Free-response PCK-Q question

SAMPLE FREE-RESPONSE QUESTIONS

    FR-CM-1

    Context: Students have learned work and the relationship between work and energy. They are applying that knowledge to answer the following question:

    "Consider a Daredevil Speedway with a number of loops and a ramp. A toy car can be wound several times. If the car is wound, there is a force pushing the car forward while it is in motion. But the force keeps changing. Consider a wound car started with a launcher. It has a mass of m. Its initial and final velocities are vi and vf. Its initial and final height are yi and yf. If friction is negligible, write an equation for the work done by the force pushing the car forward after it leaves the launcher."

    You move to a table and notice that the students put on their white board the following equations:
    Wnet = Wpush + Wgravity + Wnormal
    Wnormal = 0
    Wnet = 1⁄2mvf2 - 1⁄2mvi2
    Wgravity = mgyf - mgyi
    Wpush = Wnet - Wgravity = 1⁄2mvf2 - 1⁄2mvi2 - mgyf + mgyi

    You ask the students to explain their answer to you. They say that “There are three forces in this case, gravity, push, and the normal force. The normal force does not do any work because it is always perpendicular to the motion. The work of the net force is the difference in kinetic energy. The work of the gravity is the difference in gravitational energy. When we plug them in, we get the work of the pushing force.”

    a. What can you conclude from the information provided about the students' content knowledge? What are the students' strengths and difficulties?
    b. How would you respond to the students? Please use direct quotes of what you would say. What is the reasoning behind your response?

    FR-CM-2

    Context: A group of students are conducting a lab about free falling. They are required to use a motion detector to draw position vs. time (s-t),velocity vs. time (v-t), and acceleration vs. time (a-t) graphs of the free falling of three different objects, a book, a small basketball, and a box. The motion detector is held above the objects, facing downward. Moving away from the detector is recorded as the positive direction.

    chart

    You approach this group to check whether the students understand the relationship between s-t, v-t, and a-t graphs. Below is the conversation you have with the students

    You: What does the position graph tell you?
    Student: It hit the ground and stopped.
    You: OK. Does the velocity graph match the position graph?
    Student: Yes, because it increases
    You: OK. Does the acceleration graph match the velocity graph?
    Student: Yes. If you are increasing at a constant rate, you cannot accelerate. Right?
    a. What can you conclude from the information provided about the students' content knowledge? What are the students' strengths and difficulties?
    b. How would you respond to the students? Please use direct quotes of what you would say. What is the reasoning behind your response?

    FR-EM-1

    Context: Students have studied electric flux both qualitatively and quantitatively. They are qualitatively deriving Gauss's law by drawing field lines through a closed surface.
    The students are given the following instructions: "Consider the illustrations shown below. Each picture contains one positive point charge and an imaginary box. In each case, determine if there is net flux through the box. The total electric flux through the imaginary box is the sum of the electric flux through each surface of the box. Remember that when the angle between the area vector of the surface and the direction of the electric field is greater than 90°, the flux is negative. What does the flux through the box depend on? When is there more net flux, less net flux, and zero net flux?"

    chart

    You approach a group of students and have a conversation with them to check their understanding

    You: Looking at the left picture, when the point charge is outside the box. What do the field lines look like?
    Student: Radiate out from the positive charge.
    You: OK, so what is the net flux?
    Student: I think it's negative, because the left side of the box is closer to the point charge, so the flux into the box should be stronger than the flux out.
    a. What can you conclude from the information provided about the students' content knowledge? What are the students' strengths and difficulties?
    b. How would you respond to the students? Please use direct quotes of what you would say. What is the reasoning behind your response?

    FR-EM-2

    Context: Students are exploring the forces exerted by two identical charged pith balls on each other in different cases as shown in the figure below.

    chart

    You approach a table of students and have a conversation with them:

    You: In the case when both balls have the charge of Q, what is the relation between the angles of θ1 and θ2.
    Student: They are the same.
    You: Why?
    Student: The two pith balls are identical. Same mass, same charge. So the gravitational forces, electric forces, and pulling forces are all the same. The force diagrams on the two balls are symmetrical, like looking into a mirror.
    You: What if Ball 1 has Q and Ball 2 has Q/2? Are θ1 and θ2 the same?
    Students: No.
    You: Why not?
    Students: Because Ball 1 is exerting less force on Ball 2 and Ball 2 is exerting more force on Ball 1. So the angles would be different.
    You: What is the electric force on Ball 1 and Ball 2 respectively?
    Students: From Ball 1 to Ball 2, it is k(Q/2)/r 2. From Ball 2 to Ball 1, it is kQ/r2. The former is smaller.

    a. What can you conclude from the information provided about the students' content knowledge? What are the students' strengths and difficulties?
    b. How would you respond to the students? Please use direct quotes of what you would say. What is the reasoning behind your response?

GRADING RUBRIC

    PCK-Q maximum score = 8 points

    COMPONENT DEFINITION SCORE DESCRIPTION
    Orientation (O) Teachers' awareness of the importance of questioning in inquiry-oriented physics teaching, which is evidenced by their preference of using questions during their interaction with students. 2 pts The respondent asks content-specific question(s) that refer to a specific physics concept
    1 pts The respondent asks content-free question(s) that do not refer to any specific physics concepts
    0 pts The respondent does not respond with a question.
    Knowledge of curriculum (C) Teachers' knowledge of physics/science content associated with a lesson objective. 2 pts There are clear and accurate statements of physics/science in responses, which suggests that the respondent holds strong physics/science content knowledge about the learning objective.
    1 pts There are no clear statements of physics/science in responses, which is insuf- ficient to infer whether the respondent holds strong physics/science content knowledge about the learning objective.
    0 pts There are erroneous statements of physics/science in responses, or the state- ments are unrelated to the learning objective, which suggests that the respondent holds misconceptions about the learning objective.
    Knowledge of students' understanding (S) Teachers' knowledge of students' strengths and difficulties in their understanding of physics/science concept(s). 2 pts The respondent accurately identifies both the strengths and difficulties in students' understanding of physics/science concept(s) associated with the learning objective from the given information.
    1 pts The respondent accurately identifies either strengths or difficulties, but not the other, in students' understanding of physics/science concept(s) associated with the learning objective from the given information
    0 pts The respondent fails to identify either the strengths or difficulties in students' understanding of physics/science concept(s) associated with the learning objective from the given information.
    Knowledge of instructional strategies (I) Teachers' knowledge of appropriate responses to students (including questions) that could effectively help students make a progress toward a learning objective. 2 pts The respondent's response(s) to students are aligned with the learning objective and could potentially scaffold students to make thorough progress in their learning in terms of realizing their misconception and the direction for correction.
    1 pts The respondent's response(s) to students are aligned with the learning objective and could potentially scaffold students to make initial progress in their learning in terms of realizing their misconception.
    0 pts The respondent's response(s) to students are unaligned or have no potential to scaffold students to make initial progress in their learning