Box Theatre: Grade 4-6 Ideas and Engagement

This morning, I helped out with some outreach program at MTSU for grade 4-6 students. I had 4 groups of about 10 students each come through for a science activity lasting about 40 minutes. We, of course, talked about and investigated with pinhole theaters.

Here is what the children predicted they would see (collected across all four groups that circled through the activity):

(1) A small circle of light (because it takes the shape of the hole)

(2) A dimly lit box (because light spreads out to fill the box)

(3) You will see nothing. It will be a completely dark box, (because the hole is too tiny to let light in) / (because your head will block all the light)

(4) A shadow of your head, (because your head will block some of the light, but not all) / (because some light will go around your head)

(5) You will just the see the inside of the box, because even if it’s dark you can still see a little.

(6) The box will be dark at first, but as more and more light gets in it will be light everywhere inside

(7) At first it will look dark, but our eyes will adjust, and we will eventually see something.

(8) You will see a shadow or picture of whatever is outside the box

(9) The shadow or picture of whatever is behind us will be seen upside down, because it’s like an eye.

(10) There will be colors or a rainbow, because of the reflective tape.

Here is what students noted that they saw:

They saw the window, and trees, branches, leaves, and the sky and clouds, and people, and buildings, and grass, and some saw colors, and some noted that it was upside down. Other swore it was right side up. And others only saw it in black and white. One child got scared when a person walked behind them and they swore they saw a ghost.

Here is what students had to say after the observing and drawing:

The white paper reflects the outside like a mirror.

The glass window makes it go upside down (note: it was too cold to be outside, so we looked out a window)

The hole makes the outside squeeze down and go inside the box

Our brain is being tricked into seeing it upside down

The box is like an eye without a brain

The hole being at the top of the box (not the middle) is why

The colors that are blue go in blue (like the sky), and the colors that are white go in white (like the clouds), and they go in and paint a picture

The image is black and white (and not colored) because the paper is white, and it can’t show colors.

The reflective tape is acting like a mirror

After we predicted, observed, and shared our ideas, not a single child asked me what the answer was. Many lingered around to tell me about their ideas, many came over to tell me what they were wondering about, and many told me about who they were going to share their discoveries with when they got home.

Engagement as  Social Construct

Of the 4 groups, only one was disinterested. They didn’t want to share their ideas. As a class, they only came up with three ideas: the box would be dark, we’d see the paper, or we’d see light. They balked at the idea of trying to draw what they would see. Many chose to just free draw instead, and many complained that they didn’t know how to draw, or that they had no ideas about what they would see. Not a single student in any other group had this problem, but over half the students in this group were disengaged in some way. They weren’t even excited to see images in the box, and had no interest in trying to draw or talk about what they saw. This group was very different than the others groups, who were excited to think, and share, and draw. They were excited about their discoveries, and happy to share possible explanations.

So what was the difference? Why would one group be so different? Was it something different about the students? Did I do something different?  Was it just later in the day and students were brain-zonked? To tell you the truth, I don’t think any of those things explain I saw. I actually believe that the difference was largely due to the chaperones. In the disinterested group,  the adults in the room stayed in the corner playing with their i-pads and i-phones. They didn’t look up, or listen to the students. One of them kept walking in and out of the room with his phone. There were also two high school aged students in the classroom who were showing vivid signs of contempt, sarcasm, and disdain for being there. I think children (and people in general) are very aware of these behaviors and the social cues they send, even if it is subconscious. Those signals were clear–the activity was not interesting or worthy of their engagement. And those children suffered because of it. Of course, I can’t be sure about that. But that’s what I saw. See, In the other groups, the adults were engaged in the activity. They were responsive to me and my invitations to be part of the activity, and they were attentive to the children. The children’s excitement was reciprocated by all the adults in the room. That sent the message that it was not only OK to be excited, but that it was something worthy of their time, excitement, and engagement.

Rules for Light

In Inquiry class, we spent most of the day trying to agree on “rules for light”. Here’s what agreed to:

(A) The path taken by light is straight

  • This means that light doesn’t curve around things and that’s it not wavy
  • We discussed how shadows and tanning are good everyday examples of this
  • A more contrived, but strong piece of evidence, is how a bulb held high shines down through a hole, and vice versa.

