Many of us have become good at coming up with simple physics questions that students will struggle to answer correctly, definitely before instruction, probably during and even after instruction.

I want to hear about a question that you think students will likely answer correctly before instruction, but are likely to do worse after some instruction. I’m curious what the question is and why you think students will fare worse after (at least initial) exposure to instruction.

This week’s online pre-class question:

An object is dropped from a height of 45m and takes 3 seconds to hit the ground. Explain why someone might think the object’s speed just before hitting the ground is 15 m./s. Then explain why that can’t be correct.

Three responses representing very different places students can be:

“First of all, wow! That’s the exact answer I had in mind and that is because if it’s dropped from a height of 45 meters and it takes 3 seconds to hit the ground you would want to divide the 45 meters by the 3 s to speed per second (15 m/s), but that is if it was going at a constant speed. So you also have to keep in mind that it was dropped at rest/zero so the speed will increase slowly not constant. I’m still confused.”

“Someone might think it is that because they would divide distance (45m) by time (3 s) which would come out to be 15 m/s. But that would be the average speed.  To find the final speed you would take the initial speed (0 m/s) and add it to the acceleration (9.8 m/s^2) multiplied by the time (3 seconds). The final speed of the ball before it hits the ground would be 29.4 m/s.”

“Because most people would think just divided 45 into 3 to get 15m/s but we haven’t put in  our minds about the acceleration of gravity, which is 9.8m/s that can round up to 10m/s then if you was to times 10m/s by 3s you would get 30m not 45m.”

Initial ideas about what we would see

#1 We’ll see a dot, a circle of light, probably bigger than the hole itself.

Light seems to spread out, like a flashlight

#2 We’ll see the white piece of paper, maybe even with the brightness fading as it gets to the edges.

Like a flashlight lighting a room

Like a streep lamp lighting the ground

It only takes a little bit of light getting in to fill the whole space (like a cracked door)

The light might even bounce of the paper and onto your face, lighting your face

#3 Depending on the position of the hole and the head, you might see a shadow of the head

#4 You will see whatever is behind you–for example a tree

#5 Maybe things will be backwards.

#6 It might depend on the kind of light or the amount light

Inside vs Outside Light

Sunny vs. Non Sunny Day

Bright vs. Dim Light

#7 We might see images or colors on any pieces of shiny tape that were used

Those images might be backwards because shiny tape acts like a mirror or reflection

Observations:

We saw what was behind us, but everything was upside down: The lamp-post, people walking by, the sky, buildings, etc.

We not only saw images, but we saw moving images (e.g., people walking by, the bus going by)

Everything might also be left-right backwards… On group saw that a bus moving from left to right was seen going from right to left in the box

With a hole in the top right corner, you saw the shadow of your head in the bottom left corner.

Things that were far away seemed to be clearer than things that were close up (seems opposite of real vision… far away things are blurrier)

We could see color, at least sometimes. Color was easier to see when the hole was bigger, but it also made the image less clear. Color also seemed easier to see for far away objects than closer objects.

With a small hole, it was only easy to see certain things (like sun and trees). As the hole got slightly bigger, it was easier to see everything and in color. When the hole got even bigger, the colors became more vibrant but the imagine got more distorted

Questions:

Why is everything upside down?

Does this work like a projector? (the fact that blurriness depends on distance of objects)

Does the image come in through the hole and then bounce off the white paper like a pingpong ball?

Does this have anything do with how our brains and/or eyes “flip” the imagine when we see?

Will this work inside?

Why is the “level” of the image not right with the world behind us? (e.g., high things appear low).

Are farther things really crisper and closer things blurrier? If so, why?

Why does the size of the hole have an effect on the color / blurriness?

Are the images just upside-down or upside-down and left-right backwards?

Is the image always upside down or does it depend on the angle you hold things up?

Student Rights

To participate in class in your own personal way

To express your ideas and opinion

To have your ideas taken seriously

To not be interrupted or shutdown during discussion

To be treated as an adult (and not like a child)

To ask questions and seek clarification

To be excused from class when deemed necessary

To have a snack (or two)

Student Responsibilities

To listen while others are talking

To disagree with others in a respectful manner

To be prepared and engaged in class

To be punctual

To come to class with an open mind

To make sure you are understanding ideas

To contribute to your group’s work

To contribute in a way that allows other to contribute as well

To clean up after yourself

Teacher Rights

To be respected as a teacher

To have students’ attention when needed

To set high expectations

To change the direction of the class if need be

To disagree with the class or hold differing opinions

To have a snack

To set rules and establish consequences

Teacher Responsibilities

To keep things interested

To provide learners with a prepared learning environment

To provide opportunities for students to learn what is expected of them

To respect both the class and individuals in it

To grade fairly and assign meaningful work (not busy work)

To manage class discussions

To speak clearly

To keep the class on track

To make connections to their future careers as teachers when possible

To clarify expectations, especially for assignments

To be attentive to student ideas and opinions

To make sure we are progressing toward “scientific” understandings

Here is the list from last semester for comparisons

Why did we need to do research on student difficulties? We could have just asked them.

