According to this paper, there can be no relativistic quantum theory of localizeable particles ("relativity plus quantum mechanics exclusively requires a field ontology"). Sean Caroll has also argued that fundamental physics should be conceptualized in terms of fields, not particles. Here is another paper on the subject as well, and two other related questions on this website.
My question is primarily about learning and conceptualization: Quantum fields, not particles, are the fundamental constituents of nature (at least as far as we know), yet particles are often the conceptual tool used to teach field theory/particle physics. What concepts do particles help explain where fields fail? And conversely, where do fields succeed while particles fail?
Relevant article: Pitfalls in the teaching of elementary particle physics.
Elementary particle physics is gradually implemented into science curricula at the high school level. However, common presentations on educational, semi-technical or popular level contain or support severe misconceptions. We discuss in particular the notion of 'particle', the interaction between them and the use of Feynman diagrams. In many cases the true novelty of particle physics (i.e. quantum field theory) is largely ignored. We also suggest reasons for this widespread distortions of particle physics in popular accounts.