I've previously suggested that schools should focus more on developing cognitive skills rather than the rote memorization of facts. As another aspect of this, we might consider how the facts are taught. Typically they're simply presented as unsupported testimony, ultimately resting on the authority of the teacher or textbook. This is lamentable in two respects: (1) It fosters bad intellectual habits: students should be taught to probe and question, not merely accept assertions at face value. (2) It does little to advance students' understanding of the topic at hand. Rather than baldly reporting the facts as we take them to be, educators should also impart how we came by the knowledge in the first place, and thus how curious students could (at least in principle) test it for themselves.
Situating knowledge in its historical context would give students a greater understanding and appreciation for their disciplines, and for how intellectual progress is made. It is no longer a "black box", as if facts found their way into textbooks by some inexplicable magic. By showing progress and discovery to be an ongoing human endeavour, more students could come to fully realize that this is an endeavour that they could contribute to also. For example: for many school students, the "scientific method" - the way they're taught to do science - consists in memorizing textbooks and rotely performing predefined lab tasks. Sometimes they're told to write up a lab report in terms of "hypothesis testing", but this seems tacky and artificial when it's so divorced from the way that everything else in their science class has been presented. Teaching science as a closed book fails to make clear to young students the vital role waiting for them if they choose to pursue the subject further. (And of course the same could be said of other fields too. A history textbook might be presented without any explanation of where it came from, or how actual historians go about their work.)
A more engaging style of teaching might go something like this: Begin with a problem, and explain why it's important. Brainstorm possible solutions, or ways one might begin to inquire further. (In early sessions, students may have no idea what to say here. But hopefully they would develop the skill after further exposure to this teaching method. If so, that would be a significant educational achievement in itself.) A skilled teacher might be able to subtly guide the class discussion in the right direction, ultimately enabling them to "solve" the problem themselves. In any case, you can offer a basic account of historical methods for resolving it. The crucial point here is that you teach more than just the end result -- the "brute facts" accepted by relevant authorities. You also teach how they know it.
By teaching disciplinary methods to young students, the hope is that, in addition to better understanding the discpline, they will also be better prepared to use the methods themselves. Science classes should teach students how to be scientists, not merely indoctrinate them with what The Scientists have said. Similarly for history, and so on. Of course, part of this has to include a healthy respect for past research, and an adequately comprehensive knowledge of what those findings were, so I'm not advocating a total upheaval here. But it does seems to require an important change in perspective from the pure fact-imparting model of contemporary "schooling".