Measuring and improving Pedagogical Content Knowledge of student assistants in introductory physics classes

LIKERT-SCALE QUESTION CATEGORIES

CATEGORY	DEFINATION	SAMPLE ITEMS
Effective guiding question	An effective guiding question directly addressing students' difficulty.	A. If we drop a book, does the gravitational force on the book do positive or negative work?
General definition question	An overarching question regarding the definition of the key concept involved in a scenario without specific directions.	B. What is the formula of work? How does it apply to this problem?
Circumventing difficulty question	A question prompting students to extend their thinking without resolving their difficulty yet.	C. What if the friction is not negligible? How would that change your equations?
Correction through direct instruction	Addressing students' difficulty by directly conveying the information that students need.	D. Work done by the pushing force should be the change of mechanical energy.
Erroneous statements	Direct instruction that conveys erroneous information to students.	E. Work done by the net force is not the change of kinetic energy.

SAMPLE LIKERT SCALE QUESTIONS

LI-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 v_i and v_f. Its initial and final height are y_i and y_f. 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
W_normal = 0
W_net = ¹⁄₂mv_f² - ¹⁄₂mv_i²
W_gravity = mgy_f - mgy_i
W_push = W_net - W_gravity = ¹⁄₂mv_f² - ¹⁄₂mv_i² - mgy_f + mgy_i

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.”

Your job as an LA is to identify students' needs or difficulties and guide them to make a progress in their learning. At this moment, how likely would you use the responses below to continue the conversation with the students? Indicate the likelihood of each response on a five-point scale of 5(very likely), 4(likely), 3(Neutral), 2(unlikely), and 1(very unlikely).

A. If we drop a book, does the gravitational force on the book do positive or negative work?
B. What is the formula of work? How does it apply to this problem?
C. What if the friction is not negligible? How would that change your equations?
D. Work done by the pushing force should be the change of mechanical energy.
E. Work done by the net force is not the change of kinetic energy.

Hypothetical impacts of Items A-E on students' learning

Emperical equations to derive PCK-Q from Likert ratings

The following empirical equations were derived from one case study since they generated O-C-S-I that highly correlated with the same components measured by free-response questions. These equations need to be examined in further empirical studies.

Orientation (O) = (Rate A - 3) - (Rate D - 3)
Knowledge of Curriculum (C) = - (Rate E - 3)
Knowledge of Students (S) = Rate D - 3
Knowledge of Instructional Strategies (I) = -(Rate B -3 ) - (Rate C - 3) - (Rate E - 3)
PCK-Q = O + C + S + I = (Rate A - 3) + (Rate D - 3) -(Rate B -3 ) - (Rate C - 3) - (Rate E - 3)