I’m having problems trying to figure out the difference in acceleration and velocity. They seem as if they are identical when reading the definitions. If velocity is the change in position, and acceleration is the rate of the object changing its velocity or “position,” then they sound like the same thing to me. Im confused about velocity and acceleration.

The text said that “velocity is a measure of how fast an object’s position is changing with time” and that “acceleration is a measure of how fast that object’s velocity is changing with time”. Does this mean that acceleration is the change in position as well? And if not, then what is the difference between acceleration and velocity? I took a guess in my answer above, but I’m not sure that it is correct.

I’m confused with acceleration and speed; I think I know what it is but I still need to take a second to make sure I dont get them mixed up because the definitions are similar.

(added later): I want to emphasize that I’m posting these quotes (from my online / pre-class reading quiz) because I’m in awe of how articulate and aware these students are about what’s confusing them. I’m not posting them because I’m trying to parade around examples of how students don’t understand things. The ideas of velocity and acceleration are incredibly subtle and difficult to grasp. These students are mature in monitoring their own understanding, and are better off for having located the areas in which they don’t feel like things are making sense. They also think that this should make sense, which is something we want to see in our students. The second reason for posting this is because these students are not just articulate about what might be confusing them, they are (according to research) quite accurate. Certainly, it’s a good thing for me as a teacher to know about the things that my students are struggling to understand, but it’s likely a better thing that students know what they are struggling to understand.

This past week, students in my teaching physics course spent a fair amount of time examining student responses to MC physics, and reflecting on what all of that meant, and how well they were at predicting student responses and the difficulty of those items.

Today we tried to gather together all the things they noticed during discussion. Here’s what they noticed:

Students have trouble with circular motion… sometimes thinking that objects can keep curving even when forces aren’t present (maybe they are thinking about something like a curveball that can keep curing after you throw it)… or thinking that objects will get thrown out of a circle (they mentioned the term “centrifugal” force).

Students have trouble with force:

Students think that contact forces can continue to have influence on objects even after they are no longer in contact. Some thought that maybe students were confusing the concepts of force, momentum, and inertia.

Students think that a force (or more force in the case of competition) needs to be in the direction of motion.

Students have trouble with Newton’s 3rd law: They might think that heavier things exert more force, or that more active things exert more force.

Some students don’t seem to think that a surface can exert a force. Some of us thought no students would, but others thought students would definitely.

We can look at pairs of questions and see that questions that we think are similar are not similar to students:

For example they might think that a ball keeps curving in one circular motion question but that it gets thrown out of the circle in another. We might have thought that students answer inconsistently.

By looking at student responses to shape of trajectory for impulsive and continuous forces, we can see they don’t necessarily understand the difference between impulsive and continuous forces. We couldn’t have know this by looking at one question.

Students sometimes give wildly unexpected answer… like answering that an object dropped out of plane would fall backwards. Sometimes it’s hard to remember what it’s like to “not know the physics”. But on the other hand, if we think about it we can often come up with reasons why a student would answer that way (e.g., from the perspective of the plane, the cargo would fall backwards).

Some questions have one really common incorrect answer, while others there are more scatter.

Many of the wrong answers are similar across different questions: There are many questions where students indicate a force in the direction of motion.

Next, we focused in a bit on some specific questions and tried to come up with rules for what students might do when faced with  similar problem. Here is what they came up with for a velocity question.

They might think that same position at the same time means same speed

They might just look for some really obvious pattern in the representation and based an answer off that

Here is what they came up with for an acceleration question.

They might think that velocity is the same as acceleration

The might think that velocity and acceleration are closely related, but not the same (i.e., more velocity implies more acceleration, or velocity implies acceleration, or acceleration causes velocity)

I then gave each pair of students a new question to work on. They had to solve the problem correctly, and then try to solve the problem as they imagine a student might. While the problems we inferred the rules from were for “strobe diagrams”… I gave them questions that mostly involved graphing problems. Groups shared out what they did. For the most part, we found that our rules worked pretty well even for other problems. We did however need to add a rule and modify a rule them slightly, including

“Students might calculate velocity as position/time”,

and that they might think that “being ahead means moving faster” in addition to “having same position means same speed”

As a researcher who thinks about how it is that we come to tell stories about student thinking, I’m struck by many things. First, How similar my class’ ideas about student thinking are with the Canon of PER. This is in two senses: First is the specific categories of difficulties they come up with are very similar, but second is that the tone of students have “difficulties” is similar.

One possibility: The similarity is natural… because that’s what student do, and when presented with the data, we naturally notice those patterns.

Another possibility. The similarity is artificial….  it is a by product of the fact that they are analyzing data, taken using instruments that presume those categories and ways of thinking about student thinking as difficulities.

I think it’s got to be a bit of both, but I do worry. Am I training these future teacher to think about student thinking in ways that are quite natural, or am I training them to think about student thinking in a narrow way that is merely a by-product of the particular methods (and underlying assumptions) of the data and how it was collected. Is this the most productive entry point into examining student thinking?… I wonder.

