So how should we think about fundamental particles? Are they points in space or are they waves of probability? One person I read recently said that it just depends on the type of experiment. If you want a wave then make a wave experiment, but if you want a particle then make a particle experiment. This may seem like a simple explanation except for the fact that in some cases they behave like particles in wave experiments and also behave like waves in particle experiments.
So how do I think of particles in the particle-wave duality debate? The way I see it, they behave like waves when they travel, but they behave like particles when they interact with other particles. So when I explain it to students I say, "It travels like a wave, but interacts like a particle."
As a side note, this is an interesting way of looking at it since it would seem that particles travel like they have mass, but when they interact, they interact like they have no mass. Hmmm... so the wave nature of particles give them mass? There's an interesting thought.