(B) There are many (maybe even infinite) paths of light going out in all directions from a source of light

  • In all directions means that light doesn’t shoot out in a beam with all the rays going straight together.
  • We talked about how a ceiling light lights up the whole room
  • There was some discussion a solar eclipse, and how that blocks the rays going toward the earth, which is why it gets dark, but there must be rays going in other directions. We wondered if we could see those rays going in other directions during a solar eclipse.

(C) When light hits a surface or an object it must either bounce (go off somewhere else) or be absorbed (stops), or possibly both

  • We discussed tanning as a good example of light absorbing
  • We discussed that word “bend” shouldn’t be used to describe what the path light does at a surface, because it seems like it should “kink”. We agreed that bending made it sound like it was “curving” the way a ruler bends when you grab its end up pull, which would violate our rule that light travels straight.
  • Some groups have suggested that there must be two different kinds of bounces. One bounce that allows images or reflections to be seen (like in mirrors), and another kind of bounce that allows objects to be seen (like grass).
  • Other groups have suggested that absorbing is when you see objects like a table, and bouncing is when you see light glaring off a surface or when you see a reflection.
  • We discussed how if you were outside tanning with tanning oil on, there might be three things happening with light. Some of the light is being absorbed, causing you to tan. Some of the light might bounce of the oil, causing a glare or reflection. And some of the light would be bouncing off your skin, allowing other people to see your skin.

(D) When light goes through a small hole, each path just keeps going straight through the hole

  • We decided that each piece of light doesn’t get “squished” through the hole, but rather all the light coming from different places get closer together as they move through the hole.
  • We struggled with what words to use… during discussion we sorted through the words “squish”, “close in”, “funnel”, “focus”, “cross”…  I still think we haven’t fully come to agreement, but I think we are leaning toward the idea that any given path of light either gets through or it doesn’t. If it gets through the hole, it just keeps continuing in its straight path. If it doesn’t get through, it’s because it hit the surface, which acts like a barrier to getting in the box. Many paths get through, and those that do just happen to get close together. They are forced to cross, as they go through because of the angles involved.

We spent the end of class trying to apply our rules for light to a novel situation they had not considered before: A long filament bulb through a small triangular hole, and what would change on the screen as we began covering up the more and more of the long filament bulb (from top down) until the just the very bottom of the long filament bulb was still left uncovered.



Inventing The Tiring Index

Over the weekend at the PhysTEC conference, I participate in a very fun workshop on using invention tasks to help students engage in proportional reasoning in physics. One of my favorite tasks from the workshop was trying to invent an “inefficiency index” for companies that wash cars, taking a certain amount of people a certain amount of time to wash a single car.

Today, while running with my dog Rudi, I invented the “tiring index”

I was running and getting tired, and started to think, “How tired am I getting?” Anyway, while running, I started to imagine myself running a 5-min mile in the first mile, then a 7-min mile in the next, and then a 9-minute mile in the third. And I wondered if I could quantify how tired that person was getting.

So I invented, the “tiring index”. This person’s tiring index would +2 , or 2 min/mile per mile, because they are taking an extra 2 minute per mile every mile.

Then, I got to thinking about what a negative tiring index would mean. Well, I thought about a person who starts off running a 10-minute mile, but then they run a 9-minute mile, and then a 8-minute mile. This person isn’t tiring at all. In fact, it’s quite the opposite, which is their tiring index would be -1 or  -1 min/mile every mile, or -1 min/mi²

I have learned that inventing indexes is really fun.

Now, I’m thinking about whether the tiring index should be a percentage of the pace rather than a linear rate, and I’m wondering what the “tiring index” is for normal people who run. And I’m really curious… Like, what’s the tiring index for a ball thrown in the air? It can’t be constant. And now I have to eat dinner… ah!

We should all be inventing more indexes… all the time, and being curious about them.

