Considering Incorrect Answers: How students responded?

In my summer physics class, I asked students the following question about motion online, in which they were asked to consider a wrong answer, explain why someone might think it, and then explain the incorrect answer away.

Here is a physics problem! Imagine you are driving a car along a long straight. Your friend in the passenger seat is recording where you are every hour of the trip.

 Clock Reading   Mile-marker 

2:00 PM


3:00 PM

4:00 PM


5:00 PM


6:00 PM


Explain why your friend might reach the conclusion that the speed of the car at 3:00 PM was 24 miles/hour.

Then explain why that answer is probably not correct.

Here are different ways that students responded to the task:

Describe the Mistake Process and Explain the Correct Way

Someone might have tried dividing the mile-marker number (72) by the time on the clock (3pm). The answer cannot be correct because during each hour, the car has advanced to a mile marker 52 miles away.  The time on the clock can only be used to determine the interval between time: 3pm-2pm =1hr and to find the speed, the initial mile-marker needs to be subtracted from the final mile-marker: v= (72mi-20mi)/1hr = 52mi/hr

Describe Mistake Only

Because they divided 72 by 3 thinking that they had traveled 72 miles in three hours.

Describe Mistake Process and Underlying Misunderstanding

If they confused 3:00 PM with 3 hours, they might be tempted to divide 72 by 3.

Show that Wrong Answer implies Something Else Incorrect

If the car were traveling 24 miles per hour at 3 pm then from 2:00 pm until 3:00 pm they would have only traveled 24 miles leaving them at mile marker 44 instead of 72.

Identify Hidden Assumption in Process and Explain why Wrong

If someone took the mile marker 72 and divided it by 3pm they would come to 24MPH however this would be assuming that the car had started at noon and had started at mile 0. however we do not know where the car started, only where it is now and where it was an hour ago.

Explain Correct but neither Describe or Explain the Mistake

I don’t know why someone would think that they were moving at 24 mph at 3 pm, but the time is given in increments of an hour. So obtain how fas they are moving you would subtract the mile marker number from the number of the previous mile marker of the previous hour. From 2 pm to 3 pm the car traveled 52 miles within the hour , so the car was traveling 52 mph.

State Correct Answer without Explanation

I don’t know why someone would think the speed of the car is 24 miles per hour. If you look at the data it’s clear that they are traveling at 52 miles/hour.


I’m curious: Which kinds of responses do you think are most productive? Which are the least? How could the task be re-written to encourage more of the productive kinds, and less of the unproductive kinds? OR What feedback would you give to students, or do in class the next day, as to encourage the more productive responses on later assignments?

KA: Why you don’t even need to watch the videos to understand why it’s more of the same

Sorry for the long title. OK, so I’m obsessed with mining the KA comments and questions for evidence of student thinking, questioning, engagement, and interaction. Who cares about the videos. Seriously. You don’t even need to watch them.

A student on KA, after watching a video on the difference between average speed and average velocity, asks:

“Im confused with the original question and the reason behind needing the answer you came up with, isnt his average velocity 5km an hour either way?”

This seems like a wonderful question to ask: Why would we need two ways to think about speed? I don’t understand the premise for needing two approaches. Isn’t it 5 km/hr either way?

Here is some of the feedback this student gets:

#1 When you go on to study more complex things it will be important, so just cram it in your head for later

“The fact is that 5km/h and 5km/h North are very different when things gets more complex, so you just have to get the idea in your head.”

#2 Just think about it like this, and worry about how to make sense of it later. 

“The main thing to realize with this is that velocity means speed AND direction. it’s a very fancy thing for a very simple process. You’ll get the intuitiveness of it later, but for now just think about it like this: Speed = Direction does not matter.”

#3 The question asked for something specific and you should learn to give correct specific answers to questions asked.

“The reason is that 5km/hour is a scalar quantity (only has magnitude) but the question asks for the average velocity which is a vector quantity (has magnitude and direction). The correct answer is 5km/hour north because it has both the speed and the direction that Shantanu traveled in an hour.”

“The difference is without the direction it’s only speed but the question asks for the velocity”

#4  It is important to know equations so you can solve problems with different numbers

“The point was to show the equation, and that you could change the velocity or the time to whatever and you will be able to solve for average velocity with that information.”

