’t your brother-in-law take snapshots of particles with his cyclotron? Is that like what we’re doing here?

I guess so. I don’t really know what he’s been working on lately. But it sounds kind of like what we’re doing right now, yeah.

It’s funny how you two don’t talk more about this stuff, you’re both physicists after all. It’s weird.

Granted! But back to our game—

Wait, I’m confused again. Why do we multiply $v_{\text{current}}$ by $\Delta t$ ? Why don’t we add?

Good question. See, velocity is the rate of change of your position in time. If you’re moving along at some velocity for an amount of time, you’re going to go a certain distance. How far you go depends on both your velocity and your time. If you are going 5 meters per second for one second, you’ll travel 5 meters. But if you go 5 meters per second for 0 seconds you’ll go 0 meters. We need multiplication because $5\times 0 = 0$ but $5+0 = 5$ , which would give us the wrong result for our purposes here. It’s also because velocity is defined as the ratio of ——

No, this isn’t working. This is like when I learn a new board game and everyone wants to explain the rules to me. I always get frustrated because I just want to start playing and figure it out as I go. Can we just start the game?

Yes, I think we should. Go stand at -1.5 meters, and note down that your starting velocity is 3.

Starting the game

Now I’ve got my paper and my calculator and we can start. Tell me your position and velocity. -1.5 and 3. Good, that makes your new position and velocity -1.2 and 3.

Okay, I’ve moved to -1.2 and my velocity is 3.

Then your new position is -0.9 and your new velocity is 3. Got it, -0.9 and 3. Now with that position and velocity you should move to -0.6 and keep velocity 3.

The table of positions and velocities for the first try. Note the author’s inability to draw a straight line.

I think I see the pattern in the velocity. It just stays at 3 every time.

Correct. What about the pattern in the position?

I don’t see that yet. Wait! Oh! It changes by positive 0.3 every time!

Yeah, you’ve got it. So what’s the next position and velocity I’m going to give you?

It must be -0.3 and 3.

Yes! Good job. You just did physics! You observed some data, noticed a pattern, formulated a rule that possibly explains the pattern, and then made a prediction using the rule. That’s basically all of physics right there.

This pattern is called “constant velocity.” The rate at which you change your position doesn’t change, so when we look in steps of equal time, you always move the same distance.

Constant acceleration?

Okay, that rule was pretty easy. Now let’s start over and I’m going to use a new rule. Start at -1.5 again, but with velocity zero. [Editor’s note: this time I’ll just list out the positions and velocities for each step in a table. See if you can see the pattern yourself]

The positions and velocities with the new rule. What’s the pattern?

Oh! I think I see it! So my next velocity is 0.9, and my next position is 0.9. No, wait, 0.75

Yes! That’s it! Good job. Now, can you explain to me the rule you used to get that?

The velocity increases by 1.5 every time. For the position, you take the position in the previous row and add the velocity from that row, but multiplied by 0.1

Perfect. That’s the rule I’ve been using. In fact, if you write down what you just said with mathematical language, you get the formulas I tried to show you earlier. Let’s go back to those now that you’ve figured it out yourself.

$x_{\text{new}} = x_{\text{current}} + v_{\text{\current}}\times 0.1$
$v_{\text{new}} = v_{\text{current}} + a\times 0.1$

All I did this time was use $a = 15$ , so that $v$ increases by $1.5$ each time. That term $a$ is called “acceleration.” Acceleration is the rate of change of the velocity, just like velocity is the rate of change of position. A big acceleration means your velocity changes a lot every time step. And notice that if we take $a=0$ , then there’s no acceleration, the velocity is constant, and we get the rule for the first round we played. Both rules have the same form, just with a different value of $a$ .

Graphs and prediction

Okay, there’s one more thing I want to do, but it involves graphs.

Bring it on.