Plunging into Forces…and ready for a bruising

In my physics class, we go way too fast and jump in way too deep on the first day of forces. Think about it: Our first day with forces jumps right into two-dimensional forces on ramps. This means we have to introduce the concept of force, understand different kinds of forces, draw force diagrams, find the components of forces along angled axes, figure out how the angle of ramp translates to angles in diagram, discuss how and why to sum forces, and finally apply Newton’s 2nd law for x- and y-directions. It’s going to be a mess; I can guarantee it.
I’m very much inclined to spend today’s class discussing and working problems with forces in one dimension. It would be nice to just make sure we have some time to discuss how to identify forces, to consider the mechanisms for normal and friction forces, to grapple with how a single force influences an object, and to introduce the idea that we can think of multiple forces as acting as if it were a single force. I could even foreshadow the need for a clever way to think about how to do this in 2D.
I haven’t quite settled on what I’ll do, but I’ll have to figure it out soon. For context of where my students are at after an hour of lecture and a reading, below are some student responses from my pre-class reading quiz:

I’m having trouble with understanding how forces effect the movement of that object.

How can both force and friction be in the same direction up the ramp and the object still slide down the ramp?

Based on the readings, I don’t grasp of the concepts of the forces that act on an object that is on a ramp.

In lecture today, Professor X was talking about the forces that do or do not act on an object while it’s at an incline and I didn’t understand how to determine whether or not the force is present.

With simulation, sometimes when I kept the applied force the same it kept speeding up.. I don’t get why it did that.

It is not much of a question but more of a wanting to know a deeper understanding on how an object on a hill creates a force of friction without having to move since force tends to be based on some acceleration.

Real Life

How is it possible that a ramp can have a perpendicular upward force?

Is ice the only surface that cancels out friction?  What about a waxed bowling lane or an oiled skating rink?


If an object is on a ramp and we are trying to find the acceleration, will the equation always be g sin or cos of the angle incline?

I don’t understand when the inverse of sin, cos, or tan should be used.

When drawing an FBD to represent the force of something on a ramp how do you determine the angles of the vectors if they are not already given.

When can we ignore the Y axis forces and when can we ignore the X axis forces?

I just want to know how do you figure out or what determines where the object that is being pushed up a ramp will end at the bottom of the ramp.

I really don’t understand how to apply the free body diagram.

Go play and tell me about it…

Online quiz this week asked students to play with this online PhET Sim, and then tell me something they learned, something they noticed, or a question that arose.

Here is what one student wrote in response:

“Sometimes when I kept the applied force the same it kept speeding up…I don’t get why it did that.”

What a great thing to notice, and what a great thing to ask about.

Replacing Computer Exercises, with What?

I have been mulling over Student Feedback from my Physics Class:

Mostly, I’ve been thinking about what I’m going to have students do while I write feedback on their standards-based assessment quizzes.

Right now, I’m usually sending them back to work through the computer exercises. I don’t really like the computer exercises, and it was by far the most prevalent thing students said was not helping them to learn.

My options are:

  • Give them self-contained review activities or problems to do instead. Since it’s practice of previous material, it will be less likely they will need my assistance. Plus, we spend too little time in this course cycling back to concepts anyway.
  • I could ask them to use this time to make progress in their independent projects, which are going to start up soon.
  • I could have some hands-on exploration (or Phet Simulation) that I can connect to the sample problem I’m supposed to do that day. I would imagine keeping it a fairly free exploration, with each group having to contribute one thing they noticed or question that came to mind as they were exploring.
  • I could still (at times) choose to send them back to the computer files.

I’m leaning toward being flexible, giving myself options, and students options at times. I’m thinking, If I can come up with an exploration or find a simulation that will lead nicely into the sample problem, I’ll likely do that. If I can’t, I can give students the option to either discuss/work on their projects or they could choose go back to the computer stations, instead.

I like the idea of having students doing some review, and I think I’ll save this kind of thing for the right moment. Maybe when the sample problem is going to drum up some concept we haven’t talked about in a few weeks, or if there’s a particular standard that lots of students are struggling to show mastery with.

Anyway, what do people think? What’s the best use of my students’ time? How do I balanced that with not agonizing over developing or selecting new materials too much?

Other wise with the feedback, student seem pretty happy with things. Got some positive responses about the quizzes (and no negative responses). Got some positive responses about focusing on thinking, reasoning, and ideas over equation, and only one comment suggesting they wish I did more equation work. Got lots of positive responses about doing problems, working with others, and getting to hear how other students thinking and work problems, with only one comment about group work being a pain. Labs were a mixed response, with a fair amount of negative responses. The labs aren’t “cookbook” labs, because they don’t have steo-by-step instructions, but they are purely “confirmation labs”… The labs are never to discover something, they are never a result of student ideas or questions; they are never to develop a model… We always know the model a head of time, and seek to take data to confirm a value, and practice error propagation.


