Conceptual Difficulties with Acceleration

Conceptual Difficulties with Acceleration
by Don Pata

The other night I received an email from Mark Davids.  For those who do not know Mark he is a recently retired physics teacher who taught at Grosse Pointe South high school for over 30 years.  He was a master teacher and a practitioner of the Modeling Method.  He won the PAEMST (the Presidential Award) and was an Einstein Fellow.  Most importantly he was the heart and soul of the DMAPT for many years.

Although he has been retired for a couple of years he was missing being in the game and convinced some teachers in Tennessee - which is where he and his wife retired - to run a modeling workshop last summer.  Once he got back in the game I knew he couldn't stop.

He emailed wondering how we dealt with the conceptual difficulties that students persistently have with acceleration.  He sent the following as a plan to deal with these conceptual difficulties.  His contention is that the kids have problems mainly due to the way that we teach it.

His suggestion is to emphasize that constant acceleration is simply a constant change in velocity each second.  Here are a few specific ideas to improve student understanding:

1.  Always make a data table (time and velocity). 

2.  Then make a velocity vs. time curve.

3.  The slope of a velocity graph is always to the acceleration.

4.  The area under the curve is always equal to the displacement.

5.  The formula: (Dx = ave. velocity * Dt) still works for constant acceleration.

     (Students are familiar with these ideas from the previous unit!)

6.  Keep local gravity –10 m/s/s and separate it from the gravitational field strength of 10 N/kg

7.  Refer to accelerations as 2.0 m/s each second or 2.0 m/s every second

8.  When students are asked to predict (or match) graphs of position, velocity, and acceleration suggest that they always begin with the velocity curves.

9.  Avoid stock formulas (Dx = V_ot +1/2 at² and V_f²– V_o² = 2 a x)

(Most students do not have any conceptual understanding of where these came from or how and when to use them; i.e.can you make a drawing that explains the last equation? Can you apply the last equation when the acceleration is zero?, etc.)

I learned everything that I know about teaching from Mark so looking at this list, I am not that surprised by any of them and in fact my thought is, "Doesn't everyone do it this way?"

But I think not.  I am sure that there are plenty of physics teachers out there who still roll out the equations on day 1 and work for the next week to have students verify them.  Or that their unit on acceleration consists of drilling and killing kinematics problems.  We know that proficiency in solving kinematics problems does not necessarily coincide with a conceptual understanding of acceleration.

So I guess my question is; what is your goal when teaching acceleration?  If real deep understanding is what you're looking for consider Mark's list above as a real approach to getting your kids to deeply understand what it means to "accelerate".

DP