Good PD is Hard

This week, in addition to teaching, I am helping out with a week-long professional developmentthing (?) for middle math and science teachers. There was not a lot of time for the organizers to put it together, but they are making do. The physical science content is mostly around simple machines (and measurement), and the math content is mostly around graphing and patterns. Teachers work in pairs from a school (math and science together).

Here is some critical perspective toward what we are doing:

  • There is a tacit assumption in the way some of our activities are conducted that teachers are  more familiar with content than they are. An example of this is, teachers were doing an investigation into how much weight it would take to lift a brick (using a lever) with the fulcrum placed at different positions along the lever, largely in order to determine the position with greatest mechanical advantage. The activity is structured such that they start at the most effective location (but they don’t know that necessarily). When I walked around and talked to teachers about whether they would have to add mass or take away mass at the next position, it was nearly a 60/40 split. Cool thing to talk about, to hear ideas, arguments, etc. However, one of the instructors commented off the cuff about the next position in a way that suggested everyone in the room new we’d have to add mass. Some caught on to what the instructor said and changed their predictions, but their thinking was never engaged about why they thought one thing and why they now might have changed their mind). Some, and I’m more proud of them, maintained their original idea (probably because they didn’t hare), and got to be surprised about what happened. One teacher said to me, “I was only thinking about the distance, not about the brick on the other end, and how that might change, too. Now I’m thinking this is more like a see-saw.”
  • There are many “tools” being given out for teaching with no help in developing teacher’s thinking about those tools. One example of this is a brief technology session, in which a bunch of websites and apps were presented. There was no framework for thinking about the role of that technology (or any technology) in the classroom. None of the conversation was about how to change the manner in which students relate to content or how you relate to them (and content), but how to merely make class time more “efficient”. I’m all for efficiency, and sharing cool technology, but that’s not professional development.
  • Some of the pedagogy being modeled is difficult (for me) to see as productive.  An example of this is how we used a KWL chart. The question asked was, “What do we know about levers?” and the teachers who new about levers spit out vocabulary words and facts about levers, and those correct vocabulary words and facts were written on the board– Facts such as there are three different kinds of levers, levers have a fulcrum, levers are simple machines, etc. This kind of modeling misses the whole point of the K in KWL, which is bring the surface IDEAS, ways of thinking, real-life experiences, for the purpose of having them within the public arena of the classroom. To me, one of the worst way to activate prior knowledge is to ask, “What do you know about topic X?” and then proceed to write down canonically correct statements made by the few who happened to know them.
  • A lot of our time is spent rapidly oscillating between teachers being “students” engaging in a lesson and teachers being teachers, listening to meta-commentary about the teaching the lesson. I think it is easier to feel immersed in learning if you aren’t having to constantly shift frames from, thinking about levers to thinking about some advice about how to teach this lesson. I’m not saying we shouldn’t shift frames, but that we shouldn’t shit so rapidly in the moment. It’s dizzying even to me.
  • There is a lot of variety to what teachers do throughout the day. And while variety is good, variety is probably coming at the expense of coherence and meaningful learning. Teachers did a lesson on probability, then a lesson on graphing, then a discussion about technology, then a lesson on simple machines, etc. It was all disconnected for the most part. I could be wrong, but I don’t think ideas are not being pursued, refined, and developed over time, throughout the day and throughout the week. I fear that we are doing to these teachers what the school day does to students.

I am not in anyway suggesting that the people I am working with aren’t knowledgeable of many aspects of PD and aren’t hard-working and committed. I am suggesting that professional development is very difficult. So here are, at least, some very positive things:

  • Teacher seem, for the most part, very happy about the professional development (based on anecdote and daily feedback)
  • Teachers like the variety of activities they are doing
  • The week is extremely well organized and structured because of the organizers (I couldn’t pull that off).
  • Teachers time is well respected–there is little down time, they are being compensated, and lunch is provided, etc. (Very important)
  • The team is developing good rapport with the teachers, and the feel of the community is good (Maybe the most important)


A joke, but not really…

If we taught motion like we often teach energy, it might look something like this.

We say that displacement is done when a velocity persists through an amount of time. Quantitatively we can define displacement as D = V Δt. This equation is valid as along as the velocity persisting through that time is constant. For non-constant velocity persisting through time, see the appendix.

Given this definition  of displacement, we can now proceed to talk about the change-in-position-displacement theorem, which states that when a displacement occurs, the amount of displacement is just equal to the change in position. For a proof of this theorem, see the appendix. The change-in-position-displacement theorem can be written as the following equation,

D = Δx

where Δx is understood to be equal to xf -xi. It is a surprising result that the act of displacing an object with a velocity through a time is merely equal to the change in position.