Me learning to examine the pedagogical thinking of future physics teachers

I have never taught a teaching physics class before. An interesting thought keeps popping into my mind: As the students in that class are learning to attend to student thinking about physics, I am learning to attend to their pedagogical thinking.

Anyway, here is a bit of my thinking about their thinking…

Last week for homework, I asked students in my teaching of physics to work through the University of Washington 1D acceleration tutorial with a classmate. I asked them to discuss what they learned, where in the tutorial they learned it, and how the tutorial helped that learning to occur.

Then I asked them to analyze the tutorial in terms of the difficulties that students might have opportunity to work through.

Here are some snippets of what three students wrote (emphasis added):

“I really don’t think that these questions would help most students overcome difficulties in their understanding of motion. These problems would be better for revealing what difficulties students have.”


“Problems like these confront students with contradictions between their common sense and the laws of physics. Students can reconcile the two, provided they get reminders about what acceleration and velocity are. These problems are valuable in progressing the students’ abilities to distinguish physical quantities. However, there should be considerable discussion on each question. These questions should not be rushed.”


“I think this is an excellent worksheet that progresses students through some situations that will make them make them face some common misconceptions and (hopefully) reconcile them…Making the students draw the graphs next to each other for the scenario makes them think through…I really like how the worksheet makes the student flip the direction of the positive-direction. Having students actually reproduce something they have already done with the direction flipped is far better learning tool then just telling them to remember it is dependent on how you set up your axis… I really like where it asks you to agree or disagree with an incorrect  statement–questions like this go deeper than a number answer. They address concepts, not just equations.”

I really appreciate aspects of all three of these very different responses

The first is focused on what a knowledgeable instructor would be able to discern from students making mistakes while doing the worksheet. The responder, however, doesn’t seem confident that students would be in a position to notice or work through those difficulties themselves. The response suggests that an expert must be around to notice and make the most of teachable moments. I see this response as the beginnings of asking, “What is the role of the instructor when students are doing this worksheet?” and I think that this future teacher will likely benefit from more opportunities to watch students working things out for themselves.


The second response is focused more on the possibility that students could be able to work it out themselves, but that it might require something–some scaffolding that draws their attention to the disciplinary ideas of acceleration and velocity, as well as, thoughtful discussion among students I see this response as the beginnings of asking, “What can we do to promote student discussion and meaningful engagement when they do these kinds of activities?” I’m curious how this future teacher is thinking about that question.


The third is focused mostly on specific features of the worksheet that make it likely that students will have an opportunity to wrestle with some difficulty or to notice some inconsistency. The student sees value in having students coordinate among multiple representations, in having them look at the same problem from a new perspective, and in having students considere and respond to reasoning. I see this response as the beginnings of asking, “What kinds of problems, questions, activities are likely to engage students in meaningful learning?” I also notice in the students’ writing the phrase “make them face”… and “make them think”, and I’m thinking about the use of the word “make” in particular, and I wonder what that means in relationship to the first two students who think you can’t “make” them do it.


More Reflections on Inquiry Class

Yesterday was a big emotional day in inquiry.

Students were really digging in to their investigations. Many were so excited about what they were discovering and excited about the ideas they were having. Several groups just continued working through our 20-minute break. Even I took a break. One group kept investigating around a new discovery they had just made, while two other groups felt the need to get their ideas down on the whiteboards now, while they were fresh in mind. There are some really awesome insights students are having and discoveries students are making; so many in fact that I think it will take some time to sort through them all. Students are also beginning to call me over just to tell me about their idea, and to ask whether I understand them. Several students have commented about how they have never felt good about or excited about science until this class. We are in a really good place, especially in terms of affect, engagement, and intellectual seriousness.

Yesterday was also emotional because it was the first somewhat heated debate we’ve had. Near the end of class, students were disagreeing about whether some new evidence meant that one of the students’ theory had been proven wrong. Things didn’t get out of control (not at all in my mind), but tensions were a bit high. I loved that another student stepped in and said, “Do you guys even know what you are disagreeing about?” It was said in just the right that we all sort of laughed. It was true… they weren’t really listening to each other, they were talking at and past each other. The laugh didn’t completely diffuse the tension, but it helped point to what was happening. I think many left class feeling a little deflated.