Alright, then let’s do it. We’re going to make a graph of your position versus time. So we draw time on this horizontal axis, and I’ll mark out the specific times we looked at: 0, 0.1, 0.2, 0.3, etc. Then I put position on the vertical axis. Remember it can be positive or negative. Now we look at the tables you made and put the entries on the graph as points. Let’s do the constant velocity one first.

The “constant velocity” position-versus-time graph in blue, and the “constant acceleration” one in red. Luke accepts all responsibility for the mess.

Now I have a question: looking at the blue curve, if this pattern continued, where would you end up after a hundred steps, approximately?

Way over in your neighbor’s house, right?

Right. Good, you can extrapolate the pattern on the graph. Now let’s put the constant acceleration data on here so we can compare. Same question, but with the red curve: where would you end up after one hundred steps?

Still in the neighbor’s house.

Which rule would take you further?

I guess the constant acceleration rule because my speed keeps increasing. This graph keeps curving up but the other one just goes up in a straight line.*

Right. If the first rule takes you in the neighbor’s house after one hundred steps the second rule will take you all the way down the street.

This is another key lesson! All we did was change the acceleration and we got vastly different behavior from our particles. We’ll see this over and over in physics. Small variations in the rules can produces remarkably varied results.

Enough for now, plus some rambling.

This is probably a good place to stop for the night, but first I’ve got to give you your homework.

Can I ask a tangential question first? We’ve been talking about particles, and you’ve mentioned that everything is made up of particles moving around, but what exactly is a particle? Are they atoms? Did Newton know about particles?*

Sure, good question. Unfortunately “particle” is a word that means different things depending on what kind of physics you’re talking about. The way I’m using “particle” now is very different from the way I use it at work, where I’m a theoretical particle physicist, which Newton would have known nothing about.

For our purposes, a particle is an object that doesn’t break apart when you push it. That includes a lot of things! An atom is a particle, but so is a baseball, or this chair, or the moon. On the other hand, water is not a particle, because it ripples and breaks apart when you try to move it. Though, it turns out if you model water as being made up of lots of little particles you can do very well at predicting its behavior. That sort of thing is the first sign that people had that everything is made up of little particles.

And one more thing, if the chair is made up of tiny particles, what makes it a chair? Why doesn’t my hand just go through it?

It’s all about the rules the particles follow. We just saw how different rules can result in very different behavior. The particles that make up the chair are following a rule that makes them want to stick together, so they resist when you press on them. The particles in water are following a different kind of rule, so they do move out of the way when you put your hand in.

Huh, well that answers a lot of the debates my students used to have in my Theory of Knowledge class.*

Ha. Glad I could help.

Homework

You did an excellent job today figuring out the rules that you were following. Your homework is to apply the rules yourself. I’ll write down the formulas for you, and you need to use them to generate a table and a graph for the motion of some particle. You can use any rule you like for the acceleration. You might want to start simple, like with constant $a$ , but in principle there are no limits. You can show me your table and graph when we meet next week.

Okay, I’ll try!

Next post: Lesson 2 - More on position, velocity, and acceleration.

Saturday, February 4, 2017

"What is Teaching Physics" and Other Pre-amble

In this post: General musing on physics teaching and then some gritty details about my lesson plans. Kind of like those boring college classes where the professor reads the syllabus even though the last half of it is exactly the same for every other course you've ever taken .

What is "teaching physics"?

Now that I've decided to try to teach my mom physics (and she has decided to let me), I have to determine what exactly I mean by "teaching physics." What do I hope to accomplish by the end of this project?

In my mind "teaching physics" means two separate, but closely related things. First, it means teaching the rules that appear to govern the physical universe. It seems to be a fact that all the rich and beautiful and amazing behavior of our universe is governed at the most basic level by a collection of simple rules.

Knowing these rules has value on many levels. It helps engineers build things that work precisely and consistently (you can't get a man on the moon by guesswork, or even a GPS network in the sky). It helps you quickly assess the feasibility of political proposals (can we replace our power grid with solar arrays? Conservation of energy says "outlook poor"). And it seems to satisfy a deep human spiritual need to know. The Greeks couldn't build rockets, but they still wanted to understand the stars.