Here is a question on my pre-class reading quiz: Describe something you found confusing or difficulty to understand from reading. What specifically about it are you having a hard time understanding?

A student writes, “I’m finding it difficult to make sense of any of the kinematic equations or why they work, and because I don’t know why they work it is very hard for me to think about using them to solve a problem unless the question has specific instructions to refer back to the list of equations.”

I know it, students know it, but this is still how we are expecting them to learn.

Future physics teachers’ initial explanations for why a student might say that a dropped stone falls and quickly reaches a constant speed:

“A student could think that since it’s a rock or a heavy object as compared to a sheet of paper or a feather that it would fall faster and might reach terminal velocity faster.”

“A student may put this because they understand the concept of terminal velocity but assume that it happens quicker than it actually does.”

“Students would choose this because of their understanding of objects reaching terminal velocity”

“Someone who has taken some physics and has some knowledge of terminal velocity can easily choose this answer. Someone without experience in physics might still pick this answer because from personal experience, it is difficult to notice objects accelerating as they fall.”

“This might be chosen because if you imagine the situation, the stone falls for such a short time, that you can’t really tell that it’s speeding up. You might think that it quickly gets up to speed.”

“A student might pick answer A because they know about terminal velocity but not realize that 12 feet is not nearly high enough for a stone to reach terminal velocity.”

“If a student had an incomplete understanding of terminal velocity or the distances involved than they would choose this answer.”

Some thing I notice:

Many of the students are situating student responses in terms of the disciplinary concept of terminal velocity… some saying that they might know about terminal velocity, but not understand the conditions in which it is likely to apply and other suggesting that such a student has an complete understanding of terminal velocity. One student suggests an intuitive explanation for why someone might think terminal velocity happens quickly for a heavy object-that because it falls faster (being heavy and all), that it would also reach its top speed rapidly.

I also notice students situating this answer with respect to everyday experience and constrains on our ability to closely observe what’s happening. One suggests that falling happens so quickly that it’s hard to tell that it’s speed up, and another suggesting that it’s hard to notice acceleration.

These two ways of making sense of student ideas are different: One is rooted in student misunderstanding or misapplying disciplinary knowledge. The other is rooted in pointing to a feature of our everyday experience and the consequences of that experience for how we might think about falling objects. Of course, these two might interact.

Both kind of ways of seeing student thinking is important: How does this make sense form students’ experience and set of ideas? What relationship does this have with disciplinary ways of knowing?

One thing I see missing here is how this everyday experience and idea can interface with students learning that the acceleration due to gravity is a constant 9.8 m/s/s. Many students I encounter interpret this as meaning that objects fall at the speed of gravity, which is 9.8 m/s.  Some will even interpret this to meant that it takes a second for a falling object to reach the speed. Some will say that air resistance results in the speed being less than 9.8 m/s.

This last piece here is a third way of seeing student thinking: How their everyday experience and ideas can interface with learning formal physics concepts?

Students took the FCI in my teaching physics class, the three ways I outlined before:

Overall, students did quite well, all students scoring above 70%, with the group averaging 83%. The most common stumbling blocks were indicating force in the direction of motion; distinguishing position, velocity, and average velocity; difficulty comparing the magnitude of force pairs under non-equilibrium situations, and reasoning consistent with force as proportional to velocity.

After everyone finished, we worked through trying to reach consensus, and got as far as the first 20 questions. There was only one question that consensus could not be reached, and the arguments went back and forth for quite some time. Based on the particular question and arguments we were working with, it’s fair to say we’ll be visiting the horse and the wagon paradox. I feel like I did a good job of maintaining  a neutral position with respect to that answer, while still pressing upon and helping to clarify the arguments.

For the first day, things went well in terms of willingness to share, argue, listen, and respond. I was happy that for the most part that we were focused on the arguments and having reasons for changing one’s mind; although changing one’s mind for peer pressure reasons was certainly happening here and there. I usually pressed for what arguments had convinced people to change their mind. In class, I also had a chance to point out some important elements of our discourse, including some nuances in construction of counter-arguments, calls for using representational tools to resolve disputes, and being able to explain or argue for an answer in multiple ways. Some of the arguments I had never considered myself, which was nice. At one point I was able to point out that, at least for one question, that we were mostly in agreement on the answer, but with contradictory explanations for that answer.

As we worked through consensus, our conversation naturally spilled over to explaining why someone might think wrong answers. I heard lots of good beginnings for making sense of how students think. It is nice that we began this conversation in class, because this is what students are going to do for homework–empathize with the thinking of students to account for the range of alternative answers.

Tomorrow, students in my physics course get the FCI and we’ll get to see how they faired at predicting what incorrect answer students will give and predicting the difficulty of the question.

Here is Galileo (in the Two New Sciences) writing on some properties of naturally accelerated motion which are worth knowing:

“That the distances traversed during equal intervals of time by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity

Amid deepening consultation with Galileo, I am inclined to think that non-calculus-based physics would benefit from a framing in terms of integer sequences and series rather than the changing of d’s to Δ’s.