Imprinting, and teaching spring energy before spring force

The first day on which you introduce a new topic imprints on your students’ brains, the same way a duckling imprints on its mama.  If from birth you replace mama duck with, say, a dog, then the duckling follows the dog around in an adorable manner.  

Similarly, students imprint on your first lesson in a new topic.  Though less adorably.

In electrostatics, if your first lesson is about Coulomb’s Law, then F = kQQ/d^2 becomes the starting point for every single problem, even those that don’t involve forces or point charges.  So instead, I make the first lesson a conceptual introduction to the meaning of an electric field using F = qE (with PE = qV following up on day 2).  The force between point charges follows a week or two later, once the concept of electric field in general has been well established.

In energy, if your first lesson is about work, then every energy problem starts with W = Fd, even those that don’t involve a steady force (or any distance to speak of).  So instead, I make the first lesson a conceptual introduction to energy bar charts.  Work becomes the thingamajigger that changes mechanical energy in a bar chart.  Later, once students are well used to creating, annotating, and using bar charts, I mention the fact that work is the area under a force vs. distance graph.  That becomes W = Fd if a force is steady.  

I’m going to try to fight another imprint that my AP reading colleague Peggy Ankney brought to my attention.  Haven’t we all been frustrated that every spring problem starts with F = kx?  Even when the problem asks for a speed rather than a force or distance, even when the problem explicitly discusses the potential energy of an object-spring system?  

This coming school year, I’m going to invert my first-time approach to springs.  Instead of a laboratory exercise with F = kx, I’m going to start with lab exercises using PE = ½kx^2.  I’ll introduce and use the formula for spring energy well before we ever discuss the force of a spring!  I want the default for my students to be to use an energy bar chart when they see a spring.  Students tend to consider force and motion methods before energy methods – because we *start* with force and motion.  Imprint again.

If I can get students habituated to the reflex that a spring implies use of energy methods, then hopefully (a) they’ll get most problems right because in fact a spring problem more often than not requires the use of energy, and (b) they’ll have an easier time recalibrating to the familiar concept of force than if they had to readjust once they’ve already grabbed the hammer that is F = ma.