How much math? So much math.

Second, "teaching physics" means teaching how to think like a physicist. Every field of study has its own ways of thinking. Physicists think about things differently from engineers, and both think differently than historians, and also music teachers, and so on. These different ways of thinking have been carefully cultivated over millennia of human thought to solve the particular problems their respective fields.

For example, historians try to extract what truth they can from extremely limited information while avoiding bias and assumption. Physicists try to find simple, consistent explanations for the all manner of seemingly unrelated phenomena. And to accomplish this, we have developed tricks and techniques to help us, very few of which come naturally. We use math, we devise simplified models, we do experiments, and thought experiments, et cetera and so on. Every physicist carries a "toolbox for his or her brain", and the more tools you have in your toolbox the more you can accomplish in every part of life. If you're skeptical that thinking like a physicist is useful, just remember that "physicist" is basically a by-word for "smart."

Take that, humanities!

That all sounds great, but I need a strategy, and specific goals.

The gritty details

The Rules of the Universe

First, I want a list of concepts I would like my mom (and everyone) to understand about our universe.

Everything is made up of particles whose motion is governed by simple laws.
Motion is relative (Newton's first law).
Motion is determined by forces, and momentum is conserved (Newton's second and third laws).
Energy is conserved (and everything is energy!)

To me, these are the fundamentals. Pretty much every other interesting thing that happens in our universe is a manifestation of these laws. (Unfortunately they're not all true! (1) breaks down at the quantum level, or even in classical electromagnetism, and (3) and (4) aren't strictly true in general relativity, at least without a more advanced framework)

From these basic concepts, we can add on the principle behind various interesting phenomena. Gravity is a great subject for learning to understand forces and acceleration, so I'll probably include that. I have the luxury of asking Mom what she would like to understand and going from there. We will almost certainly spend quite a bit of time investigating acoustics because we both love sound and music. I'll decide on learning goals

Every goal needs a metric, and unfortunately it can be tricky to determine whether or not someone has actually learned a concept. Thankfully, there are plenty of other experienced physics teachers who have worked on this problem and created standardized assessments. They are designed to probe common misconceptions and concept-level understanding. I would like to use them, at least in part, partly because it saves me the work of designing my own, and partly for my own personal learning (translation: I am a huge nerd and enjoy reading academic papers on physics teaching). For some topics, like acoustics, I might have to design my own assessments, but I will deal with this problem as I come to it.

Thinking Like a Physicist

Things get a little more abstract here, so it's especially important to have concrete goals. I'm going to focus on specific tasks that I would like Mom to be able to accomplish. To start with:

Given a simple phenomenon, devise a mathematical model to describe the phenomenon, including picking relevant quantities.
Make plots to help discover relationships between physical quantities.
Use a mathematical model to predict the results of some situation, including identifying relevant formulae and using algebra to isolate variables of interest.
Design and perform an experiment to distinguish between competing hypotheses.
Given a phenomenon, devise an explanatory hypothesis and devise a way to falsify or confirm it.

These learning goals are perhaps easier to assess because they focus on producing a concrete result -- a plot, a successful experiment, a solved equation.

My hope is to teach these skills in conjunction with the physical laws. This should happen relatively naturally; after all, these are the things physicists of old did to discover the laws we know today.

I will be taking care that my lesson plans always work towards a learning goal from both bins, and when I post a lesson plan I will try to identify explicitly which points I am addressing. There might be a few lessons where this is not possible, but it's a personal goal anyway

Homework

I fully intend to assign homework. Just as you cannot learn to play the piano without actually playing the piano, you cannot learn to think like a physicist without thinking like a physicist. I suspect that you can't get a good understanding of physical law without practice either -- physical law is not intuitive, and it takes practice to retrain the brain to have new intuition. Nature doesn't seem to change itself to fit the way we prefer to think, so we've got to do it the other way around.