Together the definition of displacement above and the change-in-position-displacement theorem allow us to solve many problems involving moving objects. Before we do so, however, we need to discuss a special kind of velocity called a conservative velocity. A conservative velocity  is one that can be defined as the negative time-derivative of a displacement function. When such a function exists, mechanical displacements are said to be conserved. For this reason, we say that space can never be created or destroyed.

The conservation of space makes it very convenient to solve problems about motion, because we can now define a number line in space with an arbitrary zero-point. It may be confusing to think about negative position, but remember only changes in position through space are important.

Problem #1: A velocity of 4 m/s persists backwards in time for 4s. What is the displacement? (Hint: The velocity is persisting in the opposite of time’s conventional flow, so be careful with your signs!)

Problem #2: Apply the principle of conservation of space to determine how far an object has displaced if it started at the arbitrarily defined 5 m position, and underwent a displacement of 6 m.

Problem#3: When an object moves at with a velocity of -12.8 m/s for 4 s, how much of the displacement is stored in potential space?

Student Solutions from Today

Students practiced a problem today where a child goes down a slide that is 4m high. Students are asked to first calculate what the speed of the child at the bottom should be if there were no friction. Then they are given the actual speed data and asked to determine how much energy was “lost” due to friction. Everyone gets the first part right, so I want to talk about solution paths to #2

Solution Path #1:

Calculate the theoretical kinetic energy at the bottom and subtract from that the actual kinetic energy at bottom based on actual data.

Solution Path #2a:

Construct the Equation PEi + W = KEf (often based on pie charts), and solve for the work done by friction.

Solution Path #2b:

Construct the equation PE + W = KEf, and actually try to solve for the symbol f, by using W= f Δx, and often (mistakenly) plugging in 2m (which is height not distance along which friction acted). Some students go so far as to try to calculate μ, using f =  μ N.  I try to refrain from saying that these students are trying to solve for the force of friction or the coefficient of friction, because I think they are just solving for variables, not trying to determine any quantities in a physical sense.

Solution Path #3:

Calculate the Initial Energy (all PE), Calculate the Final Energy (All KE), and look at difference.

Solution Path #4:

Subtract the theoretical speed from the actual speed, and use that difference in speed to calculate a kinetic energy (essentially doing KE = 1/2 m (Δv)²

Solution Path#5:

Ignore the actual data. Calculate potential energy and then the theoretical final energy (based on speed answer to part one), and then examine the difference, actually finding a very small one due to rounding.

Solutions #1, #2a, and #3 all work. I find that Solution #1 and #3 are more thoughtful. Solution #2a can be thoughtful for some, but for many its just a routine. Solution #2b sends signal to me that student is in “algorithm of an energy problem mode”. They aren’t thinking; they are just doing. They probably also don’t understand what the difference between Work due to friction, force of friction, and coefficient of friction. Solution #4 is incorrect, but I still like it. It’s a plausible idea, and shows me they are thinking. There’s also something to build off, to learn from, etc. Solution #5 is odd. I suppose it’s good that they are trying to look at a difference, but they act of not including anything about the actual speed of the child sends a signal to me that they are also not thinking, they are just doing.

What do you all think?

Three Questions

Week one in physics, we probably discussed the following question for about 20 minutes:

If a physics textbook is dropped from a certain height, and an identical textbook is thrown straight down and released from that same height, which book will have gained more speed while in the air? (Air resistance ignored).

Then, earlier this week we discussed the following question:

Starting from rest, a ball can either roll down a steep ramp or a shallow ramp that both start at the same height above the ground. Which ramp should you send the ball down so that it gains the most speed by the time it gets to the bottom?

Then today, we probably spent about 20 minutes discussing this question:

If a physics textbook is dropped from a certain height, and an identical textbook is thrown straight down and released from that same height, which book will have gained more kinetic energy? (Air resistance ignored).

Each question alone is perplexing and interesting in its own way, but the real perplexity lies in the collection of answers and arguments among them.



Coaching Day

Today in physics, we took a break from the fast-paced, move-on-to-the-next-topic-everyday schedule. Instead, we had a coaching day.

I just wrote up a bunch of problems. Students worked on them as individuals, but they could come discuss with me what they were doing, or get suggestions from me if they got really stuck, or just check a solution if they felt they had figured it out. Initially, most of the coaching was given by me, but as the day went on, there was more and more student coaching. Before all of this, we had a conversation about coaching, and why athletes do certain kinds of training on their own, but why (in fact) they do a lot of their training with a coach nearby. We also talked about the role of veteran players in mentoring rookie players–the veteran don’t do the workouts or practice for the rookie when they are struggling. It would be silly for another player to lift the weights for you, or to run for you, or to practice some skill for you. Veterans can be around to give some feedback, some perspective, or even encouragement.

