Particles and Waves
While the motions of the latter can be calculated (more or less) accurately, with the first we have to be satisfied with probabilities. Waves are relatively easy to understand, they can be in many places at the same time. Particles though can only be understood if they behave as such. 
The difficulty particles represent is obvious in the choice of words Feyman ("Feynman Lectures on Physics: Quantum Mechanics") uses to describe a gun shooting bullets, or a heated wire emitting electrons. They do no not behave like we would expect guns to behave rationally, but more like an automatic weapon out of control. In fact, guns behave just like waves, even if they shoot single bullets: "It is not a very good gun, in that it sprays the bullets (randomly) over a fairly large angular spread".
Which makes me say: the problem is not with the bullets, but with the gun! The nicely short and beautifully clear review by Gieorgio Matteuci ("Interference with electrons- from thoughts to real experiments", 2013) reinforces my conviction. He confirms Feyman's perspicacity with the two-slit experiment, but also adds this fundamental precision: interference patterns are built up not only from thousands of electrons, thereby reinforcing the wave-view, but also from the successive impacts of single electrons. The latter being an experimental proof of the particle character of electrons.

We arrive at the following, apparently contradictory remarks. The particle-gun has to be interpreted as a wave-gun, but waves themselves appear to be the product of successive or simultaneous particle impacts. This seems to give much more credibility to the image of a gun that shoots bullets in a wide range. That could mean that not the properties of the electron are essential, but the way each electron is emitted, and its subsequent trajectory (it could be of course that the properties determine the trajectory, but I will leave that to the scientists]. The dichotomy particle-wave would, more than ever, be a false one: individual electrons are particles, but as a group they behave like a wave, just like spectators in a sport arena.

The first image therefore, that of an automatic weapon slightly out of control, would seem to be very accurate. We could even find a very simple explanation for its behavior. Just like the hand of a shooter is never completely still, so is any source of emission of electrons forever trilling in the quantum dimension. Those oscillations would then explain why electrons seem to behave more like a wave than like particles.
Very simple, and therefore probably quite wrong. Better hear it from the experts.