Edit: I was inspired to ask this question while thinking of the communist manifesto, where Marx writes out about history as if its as story of the different social classes fighting etc. And I then thought maybe cause and effects in history are either far simpler than they seem(like, say, starvation was the vast overwhelming cause of the french revolution and everything else was just rationalization) or much more likely, that the actual causes are far too complicated and chaotic to actually figure out and in fact impossible to know. (And something about the butterfly effect-seemingly inconsequencial changes causing huge differences down the line) And I was also thinking that a non-narrative framework would be the perfect tfodder for some young aspiring postmodernist to tackle (andthat someone probably has) and that I would be interested in knowing what that framework was.
In direct answer to your question, current historical practice shies away from narration, though chronologies still do play a part in organizing thoughts. There are a number of different frameworks we use to bring up questions and organize how we present research. Many are modes of thinking, for example dialectics (mutually influencing relationships, for example between technology and people, or between cultures), gender approaches (thinking about how cultural constructs inform source material and our reception, among a huge number of other areas informed by feminism), materiality (more closely considering the role of material objects in humans' lives).
As a semi-side note, Marx's class conflict is a form of dialectics, so Marx wasn't entirely narrative either. But the idea of social evolution, what you're seeing as narrative in Marx, is something that still pops up in scholarship. It seems to be one of those underlying assumptions some scholars have that they're not aware of.
Those are just the ones that came up first as I was thinking, and I don't want to leave a huge wall of text. But these are all different ways to think about the past beyond A happened than B happened, or A caused B thus C. If you read the vast majority of historical writing, it's far less linear. Here's an example from my own work, starting with a chronology.
Thesis: Japan is made up of islands, and as such the role of maritime violence is important in thinking about the islands' history.
In explaining this, I could give a number of paragraphs starting with each era and showing the extent of maritime violence in this period. This would support my argument and be linear... but not only is it boring, it fails to raise any questions in addition to my main question (what role did maritime violence have in Japan?). I might write that first to give myself a clearer understand of the chronology, but historians are looking more for themes. What forms did that violence take? Who was involved? (Men, women, locals, "foreigners", wealthy, poor, a mix of these? How old were they? This is where gendered approaches come in) Where was it occurring? Why was there violence? What did said violence influence? (Those last two are the dialectics I mentioned above.) In this approach, I would probably structure my paper around these types of themes.
I don't honestly have a good theory book for history, but this book lays out some of the frameworks art historians use. While they're asking somewhat different questions, (some historians will argue that art historians aren't "real historians", some art historians consider themselves historians, we all study the human past) the fields really follow a lot of the trends like Marxism, feminism, and post colonialism. I found it very thought provoking.
Hayden White is generally the historical philosopher one goes to when one wants to talk about "narratology" in history — philosophical takes on the types of narratives historians deploy. I'm not sure White has ever suggested what a non-narrative history might look like. I think he would say that history is defined by its use of narratives, and so non-narrative history is, by definition, not history. White's main argument is that historians should be reflexive about their use of narrative (that is, recognize you are doing it, acknowledge it, don't let the narrative get in control of you), not get rid of narrative. Even a narrative of non-causation is still, technically, a narrative.
As an historian of science, I'd also be quick to point out that even science papers have narratives (albeit pretty thin ones, usually). Raw data often has no narrative, but without a narrative telling you how it was created, why it was created, and so forth, it lacks context — and thus lacks meaning. (Whoa.)
Care to elaborate on your question? :)
What would an alternative be?
If I may ask a question of my own, what exactly is a "narrative school of thought?"
