You would be wrong.
For the sake of argument assume we're just looking at the last ~150-175 years or so of widespread public education in the US and chunks of Western Europe and ignoring the massive swaths of history where education was a) only for the wealthy elite b) religious or c) both. Even then the average somewhat educated individual had a decent grasp of whatever the curricula of the time deemed important, but little else. Heck, let's restrict it to just the period after the 40s, well after public education had been established in the US.
You have an absolute explosion in educational attainment in the US between 1940 and 2000 with the proportion of the population graduating high school almost doubling every two decades. Now, I will be the first to admit that this is a messy proxy for what you are talking about.
Here is a snippet of something that I had left over from a research project many years ago. It paints the picture pretty well. All data published by the US Census.
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The picture gets a lot more complex when you start looking at male vs female, by racial category, and geographic area (the South in particular had really dire public schooling even for white students for a very long time), but that's the broad strokes. I'll also add that something similar can be seen if you look in the 19th century, roughly 1865 - 1895. Also Germany ~1800-1865 and the USSR 1917-1938. Educational explosions like that are amazing for how they reshape societies.
Someone who drops out of middle school might nonetheless spend a lot of time at the library and know far more about history than a disinterested student who finished high school. But, be that as it may, it is still a useful rough gauge. There is also a very big difference between what we can describe as the basic, basil level of knowledge a person might have about a subject through cultural osmosis vs. more in-depth knowledge. To use an easy historical example, most people have at least a crude knowledge of what a Nazi is based purely on cultural references, but far fewer have a reasonable grasp of German politics in the 1930s and the crises that ushered in Hitler's dictatorship.
What you're likely perceiving is the change in curricular goals between now and when you were in high school. It's fairly likely, for example, that some of the people you are lambasting for having deficient knowledge of history know a fair bit more than you do about a number of other things.
Anyways, I'll cut it off here. The history of education is something that I can go off at length about. It was one of the first major areas I did significant research, and remains a topic I'm passionate about. The long and the short of it, however, is that the world in general - and even the US - has never been more educated than it is today. This is doubly true if you're part of a group that has traditionally been denied educational opportunities.
edit: here's the table for educational attainment for women by race - this really puts it into stark relief. The jump, for example, in Native populations is staggering. Keep in mind this is all within living memory. When families start moving up the educational ladder it can happen quickly and have some jarring consequences. I say this as someone with a doctorate who's grandfather was a sharecropper who dropped out of the 4th grade. That sort of inter-generational mobility can cause some whiplash.
edit 2: oops, I cut the years off of this when I screen capped it. The columns are the same as above. Far left column (starting 28.1 for white women) is 1940, the far right one (starting 83.7) is 2000, with each column in between being the intervening decades in order.
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There is a similar story to be told about post-secondary education as well. The long and the short of it is that in the years before WW2 you are looking at less than 5% of the population with a bachelor's (with the usual caveats - lower for women, MUCH lower for African Americans and Natives). By 2000 almost a quarter of the US had a BA/BS and the racial disparities, while still very significant, were much lower in scale.
I wish I had good data for how it breaks down by economic class, but the US Census just doesn't track that as well as I would like, especially before the 70s or so. Still, it very much is there. Looking at the data for an impoverished area of rural Appalachia looks very different from a professional-heavy suburb outside of Boston. The general picture I've painted holds true there as well, though, with the caveat that the magnitude of the changes are less pronounced in areas that were already starting from a higher baseline.
edit 3: Ernie, I want to be clear that this isn't an attack on you or me trying to show you up. But this is something I hear a lot and it's just wrong. For what it's worth, old people complaining about kids these days is a tradition that literally goes back to antiquity.