Skip to main content

Table 7 Sample responses from one student for Acceleration simulation for all framework levels

From: Cognitive framework for blended mathematical sensemaking in science

Level

Description

Pattern

Mechanism

1 Qualitative

I apply a certain force, and after I increase mass, that’s kind of subtracting away from acceleration

With greater mass in order to keep the same acceleration I would need greater force

With greater force comes more acceleration

2 Quantitative

Note: student didn’t demonstrate this level but defined quantitative patterns (see next cell) right away

Force and mass will be directly proportional to one another

Note: Student didn’t struggle to explain why division makes sense in the formula, was assigned level 3 mechanism (see the cell below)

3 Conceptual

With a lot of friction, even with a lot of force we can see that the acceleration is not as great. We are at about 8 m/s2, but as we increase friction, it’s only 6 m/s2

Acceleration is directly proportional to force, but mass is inversely proportional, so I can form a = F/m

Application of a force on an object creates acceleration, and that is a certain value, and can vary with friction. What causes acceleration is the interaction between how much force is applied onto the object because it contributes positively or negatively to the overall acceleration. Currently it is a = Fnet/m, so maybe I can break down Fnet into applied force and frictional force to yield a = (Fapplied-Fnet)/m. Acceleration is just a rate of speed increases, and with higher friction acceleration will have a lower rate of increase