“If you had the same exact problem, except with different times and distances, you would have to go through all of this the same way. While the numbers would come out differently, the method would be the same.”

#5  In order to answer questions correctly, you need to know the vocabulary words associated with question. Those vocabulary words are best defined in terms of other vocabulary words.

“The reason is that 5km/hour is a scalar quantity (only has magnitude) but the question asks for the average velocity which is a vector quantity (has magnitude and direction).”

#6  If I repeat the point to you again, perhaps you will understand why it’s important

He was just trying to make the difference between speed and velocity clear

One way of looking at KA is to analyze the content presented. Another way is to look at the activities that occur around and are stimulated by that content. From this perspective, it also looks like more of the same. What do you think?

** Seriously still not trying to get myself in trouble by analyzing KA stuff, just noticing and wondering **

Crowd-sourced Questions and Answers with KA Physics Videos

I have recently been browsing user questions to Khan Academy Videos, because they are pretty interesting. For example, here are some student questions from his video on acceleration.

With these questions, users can vote the question up and down, such that the question “importance” is crowd-sourced.

So where does this fall short?

One reason this falls short is because the bottom question would be (to me) the most generative, interesting, and significant question for my students to  pursue. That’s not to say that the other questions aren’t important. Understanding vectors vs. scalars and understanding why division can be thought of as multiplying by inverse are both relevant questions, but those questions are probably not going to lead to interesting pursuits. In contrast, the question of how to find acceleration with distance information is a real puzzle–one that requires some real digging into. The question about velocity and speed are likely the result of that vocabulary being introduced, with “pat” answers that aren’t very meaningful.

Part of the job of me as teacher is see the significance and generativity of my student questions: Does this question concern significant disciplinary ideas? Does it represent a significant difficulty or misunderstanding from which we can learn? Will this question lead to meaningful inquiries? For those purposes, not all questions are equally good and students don’t necessarily have the perspective and expertise to discern the difference.

Not only question, but Answers to Questions

Users can also post answers to questions. Like questions, those answers can moved up or down in importance as users vote on best answers. To follow up on our question, here are three answers to the question about how to find acceleration given distance information.

Why does this fall short?

Of these three responses, the one voted to the bottom is probably the best one–even if you don’t think it’s great, it’s still much better than the first two. The first two simply refer to using an equation and plugging away. The last one, although cursory in exposition, at least leverages the use of an important idea: average velocity.

Additionally, students in physics are prone to “look for the equation” to use. Here we see that the users have simply vote up answers that fits their expectations about what a good answer should look like: It should provide you with the equation to use. Crowd-sourcing might then just be a way to reinforce such views.

Anyway, I suppose I should just add that this isn’t an “attack” on KA. It’s just some thoughts about how teachers vs crowds prioritize questions and explanations for learners.

Fractions Conversations (Or Christopher Danielson will like this)

In the car, while I was driving, my wife was finishing up the border of a quilt by hand. During the drive, I would keep asking how far along she was on finishing the border, which had four sides of equal length.

Sometime in the morning she says, “I’m about half way to a quarter, so an eighth.”

Later she says, “I’m a quarter of the way.”

Later she says something more interesting, “I’m half of the way, to the halfway,…”

“Huh?”, I inquire. “Isn’t halfway to halfway equal to a quarter of the way, which is where you were an hour ago?”

She adds, “No, Im half of the way, to the halfway from when I was at a quarter.”

I pause and think about this for a while, saying, “OK. From where you were before. You’ve made half of the progress to half based on being a quarter of the way…. That’s an interesting way to think about it. So, you are 3/8th of the whole way, right?”

She thinks about it for awhile, and says, yup.

She then want to explain how’s she been thinking about it, “I’ve been thinking about each side of the quilt as one. So, I was half way into completing the second side.”

“OK. I see. You were half way into the second 1/4,… which I think is why I said it’s an 1/8th, or rather the 3rd 8th.”

She thinks about that for a while and agrees.

So now, I’m curious about her way of thinking about it, and I ask, “Let me know when you get half of the way to the halfway from being half of the way to halfway from when you were at a quarter.”

She thinks about it for a while, stopping me several times from interrupting her,

After 20 seconds or so, she says, “So you want to know when I’m 7/16th of the way?”