I will try to make sure that every lesson has a few exercises at the end. We can go over the answers at the beginning of the next lesson.

Experiments

I would like for this project to be experiment-heavy. This isn't always easy, because really good experiments require really good equipment, sometimes custom made. However, the point of doing experiments is not to simply go through steps. My focus is on designing good experiments, identifying what makes an experiment able to distinguish clearly between hypotheses, and what makes good experiments difficult. Hopefully we will be able to build a few of our own. But sometimes we may design an experiment and then find a video of someone else performing a similar one, or I may just reveal what the results would be if we did it for real.

In summary

From here on my posts here will be a mix of my lesson plans and descriptions of our lessons. I have not yet decided on the exact format of the posts, but I will try to make it so the reader can enjoy our antics but also learn a little physics at the same time. The homework exercises will be included, and I encourage anyone reading this to give them a try!

Next post: The first lesson -- Position, Velocity, and Acceleration or The Physics Simulator

Thursday, February 2, 2017

Teaching Physics to my Mom: An Introduction

I have decided to attempt a great feat. I fear I may fail, but I also feel an irresistible compulsion to try. I know of no one who has come close to succeeding in almost half a century. It's a little scary, but the potential rewards are high.

I am going to try to teach physics to my mom.

My mother is a brilliant woman. She earned a PhD in political science back in the 80's. Later, when her kids were getting older, she went back to her true favorite subject and earned a music teaching degree. Since then, she has directed school choirs all over the world, overseen district music programs, only pausing now and then to teach IB history and philosophy classes.

The author's mother in her element. That's about to change.

And yet she is just awful at physics, and even worse at math.

When she went back to school for her teaching degree one of her worst recurring nightmares came true and she had to take a college-level algebra course. I was in middle school at the time and I remember sitting up at nights helping her with her math homework. My older sister and I would take turns trying to help her. My father, an economist, was not allowed to help as all his attempts led to, shall we say, frustration.

The last time she tried to learn physics was her first time though college. Here are her words:

I took my first test. There was a question about a fly and a truck having an encounter. I know I was supposed to use numbers and a formula of some sort but my trick of memorizing problems didn't work because we were supposed to write out what we understood as we were solving it. Fortunately, for me there was a lot of room on the paper. I remember drawing the windshield of the truck, the fly, its smashed remains slowly moving down the windshield leaving a squashed streak. And I actually thought I had answered the question. Imagine my surprise when I got a U-- a U!-- on the test. I had never seen a U in my life. I didn't know it was possible.

So why try again? Well, we each have our reasons. For my mother's part, she's older now, hopefully wiser, and no long being graded or judged. She's recently started to consider herself retired, and one of the things she wants to do with her time is to learn things. She's already learned to play the organ, done in-depth research on World War I, and become a certified hospice-worker. Since stuff all comes naturally to her(!), she's ready for a challenge.

As for me, I like physics, and I like math, and I like to teach. I've spent the last 6 years setting myself on a career track that is likely to include a lot of teaching physics to people who are bad at physics so I could use some good practice. Also, unlike with the 100-level college classes I teach as a grad student, I will have complete freedom over the syllabus here. That means I can experiment with teaching techniques and conceptual approaches. I spend a lot of spare time thinking about effective ways to understand the most basic concepts in physics, but I rarely get to see if my ideas help anyone but me.

Besides, my mom taught me how to read, how to sing, how to wipe my butt, how to make friends, how to bake, and even how to teach, so if there's something I can teach her I guess I owe it to her. Plus, it might be really funny when she screws up.

The author demonstrating that he really owes one to his mother.

This blog is where I will document our attempts. We'll have lessons approximately weekly, and I will share my lesson plans here, along with commentary on how they went. Hopefully Mom will chime in from time to time with thoughts on what she thinks she is learning (or not learning!)

Next post: Teaching philosophy and learning goals