We’ll have a conversation next week about the need to be critical of ideas, and how to keep that criticism focused on ideas and not on people, and also what can do we if we feel uncomfortable about the direction of a conversation. Overall, I’m happy the disagreement was about something deeply connected to scientific epistemology and the nature of science. I mean seriously, the disagreement was about the meaning of evidence in relation to theory. Could it be any better than that?

Without going into detail, I see yesterday as largely about trying to figure out whether the “hole” does something, or whether its the “material” around the hole that does something & while hole that does nothing. Students haven’t quite framed the conversation that way, but this is sort of where its headed: Does the “hole” angle the light? Does the hole “bend” the light? Does the whole “flip” the light? Does the hole “focus” the light? Or does the hole just not stop light?

In the debate, it turns out that the meaning of our new piece of evidence really hinges on what we think that hole is doing, and importantly what students think other student think about that. The disagreement, I think, was about what one student interpreted another student to be saying about what the hole does or doesn’t do. Fortunately, the argument and misinterpretation, will allow me to bring this up explicitly next week: What do we think the hole is doing, if anything at all? And what evidence do we have to support that?

All the Feedback from Students in Physics

Here are the three questions I ask students for mid-semester feedback. Below is what they wrote.

What do we do in this class that seems helpful for you in learning? Why is that helpful for you?
“The group problems tied with sample problems seem to help a lot. Ideas that I might not have thought of before are shared and I learn a lot.”
“The quizzes because we do them over in order to better our skills.”
“Doing a lot of work with the class.”
“You explain things more than one way that helps to think about things in a different way, and also gives us options in how we’d like to solve it.”
“The fact that we get to take quizzes over. It shows that we have mastered that task and we can move on.
“The sample problems we do in class are very helpful. They allow me to see more types of problems that may come up. I tend to learn by doing examples.”
“Time spent doing problems. Additionally, the manner in which it’s presented, not just focusing on plugging numbers into equations but rather comprehension”
“The instructor goes into depth with each problem.”
“The analogy for average speed and average velocity as “ghost racers”. It helped make an abstract physics definition easier to visualize and understand.”
“The example problems that we do on the board. They are helpful because explain 2 ways to do a problem.”
“I believe the group problems help me most. It really helps when things are broken down”
“Working through the sample problems on white boards, and hearing how other students go about solving a problem helps to learn multiple methods and also be able to see what areas I have problems with”
“Practice problems that we do on boards. I do better learning by doing than talking.”
“Working through some of the problems by going over several scenarios, right or wrong, helps me understand the right way more and helps me train my thinking.”
“The quiz and reassessing. The quiz helps me see the mistakes I make and reassessing helps me correct them.”
“I like going over sample problems as a class and then individualized problems in our groups. This is because you break down the complexity into terms we non-physics majors can understanding. The groups problems allow us and me to see if we really comprehend all the info.”
“You show us how to think, how to use concepts logically, instead of just plugging into equations. I find this very helpful because I learn why these laws of physics work and understand them much more in real life.”
“I like how you do all the problems on board showing all the steps and explaining all the parts. Then we will do a similar problem in our groups.”
“When you do a problem at the board in a few different ways. It allows me to choose the way that makes sense to me. This is helpful because I don’t always solve problems the same way.”
“Just doing things in class is helpful. For example, you brought out the hovering soccer ball. It became much easier for me to see how forces work.”
“I enjoy quizzes before and after class. They show me where I might not understand things that seem clear from the reading, and sometimes it turns out I’ve completely missed it.”
What do we do in class that seems not helpful for your learning? Why is this not helpful for you?
They’re is probably no way to do this, but I feel the lab manual is not very helpful.
When we make excel graphs. It is frustrating dealing with the computer.
The computer files in class don’t help me too much.
There is a lot of down time for certain groups, and I’m not sure there is much you can do about it. If you can find productive things to do during down times, I would be completely accepting of extra work.
The computer questions aren’t helpful because they’re worded in a way that I can’ understand what they are asking. It also doesn’t explain why you go the answer right or wrong, just whether you are right or wrong.
I don’t like doing the computer problem at beginning of class.
I don’t think the computer exercises we do at beginning of class are very helpful. Cause we don’t understand something, but we get the right answer anyway, and then we fool ourselves into thinking we understand
The computer questions seem like they’re taken from some generic physics course that’s not about what we are learning.
The computer stuff isn’t helpful because if we do get a question wrong, it doesn’t really explain it.
Some of the experiments, although interesting, don’t give me a better understanding of why.
The lab activities are related, but they don’t help when it comes to learning. Also, the computer exercises are mostly confusing.
I really do not think the labs help me much.
The computer assignments are not a good learning device.
The skill packets on the computer are not helpful. For me, the wording of the questions and the graphs that they present always confuse me.
The computer programs doesn’t help. It asks more questions than it answers.
The computer problems seem to offer the least benefit. They end up merely being a race to get it done rather than a task that aids in comprehension or understanding.
The exercises on the computer don’t help me much just because they are different that they way questions are asked in class.
When you skip steps in the math, it gets confusing sometimes.
I would like it if you used more formulas
The computer exercises are more of a hassle than a tool for learning. It frustrates me when our answers are wrong and no explanation goes along with it.
Everything we do is helpful. But some of the labs don’t really impact my learning. Just recording information in a notebook can’t effect learning.
I don’t feel like the computer activities are helpful at all. I would rather do more problems in group with that time.
I think you’re pretty helpful
Practice problems take a lot of time. Posing shorter problems may be better.
I don’t like group problems; different opinions just confuse me.
When we go back to the computer. I would rather do things that work better for us.
I don’t see to learn from the computer assignments, it just seems like a tedious task and the questions aren’t always worded efficiently.
Is there anything else you’d like to tell me about? Something you wish we did that we don’t? Something that’s been on your mind?
I might add more sample problems.
I would like to see more simple problems worked out step by step.
I learn better when you do sample problems. There should be more of that.
Do shorter practice problems, but more of them.
Sometimes I feel like we breeze through things as if we try to do soo much in 2 hrs and 20 min that I walk away half the time not understanding we went over.
Everything is fine
I appreciate your partience. Also, thanks for taking our ideas into consideration.
I wish we did more problems in class.
Thank you for changing the time of quizzes to 2am instead of midnight. The readings are hard and I work late.
Do I need to know this stuff for the MCAT?
Get out early on Fridays?
Just to do more example problems as a class, where people offer opinions on how to solve. This helps me understand physics better.
You’ve really helped me out a lot. So far ! yay!
You explain things really well & make material so much simpler. Thanks for being patient.
Our lab class seems to have a lot of people who are really trying.
I like that you accept feedback
Thanks for changing the quiz time to end at 2am
I wish we would more problems on the board.
I would benefit from a site with more examples problems with solutions.
I would like to tell you that I think I did pretty well on the exam and after turning in today’s standards I remembered how to do the answer I turned in blank.
It would be nice to do a homework problem that may have given us problem

