My youngest daughter is taking algebra based physics in high school. The middle one is taking AP calculus in high school, and the oldest is taking honors calculus-based physics. They are keeping me busy.
My youngest was asking me about conservation of momentum problems last night. The book did something that I liked. It did not ask for actual numerical answers, but instead asked if the available information was enough to solve the problem. For example, you know the masses and momenum of two objects before a collision and the velocity of one after the collision. Can you find the velocity of the other after the collision. After doing a few of these I instructed her to write the equation for conservation of momentum.
m1v1i + m2v2i= m1v1f + m2v2f
Now cross out each item that you know and ask if there is only one unkown left. I get to cross out both terms on the left side since I know the initial momenta and I can cross out m1,m2, and v1f. I am left with just v2f so I can solve for it.Well it turns out that writing that equation which is just second nature to me is a big stumbling block for a new student. I immediately switch to abstract thinking. There is a lot of content in my choices of labels. 1 and 2 indicate that there are two different mass objects and they can have different velocities. The i and f indicate that the velocity can change in the collision. The fact that there is no i and f on the masses means that objects do not stick to gether or fall apart.How does one encourage that conceptual leap? Do you do many concrete examples and hope the student begins to infer the abstraction or do you lead them through it?
Update: I think some experimental introduction is probably the best approach. Measure a bunch of momenta before and after a collision and see that the momentum is always conserved.