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3.3 Thinking in models

Example: Free fall

Course element Work Learning activity
Development of a model
Quantities and variables
visualisation of the mathematical description 		Identification and selection, together with the students, of relevant quantities and relationships
Creation of a visual model of elements and processes
Linking with known relationships and principles
Formulation of testable expectations about the behaviour of the model
 Class discussion

Mindmap

Conceptual assessment

Presentation

Based on the assumption that the gravitational acceleration g is a constant, the falling motion can be constructed stepwise for given initial values by filling out Table 2 from right to left. Student calculate the velocity and the displacement for a few time steps and can compare the numerical results with the experiment by adjustment of the initial values. Students create a visual representation of the procedure followed.

Initial values:  t=0, y( 0 ) = 10 m, v(0)=0, g=9.81  m/s 2
Step size: Δt=0.4 s
TIME STEP


#
POSITION

(cm)

 y
CHANGE OF
POSITION
(cm)
Δy
AVERAGE
VELOCITY
(cm/s)

 Δy/Δt
CHANGE OF
VELOCITY
 (cm/s)
Δv
ACCELARATION
OF FREE FALL
 (m/s2)
 
Δv/Δt
1



-g
2



-g
..



-g

TABLE 2.  Construction of the falling motion in time steps

The learning goal is that students can explain that the change in velocity per time step follows from the Newton's second law of motion

Δv=− F z m ⋅Δt=−g⋅Δt

and that the change in position is computed with the formula

Δy= v ⋅Δt

Depending on the level of the students, the teacher can further formalise the computational method using the notion of dynamic model.