Encouraging Autonomy–Lessons from Parenting

From, “How to Talk to So Kids will Listen and Listen so Kids will Talk“, Faber & Mazlish

To Encourage Autonomy:

1. Let children students make choices

2. Show respect for a child’s student’s struggle

3. Don’t ask too many questions

4. Don’t rush to answer questions

5. Encourage children students to use sources outside the home classroom.

6. Don’t take away hope

To Praise

1. Describe what you see (instead of evaluating)

2. Sum of the praiseworthy behavior with a word

To Free Children Students from Playing Roles:

1. Look for opportunities to show the child student a new picture of himself or herself

2. Put children students in situations where they can see themselves differently

3. Model the behavior you’d like to see

4. Be a storehouse for the child’s students’ special moments

To Engage Cooperation:

1. Describe what you see or describe the problem

2. Give information

3. Sum up the situation with a word

4. Write a note

I’m likely going to use Chapter Four (encouraging autonomy) in my teaching of physics class. Here’s are two snippets:

And how could I let my children make mistakes and suffer failure when all they had to do was listen to me in the first place? You may be thinking, “What’s so terrible about helping children tie their shoelaces,or telling them how to resolve an argument,or seeing to it that they don’t make mistakes? After all children are younger and less experienced. They really are dependent on adults around them.

As much as we understand the importance of our children being independent, there are forces that work against us. First, there’s the matter of sheer convenience. Most of us today are busy and in a hurry. We usually wake children ourselves, button their bottoms, tell them what to eat and what to wear, because it seems so much easier and faster to do it for them. Then we have to cope with our strong feelings… We have to fight against seeing their failures as our failures. It’s hard to allow those so close and dear to us to struggle and make mistakes, when we’re certain that a few words of wisdom could protect them from pain. It also takes great restraint and self-discipline on our part not move in with advice, particularly when we’re sure we have the answer. I know to this day whenever one of my children asks, “Mom, what do you think I should do?” I have to sit on myself


Naming Inverse Mass

I asked on twitter what people might name inverse mass. Here’s what I got so far

Alacrity (@bvancil):

Mechanical Conductivity (@kellyoshea):

Capriciousness (@almeidaphysics):

Ertia (@fnoschese):

Mobility (@chrisgoedde):

Breeze (@chrisgoedde):

Wisp (@chrisgoedde):

Dispatch (@chrisgoedde):

Coefficient of Acceleration (@calcdave)

Force Responsitivity (@brianwfrank)

What do you like? What you would add?

Added from the comments

Acceleration propensity (LJ Atkins)

Acceleration susceptibility (LJ Atkins)

Influentia (LJ Atkins)

Accelerability (Dan Goldner)

Photoelectric Effect Difficulties

An undergraduate student has been working on a research project on student understanding of the photoelectric effect. One of the challenges has been helping the undergraduate student to develop enough of a deep and meaningful understanding in order to navigate through an analysis of written data and interview data. It’s hard to understand others’ confusion when you are still working out your own. I am actually leaning toward making the student right up a section in his thesis about himself as a research subject, in which he discusses and analyzes some of the major misunderstandings that he’s had to work through.

Anyway, here’s quick list of some observed difficulties that physics majors have had in making sense of photoelectric effect phenomena.

#1 Associating speed of ejected photoelectrons with the measured electric current flowing in circuit; difficulty understanding how the current can only depend on the rate of photoelectrons emission (and not their rate of travel).

  • Predicting that decreasing the wavelength will result in an increase in the current, because the photoelectrons will be more energetic, thus faster, thus produce a greater current
  • Believing that driving the stopping voltage in the other direction will result in an increased current, because the emitted electrons will become more energetic, and move faster, producing more current

#2 Incorrectly associating intensity exclusively with the number of incident photons or energy of individual photons (not both); not having a clearly defined classical interpretation of intensity to fall back on, and relate to quantum energy associated with a single photon:

  • Struggling to understand in thought experiments what it means to “hold” the intensity constant or “hold” the number of photons constant
  • Believing that an increase in intensity alone can produce photoelectrons

#3 Incorrectly associating the “work function” with a function that describes how the binding energy of electrons varies with depth

  • Associating the surface levels electrons with zero work function
  • Struggling to understand why the the standard equation describes the maximum kinetic energy of electrons.

