# Algebra Help

So we’re just over 1/3 of the way through Physics 11. Despite my intentions to ward off predictable problems, they nevertheless continue to appear. One of them is Hooke’s Law.

My students did a lab to see the relationship between force and how a spring reacts to the applied force. They could graph the relationship and figured out that the slope was the stiffness of the spring. Most students also go an equation of the line from their graphs and I helped this process along by generalizing the equation to Fs = kx, aka “Hooke’s Law.”

When deploying this model, I had too many students asking telling me they didn’t know what to do. Given a force and extension they seemingly had no idea how to get the spring constant. We worked through that, but I was scratching my head. This is the fourth year kids have been using three variable equations, the first being density = mass/volume. This year alone we’ve worked with d=vt, v=at, Fg=mg.

We subsequently had a quiz on Hooke’s Law with similar results. “I don’t get it.”

There is a complete disconnect from using language and discussion around how force and extension are related, and doing a bit of math with these ideas. Worse yet, it’s a three variable equation! What prevents a student from basic problem solving like, “well the force is where the F is, and I know that k is spring constant, so…”

What are the conceptual problems that kids have algebra? What are the main things that prevent a fluency in working with an equation? In a few weeks students will have learned Ff =uFn and Fg=Gmm/r^2, and all hell will break loose.

FWIW, I fully support students solving any problem graphically but they are extremely reluctant to do this.