See usually in our class, so much of the work we do is in groups that it’s hard for me to give individualized feedback on problems. The standards-based approach I am using gives students written feedback on rather isolated standards, but not as much “in-the-moment”, “while actually solving the problem” verbal feedback. And because its often one-way feedback, I can’t tell how they are understanding or responding to my feedback.

I also think we also just all needed a break from the onslaught of those assessment quizzes. In the summer course, the assessments come too quick, and at some point this week, it got simply over whelming. So today, we took a quick break from written standards quizzes and just spent the whole day working on problems with teacher and peer coaching. All and all, I think the students who have been struggling got some much needed personalized time and feedback, and we all got a day not to be run over by new assessment and new topics.

More on celebrating mistakes…

I want to write about my response to an (incorrect) student approach today that I forgot to make big deal about–by that I mean I failed to get excited about the mistake, failed to celebrate the discovery of a very reasonable strategy that doesn’t work, and failed to share that students’ discovery with the class.

A little context: We have be doing conservation of energy problems this week and turned today toward momentum problems. We worked a lot of momentum problems, and then I gave them a more challenging problem. The problem they were working on near the end of class today involved a 3kg object sliding along with a speed of 10 m/s into a 7kg object, and then the two objects (now stuck together) fall off an edge through a height of 4 m. The question asks about the speed of the two masses. All of the students correctly used conservation of momentum to solve for the speed of the mass after the collision (3 m/s), but about half of the students failed to use that speed to calculate the total energy after the collision. These groups simply set the potential energy at the top equal to the kinetic energy at the bottom, forgetting to include the kinetic energy it initially had.

One group however, realized they made this mistake and went to correct it–not by going back and re-working the problem, but by simply adding the 3 m/s to their final answer. The strategy (while wrong) makes sense. They saw themselves as calculating how much speed it would have gained if it didn’t start with any speed, so why shouldn’t they just be able to add the initial speed back in? I’m mean we’ve spent the entire semester doing that essentially– with equations like  xf = xi + vt, and vf = vi + at, etc. Figure out the change and add that to what was there to begin with.

It would have been a cool thing for me to share with everyone what the approach was, why it seems like a reasonable thing to do, helped to point out that it led to a different answer, and leave it as an open puzzle about why. In the moment of teaching, however, I merely gave quick lip service to strategy as being reasonable, and gave some silly explanation about why it won’t work. Believe it or not, I said something about how it had to do with the fact that √( a² + b²) ≠ a + b.  I quickly reared them back to the correct strategy. Now granted, there were only 4 minutes left in class. I didn’t have a lot of time, but I know that wasn’t the reason I didn’t do it. It’s that I really didn’t recognize how cool of an idea it is, and I didn’t think about the impact that my tone of voice and response would have on that student, their group, etc. I just sort of reacted. And what weird about me not recognizing it as a reasonable approach, is that I’ve even talked about this mistake before.

So tomorrow, I get to try to redeem myself. It’s going to be the first thing we talk about.



Writing in Intro Physics

My experience teaching this summer has led me to re-think many things. Here is just one thing on my mind I don’t want to forget about:

I’d really like to include more writing in the physics curriculum. By that, I don’t mean more lab reports or more independent projects with papers, which we do have. I’d like students to have opportunity to practice formulating written explanations of phenomena and evaluating explanations and arguments. I want to give them feedback on that writing, and I want to hold them accountable to learning to do it well. Now, I have been having students write a lot online as part of pre-class reading assignments. I’ve been sharing a lot of what students do write in posts. In many cases, students are asked to make predictions and explain their reasoning, or students are asked to make some observation and have to try to explain what they observed. Some of the time I’m asking them to begin with their everyday thinking, while other times I am looking to see if students are framing their explanations in terms of physics concepts. None of that is graded or given much feedback. I use it to inform what I do in class in a JiTT-style. In class, as well, we discuss clicker questions, which often involve forming arguments, listening to arguments, responding to arguments, and reconciling competing ideas. While we do all this to learn, I’m beginning to be concerned that these aren’t explicit learning goals–ones that students practice, get feedback on, and are held accountable for being able to do.