SBG Update

Random Collection of Observations

Last year, on the first physics exam, I had about 65%  of students answer correctly when asked about the sign and direction of the acceleration for an object in free-fall, both on the way up and the way down.  (Big Big correction: Last semester, only 30% of my students answered both correctly. 65% last semester gave either both correct OR incorrect in a way that implied negative acceleration meant slowing down.)…

This year, one of my standards specifically addressed this, and there are no surprises. This year, with very similar questions, 93% of my students got the two questions correct. The students who didn’t get it right, chose not to re-assess after an initial unsuccessful attempt.

So those two questions were very similar to the standard. A harder and less similar question was about making sense of what an acceleration of – 2.7 m/s/s tells us.  Students had to choose a correct statement about the motion from a list of option. The right answer to choose was that there is not enough information to tell whether its speeding up or slowing down. On this question, 70% of the students got that answer correct, with the two most common wrong answers being that it’s slowing down and that it’s moving at constant speed.

Looking to the open-ended problem with free-fall, 100% of students chose the correct direction for the acceleration due to gravity in the problem and 0% of students tried to solve for acceleration as if it were unknown in free-fall. I don’t know exactly how many students did this last year, but it was significant enough for me to notice.

On another note, I did not have any standards for interpreting graphs, and students did poorly on a simple question about a position vs. time  graph. Many of them, I suspect, were simply remembering an answer from a practice test where it was a velocity vs time graph. It was the same question about where does the object change direction.

Most recent update:

The sign for acceleration due to gravity on the way up and down: 93% vs. class average of 66%

Whether negative acceleration means slowing down: 70% vs. class average of 42%


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