And I'm not talking about usual fringe battle-fronts like creationism or flat-Earthers, I'm actually talking of much more down-to-Earth topics like climate change for example. The fact that we might be fast approaching an era where the staple defenses such as evidence and not being suddenly censored are probably going to be under increased threat, is not helping much in that respect, either. Something tells me it'll be ever harder to argue with people who don't even know the full extent of what they don't know - and on top of that, do not want to know.
A recent (and quite intriguing) paper called "When science becomes too easy: Science popularization inclines laypeople to underrate their dependence on experts" argues that it's the rise of science communication that might be the cause of rising distrust in experts, which is quite a unusual thought, but it may have a point when you think of it. Again, the disadvantage of science communication is that it's full of words like probably, maybe, possible, roughly, estimated, hypothesized - which hardly sounds convincing enough to the layperson, who, like I said, would rather deal in absolutes. Be it due to intellectual laziness or some other reason.
So how do we deal with this problem? Before a rather lengthy rant - here's an informative laugh with John Oliver on the subject:
Now. First off, I think it's become evident by now that science in school should be less about teaching kids to recite dates and numbers in order to get good marks. The end of the last ice was how long ago? 10 thousand years is the "normal" way to "teach" it. A number that started off from varve counting in the Baltic Sea - later "more or less" confirmed by C14 dating. But a carbon-year is not the same as a calendar year - so when you take 10K C14 years and calibrate it to Earth orbits, you get a number that is well in excess of 11K. But when you start to think about it, the North American ice-sheet kept melting until 7K years before present. And the modern ocean circulation can be described as leaving the glacial mode as late as 6K years ago. We know for example that the "8,200 year event" is linked to glacial modus operandi. What to learn from this? That science does not know when the last ice age cycle ended within error bars covering 5-6K years? HELL NO! That's not what I just said.
Science is not a place for those who demand "the answer" (which of course is 42). Which is why it tickles certain religious groups in need for absolute truth so much. Deniers will use rhetoric such as "what is the exact climate sensitivity of one CO2-molecule", knowing full well that science only can give the unsatisfying answer "it is probably", .and, "it depends". Then they can play their smug gotcha game and feel good about themselves.
Science in school should teach that probability and uncertainty is not the same as not knowing. Probability and uncertainty is in fact how knowing is described. Science in school should teach philosophy of science: The difference between an analogue and a homologe. The difference between induction and deduction. The difference between a scientific hypothesis and a theory. The difference between falsification and verification, or indeed, what "proof" is. It should teach the structure of logic. It should teach the demarcation line. To make kids aware of the need to question the premise.
Kids do not necessarily need to learn how to solve diff-equations. But they do need to understand how to separate information. They must learn about fallacies that come in so many forms (even fun tricks allowing "proof" that 1=2 or that 1+1=1). Because these building blocks of science are publicly unknown, deniers and "alternative truths" can roam public space. They can troll - by sharing information (that per se can be correct) that seemingly falsify or significantly "weaken" any theory.
Admittedly, it's too tempting to blame the ever changing education targets for this as well. It's easy to measure "targets" by teaching kids to answer yes/no or multiple-choice questions. So kids grow up with thinking they understood the topic by 56%, 78% or 96%. The entire population is learning that there is some 100% answer key that science possesses. This is of course wrong.
In mathematics, because it is (most likely) a human construct (though some philosophers argue that mathematics is a real entity that can be discovered - similar to a fossil) this might be true to an extent - until one buries themselves deep into number-theory and starts to understand that there's some pretty interesting epistemological stuff at the bottom of it - called axioms. Epistemology, even though it at first glance provides information that makes any idea look as likely as any other idea, is quite important to be aware of. These inner structures of knowledge are seldom discussed in scientific papers. They are treated as shared by all by default. They're usually silently represented by how science is done/acted out - simply because they're known by everyone else, and they "stand to reason". Even mathematical papers don't start with proving that 1+1=2 (Whitehead and Russell spent 400 pages of set-theory in an attempt to prove it to be true in the early 20th century, and besides, one really needs to get back to the axioms of Peano to truly start to appreciate that 1+1 is 2.
So here is what science is like - and to many people, it doesn't look good. It's hardly satisfying. Particularly because we use all these words that are the same as used in daily speak. Theory, for example. Error, for example. And if no one ever explains what is meant with a scientific theory or what error-bars (or residuals) mean in science - all they hear is that some scientist has a theory with lots of errors and unexplained residuals hanging around!
Finally, culture has developed a certain liking of the myth of the lone brilliant genius. You know, Einstein, who according to popular culture did not understand math and was rejected from science, thus discovering truth without any links to science itself in a patent office. These myths are harmful and wrong. Einstein knew math very well - and he was updated very well on the current science. He actually based his work on the current science at the time. He communicated massively with other scientists. Science is a web. It's a deeply structured global collaboration. It's a ladder - you can't leap from the base straight to some abstract highest point that you can call truth. You need to step on the preceding steps first. And start climbing.