#4 Struggling with the apparent similarities between the frequency dependence with Bohr model (i.e., absorption spectral lines) with frequency dependence of photoelectric effect

  • Believing that there is a resonant frequency that will result in maximum photoelectric effect, because the metal *prefers* particular energy transitions

More posts to follow for sure once the thesis takes some more definite shape, but just wanted to get this down before I forget.

Understanding the Pressures Against Whiteboard Meetings

An interesting phenomena in our department is the following one:

Our introductory physics sequence makes use of whiteboards. The typical mode is this:

  • The instructor models how to work a problem based on the reading students did the night before (the reading was incentivized by use of reading quiz when students show up).
  • Student groups are randomly assigned to do 1 of 4 possible problems. Students are expected to work on the problem collaboratively on whiteboard. Typically they are expected to show how they set-up the problem, but not show grueling detail of any algebra or math.
  • Students are expected to stack their whiteboards at the front of the classroom.
  • Then there is a class discussion or whiteboard meeting of some sort–my understanding is that, in implementation, the typical format of the discussion is the instructors picks one or two group to stand up and explain how they solved their problem.

The course has been using this for a couple years now (not sure exactly how long). Over this time, there has been a uniform movement away from having whiteboard meetings / class discussion. All instructors still use whiteboards for problem-solving and see value in it, but there has been a fewer and fewer instructors do the discussion part. Some instructors still do the discussions, but even among them, the feeling is that the discussion are not useful and productive.

There are many possible factors that drive this shift away from holding discussions. Here I want to lay out some and see what other people think:

#1  Professional Development Collectively, there has been little to no training, apprenticeship, feedback, or support in developing effective practices with structuring and facilitating whiteboard meetings. This is true for both faculty and undergraduate TAs, and more generally of all interactive engagement methods that instructors are expected or encouraged to use. This isn’t to say there has been no professional development in some cases. In most cases, however, no instructors have never even observed anyone else running a whiteboard meeting, not to even mention an effectively run one.

#2  Substance of White-boarding Problems: The particular problems students are assigned to work on were not necessarily designed to support productive discussion; rather they were designed around chapter topics. They are also not necessarily designed based on physics education research or specific learning objectives; or, if they are, such design features are not clear to their users. Well-chosen problems can go a long way to helping promote useful discussion.

#3  Values and Priorities: Explicit conversations about the value and importance of whiteboard meetings for student learning and classroom community are mostly absent in our department. With very real pressures for time that instructors face and their growing sense of the ineffectiveness of whiteboard discussion, whiteboard meetings become one of the first things instructors will stop doing. The reality is that it’s hard to persist in doing something if either the individuals involved (or the community at large) don’t value that thing. Instructors, I believe are doing what they see is best for their classrooms and students.

#4 Classroom Constraints: Our classroom space is a large, wide-open space and there are 32 students spread out among that space. This makes white-boarding meetings difficult.  Managing a classroom discussion with 32 students is different than managing a classroom discussion with 10, 15, or 20. In addition, the tables in the class are also not conducive for rearranging the space. Large rolling chairs make it difficult to find space where everyone could be a circle. Designing spaces that support particular kinds of social interactions can go a long way to promoting productive conversation.

I would imagine that these constraints are common to many institutions, classrooms, and instructors. Understanding how these constraints operate on us and how we can change these constraints becomes really important. I can’t imagine significant movement toward developing effective classroom discussion with whiteboards without changes at all of these levels. What do you all think?

* I should note that I am subject and influenced by these same constraints: An environment/community that doesn’t explicitly communicate the value of the practice. A classroom space that is not conducive to effective practice. Content that is not design to support the practice. And lack of professional development (specifically about what it means to engage in this practice at our institution in our courses). These pressure have driven me away from consistent use of effective classroom discussion with whiteboards. I write this post, because in the fall, I am re-commiting myself to making this work in my classroom.

Test Score vs Time Spent

So let’s say you gave a certain test to your students. There were 30 questions on the test. They were all multiple-choice each with 5 choices. The test is ungraded but students are required to take the exam. The exam is used solely for evaluating the effectiveness of instruction.

Let’s say you plotted for each students “Test score” vs. “Time spent taking the test”. Let’s say the plot looked like this:

What do you make of it?

Equation of Best Fit:  Score = (0.35 Points / Minute) * Time + 6.5

Correlation Coefficient:  R = 0.71

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