I know there’s a lot of literature out there on writing in the sciences, and I’m tasking myself with reading up on it and beginning to formulate a plan on what might work at our institution. The truth is that I am more interested in helping students to use physics concepts to explain the world around them then to solve problems (which is our primary way of assessing students right now). I’m not saying that problem-solving shouldn’t be assessed, I’m just saying that right now it’s given way to much attention–in the substance of the course, the practice students get, the feedback they get, and the ways in which they are assessed.

Anyway, I’d appreciate any ideas, papers, blogposts, strategies, etc. There’s a lot to think about, and I could certainly use some help.


Here are some challenging multiple choice questions I have asked my student this year… figured I’d share.

For each situation below, circle all of the statements that you would identify as accurate scientific statements about the situation. You can circle more than one explanation as scientifically accurate. If you think none of the statements are scientifically accurate, then select only that option.

Situation #1

A heavy stone and a light stone are dropped from the same height. Both reach the ground at the same time, because

(A) The gravitational force from the earth is the same on all objects independent of their mass

(B) All objects fall toward the earth with the same constant speed

(C) The heavy stone is so large that the air below it pushes up on it, causing it fall slower than it would otherwise

(D) Each stone experiences a downward force proportional to its mass

(E) I believe that none of the above explanations are scientifically accurate

Situation #2

A heavy cart moves quickly along a horizontal track and then crashes into a light cart, which is at rest. During the collision, the light cart changes its speed much more than the heavy cart changes its speed, because

(A) The heavy cart exerts a much larger force on the light cart than the light car can exert back on the heavy cart.

(B) The heavy cart carries with it a very large force that is imparted onto the light cart

(C) The light cart has such a small mass that it responds with a very large acceleration in response to the force exerted by the heavy cart.

(D) It is easier to change the motion of objects that are stationary than objects that already are moving.

(E) I believe that none of the above explanations are scientifically accurate

Situation #3

Two identical sleds move along frictionless tracks. One of the sleds is moving faster than the other sled. Circle any statements you believe to be scientifically accurate statements about the situation.

 (A) The faster sled carries with it a greater force than the slower sled does.

 (B) The faster sled must have experienced a larger force in the past that that slower sled experienced in the past.

 (C) The faster sled is currently experiencing a larger force that the slower sled is currently experiencing.

 (D) The faster sled must be lighter than the heavier sled.

 (E)  I believe that none of the above explanations are scientifically accurate.

 Situation #4:

A sled is pushed along a horizontal frictionless track in such a way that it speeds up at a constant rate. This could happen if

 (A) A constant force is applied to the sled in the direction of motion

 (B) A force of decreasing magnitude is applied to the sled in the direction of motion

 (C) A force of increasing magnitude is applied to the sled in the direction of motion

 (D) No forces are applied to the sled

 (E)  None of the above conditions would make it possible to speed up the sled.

We haven’t talked in class about Newton’s 3rd Law… but we will

Below are just some of the student responses to a question about the forces exerted between a bowling ball and a pin compare.

There is a greater force from the ball to the pin than from the pin to the ball. If they were equal forces then the pin wouldn’t fall, and if the pin had a greater force then the ball would go in the opposite direction.

The force exerted on the pin from the ball will be much greater than the force exerted on the ball from the pin, this is because the ball has a greater velocity and mass than the pin, so it would have more force.

I think the force on the pin from the ball will be smaller than on the ball from the pin. Since the pin is sitting at rest and the ball is being thrown down the lane, there has to be more force to get it there.

The bowling balls force will take out the single pin and give some of its force to the pin to fall while the ball will keep moving.

The force from the ball to the pin will be greater from the pin to the ball.

The bowling ball would hit the pin and knock it over. The weight of the ball will push the pin.

The force on the pin from the ball will be much greater than the force exerted on the ball from the bill, because the ball has larger mass and speed.

The force on the pin to the ball is less than the ball on the pin which is why it flew backwards.

Assuming the ball has a bigger mass than the pins then the force exerted on the pin from the ball would be less than the force exerted on the ball from the pin because the ball is moving the pin the pin and therefore forcing the pin more than the pins are forcing the ball.

The force exerted on the pin from the ball will be greater because it has more mass and velocity.

There would be little force exerted from the pin to the ball because it’s at rest. The ball is speeding towards the pin and would exert a greater force on it causing it to fall down.

Since the pin is at rest, the force to the ball should be zero. But the force from the bowling ball is greater than zero because it is moving.

I think that the force exerted on the pin from the ball would be quite a bit more because it is actually moving at a good speed and the pin is sitting still so when the pin is hit then it is thrown back.

The force exerted on pin from ball will be greater than ball from pin because of the masses.

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